Michael Eineder

Reconstruction of Alpine Digital Elevation

Models From Interferometric SAR Data

September 2004

Reconstruction of Alpine Digital Elevation

Models From Interferometric SAR Data

Dissertation

zur Erlangung des akademischen Grades

eines Doktors der Naturwissenschaften

an der

Leopold-Franzens-Universität

Innsbruck

eingereicht von

Dipl. Ing. Michael Eineder

September 2004

Vorwort

Die Idee zu dieser Arbeit entstand auf einer Bergtour 1999. Beim Anblick der steilen Wände

und Schluchten wurde mir bewusst, wie schwer es sein würde, solche Gebiete mit den

Instrumenten der bevorstehenden Shuttle-Radar-Topographie-Mission zu vermessen. Denn

die Algorithmen würden mit ähnlichen Schwierigkeiten zu kämpfen haben wie ein

Bergsteiger, der eine neue Route zum Gipfel sucht. Zunächst erscheint die Wand absolut glatt.

Bei genauerem Hinsehen finden sich erste Haltepunkte. Dann gilt es herauszufinden, welche

davon in einer Ideallinie zum Ziel führen.

Mich selbst hielt diese Arbeit meistens im Tal und am Schreibtisch. Deshalb danke ich allen

Freunden und besonders meiner Lebensgefährtin, die es mir nicht verübelten, dass ich so viel

Zeit am Computer verbrachte und so wenig mit ihnen draußen in der Natur.

Ich danke weiterhin Richard Bamler, der mich zu dieser Arbeit ermunterte und mit dem ich

meine Ideen jederzeit diskutieren konnte. Herzlichen Dank auch an Helmut Rott für die

freundliche Aufnahme am Institut für Meteorologie und Geophysik sowie für die Zeit, die er

meiner Betreuung widmete. Der frische Geist in seiner Arbeitsgruppe hat mich immer wieder

motiviert. Merci auch an Thomas Nagler für die praktische Unterstützung vor Ort.

Schließlich danke ich meinen Eltern, die in mir die Liebe zu den Bergen und das Interesse für

die Naturwissenschaften geweckt haben.

Section A 1

Abstract

When compared with the established optical stereo methods then Interferometric Synthetic

Aperture Radar (InSAR) is a rather young technique to generate Digital Elevation Models

(DEMs) of the Earth from satellite or airborne radar data. In the last 10 years systems and

algorithms have continuously improved and today InSAR has become operational status for

DEM generation in areas with moderate or undulating topography. Rugged mountains how-

ever still pose severe limits on the current algorithms and the available systems. The intention

of this thesis is to investigate the limitations and to find new solutions to overcome them.

Firstly, the geometric imaging conditions and the limitations of radar systems are investi-

gated. From the results viewing geometries for the available satellite systems are proposed

that will optimize their performance with respect to DEM generation.

Secondly, an accurate and efficient InSAR phase simulation algorithm is described that allows

the test of advanced reconstruction algorithms.

Thirdly, new improved algorithms for the reconstruction of DEMs from the observed data are

investigated. Special interest is given to the fusion of data from different viewing geometries

in order to overcome radar shadow, layover and phase unwrapping problems. A novel algo-

rithm for the reconstruction of radar shadow areas is one of the major results. Furthermore, a

novel general solution for the parallel fusion and phase unwrapping of multiple imaging ge-

ometries based on a maximum likelihood approach is described. It is successfully tested with

real data from the Shuttle Radar Topography Mission.

Finally, technical improvements for future SAR sensors are proposed in order to make them

more suitable for interferometry. A split bandwidth approach is described that might simplify

phase unwrapping for DEM generation and for all other disciplines of SAR interferometry.

Section A 2

Table of Contents - Section A

Introduction 3

1. Contents and Structure 4

2. Analysis of InSAR Imaging Geometry in Alpine Terrain 4

2.1 SAR Layover and Shadow 5

2.2 SAR Interferometry in Alpine Terrain 10

2.2.1. SAR Geometry and Phase 10

2.2.2. Interferometric SAR Geometry and Phase 13

2.3 The Wavenumber Shift 16

2.4 Temporal Decorrelation and Propagation Medium 17

3. A Novel Interferometric Phase Simulation Algorithm 18

4. DEM Reconstruction Algorithms 24

4.1 Puzzle Fusion Algorithm 27

4.2 Interferometric Shadow Reconstruction Algorithm 32

4.3 Split Band Interferometry 36

4.4 Maximum Likelihood Hybrid Geometry Stacking 41

5. Summary and Outlook 44

References of Section A 46

References of Sections B-G 52

Enclosed Publications – Sections B-G

Section B: Interferometric DEMs in Alpine Terrain - Limits and Options for ERS and

SRTM, IGARSS Conference 2000.

Section C: Problems and Solutions for InSAR Digital Elevation Model Generation of Moun-

tainous Terrain, ESA FRINGE Workshop, 2003.

Section D: Interferometric DEMs in Alpine Terrain, IGARSS Conference, 2001.

Section E: Efficient Simulation of SAR Interferograms of Large Areas and of Rugged Ter-

rain, IEEE Trans. on Geosc. and Remote Sensing, Vol. 41, No. 6, 2003.

Section F: Recovering Radar Shadow to Improve Interferometric Phase Unwrapping and

DEM Reconstruction, IEEE Trans. on Geosc. and Remote Sensing,

Vol. 41, No. 12, 2003.

Section G: A Maximum Likelihood Estimator to Simultaneously Unwrap, Geocode and Fuse

SAR Interferograms From Different Viewing Geometries Into One Digital Eleva-

tion Model, Accepted for publication in the IEEE Trans. on Geosc. and Remote

Sensing, 2004.

Section A 3

Introduction

This study is dedicated to the problem of alpine terrain reconstruction using radar interfer-

ometry. Terrain reconstruction or digital elevation model (DEM) generation is today an im-

portant application of synthetic aperture radar (SAR). The original idea to exploit the differ-

ential phase of two coherently processed SAR images for terrain reconstruction was published

by Graham [30] thirty years ago but it took some additional years until considerable results

were published, e.g. by Goldstein and Zebker in 1986 [26]. It took another couple of years

until satellite based data of high geometric quality and of large quantities were available to

scientists. The most important radars were those on the European Remote Sensing Satellites

ERS-1 and ERS-2 launched in 1991 and 1995, respectively.

A highlight was their operation in an interferometric tandem configuration between 1995 and

1998. With those satellites in space, the exciting SAR interferometry technique increasingly

filled the programs of scientific conferences and the development of the quite complex proc-

essing techniques leaped forward. Up to the year 2000, only repeat pass interferometric satel-

lite data were available for DEM gener ation, i.e. the two observations from different positions

in space had to be acquired at different times. For a single ERS satellite the time lag is a mul-

tiple of 35 days and also the acquis itions of the ERS tandem mission are separated by 1 day.

Soon, the first enthusiasm was replaced by scientific thoroughness and a number of severe

drawbacks were discovered: even small geometric changes of the scatterers between the two

observations decorrelate the interferometric phase and also changes in the propagation me-

dium severely distort the measurement.

Both problems could be solved with the Shuttle Radar Topography Mission (SRTM), a SAR

system with two spatially separated antenna systems that flew on a space shuttle in February

2000. Within 11 days this system mapped the earth between +60° and -54° latitudes with a

quality, speed and homogeneity unknown so far. But also in SRTM, the overall success and

the enthusiasm did initially hide some systematic difficulties unsolved so far. At the same

time the expectations what can be done with SAR interferometry rose even higher. In fact,

the reconstruction of terrain in those places where it is especially interesting, namely in

rugged mountains, steep canyons and also urban areas is still not yet solved satisfactory.

In the SRTM DEMs published both by NASA/JPL and by DLR many regions in mountainous

areas are marked as invalid or erroneous. The reason is that a SAR has a special viewing ge-

ometry and a number of other limitations when compared with an optical system. Under the

Section A 4

rugged conditions in alpine terrain the available systems and the existing algorithms, devel-

oped with flat or moderate terrain in mind, are not always suitable.

In this work the conditions in mountainous terrain are studied in detail and several new ap-

proaches are developed to overcome or at least to minimize the difficulties encountered. Fur-

thermore, new efficient codes for simulation and for terrain reconstruction are developed.

1. Contents and Structure

The work in hands has been performed in units that have been individually published in con-

ferences and in reviewed journals. Therefore this document is structured as follows: section A

introduces into the topic , summarizes the major findings, problems and solutions and provides

a final critical evaluation in the overall context of the work. The following sections B to G are

the original publications. Because those have been written sequentially, they are internally

consistent but contain only references to sections written earlier and the nomenclature and

variables may not always be consistent across the publications. Fig.1 shows the logic and the

overall structure of this work.

InSAR reconstruction in alpine areas

Summary, Section A

Systematic analysisof effects

Section BIGARSS

Optimization of viewing geometry

Section B+GIGARSS+TGRSS

InSAR simulation

algorithmSection E

TGRSS

Reconstruction algorithms

for rough topography

Shadow reconstruction

Section FTGRSS

Hybrid geometry fusion

Section GTGRSS

Split bandwidthsystems

Section C (Patent pending)

Puzzlealgorithm

Section DIGARSS

Fig.1: Block diagram of thesis structure. Section A provides a final summary of several associated publications and a pending patent. Dark boxes mark, in the author’ s view, significant and innova-tive contributions to the topic.

2. Analysis of InSAR Imaging Geometry in Alpine Terrain

It is assumed that the reader is familiar with the basics of SAR imaging, geocoding and with

SAR interferometry. Good textbooks and articles for this background are, e.g. Curlander [8],

Section A 5

Schreier [48], Bamler and Hartl [1], Franceschetti and Lanari [23], Rosen et al. [45] and

Hanssen [33]. Only a very brief introduction to SAR and InSAR theory is given in the follow-

ing. Especially the concept of the interferometric phase field is introduced to guide the reader

through this work and help to understand the problems and the solution strategies proposed.

For the purpose of this study it is sufficient to understand that a synthetic aperture radar

(SAR) transmits a sequence of microwave pulses to the earth and records the reflected echoes

coherently with the phase of the transmitted signal. An image in the range (=distance) direc-

tion is formed by recording the time and the intensity of the echoes. By moving the antenna

along azimuth, i.e., the satellite flight track, a two dimensional image is reconstructed. The

achievable resolution in azimuth is much higher than the physical antenna beam width deter-

mined by the real aperture because the echoes are recorded coherently in phase and hence a

larger aperture can be synthesized. This is done in a SAR processor, i.e. a computer program

that generates a focused complex valued image from the sensor data and from the knowledge

of the flight trajectory.

The SAR interferometry technique uses the differential phase of two SAR images taken from

different positions. The effective distance between both observations, the so called baseline

may be relatively small compared to the distance from the scatterer because the distance be-

tween antenna and scatterer is measured with high precision in the scale of the wavelength.

For typical microwave SARs the wavelength is in the range between 3 cm (X-Band) and 24

cm (L-band) and the baselines are in the range between tens of meters to kilometers. Even

larger and smaller wavelengths are used for special purposes.

2.1 SAR Layover and Shadow

A well known problem with SAR in mountainous terrain are the effects of layover and

shadow, consequences of the projection of three-dimensional object coordinates to the two-

dimensional cylindrical coordinate system of the radar. As described by (Curlander [8], Bolter

[4], Schreier [48], Kropatsch [36]) and here in section B, layover is caused by different ter-

rain facets with equal range distance and it occurs when the terrain is steeper than the inci-

dence angle.

Section A 6

b)

b)

Fig. 2: a) Radar shadow is caused by missing “echoes” without illumination. b) Shadow example marked with a circle. Data: SRTM X-SAR taken at 54° incidence angle in Ötztal/Austria.

Fig. 3: a) Radar layover is caused by multiple superposition of echoes. b) Layover example marked with a circle. Data: ERS-1 taken at 23° incidence angle in Ötztal/Austria.

In mountainous terrain and at small radar incidence angles θ (see Fig. 3) the layover effect is

a severe problem in SAR imaging and hence also in SAR interferometry. As shown in Fig. 3

layover is caused by the terrain facet between x2 and x3 that is tilted towards the radar with a

slope α that is larger than 90°-θ.

Ground space coordinate system x

schematically

θ

missing echoes

schematically

multiple echoes

x 1 x 2 x 3

θ

α

x 4

Radar time coordinate system τ

τ 1

τ 2

x 1 x 2 x 3

Radar time coordinate system τ

Ground space coordinate system x

τ 1

τ 2

α

a) a)

range

azimuth

range

azimuth

Section A 7

The term slope is used here in the geospatial convention, i.e., it is measured along the maxi-

mum gradient direction of a terrain facet. In consequence, the slope is always positive and

ranges between 0° and 90°. The orientation of the slope in the horizontal plane is given by the

aspect angle measured clockwise from the north direction.

For the image facet causing layover the imaging process is reversed ( 0<∂∂

xτ ) and therefore

other facets between x1 and x4 are overlaid. These areas are also called passive layover.

In consequence, when measured in the ground coordinate system, a much larger surface area

is affected by layover than just the area of the steep slopes. For example, in alpine terrain

more than 40 % of the surface area are unusable due to layover effects when imaged by the

European Remote Sensing Satellite ERS with 23° incidence angle [18].

