In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3A/V4 — Paris, France, 3-4 September, 2009 
identify automatically, while layover areas still carry useful 
information, even if this is embedded in clutter (see the example 
of a repeat-pass TerraSAR-X interferogram in Figure 1). 
Moreover, the incorporation of additional knowledge about 
buildings may help to separate useful signal from clutter, 
especially as buildings have regular shapes and, often, digital 
maps indicating the building footprints are available. 
Multi-baseline and multi-aspect approaches show great 
potential to reconstruct buildings with high accuracy and level 
of detail. However, the time needed to acquire the necessary 
images is usually too long for rapid mapping, especially in the 
context of providing crisis information. Consequently, the 
analysis in Section 3 concentrates on accuracy aspects of single 
pass interferometry. The building heights are expected to be 
computed from the interferometric signal of layover regions. 
The inherent contribution of clutter in these areas is 
accommodated by some loss of interferometric coherence, 
which is also taken into account for the final height accuracy. 
Figure 1 : Interferometric fringes in layover area of tall buildings 
computed from dual-pass TerraSAR-X interferogram (courtesy 
M.Eineder, DLR). 
3. HEIGHT ACCURACY OF INSAR MEASURMENTS - 
THEORY 
In this section we revise the mathematical theory for relating 
specific sensor and scene parameters with the desired height 
accuracy for the case of space-borne SAR. A detailed derivation 
of the formulae can be found in (Bamler & Schattler, 1993; 
Bamler & Haiti, 1998; Gumming & Wong, 2005). Figure 2 
(left) depicts the typical geometric configuration of across-track 
interferometry. The phase values of the two acquisitions can be 
derived from the well-known two-way range equation 
... 
0i=—— 2/? + 0 scatli (1) 
<h =— 2 (* + /№)+*, 
(2) 
where (f)^ and are the SAR phases at a certain pixel, A is the 
wavelength, R is the range between one antenna and the point 
on ground in viewing direction 0, and AR is the range 
difference induced by the baseline vector B and its component 
perpendicular to the viewing direction B ± , respectively. Under 
the assumption that the unknown phase contributions caused by 
random scattering (/> scatt x and <ft scatt 2 are identical 
t scatt, 1 ft scat t,2 
(3) 
one can express the interferometric phase (J) for a certain point 
by 
0 = fi-0 2 = — AR (4) 
A 
In order to convert the this phase into height values Z , it is 
useful to first formulate the functional relationship between 
AR and the direction perpendicular to R on ground