The counterpart of layover, if not as destructive, is shadow as depicted in Fig. 2. Shadow oc-

curs, when the terrain slope between x1 and x2 is tilted away from the radar and the slope α is

larger than 90°-θ. Also shadow affects additional areas outside from the area that causes the

shadow.

The quantitative effects of shadow and layover are investigated in section B by explicit com-

puter simulation and in section C by a statistical analysis using a simplified geometric view-

ing model. Both methods confirm the obvious fact that an incidence angle of 45° minimizes

the probability of layover and shadow. The statistical analysis can further be used to optimize

multi observation mapping scenarios, e.g. from ascending and descending orbits or from dif-

ferent incidence angles.

As shown in section C, the terrain gradients in the range direction that are visible in one SAR

observation are inherently limited to the interval ]θ-90°, θ [, i.e., a range of 90 degrees. In

order to allow negative values the term gradient is used here to distinguish it from the geospa-

tial term slope. Because natural terrain may contain gradients between -90° and +90°, multi-

ple passes with different incidence angles are required to map it without gaps. In section C a

novel method is proposed to select optimal incidence angle combinations to efficiently map

terrain with a given two dimensional slope probability distribution function. It is based on the

idea of maximizing the coverage of the two dimensional slope probability density function

(PDF) of the terrain with the joint field of view of the different SAR observations. An inte-

grated slope PDF is shown in Fig. 4. Assuming isotropy it was derived by averaging along all

Section A 8

aspect directions the numeric gradients derived from a precision DEM of Ötztal / Austria [47],

an extremely rugged area. Fig. 5 depicts the concept for the configuration of a single SAR

acquis ition. The polar diagram shows the field of view perceptible by a SAR. Blue circles

indicate the percentage (90 %, 99 % and 99.9 %) of undistorted coverage of an alpine area for

an imaging system with an isotropic slope coverage, e.g. a nadir looking optical camera. Even

if a side looking radar has an eye-shaped pattern in this diagram, the circles are still helpful to

assess how much of the slope diagram is covered by a specific imaging configuration and

what has to be done in order to optimize the viewing conditions. The 23° incidence angle of

ERS shifts the “eye” away from the optimal central position and leads to large non covered

areas (losses) of 14 %. The central position is the optimum because there the slope PDF is

maximal.

Generally with this method the losses due to layover and shadow are underestimated because

only the direct layover and shadow areas are accounted for. Therefore in practice the loss-

percentage has to be scaled by a factor of approximately 2.5 for layover or 1.8 for shadow in

order to consider also the areas of passive layover or shadow. These numbers are empirical

results of exper iments performed for section B. Precise loss values can only be derived by

complete simulation of the viewing geometry as has been performed in section B and section

E.

shadow

layover

field

of view

aspect

slope

0.9

0.99

0.999

Fig. 4: Integrated slope PDF of Ötztal area. Isotropy is assumed. The lines show characteris-tic slopes with integral values 90 %, 99 % and 99.9 %.

Fig. 5: Polar slope/aspect field of view of an ascending pass of a right looking ERS acqui-sition with 23° incidence angle. Radial coor-dinate: slope angle 0°-90°. Polar angle: aspect angle. Blue circles: characteristic slopes. The loss is: 14 %.

Section A 9

In order to cover also the problematic slopes of an area, acquisitions with different viewing

geometries must be combined. Typical combinations are for example ascending and descend-

ing polar orbits as shown in Fig. 7, left and right looking antennas (Fig. 6) or crossing orbits

of non-polar systems like SRTM (Fig. 9).

0.9

0.99

0.999

0.9

0.99

0.999

Fig. 6: Slope field of view of ERS (virtual) left and right looking ERS passes for θ=23°. Loss: 0.22 %.

Fig. 7: Slope field of view of ERS right looking ascending and descending passes for θ=23°. Loss: 0.22 %.

In conclusion, a SAR system is inherently limited in its capabilities to map rough structures

due to shadow and layover effects, the latter being more destructive. If only one SAR obser-

vation can be afforded, an incidence angle of 45° is optimal to map mountains. Multiple ob-

servations from different aspect and different incidence angles are required in order to achieve

gapless mapping.

Section A 10

0.9

0.99

0.999

0.9

0.99

0.999

Fig. 8: Slope field of view of ascending SRTM left looking pass with θ=54°. Loss 4.8 %.

Fig. 9: Slope field of view of ascending and descending SRTM left looking passes with θ=54°. Loss 1.4 %.

2.2 SAR Interferometry in Alpine Terrain

2.2.1. SAR Geometry and Phase

Synthetic aperture focussing of satellite data is conventionally performed in the zero Doppler

plane, i.e. the plane orthogonal to the flight track in an Earth fixed coordinate system. In con-

sequence, a scatterer will appear in the image at the azimuth location where its distance to the

radar is minimal and hence, the time der ivative of range is zero. In this plane a single scatterer

(point scatterer) will result in a measured phase of

scattPTR φλ

πφ += 4 , ( 1)

where R is the distance between antenna and scatterer, λ is the effective wavelength includ-

ing potential inhomogeneities of the propagation medium and scattφ is a constant phase contri-

bution specific to the scatterer. Phase inhomogeneities of the antenna are not considered here

and equation (1) is only valid for the narrow far field of the antenna, a valid assumption for

space borne SAR systems.

Fig. 10 shows the basic configuration of a SAR in the zero Doppler plane. The sampling (here

set equal to the resolution cell size) intervals are shown as black lines and the colors represent

the cyclic phase value (see Fig. 11) that would be measured for a single point scatterer

(marked with a star) at this position. For the further it is important to note that iso-phase lines

Section A 11

are circles around the antenna. Because those radial fringes are concentric with the range

sampling grid, the phase does not provide additional geometric information that could be used

for 3D reconstruction.

The situation gets more complicated if several scatterers contribute to one resolution cell, i.e.,

one echo sample of the SAR. Since the wavelength is much smaller than the resolution cell,

each scatterer contributes with a different phase and the total phase of the resolution cell is the

phase of the coherent sum of all scatterers in that resolution cell:

= ∑+

i

R

iDS

iscatti

eA,4

argφ

λπ

φ . ( 2)

Here Ai denotes the amplitude of the scatterer i and Ri its range from the antenna. In

natural environments the intensity and spatial distribution of scatterers in a resolution cell are

random. Hence, the phase of each individual pixel in the SAR image is a random number.

This mechanism is visualized in Fig. 10. ERS parameters (see also Table 1) are selected but

the wavelength is scaled by a factor of 10 to 56 cm because the true ratios could not be visual-

ized reasonably on a page. Black lines indicate the sampling intervals of 7.9 meters (18.96

Mhz). The fringes correspond to the half wavelength due to the two-way effect. All scatterers

within a sampling interval (more precisely: in a resolution cell) contribute to the total phase of

this cell with their phase (color) weighted by their intensity. This is the general case in SAR

imaging: usually several scatterers on the terrain surface (white line) or in a volume (white

circle) close to the surface contribute. A volume scattering layer may be caused, e.g. by a

vegetation that is semi transparent to microwaves.

Section A 12

zero Doppler plane

R

SAR antenna flight direction(azimuth)

Fig. 10: Schematic configuration and phase field of a SAR in the zero Doppler plane. A point scatterer (star) will return a phase corresponding to its geometric distance (color) while several distributed scatterers will return the coherent integral. Black lines: echo sampling interval. Colors: cyclic phase values. White: terrain surface. White circle: volume scatterer, e.g. a forest.

Section A 13

π π20 =

23π

2π

Fig. 11: Cyclic color coding of phase values used in this work.

Platform/Radar ERS-1/2/AMI ENVISAT/ASAR SRTM/

SIR-C + X-SAR

Mission time 1991- 2002- February 2000

Orbit altitude 780 km 780 km 233 km

Orbit inclination 98.52° 98.52° 57°

Orbital repeat cycle 35 days

(3 days, 176 days)

35 days 11 days

Radar frequency

(wavelength)

5.3 GHz

(5.66 cm)

5.33 GHz

(5.62 cm)

5.3 GHz + 9.6 GHz

(5.66 cm + 3.1 cm)

Incidence angle 23° 15°-45° 17°-65° + 54°

Bandwidth

(range resolution)

15.5 MHz

(9.7 m)

15.5 MHz

(9.7 m)

9.5 MHz

(15.8 m)

Table 1: Characteristic parameters of the platforms and radar systems used in this work: the Euro-pean Remote Sensing Satellites ERS-1/2, ENVISAT and of the Shuttle Radar Topography Mission SRTM.

2.2.2. Interferometric SAR Geometry and Phase

When SAR interferometry is applied for terrain reconstruction, two antennas are spatially

separated in the direction orthogonal to the flight direction and orthogonal to the radar’ s line

of sight in order to create a baseline as shown in Fig. 12. For simplicity it is assumed in the

following that the baseline vector is orthogonal to the line of sight and thus the baseline B is

equal to the effective baseline ⊥B . During interferometric processing the two images are pre-

cisely coregistered to a common geometry and for each pixel the phase difference

Section A 14

)(4 12

λπφ RR −

= . ( 3)

is calculated by complex conjugate multiplication of the images. Eq. (3) holds for 2 individual

SAR acquisitions. In the case of a single pass system with only one transmitting antenna like

SRTM only half the phase difference is measured. In the equations based on geometry this

can conveniently be accounted for by dividing the baseline B by 2. The geometric phase field

of a point scatterer in the zero Doppler plane of a SAR interferometer is shown in Fig. 12. It is

assumed that the scatterer’ s phase in both observations is equal ( 2,1, scattscatt φφ = ) and that the

propagation medium does not contribute to the interferometric phase. Both prerequisites are

satisfied when the observations are performed simultaneously. Note that compared to Fig. 10

the interferometric iso-phase fringes are now constant along the line of sight and change with

the elevation angle ς of a scatterer in the field of view of the interferometric system. The

elevation angle is measured in the coordinate system of the interferometric radar configura-

tion and is used here to distinguish it from the incidence angle which is measured in the coor-

dinate system of the terrain. The possibility to measure ς is the key to three-dimensional im-

aging in contrast to the pure range measurement of a single SAR antenna. As can be seen in

Eq. (3), the interferometric phase field can be interpreted as the difference between two of the

phase fields shown in Fig. 10 which are tilted by the elevation angle difference ς∆ . The dif-

ferential phase field is zero if the baseline is zero, i.e., an angle measurement is then no more

possible. In the far field for large values of R the an ambiguous phase corresponds to an am-

biguity angle ambς of

B

amb2

λζ = . ( 4)

Section A 15

For small angles and at a distance R from the antenna this corresponds to a radial distance of

approximately ambRζ .

R2

SAR antenna 2

Zero Doppler plane

R1

SAR antenna 1

ζ1

Slant range

sampling grid

Terrain surface

B

ζ2

flight direction

(azimuth)

∆ζ

ζambhamb

Fig. 12: Zero Doppler phase field of a cross track interferometer similar to an ERS-Tandem configuration with 100 meters baseline. The interferometer measures the wrapped phase of a point in the plane, here visualized by the color.

Some more terms and InSAR principles can be explained nicely in Fig. 12. The height differ-

ence hamb that corresponds to one fringe difference at a constant range (black line) is called

height of ambiguity. The fringe rate caused by a flat terrain (white) cutting the range lines

(black) is called flat earth fringe rate or also orbital fringes.

Section A 16

2.3 The Wavenumber Shift

With the visualization in Fig. 12 a number of important mechanisms of SAR interferometry

can be understood. In the case of distributed scatterers, SAR interferometry only works if the

scatterers contributing to one resolution cell are localized densely enough, so that the coherent

sum yields a deterministic phase value that is independent from the individual scatterers’

strength. As shown in Fig. 12 this is only the case if the scatterers are located within a limited

area of 1ς . In fact, the variation of the phase field must be less than 2π, i.e., the scatterers may

not vary more than λ R /(2 B) in tangential direction. If the random scatters are aligned along

a flat terrain as marked by the white line, it follows that the maximum baseline for a given

resolution cell size ρ and a terrain slope α is

ρ

αθλ2

)tan(max

−= RB , ( 5)

where θ is the incidence angle, equal to 1ς for a flat geometry and α is the local terrain

slope. Equation (5) describes the fundamental wavenumber shift criterion for single pass

(monostatic) SAR interferometry published by Gatelli et al. in 1994 [24]. For a terrain facet

oriented towards the sensor the fringes get denser with larger baselines and with steeper ter-

rain slopes. The maximum fringe density or frequency that can be resolved is determined by

the system bandwidth W, respectively the resolution )2/( Wc=ρ .

From Fig. 12 it can also be understood that for point scatterers the wavenumber shift is not a

problem and arbitrary baselines are theoretically possible. This advantage is used in the Per-

manent Scatterer technique published by Ferretti et al. [17] where only isolated scatterers are

used that are smaller than a resolution cell. Such scatterers allow large baselines which in turn

yields high accuracy for terrain reconstruction.

In the experience of this study and also with the processing of SRTM data at DLR [43] it

turned out that slope decorrelation is not a severe problem for terrain reconstruction even with

the relatively small bandwidth of SRTM (9.5 MHz) and the corresponding range resolution

cell size of 16 meters. The maximum slope that leads to total decorrelation for SRTM is 50.1°

(see section D) and at a slope equal to the incidence angle of 54.5° layover poses an absolute

limit. The problematic range between 54.5° and 50.1° is relatively small and in natural terrain

such steep slopes occur not isolated but in combination with even higher slopes causing situa-

tions where layover and shadow pose much harder problems than local decorrelation.

Section A 17

Future systems will have higher bandwidths (smaller resolution cells) which will reduce the

probability of slope decorrelation even more while the problems of layover and shadow will

remain.

2.4 Temporal Decorrelation and Propagation Medium

European alpine areas in elevations between 500 and 1800 meters are often covered with for-

ests and meadows. The geometric shape of the vegetation will continuously change due to

growth, wind, rain and snow [31] or even the light conditions. Due to the small microwave

wavelengths even small changes of the scatterers geometric fine structure – even on millime-

ter level - lead to decorrelation of the phase if the SAR acquisitions are not performed simul-

taneously. The experience with the processing of ERS tandem data (acquired with 24 hours

time difference) is, that temporal decorrelation is indeed a severe problem over the European

alps. Mountains in arid regions however may show coherence over several years.

Changes in the propagation medium may also distort the phase. Atmospheric water vapour

delays the microwave signal by several centimetres. This effect occurs not only in mountains

and has been investigated extensively by Hanssen [32]. A problem special to mountains is the

height dependent phase delay caused by varying temperature and stratification [33]. Also this

effect cancels out if the observations are performed simultaneously ([33], chapter 4.8).

Another effect published recently is refraction due to snow [29]. Dry snow acts like a trans-

parent dielectric medium for microwaves and the different refraction indices of air and snow

result in different wavelengths. This effect may lead to several cycles of phase difference if

the thickness of the snow layer changes between the two observations.

Both, decorrelation and propagation delays are severe obstacles for repeat pass interferometry

and severely limit its usability for operational purposes. Yet, decorrelation and propagation

effects are not investigated further in this work. Instead the focus is on geometric effects

posed by the topography, i.e. high quality single pass interferometric data from SRTM or fu-

ture missions are assumed that avoid the problems of temporal changes.

Section A 18

3. A Novel Interferometric Phase Simulation Algorithm

At this point the fundamental SAR imaging principles in rugged terrain are understood and

the associated problems have been described in a statistical sense. For the development and

test of new improved DEM reconstruction algorithms it is necessary to simulate explicitly the

interferometric phase that would be observed by a virtual InSAR system when imaging a

given terrain formation. In the sparse literature on this subject ([20], [21], [22], [50]), shadow

and layover effects are most often ignored and simplifying approximations are made like a

flat earth surface and a linear flight track of the satellite. Little has been published so far about

geometrically accurate phase simulation algorithms - maybe because the range-Doppler imag-

ing equations are easy to write down. However the solution of those equations requires itera-

tions and the computer code resulting straight from the equations is so slow, so that multiple

simulations of an area (e.g. to optimize the viewing geometry) or the simulation of large areas

is not practical. For that reason a new, highly efficient and accurate phase simulation algo-

rithm was developed. It is so efficient that it can be incorporated as a forward model in an

InSAR DEM generation system, even if multiple iterations are required. The phase simulation

method is described in detail in section E and it is also part of the maximum likelihood DEM

reconstruction described in section G.

phaseϕ(n, e, h)

Easting (e)

Northing (n)

Height

(h)

azimutht(n, e, h)

rangeτ(n, e, h)

ϕ(t, τ)

1. point for point

transformation

2. triangulation

and interpolation

range (τ)

azimuth (t)ϕ

Fig. 13: The conventional two step phase simulation approach first transforms each DEM pixel to three matrices. In a second step the matrices are triangulated and interpolated to the phase matrix in slant range coordinates.

Conventional algorithms start by transforming each point of a DEM to the radar coordinates

(slant range, azimuth) and to the interferometric phase value observed by an InSAR system.

As shown in Fig. 13 the results are three matrices, each one still in DEM coordinates. If per-

formed accurately, this coordinate transformation is expensive to compute.

Section A 19

In the range / azimuth coordinate system of the radar, the DEM points are now irregularly

sampled. Therefore, in a second step the azimuth and range coordinates stored in the matrices

are triangulated and the corresponding phase values are interpolated to the radar slant range

coordinate system. The interpolation of irregularly sampled triangulated data may produce

artefacts, especially if only linear interpolation is performed and if the resolution of the DEM

is much lower than the target resolution.

The newly developed algorithm of this work avoids the triangulation completely and acceler-

ates the time consuming coordinate transformation by careful polynomial approximations.

The transformation polynomials are computed for a dense grid, e.g. 10 by 10 pixels and they

are interpolated in-between.

First, a three-dimensional grid of the precise imaging geometry parameters of the interferome-

ter as described in [27] and [28] is computed in the slant range domain yielding 3 scalar data

cubes for the observed interferometric phase φ , the easting and northing coordinates e and n

as a function of the slant range coordinates azimuth t , range τ and a terrain height h :

),,(

),,(

),,(

htn

hte

ht

τττφ

. ( 6)

Since the dependence of each of the parameters (φ , e , n ) can be accurately described as a

polynomial function of h, the three-dimensional cubes of samples can be collapsed to two-

dimensional matrices of polynomials

...),(),(),(),;(

...),(),(),(),;(

...),(),(),(),;(

2,2

1,0,

2,2

1,0,

2,2

1,0,

+⋅+⋅+=

+⋅+⋅+=

+⋅+⋅+=

ττττ

ττττ

ττττ φφφφ

tphtphtpthp

tphtphtpthp

tphtphtpthp

nnnn

eeee . ( 7)

For example, the polynomial ),;( τthpe describes the DEM easting coordinate of a point in the

radar coordinate system at (t,τ) as a function of h.

In consequence, for each point (t,τ) in the radar coordinate system plane the parametric height

dependant trace (e, n) through the DEM matrix is described by the two polynomials

)(hpe e= and )(hpn n= and the phase is described by )(hpφφ = . The problem is now to

Section A 20

find the correct position (e, n) which is a function of the local DEM height. The solution 0h is

easily found by the intersection between the parameter h and the interpolated height z(e, n)

taken from the DEM matrix :

000 ))(),(( hhphpz en = . ( 8)

In practice the intersection can be efficiently and reliably determined by a bisection algorithm

that will always converge [41]. In the case of layover exactly one of the multiple solutions

will be found. In the case of shadow a point not visible by the radar will be determined. (Im-

proved solutions for both problems are described in section E.)

Finally, the interferometric phase is derived by evaluating the phase polynomial

)( 0hpφφ = . ( 9)

Due to the use of local polynomial approximations and the bisection this new simulation

method is much faster than the conventional triangulation method. Another advantage is that

the DEM interpolation is performed directly on the regular grid of the DEM using high order

interpolators with low distortions.

Fig. 14: Geometry grid of new phase simula-tion algorithm.

Fig. 15: Iteration of phase solution using a DEM.

The required phase accuracy can be influenced by the mesh width of the geometry grid. The

achievable accuracy was verified in closed loop tests with DLR’ s interferometric geocoding

software [46]. The tests confirmed highly accurate results with phase errors as low as thou-

(φ, e, n)

τ

t

h

northing n

h 0

e0

n0

easting e

height h

Section A 21

sandths of a degree while saving 2 orders of magnitude in the time for the geometric calcula-

tions.

Furthermore, some useful extensions to this phase simulation algorithm have been developed,

namely

- simulation of an amplitude image from the phase gradient

- simulation of the baseline decorrelation from the phase gradient

- identification of shadow and layover based on the phase

- simulation of the phase from multiple layers in layover areas

Simulation of the layover phase considering all contributing layers improves the understand-

ing of the SAR imaging mechanisms and might guide to special layover reconstruction algo-

rithms that take into account the reversed viewing geometry in layover as shortly sketched in

the following:

In layover, multiple overlaid linear terrain facets lead to multiple frequencies in the interfero-

gram spectrum. In order to reconstruct the terrain, the frequencies must be detected and the

signals filtered and separated into an odd number of interferograms, one for each facet. Each

of the interferograms is then unwrapped and geocoded using the boundary conditions that a)

the folded terrain facets must be connected at the boundaries of the layover and b) must be

connected to the surrounding non-layover areas. (See the schematic view in Fig. 3). The study

and implementation of this idea is certainly not easy and is not expected to get great practical

relevance. It is not further followed in this study.

Some example phase simulations are shown in the following. Fig. 16 shows an original

SRTM X-SAR intensity image of the mountains in Ötztal/Austria and Fig. 17 shows the inter-

ferometric phase. The noisy areas are caused by radar shadows that are also visible in the in-

tensity image. Fig. 18 shows the simulated phase. Only for the central parts a high resolution

DEM was available [47]. Outside of this area the implemented phase simulation algorithm

used the global 1 km resolution GLOBE DEM [34]. In the simulation the shadow areas can be

recognized by a reversed color cycle when transecting from left to right. Fig. 19 shows the

difference between measured and simulated phase. The shadow areas have been detected dur-

ing simulation and assigned zero phase difference. The difference image is of remarkable

quality and confirms the quality of both the reference DEM, the SRTM system and the simu-

lation algorithm. Three different distortions are visible: a) Missing DEM data in the upper left

and lower right corners. b) A red structure originating at the border of the reference DEM is

Section A 22

presumed to be a boundary artifact due to steep slopes where the precision DEM begins. c)

The blue shadows are located exactly on the glaciers Hintereisferner (HEF), Hochjochferner

(HHF) and Schalfferner (SF). The blue color corresponds to a height loss of about 50 meters

between the creation of the DEM in the seventies and the SRTM measurement in 2000. The

height loss due to glacier retreat is in reasonable accordance with results published by Span

[51]. It could, of course also have be caused by systematic errors in the reference DEM.

Summary and Discussion

A new highly efficient and accurate phase simulation algorithm working directly in radar co-

ordinates was developed in this work. The development of this algorithm helped to gain a

thorough understanding of the consequences of radar layover and shadow in the interferomet-

ric phase. Furthermore the developed software will allow to test the reconstruction algorithms

described in the following chapters. Tests with real SAR data and DEMs and additional

closed loop tests confirmed the validity of the approach. In comparison with published stan-

dard algorithms that work in the DEM domain e.g. [50], the approach delivers results with

finer details and known accuracy. A detection method for radar layover was found and even

the phase of multiple terrain facets in layover areas was simulated, but this implementation

turned out to be more difficult than the standard approach working in the DEM domain. In

contrast, shadow areas are conveniently detected “on-the-fly” from the phase gradient. This

simple method for shadow detection led later to the interferometric shadow reconstruction

method described in section F.

Section A 23

Fig. 16: SRTM intensity image of Ötz-tal/Austria (DT 093.010, February 2000). The dark areas are caused by radar shadow. Sev-eral glaciers are located in this area: Hintereisferner (HEF), Hochjochferner (HHF) and Schalfferner (SF).

Fig. 17: SRTM measured phase. In the shadow areas the phase is dominated by noise. The bar on the lower left shows the cyclic colours for phase values in the interval [-π,π[.

HEFHHF

SF

N

Fig. 18: SRTM simulated phase. Only for the marked central part a high resolution DEM is available. The remaining part is filled with 1 km resolution GLOBE data.

Fig. 19: Colors: Difference between measured SRTM phase and simulated phase. Luminance: SAR intensity. Shadow areas have been as-signed zero phase difference. The visible blue areas are DEM discrepancies located on the glaciers Hintereisferner (HEF), Hochjoch-ferner (HHF) and Schalfferner (SF).

azimuth

range

HEFHHF

SF

N

Section A 24

4. DEM Reconstruction Algorithms

The reconstruction of the topographic height from interferometric SAR data requires a coor-

dinate transformation from the range-azimuth-phase coordinate system of the SAR to the

north-east-height coordinate system of a map.

The required processing steps are depicted in Fig. 20 and shortly described in the following. A

comprehensive description can be found in [1]. Starting from two focused complex SAR im-

ages of the two antennas, the second image is registered with an accuracy of 1/10th to 1/100th

of a pixel to the first image. A polynomial is sufficient to describe the low order differences in

viewing geometry between both antennas. Note that terrain induced geometric distortions are

very small in InSAR and not visible in the intensity image.

Then, in a two-dimensional filtering step the signals of both antennas are filtered to a common

band of the object spectrum. Non-common parts of the spectrum would appear like noise and

decorrelate the interferogram that is formed by complex conjugate multiplication of both im-

ages. The interferometric phase φ is usually derived from a local sample average in order to

reduce the phase noise

∑∑ ++++= −1 2

),(),(1

(tan),(*

2121

1N

ii

N

jj

jjjiiisjjjiiisNN

jiφ , ( 10)

where ()* is the complex conjugate operator. The independent number of samples N=N1·N2 is

also called interferometric number of looks. As a quality indicator the absolute value of the

complex correlation coefficient ? called coherence is formed

}),({}),({

)},(),({),(

2*

2

2

1

*21

jisEjisE

jisjisEji

⋅

⋅=γ , (11)

where E{} denotes the expectation value. The coherence is often used in the following proc-

essing steps as a local signal quality indicator.

The difficulty of the following phase unwrapping step can not be underestimated. Phase un-

wrapping can be summarized as an attempt to estimate the absolute number of interferometric

phase cycles from the gradients to the neighboring phase values. Since the gradients are esti-

Section A 25

mated from wrapped phase values they are also potentially wrapped. Numerous algorithms

and extensive literature exists on the topic. The publications [7], [9], [19], [26] and [42] list

just a few different approaches. An overview is given in [25]. The author’ s working group has

worked with different algorithms and unwrapped more than 17000 data sets of SRTM X-SAR

using the minimum cost flow algorithm [7]. The experience is, that gradient based phase un-

wrapping only works reliably at moderate terrain under high coherence conditions [12], [52].

One approach to simplify phase unwrapping is to remove the known topographic phase using

a coarse a priori DEM [40]. However, the author’ s experience is that this method works only

in alpine terrain if the a priori DEMs resolution is close to the resolution of the SAR data be-

cause the critical gradients are contained in the high resolution parts of the spatial spectrum.

Such precise high resolution DEMs are generally not available - it is the goal of this work to

generate them.

After the phase unwrapping step systematic phase offsets from SAR instrument and orbit and

the absolute phase cycle are adjusted using one or more control points – an uncritical step.

At this point the phase values correspond to geometric viewing angles ζ as depicted in Fig. 12

and can be transformed to ground coordinates using the range Doppler equations and the

flight geometry. Well known and tested algorithms for this transformation are described in

e.g.[27], [28], [46]). Those algorithms first transform the interferogram forward into the DEM

coordinate system resulting in a cluster of north, east and height values that are irregularly

gridded in the horizontal plane of the DEM. A regridding process, usually by triangulation

and interpolation is necessary to achieve a regularly sampled DEM matrix.

An alternative and very efficient approach was published by Schwäbisch [49]. It operates di-

rectly in the DEM coordinate system and solves the transformation equation backwards. This

way the regridding step is omitted. The approach is much faster and may have lower interpo-

lation errors. The algorithm was therefore selected for geocoding performed in the frame of

this work.

Section A 26

SAR Image fromAntenna 1

SAR Image fromAntenna 2

Interferogramformation

Coregistration

Filter Filter

PhaseUnwrapping

Wrapped Phase Coherence

Phase OffsetCorrection

Geocoding

Unwrapped Phase

Regridding

Regular DEM

Irregular DEM

Fig. 20: Processing flow of a standard interferometric DEM processing system.

In alpine terrain phase unwrapping and geocoding is often extremely difficult due to radar

shadow and layover. For example, the noise patterns of Fig. 17 are caused by shadow. During

phase unwrapping wrongly estimated phase gradients propagate spatially into large areas with

wrong ambiguity number, i.e., wrong angle ζ. This wrong angle transforms into large hori-

zontal and vertical displacements in the DEM coordinate system.

In the following new algorithms are described to reconstruct the topographic height under

highly ambiguous mountainous conditions. The algorithms are aimed to situations where

standard reconstruction algorithms will mostly fail.

Section A 27

4.1 Puzzle Fusion Algorithm

The puzzle algorithm is an attempt to fuse multiple interferograms from different geometries

that help each other to bridge problematic shadow and layover areas. Fig. 21 shows the

shaded DEM of the Rhine valley in Switzerland and the surrounding mountains. The layover

areas for a descending ERS acquisition have been simulated from the DEM and overlaid in

color. Fig. 22 shows how SAR layover segments an alpine area into parts that are either visi-

ble by ascending or by descending orbits. Only the yellow parts are visible from both orbits

and can serve as bridges for the puzzle algorithm. The puzzle algorithm assumes that a quality

estimate for the gradients used for phase unwrapping exists and that the unwrapped phase can

be segmented into reliably unwrapped islands. The algorithm uses few external seed points to

determine the phase offset for one or more islands in interferogram 1 and geocodes the islands

to a fragmented DEM that will initially look like an incomplete puzzle. From this DEM – as-

sumed to be reliable - more seed points are generated for all other interferograms. Those inter-

ferograms should be acquired from different perspectives, e.g. from crossing orbits. After

iteratively unwrapping and geocoding segments from all interferograms each individual DEM

is successively filled. In parallel the quality and consistency is tested by cross comparing the

geocoded results from the different interferograms and a joint DEM is fused by weighted av-

eraging.

The puzzle algorithm was implemented as a prototype and a first result is shown in section D.

However, the algorithm was not studied in more detail because the critical decision when to

stop phase unwrapping could not be solved satisfactory within this work. If the decision is

taken too conservative, then a fragmented DEM as shown in Fig. 24 will result. If the decision

is too optimistic, phase unwrapping errors will propagate. Instead of tuning the processing

parameters to find a configuration that might finally work with only one particular data set,

the focus of this work was put on a more general maximum likelihood method described in

section G.

Section A 28

Fig. 21: DEM and layover analysis of an alpine area in (Rhine valley, Switzerland) observed by a descending ERS satellite at 23° incidence angle. The colored areas are layover in a descending pass.

Section A 29

Fig. 22: Layover analysis of ERS crossing orbits in the Rhine valley, Switzerland.. Red: no layover in ascending. Green: no layover in descending. Yellow: no layover in ascending and descending. Black: layover.

Section A 30

Segment Phase Offset Correction

Geocoding

Regridding

Regular DEM

Irregular DEM

Segmentation of consistent areas

Segment Phase Offset Correction

Geocoding

Regridding

Regular DEM

Irregular DEM

Segmentation of consistent areas

Radarcoding

Seed point

Segment Phase Offset Correction

Geocoding

Regridding

Regular DEM

Irregular DEM

Segmentation of consistent areas

Radarcoding

DEM comparison and fusion

Joint DEM

Interferogram n

Interferogram 2

Interferogram 1

Fig. 23: Schematics of a multi–interferogram puzzle geocoding algorithm.

Section A 31

Fig. 24: Color coded DEM, iteratively composed from SRTM ascending and descending passes (red, yellow: descending, two iterations; blue:ascending, one iteration. The height is coded in cyclic grey scales with 256 meter wraps.

Summary and Outlook

A novel algorithm for DEM fusion was developed and tested. Because the results were unsat-

isfactory and the algorithm showed stability problems it was not pursued longer. During the

progress of this study the SRTM C-band data at NASA/JPL have indeed been unwrapped

with a flood filling branch and cut algorithm [35]. Problematic areas in alpine regions have

been successfully masked out [39]. From their results it may be assumed that experience with

suitable phase gradient reliability criteria is available at NASA/JPL. With such reliability cri-

teria available the puzzle method might be capable to fuse ascending and descending observa-

tion layers, e.g. from SRTM and provide improved results in problematic mountainous areas.

Section A 32

4.2 Interferometric Shadow Reconstruction Algorithm

As shown in section B, a SAR image of alpine terrain is either distorted by layover for low

incidence angles or by shadow for high incidence angles. At 45° incidence angle both effects

are minimized. The incidence angle of SRTM X-SAR was 54° at scene center and hence

shadow is the only severe problem. In this study a novel solution for the significantly im-

proved reconstruction of the shadow line has been found which is fully described in section

F. Fig. 25 shows the SRTM X-SAR intensity image of the 850 meter deep crater Trou du Na-

tron in Chad with large shadow areas and a few layover regions and Fig. 26 shows a photo-

graph of the area. Fig. 27 illustrates the observation geometry: a shadow is thrown from the

upper rim of the valley to the bottom and no radar reflections are received from the range in-

terval ]r1, r2[. In consequence the phase received by each antenna is random noise and hence

also the interferometric phase is pure noise. This leads to severe phase unwrapping problems

during DEM reconstruction.

The key idea to solve this problem is that the shadow boundary line follows exactly the line of

sight of the SAR antenna. This line has a constant elevation angle ζ and hence, must have a

constant phase value – before and after phase unwrapping. Depending on the height of the

shadow throwing object and the incidence angle, the range extent of shadow areas is in the

range between several hundreds of meters to kilometers. In this range, minor deviations of the

phase field due to the non-zero baseline and due to diffraction are practically negligible in the

far field of both antennas.

Fig. 25: SRTM/X-SAR intensity image of crater Trou du Natron / Chad. Note the shadow (S) and layover (L) re-gions.

Fig. 26: Photograph of Trou du Natron (from: http://www.expeditionexchange.com/libyen/TibTrou.jpg)

Section A 33

Fig. 27: Principle of interferometric shadow reconstruction: the interferomeric phase along the shadow line is constant.

The following Fig. 28 and Fig. 29 show perspective views of the reconstructed DEM of Trou

du Natron with the operational SRTM method as sketched in Fig. 20 and with the improved

shadow method.

504 m

850 m

Fig. 28: Perspective view of DEM generated with standard methods. Shadow phase noise leads to a rough surface on the left crater rim and the crater depth is underestimated by 346 m due to phase unwrapping errors of two cy-cles.

Fig. 29: Perspective view of DEM generated from the shadow reconstructed phase. The noisy crater rim regions have been converted to smooth slopes that helped to unwrap the full depth of the crater (850 meters).

Because shadow areas can be identified rather easily using the low SAR amplitude and the

low coherence, this knowledge can be used to support phase unwrapping significantly. The

phase gradient between the start and end of shadow is forced to zero by replacing the noisy

α

Antenna 1

ζ ( r ) r 1

r 2

B ⊥

Antenna 2

r

Section A 34

phase values of all shadowed pixels with average phase values before and after the shadow

area. This simple modification of the wrapped phase data solves three major problems:

a) it removes the noise in the shadow regions that would otherwise confuse the phase

unwrapping algorithm

b) it generates high quality gradient estimates that help the phase unwrapping to climb

arbitrarily high terrain steps from the backside

c) it ensures strict phase monotony with increasing range which is required by the geo-

metrical transformation during geocoding; the final geocoded DEM in the shadow area

will follow the shadow line

The interferometric shadow reconstruction method is so simple that even the first prototype

code developed by the author improved the DEM reconstruction in the majority of test cases.

Fig. 30 shows the DEM processing chain from Fig. 20 modif ied for shadow reconstruction.

Interferogramformation

PhaseUnwrapping

Wrapped Phase Coherence

Unwrapped Phase

ShadowDetection

Intensity

Shadow Mask Shadow PhaseModification

Geocoding

Fig. 30: Modified DEM processing chain with shadow correction steps drawn in bold.

Section A 35

A further application example is shown in Fig. 31. The famous 8125 meter Nanga Parbat

mountain in Pakistan throws impressive shadows on the surrounding slopes and glaciers.

Those shadows actually augment the DEM reconstruction if the shadow correction method is

applied. The height of the peak (8125 m) was successfully reconstructed.

Fig. 31: DEM of Nanga Parbat in the Himalayas generated using interferometric shadow recon-struction. An area of 24 km x15 km was processed with 10 meter pixel spacing. The height of the peak (8125 m) could be correctly reconstructed. Superimposed is the SAR intensity where the shadow regions are clearly visible. Data: SRTM/X-SAR, 2000.

More detailed information on the algorithm can be found in section F. Here, it should be em-

phasized that the shadow areas are artificially filled by the algorithm along the shadow line.

Even if this is not the true height, it is a rather good estimate. The true height must be lower

than the shadow line and the statistical error increases towards the center of the shadow area.

The structure function of the terrain could be used to assign an error bar to the height estimate

as a function of the distance from the non-shadow boundary pixels.

Section A 36

4.3 Split Band Interferometry

As already stated, phase unwrapping is the major problem for successful DEM reconstruction

in mountains. This problem gets more difficult with larger baselines, smaller wavelengths and

larger variations of the topography. The phase unwrapping problem is mainly caused by the

small bandwidth of current systems – the measurement is almost monochromatic. If several

different wavelengths were available, the ambiguity problem could be reduced considerably.

In 1992 Madsen and Zebker published an idea to exploit the small wavelength dispersion

within the range bandwidth for the determination of the absolute phase constant of an inter-

ferogram [38]. In this study, their concept is elaborated to a technical solution for future spe-

cialized wide bandwidth SAR systems that shall allow the absolute phase determination of

individual pixels. The key idea is to use only narrow sub-bands within a wide system band-

width (Fig. 32) for multi wavelength interferometry in order to solve phase unwrapping. The

frequency difference ∆f between the sub-bands is equivalent to a second interferogram with a

wavelength of c/∆f .

frequency f1 f2

System bandwidth

f0

sub-band 1 sub-band 2

∆f

Fig. 32: Use of sub bands for split bandwidth interferometry

Even if the frequency difference of both sub-bands can be made large, the used bandwidth in

the sub-bands is relatively small. Hence, the signal can be sampled with lower frequency and

compressed efficiently for the downlink from the satellite to the ground receiving station.

The question is consequently how such a split-band spectrum can be generated. Typical SAR

systems transmit chirps, i.e. linearly frequency modulated signals. The spectrum of such a

chirp has a rectangular envelope centered at the radar carrier frequency f0. In order to optimize

the signal to noise ratio of the interferograms with a given transmit power, the SAR system

should concentrate the transmitted energy only to the sub-bands. Using standard hardware of

Section A 37

modern digital radar systems like the German TerraSAR-X [5], [53] or ESA’ s TerraSAR-L

[56] this can be achieved by either transmitting a sequential or a parallel dual frequency chirp

signal as shown in Fig. 33 and Fig. 34.

f1

f2

frequency

time

bandwidth

pulse duration

f1

f2

frequency

time

bandwidth

pulse duration

Fig. 33: Parallel split bandwidth chirp. Red: instantaneous frequency

Fig. 34: Sequential split bandwidth chirp

In the parallel variant two chirps with different center frequencies are transmitted simultane-

ously while in the sequential variant they are transmitted one after the other. Since SAR

transmitters are often operated close to the saturation level, high transmit amplitudes may lead

to distortions in the parallel variant and the sequential variant may be the favorite solution.

A DEM processing system that exploits the split bandwidth concept is roughly sketched in

Fig. 35. The sub-bands are extracted by filters from the received SAR data and processed

individually to two sub-band interferograms. Each of the interferograms can be regarded as an

interferogram acquired at a radar center frequency f1 or f2, respectively. Hence the differential

interferogram corresponds to a much lower frequency f2-f1. Therefore phase wrapping occurs

less frequently and both, the phase of one sub-band and the phase of the differential interfero-

gram can be input to an estimation algorithm for the absolute phase. This process will involve

in most cases filtering of the differential interferogram to reduce the noise that is scaled by a

large factor f1/(f2-f1) together with the phase in order to support phase unwrapping of the sub-

band interferogram. Approaches for multi-baseline phase unwrapping which is equivalent to

mult-wavelength phase unwrapping have been published e.g. in [3] and [37] and optimal ra-

tios have been investigated in [54]. Multi-baseline unwrapping algorithms should not be con-

fused with multi-baseline DEM reconstruction algorithms as described in e.g. [16], because

the latter assume that the phase has been unwrapped successfully before DEM generation.

A general approach to fuse interferograms of different wavelengths is discussed in detail in

section G and the achievable accuracy of split bandwidth systems is analyzed in [2].

Section A 38

SAR Image fromAntenna 1

SAR Image fromAntenna 2

Interferogramformation

Coregistration

FilterLower Band

FilterLower Band

Abs. Phase Estimation

Wrapped PhaseLower band

CoherenceLower band

Unwrapped Phase

Interferogramformation

FilterUpper Band

FilterUpper Band

Wrapped PhaseUpper Band

Interferogramformation

Differential PhaseUpper-Lower

Fig. 35: Modified DEM processing chain with split bandwidth processing steps drawn in bold.

Fig. 36 and Fig. 37 demonstrate the feasibility of the method even if the parameters of the

available data are not very fortunate. An SRTM DEM has been generated from standard phase

unwrapping method using the full bandwidth (Fig. 36) and another DEM has been generated

purely from split bandwidth interferometry (not including the phase of one sub-band) using

the available 9.5 MHz bandwidth (Fig. 37). Due to the extremely small bandwidth to fre-

quency ratio of 0.0009 the phase of the split band interferogram had to be scaled by a factor of

1010 and therefore the noise in the DEM is very high. Spatial averaging has been performed

to reduce this noise and to visualize that there is indeed a topographic signal in the split band

interferogram.

Section A 39

Future SAR systems will have much higher ratios like 0.03 for TerraSAR-X or 0.08 for Ter-

raSAR-L and hence will have much higher accuracy. Then, the split-band method may be-

come practicable and systems can be optimized for it. Fig. 38 shows the simulated phase field

in the zero-Doppler plane of TerraSAR-X with 280 meters baseline and Fig. 39 the phase

field that could be derived by sub-band processing.

Fig. 36: SRTM X-SAR DEM of an area of 170 km x 50 km over mountains in Iran (data take 153.260). The wavelength is 3.1 cm, the reso-lution about 30 meters.

Fig. 37: SRTM X-SAR DEM, processed using split bandwidth technique - without phase un-wrapping. The synthesized wavelength is 74 me-ters, the resolution is reduced to about 6 km in order to reduce the phase error enough so that the terrain gets visible.

Section A 40

Fig. 38: Simulated phase field in the zero Dop-pler plane of a TerraSAR-X interferogram with 280 m baseline and 45° incidence angle.

Fig. 39: Corresponding split bandwidth phase field at 290 MHz sub-band separation.

Note that the split bandwidth technique can be applied not only to DEM reconstruction but to

all disciplines of SAR interferometry where an absolute phase estimated is required, e.g. land

subsidence measurements, glacier velocity measurements or along track interferometry (ATI)

of moving vehicles. Ideally, no more spatial gradient based phase unwrapping is required and

all disciplines could profit significantly. However, up until now split bandwidth phase un-

wrapping has only been published for isolated scatterers for the estimation of snow water

equivalent (SWE) in [13] and [14].

Section A 41

4.4 Maximum Likelihood Hybrid Geometry Stacking

During this work it became clear that several interferometric acquisitions have to be combined

in order to topographically map an area without gaps, with consistent quality and with an er-

ror estimate. Different track angles and different incidence angles are required to overcome

layover and shadow. Different baselines or wavelengths are required to solve phase unwrap-

ping. Unfortunately, even if all those acquisitions were available, no method existed so far

that was actually capable of fusing all the acquisitions into one DEM.

In section G of this work a new method is described that fuses all available data simultane-

ously into one DEM. It is based on maximum likelihood estimation and a consequent ad-

vancement of the work published by Ferretti et al. [15]. The flow diagram is depicted in Fig.

40. The method uses accurate geometry transformations to predict the likelihood of a height

estimate under the condition of the measured interferometric data and other external informa-

tion like, e.g. low resolution DEMs. The final decision for the height of each pixel is based on

the maximum likelihood. This method solves in parallel phase unwrapping and geocoding of

an ensemble of interferograms on the fly. Compared to standard methods the algorithm is

computationally expensive, but quite feasible if coded efficiently. Additionally, a height error

estimate is calculated for each pixel from the likelihood function. In the implemented version

accurate knowledge of the flight geometry is required and phase variations due to atmospheric

path delay are not considered. It is therefore targeted on high quality single pass interferomet-

ric data from SRTM or future single pass interferometry missions currently being studied

[10].

Section A 42

Pre-calculateGeometry Polynomialsa1(z), r1(z), ϕ1(z)

Interferogram 1 ϕint,1(a, r)

Pre-calculateGeometry Polynomialsan(z), rn(z), ϕn(z)

Interferogram n ϕint,n(a, r)

Phase offset removal ϕ1,0 Phase offset removal ϕn,0

Phase difference∆ϕ1(z’ )=ϕint,1[a1(z’ ), r1(z’ ))]- ϕ1(z’ )

Phase difference∆ϕn(z’ )=ϕint,n[an(z’ ), rn(z’ ))]- ϕn(z’ )

Coherenceγ1(z’ )= γ1 [a1(z’ ), r1(z’ ))]

Coherenceγn(z’ )= γ n[an(z’ ), rn(z’ ))]

Probabilityp1(z’ )=PDF1[∆ϕ1(z’ ), γ1(z’ )]

Probabilitypn(z’ )=PDFn[∆ϕn(z’ ), γn(z’ )]

Joint probabilitypjoint(z’ )=pDEM(z’ )∏pi(z’ )

zmax := z | (pjoint(z) >= pjoint(z )́)

Geometric position and phasea1(z’ ), r1(z’ ), ϕ1(z’ )

Geometric position and phasean(z’ ), rn(z’ ), ϕn(z ’ )

Coherence 1 γ1(a, r) Coherence n γn(a, r)

Pre-calculatephase PDFPDF1=f(ϕ,γ, L1)

Pre-calculatephase PDFPDFn=f(ϕ,γ, Ln)

for

z’=

z min,

z max

, z+

=∆z

A-priori DEM probabilitypDEM(z’ )

DEM

Fig. 40: Flow diagram of maximum likelihood hybrid geometry interferogram stacking method. A joint DEM is calculated from a set of interferograms an a priori DEM.

In section G more details and examples for the fusion of ascending, descending and multi

wavelength data are provided. Fig. 41 shows a DEM that has been reconstructed without ex-

plicit phase unwrapping from four crossing data sets of SRTM X and C band data and with

the additional help of a low resolution DEM. The remaining distortions, visible as spikes with

high errors are mostly located in radar shadow areas where the phase information is invalid.

Those areas could be masked out or interpolated using the quality estimates generated by the

algorithm. Another interesting solution for radar shadow would be a fusion of the maximum

likelihood method from this section with the shadow reconstruction method from section F.

Both algorithms should work in good synergy because the shadow algorithm can provide an

estimate for the wrapped phase of the shadow area. And only a wrapped estimate is needed in

the maximum likelihood reconstruction method. Note that the shadow method will overesti-

mate the true terrain height. The amount of this overestimation depends on the distance of a

pixel from the shadow borders. It can be expressed by the structure function or roughness of

the area and used as an (asymmetric) PDF for the height of a pixel in shadow.

Section A 43

Fig. 41: DEM reconstructed from 4 crossing X-Band and C-Band data takes 018.080 and 093.010 augmented by the 1 km resolution GLOBE DEM. The area shows a 30 km x 15 km part of the Stubai mountains in Tyrol with heights ranging between 900 and 3500 meters.

Section A 44

5. Summary and Outlook

SAR interferometry in mountainous terrain using current space borne systems is still a diffi-

cult task if complete coverage and constant and reliable quality are required. In this work the

imaging mechanisms of SAR interferometry have been studied and the problems to be ex-

pected in rough topography have been modeled and quantified. The results confirm that an

incidence angle of 45 degrees should be selected in order to minimize layover and shadow if

only one SAR acquisition is to be used. A combination of several passes with different inci-

dence angles can further improve the coverage. A practical method based on the two dimen-

sional slope PDF is described that helps to find the optimal combination.

An important tool developed in this study is a novel interferometric phase simulator that is

both, geometrically accurate and computationally efficient.

After studying the difficulties and the imaging mechanisms, several improved algorithms for

the reconstruction of digital elevation models from existing data have been developed:

A novel shadow reconstruction method reconstructs a useful topographic signal out of the

shadow that was considered only a nuisance so far.

Furthermore, a puzzle algorithm has been developed that uses a small number of interfero-

grams from different viewing angles to bridge shadow and layover areas. Since it is based on

standard geocoding and radarcoding methods its actual performance depends on the quality of

the phase unwrapping. It is therefore not considered a very stable method.

The most promising solution for the fusion of multi-parameter interferometric data is the

maximum likelihood based geocoding and stacking method. For the first time, hybrid in-

terferograms with different wavelengths and acquisition geometry were combined and the

critical phase unwrapping step was totally avoided. The investigated method gets increas ingly

stable as more interferograms are available - a unique and attractive feature when compared to

the standard methods. The maximum likelihood method is also well suited to process data

from future missions like, e.g. the interferometric cartwheel where multiple baselines may be

available.

Section A 45

Improvements for the generation of DEMs from alpine terrain were also proposed with re-

spect to radar technology. In the near future, SAR satellites with wide bandwidths will be

available. Maybe even constellations of several satellites that could provide multiple base-

lines. For them, a special split bandwidth operation has been proposed that, together with

the proposed processing techniques would simplify or even abolish the critical phase unwrap-

ping step. This would not only solve the hardest problem in alpine DEM reconstruction but

also benefit all other applications of SAR interferometry.

In the past years SAR interferometry techniques and applications have leaped forward even if

the radar systems were not originally designed for interferometry. Their quasi-monochromatic

operation and the associated ambiguity problems severely limit the operational application not

only in the field of DEM generation but also in the fields of surface deformation measurement

or glacier tracking - whenever the motion causes phase shifts larger than a few phase cycles.

Technical solutions to this ambiguity problems have been proposed here, more will certainly

be found and implemented in the next decade.

Further work in my view should concentrate to push technology and algorithms forward

towards multi frequency and multi baseline systems. On the system side the optimal baseline

and frequency ratios for different types of terrain and in the presence of noise should be inves-

tigated. On the algorithm side the maximum likelihood fusion algorithm developed in this

work looks like one solution for all problems, but the algorithm needs to be significantly ac-

celerated for operational use on large scales.

An interesting and difficult task with – in my view – little chances to help in DEM reconstruc-

tion are further investigations on DEM reconstruction from interferometric signals in layover

areas.

Multiple baselines will not only allow phase ambiguity resolution but also SAR tomography

as demonstrated in [44]. The fusion of both techniques may deliver not only the height but

allow three dimensional imaging of volume scattering layers covering the rock such as vege-

tation, dry snow and ice. Within the next 10 years radar systems and methods will progress

from two dimensional imaging to real three dimensional scanning offering us a “perspective”

that will not be possible with classical photogrammetry, even if this established technique

looks back on hundreds of years of history [6].

Section A 46

References of Section A

[1] R. Bamler and P. Hartl, “Synthetic aperture radar interferometry,” Inverse Problems,

vol 14, pp. R1-R54, 1998.

[2] R. Bamler, M. Eineder, “Split Band Interferometry Versus Absolute Ranging with

Wideband SAR Systems”, submitted to IEEE IGARSS 2004, Anchorage.

[3] S. F. Boehmsdorff, “Unwrapping the Phase in InSAR Data by a Multibaseline Ap-

proach. Test on a Synthetic Scene”, Frequenz, 56, pp. 208-212, 2002.

[4] R. Bolter, M. Gelautz, F. Leberl, “Geocoding in SAR Layover Areas”, Proceedings of

EUSAR'98, Friedrichshafen, Germany, pp. 481-484, 1998.

[5] S. Buckreuss, W. Balzer, P. Muehlbauer, R. Werninghaus, W. Pitz, “The TerraSAR-X

Satellite Project”, Geoscience and Remote Sensing Symposium, IGARSS '03, vol. 5, pp.

3096-3098, 2003.

[6] R. Burtch, “A Short History of Photogrammetry”, http://www.ferris.edu/

htmls/academics/course.offerings/burtchr/sure340/notes/History.pdf , Ferris State Uni-

versity, accessed 2004.

[7] M. Costantini, “A novel phase unwrapping method based on network programming”,

IEEE Trans. on Geoscience and Remote Sensing, pp. 813-821, May, 1998.

[8] J. C. Curlander and R. N. McDonough, “Synthetic aperture radar: systems and signal

processing”, John Wiley & Sons, Inc, New York, 1991.

[9] G. W. Davidson, R. Bamler, “Multiresolution phase unwrapping for SAR interferome-

try”, IEEE Transactions on Geoscience and Remote Sensing, vol. 37, pp. 163-174,

January, 1999.

[10] H. Ebner, S. Riegger, EADS Astrium, I. Hajnsek, D. Hounam, G. Krieger, A. Moreira

und M. Werner, “Single-Pass SAR Interferometry with a Tandem TerraSAR-X Con-

figuration”, presented at EUSAR conference, Ulm, 2004.

Section A 47

[11] M. Eineder and J. Holzner, “Interferometric DEMs in Alpine Terrain - Limits and Op-

tions for ERS and SRTM,” Proc. IGARSS, vol. 7, pp. 3210 –3212, 2000.

[12] M. Eineder, M. Hubig, B. Milcke, “Unwrapping large interferograms using the mini-

mum cost flow algorithm”, IGARSS '98, IEEE International, vol. 1 , pp. 83-87, 1998.

[13] G. Engen, T. Guneriussen, O. Overrein, “New approach for Snow Water Equivalent

(SWE) estimation using repeat pass interferometric SAR”, IGARSS, pp. 857–859,

2003.

[14] G. Engen, T. Guneriussen, and Ø. Overrein, “Delta-k Interferometric SAR Technique

for Snow Water Equivalent (SWE) Retrieval”, IEEE Geoscience and Remote Sensing

Letters, vol. 1, no. 2, April 2004, pp. 57-61, 2004.

[15] A. Ferretti, A. Monti Guarnieri, C. Prati and F. Rocca, “Multi Baseline Interferometric

Techniques and Applications”, FRINGE ’ 96 workshop on ERS SAR Interferometry,

Zürich, Switzerland, 30 Sep-2 October, 1996.

[16] A. Ferretti, C. Prati and F. Rocca, “Multibaseline InSAR DEM Reconstruction: The

Wavelet Approach”, IEEE Trans. on Geosc. and Remote Sens., Vol. 37, No. 2, pp. 705-

715, 1999.

[17] A. Ferretti, C. Prati, F. Rocca, “Permanent scatterers in SAR interferometry”, IEEE

Transactions on Geoscience and Remote Sensing, Vol. 39 , Issue: 1, pp. 8 – 20, 2001.

[18] D. Floricioiu, T. Nagler, H. Rott, “SAR Capabilities for Alpine Hydrology”, Proc. of

IGARSS, Vol. 4, pp. 2149-2151, 1999.

[19] T. J. Flynn, “Two-dimensional phase unwrapping with minimum weighted discontinu-

ity”, Journal of the Optical Society of America A., pp. 2692-2701, 1997.

[20] G. Franceschetti, A. Iodice, M. Migliaccio, and D. Riccio, “A novel across-track SAR

interferometry simulator,” IEEE Trans. On Geosci. and Remote Sensing, vol. 36, no. 3,

pp. 950-962, May, 1998.

Section A 48

[21] G. Franceschetti, A. Iodice, M. Migliaccio, and D. Riccio, “Efficient simulation of SAR

interferometric raw signal pairs,“ Proc. IGARSS, Singapore, vol. 4, pp. 1701 – 1703,

1997.

[22] G. Franceschetti, A. Iodice, M. Migliaccio, and D. Riccio, “Simulation of SAR interfer-

ometric raw signal pairs corresponding to real scenes”, Proc. IGARSS, Seattle, vol. 5,

pp. 2653 - 2655, July, 1998.

[23] G. Franceschetti and R. Lanari, editors. “Synthetic Aperture Radar processing”, CRC

Press, 1999.

[24] F. Gatelli, A. Monti Guarnieri, F. Parizzi, P Pasquali, C. Prati, and F. Rocca, “The wa-

venumber shift in SAR interferometry,” IEEE Trans. on Geosci. and Remote Sens., vol.

32, no. 4, pp. 855-865, July,1994.

[25] D. C. Ghiglia, M. D. Pritt, “Two-dimensional phase unwrapping: theory, algorithms,

and software”, John Wiley & Sons, Inc, New York, 1998.

[26] R. M. Goldstein, H. A Zebker, C. L. Werner, “Satellite radar interferometry: Two-

dimensional phase unwrapping”, Radio Science, 713-720, July, 1988.

[27] W. Goblirsch, P. Pasquali, “Algorithms for calculation of digital surface models from

the unwrapped interferometric phase”, IGARSS, vol. 1, pp. 656 – 658, vol.1, 1996.

[28] W. Goblirsch, “The exact solution of the imaging equations for crosstrack interferome-

ters”, Geoscience and Remote Sensing, IGARSS '97, 1997 IEEE International, Vol. 1,

1997.

[29] T. Guneriussen, K. A. Hogda, H. Johnsen, I. Lauknes, “InSAR for estimation of

changes in snow water equivalent of dry snow”, IEEE Transactions on Geoscience and

Remote Sensing, Vol. 39, Issue 10, pp. 2101–2108, 2001.

[30] L. C. Graham, “Synthetic aperture radar for topographic mapping”, Proceedings of the

IEEE, vol. 62, pp. 763-768, 1974.

Section A 49

[31] J. O. Hagberg, L. M. H. Ulander, J. Askne, „Repeat-Pass SAR Interferometry of For-

ested Terrain”, IEEE Trans. Geosc. and Remote Sens., vol. 33, no.2 , pp. 331-340.

March, 1995.

[32] R. F. Hanssen, T. M. Weckwerth, H. A. Zebker, and R. Klees, “High-resolution water

vapor mapping from interferometric radar measurements”, Science, 283, 1295-1297,

February, 1999.

[33] R. Hanssen, “Radar Interferometry – Data Interpretation and Error Analysis”, Kluwer

Academic Publishers, Dordrecht/Boston/London, 2001.

[34] D. A. Hastings, P. K. Dunbar, „Development and Assessment of the Global Land One-

km Base Elevation Digital Elevation Model (GLOBE). International Archives of Photo-

grammetry and Remote Sensing, 32(4), pp. 218-221. 1998.

[35] S. Hensley and P. Rosen, NASA/JPL, personal communication, 2002.

[36] W. G. Kropatsch, D. Strobl, “The generation of SAR layover and shadow maps from

digital elevation models”, IEEE Trans. on Geosci. and Remote Sens., vol. 28 , issue 1,

pp. 98 - 107, 1990.

[37] R. Lanari, G. Fornaro, D. Riccio, M. Migliaccio, K. P. Papathanassiou, J. R. Moreira,

M. Schwabisch, L. Dutra, G. Puglisi, G. Franceschetti, M. Coltelli, “Generation of dig i-

tal elevation models by using SIR-C/X-SAR multifrequency two-pass interferometry:

the Etna case study”, IEEE Transactions on Geoscience and Remote Sensing, Vol.

34, Iss. 5 , pp. 1097–1114, 1996.

[38] S.N. Madsen and H. A.Zebker, “Automated Phase Retrieval in Across Track SAR Inter-

ferometry”, IEEE 91-72810/92$3.00, pp. 1582 –1584, 1992.

[39] U. Marschalk, A. Roth, M. Eineder, S. Suchandt, “Comparison of DEMs derived from

SRTM / X- and C-Band”, submitted to IEEE IGARSS 2004, Anchorage.

Section A 50

[40] D. Massonnet et. al., “Reduction of the Need for Phase Unwrapping in SAR Interfer-

ometry”, IEEE Transactions on Geoscience and Remote Sensing, Volume 34, Number

2, pp. 489-497, 1996.

[41] Numerical Recipes in C, The Art of Scientific Computing, Cambridge University Press,

1994.

[42] M. D. Pritt, J. S. Shipman, Least-squares two-dimensional phase unwrapping using

FFT's, IEEE Transactions on Geoscience and Remote Sensing, pp. 706-708, 1994.

[43] B. Rabus, M. Eineder, A. Roth, R. Bamler, “The Shuttle Radar Topography Mission – a

new class of digital elevation models acquired by space borne radar”, ISPRS Journ. of

Photogrammetry & Remote Sensing, 57, pp. 241-262, 2003.

[44] A. Reigber, A. Moreira, “First demonstration of airborne SAR tomography using multi-

baseline L-band data”, IEEE Transactions on Geoscience and Remote Sensing, Vol.

38, pp. 2142 – 2152, 2000.

[45] P. A. Rosen, S. Hensley, I. R. Joughin, Fuk K. Li, S. N. Madsen, E. Rodriguez, and R. M.

Goldstein, “Synthetic Aperture Radar Interferometry”, Proceedings of the IEEE, Vol.

88, No. 3, March 2000.

[46] A. Roth, W. Knoepfle, B. Rabus, S. Gebhardt, D. Scales, “GeMoS-A system for the

geocoding and mosaicking of interferometric digital elevation models”,

Geoscience and Remote Sensing Symposium, IGARSS '99, vol. 2, pp. 1124-1127, 1999.

[47] Digital Elevation Model from the Ötztal with 12.5 meter spacing, generated from 1969

optical data, kindly provided by H. Rott, Inst. for Meterology and Geophysics, Univer-

sity of Innsbruck, Austria

[48] G. Schreier, Ed., „SAR geocoding: data and systems“, Karlsruhe, Wichmann, 1993.

[49] M. Schwäbisch, “A fast and efficient technique for SAR interferogram geocoding”,

Geoscience and Remote Sensing Symposium Proceedings, IGARSS '98, vol. 2, pp.

1100-1102, 1998.

Section A 51

[50] D. Small, E. Meier, D. Nuesch, “Phase Noise Countermeasures for Synthetic Interfero-

gram Generation”, Geoscience and Remote Sensing Symposium, IGARSS '02, IEEE In-

ternational, Vol. 4, pp. 2546-2548, 2002.

[51] N. Span, „Zur Dynamik des Kesselwandferners“, Dissertation, Universität Innsbruck,

214 S., 1999.

[52] S. Suchandt, M. Eineder, “Experiences with SRTM/X-SAR phase unwrapping using the

minimum cost flow method”, Geoscience and Remote Sensing Symposium, IGARSS '03,

vol. 7, pp. 4380–4382, 2003.

[53] M. Suess, S. Riegger, W. Pitz, R. Werninghaus, “TerraSAR-X – Design and Perform-

ance”, Proc. of 4th European Conference on Synthetic Aperture Radar EUSAR, Köln,

Germany, 2002.

[54] S. Xiao, D. C. Munson, “Optimal Antenna Spacings in Interferometric SAR”, in Pro-

ceedings of SPIE, Vol. 4053, pp. 94-101, Aug. 2000.

[55] H. A. Zebker and R. M. Goldstein, „Topographic mapping from interferometric syn-

thetic aperture radar observations“, Journal of Geophysical Research, vol. 91, pp. 4993-

4999, 1996.

[56] M. Zink, “The TerraSAR Project”, Proceedings of ESA Fringe 2003 Workshop, Fras-

cati, ESRIN, 2003. http://earth.esa.int/workshops/fringe03/participants/569/paper_TSL-

INSAR_OBJ-Fringe03.pdf

Section A 52

References of Sections B-G

[57] Adam N., Eineder M., Breit H., Suchandt S., "Shuttle Radar Topography Mission

(SRTM): DLR's Interferometric SAR Processor for the Generation of a Global Digital

Elevation Model", Workshop on ERS SAR Interferometry FRINGE'99, Liège, Belgium,

1999, http://www.esa.int/fringe99.

[58] Eineder M., Bamler R., Adam N., Suchandt S., Breit H., Steinbrecher U., Analysis of

SRTM Interferometric X-Band Data: First Results, IGARSS’ 2000.

[59] Monti Guarnieri, A., Biancardi, P., D’ Aria, D., Rocca, F., Accurate and Robust Baseline

Estimation, Workshop on ERS SAR Interferometry FRINGE'99, Liège, Belgium, 1999,

http://www.esa.int/fringe99.

[60] Nagler T., “Methods and Analysis of Synthetic Aperture Radar Data from ERS-1 and

X-SAR for Snow and Glacier Applications”, Dissertation, Universtity of Innsbruck,

1996.

[61] Wilkinson, A.J., “Synthetic Aperture Radar Interferometry: A Model for the Joint Sta-

tistics in Layover Areas”, Proc. of IEEE/COMSIG, Cape Town, 1998.

[62] Ahmadzadeh, M.R.; Petrou, M.; Error statistics for slope and aspect when derived from

interpolated data, Geoscience and Remote Sensing, IEEE Transactions on , Volume: 39

Issue: 9 , Sept. 2001, Page(s): 1823 –1833, 2001.

[63] Bamler, R., Interferometric Stereo Radargrammetry: Absolute Height Determination

from ERS-ENVISAT Interferograms, Proceedings of IGARSS, 2000, pp. 742-745.

[64] Eineder, M., Holzner, J.: Interferometric DEMs in Alpine Terrain - Limits and Options

for ERS and SRTM. IGARSS '00, Honolulu, Hawai, USA, 24.-28. July 2000, IEEE,

Proceedings of IGARSS'2000, IEEE Publications.

[65] S.N. Madsen, „On absolute phase determination techniques in SAR interferometry“,

SPIE Conference on Radar Sensor Technology, 1995, p. 393-401.

Section A 53

[66] Madsen, S.N., Zebker, H. A., Martin, J., Topographic Mapping Using Radar Interfer-

ometry: Processing Techniques, IEEE Transactions on Geoscience and Remote Sensing,

Vol 31. No. 1, pp. 246 –256, January 1993.

[67] Scheiber, R., Moreira, A., Coregistration of Interferometric SAR Images Using Spectral

Diversity, IEEE Transactions on Geoscience and Remote Sensing, Vol. 39, No. 5, pp.

2179-2191, September 2000.

[68] Bamler, R., Davidson, G.W.: Multiresolution Signal Representation for Phase Unwrap-

ping and Interferometric SAR Processing”, IGARSS 97, Singapore, 1997.

[69] M. Hubig, S. Suchand, M. Eineder, „Automatic correction of baseline and phase un-

wrapping errors in SAR interferograms“, EUSAR 2000, Munich.

[70] R. Bolter and F. Leberl, “Phenomenology-Based and Interferometry-Guided Building

Reconstruction from Multiple SAR Images,” Proceedings of EUSAR 2000, München,

pp. 687-690, 2000.

[71] M. Eineder, H. Breit, N. Adam, J. Holzner, S. Suchandt, and B. Rabus, “SRTM X-SAR

calibration results,” Proc. IGARSS, vol 2, pp. 748 –750, 2001.

[72] G. Franceschetti, A. Iodice, M. Migliaccio, and D. Riccio, “Efficient simulation of SAR

interferometric raw signal pairs,“ Proc. IGARSS, Singapore, vol. 4, pp. 1701 – 1703,

1997.

[73] Franceschetti, A. Iodice, M. Migliaccio, and D. Riccio, “Simulation of SAR interfer-

ometric raw signal pairs corresponding to real scenes”, Proc. IGARSS, Seattle, vol. 5,

pp. 2653 - 2655, July, 1998.

[74] S. Fuglistaler, P. Pasquali, and D. Small, “A comparison of phase to height conversion

methods for SAR interferometry,” Proc. IGARSS, vol.1, pp. 342 –344, 1996.

[75] D. Massonnet, M. Rossi, C. Carmona, F. Adragna, G. Peltzer, K. Feigl, T. Rabaute,

“The displacement field of the Landers earthquake mapped by radar interferometry,”

Nature, vol. 364, pp. 138-142, 1993.

Section A 54

[76] J. J. Mohr and S. N. Madsen, “Geometric calibration of ERS satellite SAR images,”

IEEE Transactions on Geoscience and Remote Sensing, vol. 39, no. 4 , pp. 842 –850,

April, 2001.

[77] O. Montenbruck and E. Gill, “Satellite Orbits – Models, Methods, and Applications”,

Springer, Berlin; Heidelberg; New York, 2000.

[78] D. Petit, F. Adragna, „A new interferogram simulator: 2SIR. Study of coherence losses

for Tortured Reliefs,“ Proc. CEOS SAR Calibration Workshop, ESA/CNES Toulouse,

1999.

[79] B. Schättler, M. Eineder, W. Knöpfle, and M. Hubig, “Operational Interferometric ERS

Tandem Data Processing,” Proc. CEOS SAR Calibration Workshop, Toulouse, 1999.

[80] D. Small, E. Meier, and D. Nüesch, „Efficient Geolocation and Image Simulation for

Extended SAR Strip Maps,“ Proc. IGARSS, vol. 7, pp. 3152 –3154, 2001.

[81] H. Rott, A. Siegl, “Glaciological Studies in the Alps and in Antarctica Using ERS Inter-

ferometric SAR”, Proc. ESA FRINGE Workshop 1996, Zürich,

(http://www.geo.unizh.ch/rsl/fringe96/), 1996.

[82] U. Wegmüller, “Automated terrain corrected SAR geocoding,” Proc. IGARSS, vol. 3,

pp. 1712 –1714, 1999.

[83] A.J. Wilkinson, “Synthetic aperture radar interferometry: Amodel for the joint statistics

in layover areas“, in Proceedings of COMSIG’ 98, Cape Town, South Africa, Sep 1998.

[84] M. Hubig, S. Suchandt, M. Eineder, Automatic correction of baseline and phase un-

wrapping errors in SAR interferograms, Proceedings of EUSAR 2000, 3rd European

Conference on Synthetic Aperture Radar, May 23-25, 2000, pp. 131-134, Munich,

Germany, 2000.

[85] Ferretti, A.; Prati, C.; Rocca F.; Monti Guarnieri, A.; Multibaseline SAR interferometry

for automatic DEM reconstruction. In Third ERS Symposium--Space at the Service of

Section A 55

our Environment, Florence, Italy, 17-21 March 1997, ESA SP-414, pages 1809-1820,

1997.

[86] Ferretti, A; A. Monti Guarnieri, C.Prati and F.Rocca, Multi Baseline Interferometric

Techniques and Applications, in F̀RINGE 96' workshop on ERS SAR Interferometry,

Zürich, Switzerland, 30 Sep-2 October 1996, 1996.

[87] Just, D.; Bamler, R.; Phase statistics of interferograms with applications to synthetic

aperture radar. Applied Optics, 33(20):4361-4368, 1994.

[88] Massonnet, D.; Thouvenot, E.; Ramongassie, S.; Phalippou, L.; A wheel of passive ra-

dar microsats for upgrading existing SAR projects, , IGARSS 2000.

[89] Rocca F., Prati C., Ferretti A., An Overview of SAR Interferometry. Proc. 3rd ERS

Symposium, Florence 1997, http://florence97.ers-symposium.org.

[90] Knöpfle, W., Strunz, G., Roth, A., „Mosaicking of digital elevation models derived by

SAR interferometry”. International Archives of Photogrammetry and Remote Sensing

32, Part 4, 306–313, 1998.

[91] Krieger, G.; Amiot, T.; Interferometric Performance of a Cartwheel Constellation for

TerraSAR-L, ESA FRINGE workshop, ESA, Frascati 2003.

[92] Prati C.,Giani M. and Leuratti N., SAR interferometry: a 2D Phase Unwrapping Tech-

nique Based on Phase and Absolute Value Informations. Proc. IGARSS 90, 1990,

Washigton D.C., USA, pp. 2043-2046, 1990.

Section B

Michael Eineder and Jürgen Holzner

Interferometric DEMs in Alpine Terrain -

Limits and Options for ERS and SRTM

Geoscience and Remote Sensing Symposium, 2000. Proceedings.

IGARSS 2000. IEEE 2000 International , Volume: 7 , 24-28 July 2000

Pages:3210 - 3212 vol.7

Section C

Michael Eineder

Problems and Solutions for InSAR Digital

Elevation Model Generation of Mountainous

Terrain

ESA FRINGE SAR Interferometry Workshop, Frascati 2003.

Section C - Published in proceedings of ESA FRINGE workshop, 2003 1

PROBLEMS AND SOLUTIONS FOR INSAR DIGITAL ELEVATION MODEL GENERATION

OF MOUNTAINOUS TERRAIN

M. Eineder

German Aerospace Center (DLR), Oberpfaffenhofen, D-82234 Wessling, Germany, Email: Michael.Eineder@dlr.de

ABSTRACT

During the last decade, the techniques to generate digital elevation models (DEM) from SAR interferometry have been demonstrated and refined to a quasi-operational status using data from the ERS tandem mission. With this experience and an improved single-pass system concept, data from the Shuttle Radar Topography Mission (SRTM) acquired in 2000 have been used to produce a global DEM with unprecedented quality. However, under the extreme viewing conditions in mountainous terrain both ERS and SRTM suffer from or even fail due to the radar specific layover and shadow effect that leaves significant areas uncovered and poses severe problems to phase unwrapping. The paper quantifies the areas leading to layover and shadow, and shows innovative ways to overcome shadow and improve phase unwrapping in general. The paper is organized in three major sections. Firstly, the problem to map slopes is addressed in a simplified statistical way. Strategies to optimize the incidence angle for single and multiple observations are proposed. Secondly, a new algorithm is presented that makes the best from shadow by actively using it to help phase unwrapping. Thirdly, an outlook on the use of delta-k interferometry for phase unwrapping is given. The paper aims to improve the understanding of the mapping geometry of radar systems and the data currently available and to improve the concepts of future systems and missions.

range

azimuth

Fig. 1: Shadow areas visible as dark regions in an SRTM X-SAR intensity image of a mountain in Ötztal / Austria.

Fig. 2: The interferometric phase in the shadow areas is random noise. (SRTM X-SAR, Ötztal / Austria)

Section C - Published in proceedings of ESA FRINGE workshop, 2003 2

1. INTRODUCTION

The generation of digital elevation models (DEMs) from interferometric SAR data has become an important application of SAR technology. Compared to conventional optical stereo techniques SAR interferometry is particularly attractive because it works independent from scene contrast and illumination and under almost all weather conditions. However, when it comes to mapping mountains with high slopes and large altitude variations then SAR interferometry is confronted with specific problems that are not yet completely solved. Shadow and layover effects prevent the radar from seeing a large percentage of mountainous terrain. Even if these hidden areas are not of interest, the resulting phase unwrapping problems may cause large height errors in the visible areas. Fig. 1 and Fig. 2 demonstrate that shadow causes interferometric phase noise in SRTM X-SAR data with a rather flat incidence angle of 54.5°. In contrast, ERS-1 and ERS-2 look rather steeply with 23° leading to even larger areas of layover as shown in Fig. 3 and Fig. 4. Because of the viewing geometry the layover areas are compressed in slant range geometry and become much larger when transformed to ground range.

range

azimuth

+ π

-π Fig. 3: Layover areas visible as bright areas in an ERS intensity image of a mountain in Ötztal / Austria.

Fig. 4: The interferometric phase in the layover areas is noise or even ambiguous with reverse fringe frequency. (ERS, Ötztal / Austria).

2. WHAT THE RADAR CAN “SEE”

Fig. 5 illustrates the viewing geometry of a SAR system. The antenna moves with velocity vector Vr

and looks in

direction Lr

onto a terrain facet characterized by the normal vector Nr

. The vector Mr

is defined orthogonal to Lr

and Vr

, i.e.,

VLMrrr

×= . Three conditions must be met for successful imaging. Firstly, the facet must be visible, i.e., tilted towards the radar system:

0<⋅ NLrr

. (1)

If this condition is not fulfilled, the facet is viewed from the backside and must be hidden by some other facet because the SAR antenna is located outside of the body of the earth. Secondly, the facet must be upright in range direction:

Section C - Published in proceedings of ESA FRINGE workshop, 2003 3

0>⋅ NMrr

, (2)

otherwise the facet is imaged reversely and will be “laid over” by another facet when the slope decreases again with increasing range. Thirdly, the facet must not be hidden by another facet. This condition can not be described by the local slope alone. Ray tracing must be performed to secure this condition as done in [4]. Here, this effect is neglected for simplicity even if it accounts for a significant percentage of blind areas.

y Nr

Lr

x

z

Mr

Vr

aspect

slope

SAR antenna

Fig. 5: Schematic viewing geometry of a SAR. Fig. 6: A dome contains all possible combinations of aspect and slope. The visible areas are marked in light gray.

In geophysical applications the slope and aspect angles are generally used instead of the normal vector. Slope is defined as an angle between 0° and 90° measured between the horizontal plane and the surface and aspect is defined as the orientation angle of the slope measured clockwise with respect to north direction. A dome as shown in Fig. 6 contains all relevant combinations of aspect and slope conveniently arranged in a polar diagram. Fig. 7 shows a polar diagram of the eye-shaped combinations of slope and aspect angles that are visible to a SAR looking with 45° incidence angle to the right and flying northwards.

Fig. 7: Polar diagram of the aspect and slope angle combinations visible to a radar flying northward and looking with an incidence angle of 45°.

shadow

slopes

layover

slopes

useful

slopes

aspect

slope

Section C - Published in proceedings of ESA FRINGE workshop, 2003 4

3. DISTRIBUTION OF SLOPES IN MOUNTAINOUS TERRAIN

In order to assess quantitatively the percentage of the surface that can not be mapped by a single SAR observation, knowledge of the distribution of the slopes is required. Two test areas with slightly different characteristics are examined for that purpose. Firstly, the valley of the Rhine and Tessin in Switzerland. Secondly, the Ötztal valley in Austria. The Switzerland site is a larger area with moderate to rough alpine topography. It is assumed to represent the majority of mountainous regions in the world. Ötztal is an extremely rugged area representative for the most critical regions of the world. Switzerland test area: For this area shown in Fig. 8 a reference DEM with 100 m spacing is available. The area extends between 8030’ to 100 East and 46030’ to 470 North. Ötztal test area: The Ötztal site shown in Fig. 9 is selected because it contains some extremely rugged mountains and because it is very well known from other glaciological and hydrological studies performed at the University of Innsbruck. The available DEM covers the area between 10°30’ and 11°0’ East and from 46°45’ to 47° North covering an area of about 40 by 25 square kilometers. The DEM is regularly sampled at intervals of 12.5 m and quantized at 1 m levels. It has been generated from several aerial photos taken between 1960 and 1970. Unfortunately, the accuracy of this DEM is not completely known. However, high resolution DEMs of such areas are rare and this DEM proved to be a valuable source for this study. The high quality could be confirmed in [3]. From each DEM the probability distribution function (PDF) of slope and aspect is estimated using the 8 directions between adjacent pixels as described in [1]. The 2-dimensional PDF is rather rough because of DEM quantization and other non-isotropic effects caused by DEM generation. Therefore the PDF is averaged over all aspect values assuming an isotropic distribution. Fig. 10 and Fig. 11 show the estimated slope PFDs for both test areas.

*Rhine *Chur

*Tiefencastel

Fig. 8: Shaded view of Switzerland test area. Fig. 9: Shaded view of Ötztal test area-

Fig. 10: Slope PDF of Switzerland test area. 99 % of the slopes are smaller than 52°.

Fig. 11: Slope PDF of Ötztal test area. 99 % of slopes are smaller than 55°.

90 %

99 % 99.9 %

90 %

99 %

99.9 %

°

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4. OPTIMIZATION OF A SINGLE SAR ACQUISITION WITH RESPECT TO SLOPE

Knowing the eye-shaped mask of visible slopes in the polar PDF from Fig. 7 and the actual slope distribution, the optimal SAR incidence angle can be estimated by maximizing the coverage integral

∫∫ ⋅= βαβαβα ddmaskPDFc ),(),( , (3)

where α and β are the aspect and slope angles. Fig. 12 shows that the maximum coverage is achieved at 45° incidence angle.

Note that the curve is an upper bound as it does not include the areas shaded or laid over by other facets. Fig. 13 to Fig. 15 show examples of geocoded radar images with varying incidence angles and visualize that an ENVISAT/ASAR beam 6 acquisition with 41° reveals much less layover and shadow distortions than those of ERS and SRTM/X-SAR.

Fig. 12:: Achievable coverage of alpine terrain with incidence angles between 10° and 75°.

ASAR 41°

Fig. 13: Geocoded ERS SAR image of Ötztal area.

Fig. 14: Geocoded ENVISAT/ASAR image of Ötztal area.

Fig. 15: Geocoded SRTM/X-SAR image of Ötztal area.

5. OPTIMIZATION OF MULTIPLE SAR ACQUISITION WITH RESPECT TO SLOPE

Assuming that data more than one acquisition can be combined to achieve maximum coverage, it may be favorable to use a slightly different incidence angle than 45° in order to obtain a better signal to noise ratio (SNR) at slightly steeper incidence angles or to get a better total coverage of the PDF. Several acquisitions can be optimized similar to (3) by optimizing the integral

∫∫ ⋅ ββαβα dadmaskPDFi

iU ),(),( , (4)

where Ui

is the logical set union of the observation maps. Figures Fig. 16 to Fig. 18 show a number of reasonable

combinations of two pass slope masks of existing sensors even if left looking mode for ERS is hypothetic. It can be seen that the

SRTM 54° Shadow

ERS 23° Layover

Section C - Published in proceedings of ESA FRINGE workshop, 2003 6

circle marking 99% of all slopes can be covered with ERS date if left and right looking or ascending and descending observations are combined. However, it is not completely covered by the combination of ascending and descending SRTM data.

Fig. 16: Slope mask of (virtual) left and right looking ERS ascending passes for θ=23°. Coverage: 99.98 %.

Fig. 17: Slope mask of right looking ascending and descending passes for θ=23°. Coverage: 99.98%.

Fig. 18: Slope mask of ascending and descending SRTM left looking passes with θ=54°. Coverage: 99.7 %.

It is emphasized again that the proposed method is not precise but an upper bound for the achievable coverage. It is a convenient and illustrative method to assess the viewing geometry of different radar observations. With ENVISAT/ASAR there is the possibility to optimize the coverage by selecting the appropriate incidence angle for a certain terrain type. However the data from ERS and SRTM is acquired with a fixed, non optimal angle. In the following a method is presented that at least allows to overcome the destructive phase noise in shadow regions. 6. A TECHNIQUE TO HANDLE RADAR SHADOW IN SAR INTERFEROMETRY

Shadow in SAR data contains no echo signal and hence the interferometric phase is random. This random phase may lead to severe phase unwrapping problems and consequently, even if masked out, to coverage and phase consistency problems. Understanding that the interferometric phase gradient along the shadow line is zero helps phase unwrapping significantly. Firstly, the shadow area is no more a nuisance but actively helps the phase unwrapping algorithm to “climb” mountains from the shadowed backside. Secondly, the shadowed areas in the DEM can at least be filled with height values along the shadow line that are more reasonable than pure noise. The algorithm is described in detail in [5] and shortly illustrated in Fig. 19.

α

Antenna 1

ζ(r) r1

r2

B⊥

Antenna 2

r

The elevation angle along the shadow line is constant:

)()( 21 rr ζζ = , (5)

and hence the interferometric phase is constant, i.e., the phase gradient is zero. This can also be understood by using the formula for the fringe frequency from [7]:

( ) 0tan2

≈−

−=∆ ⊥

αζλr

cBf , (6)

because

°−= 90ζα (7).

Fig. 19: Interferometric shadow reconstruction.

Section C - Published in proceedings of ESA FRINGE workshop, 2003 7

An application example for the algorithm is shown in Fig. 20. The extreme slopes of Nanga Parbat (8125 m) could only be unwrapped correctly after correction of the phase gradients in the shadow regions.

Fig. 20: Perspective view Nanga Parbat mountain (8125 m) from SRTM/X-SAR data. Despite the large shadow areas the phase of this steep terrain could be recovered by interferometric shadow reconstruction technique. The linear geometric interpolation along the dark shadow areas is clearly visible. Still, DEM reconstruction without a-priori knowledge of the integer phase ambiguity requires phase unwrapping which gets more difficult as the baseline is increased in order to increase accuracy. A solution to avoid phase unwrapping by direct estimation of the absolute phase for each pixel could be delta-k interferometry. 7. USING DELTA-K TECHNIQUE FOR PHASE UNWRAPPING

Using an interferometric SAR for precise ranging as in the case of DEM reconstruction is inherently limited by the phase ambiguity introduced by the small bandwidth and by the single carrier frequency operation. The fundamentals of an approach to overcome this limitation have been proposed in [8], [9], [10] by exploiting the frequency dispersion available in the range bandwidth. If the bandwidth B is divided into two sub-bands with bandwidth B/2 separated by B/2, then a differential interferogram can be formed from the sub-band interferograms with a synthesized wavelength of 2c/B. For the small bandwidth systems currently in space this synthesized wavelength is so small compared to the natural wavelength λ=c/f0 that this method has little practical significance. The reason is that the small differential phase information contained in the upper and lower sub-band is very noisy when scaled to the wavelength λ. Nevertheless this method has found application in interferometric co-registration [11] and, recently for phase unwrapping of single bright targets for the estimation of snow water equivalent [6]. The technique could in principle be used for phase unwrapping of distributed targets as shown in Fig. 21 and Fig. 22 with SRTM X-SAR data. Due to the rather small usable bandwidth B/2=4 MHz, this configuration is equivalent to an additional wavelength of 74 meters besides the 3.1 centimeter X-band wavelength or to an additional baseline of 2.5 centimeters with the nominal 60 meter mast. Because of these bad conditions the DEM reconstructed from delta-k technique is very noisy and must be averaged over large areas to reduce the error. The key factor for the usability of delta-k technique for phase unwrapping is the ratio between carrier frequency f0 and bandwidth B. For SRTM X-SAR this is 1200, for ERS it is 341.

Section C - Published in proceedings of ESA FRINGE workshop, 2003 8

Fig. 21: SRTM X-SAR DEM of data take 153.260 over mountains in Iran. The wavelength is 3.1 cm, the resolution ca. 30 meters.

Fig. 22: SRTM X-SAR DEM , processed using delta-k technique - without phase unwrapping. The synthesized wavelength is 74 meters, the resolution is reduced to ca. 6 km in order to reduce the error enough so that the terrain gets visible.

Future high bandwidth systems like TerraSAR-X or TerraSAR-L will have carrier to bandwidth ratios of 32 or 16, respectively. This means that the synthesized wavelength is much closer to the natural one and can be used like a second carrier frequency for phase unwrapping. The high bandwidth transmit and receive components of future SAR systems should be optimized to use two relatively small bandwidths separated as far possible. Only one receiver and analog digital converter are required to sample these dual band signals. Such split bandwidth systems could simplify phase unwrapping enormously and provide enormous benefit to all disciplines of SAR interferometry. 8. SUMMARY

Digital elevation models from SAR interferometry have shown excellent results over moderate terrain so far. Over rugged mountains the interferometric technique still has to be improved to overcome SAR specific problems from layover, shadow and especially from phase unwrapping. Promising techniques exist that can be further developed for future, improved systems. An interferometric system optimized for mountains should operate with an incidence angle close to 45° and with dual frequency bands. 9. REFERENCES

[1] Ahmadzadeh, M.R.; Petrou, M.; Error statistics for slope and aspect when derived from interpolated data, Geoscience and Remote Sensing, IEEE Transactions on , Volume: 39 Issue: 9 , Sept. 2001, Page(s): 1823 –1833, 2001. [2] Bamler, R., Interferometric Stereo Radargrammetry: Absolute Height Determination from ERS-ENVISAT Interferograms, Proceedings of IGARSS, 2000, pp. 742-745. [3] Eineder, M., Efficient simulation of SAR interferograms of large areas and of rugged terrain, Geoscience and Remote Sensing, IEEE Transactions on, Volume: 41 Issue: 6 , June 2003, Page(s): 1415 -1427.

Section C - Published in proceedings of ESA FRINGE workshop, 2003 9

[4] Eineder, M., Holzner, J.: Interferometric DEMs in Alpine Terrain - Limits and Options for ERS and SRTM. IGARSS '00, Honolulu, Hawai, USA, 24.-28. July 2000, IEEE, Proceedings of IGARSS'2000, IEEE Publications. [5] M. Eineder, S. Suchandt, Recovering Radar Shadow to Improve Interferometric Phase Unwrapping and DEM Reconstruction, IEEE Transactions on Geoscience and Remote Sensing, in print. [6] Engen, G., Guneriussen, T., Overrein O., New approach for Snow Water Equivalent (SWE) estimation using repeat pass interferometric SAR, IGARSS 2003. [7] Gatelli, F., Monti Guarnieri, A., Parizzi, F., Pasquali, P. , Prati, C. , and Rocca, F., “The wavenumber shift in SAR interferometry,” IEEE Trans. on Geosci. and Remote Sens., vol. 32, no. 4, pp. 855-865, Jul,1994. [8] S.N. Madsen, „On absolute phase determination techniques in SAR interferometry“, SPIE Conference on Radar Sensor Technology, 1995, p. 393-401. [9] Madsen, S.N., Zebker, H. A., Automated Phase Retrieval in Across Track SAR Interferometry, IEEE 91-72810/92$3.00, pp. 1582 –1584, 1992 [10] Madsen, S.N., Zebker, H. A., Martin, J., Topographic Mapping Using Radar Interferometry: Processing Techniques, IEEE Transactions on Geoscience and Remote Sensing, Vol 31. No. 1, pp. 246 –256, January 1993. [11] Scheiber, R., Moreira, A., Coregistration of Interferometric SAR Images Using Spectral Diversity, IEEE Transactions on Geoscience and Remote Sensing, Vol. 39, No. 5, pp. 2179-2191, September 2000.

Section D

Michael Eineder

Interferometric DEMs in Alpine Terrain

Geoscience and Remote Sensing Symposium, 2001. IGARSS '01.

IEEE 2001 International , Volume: 5 , 9-13 July 2001.

Pages:2040 - 2042 vol.5

Section E

Michael Eineder

Efficient Simulation of SAR Interferograms

of Large Areas and of Rugged Terrain

IEEE Transactions on Geoscience and Remote Sensing,

Vol. 41, No. 6, pp. 1415-1427, June 2003.

Section F

Michael Eineder and Steffen Suchandt

Recovering Radar Shadow to Improve

Interferometric Phase Unwrapping and DEM

Reconstruction

IEEE Transactions on Geoscience and Remote Sensing,

Vol. 41, No. 12, pp. 2959-2962, December 2003.

Section G

Michael Eineder and Nico Adam

A Maximum Likelihood Estimator to

Simultaneously Unwrap, Geocode and Fuse

SAR Interferograms From Different Viewing

Geometries Into One Digital Elevation Model

Accepted for publication in the

IEEE Transactions on Geoscience and Remote Sensing, 2004.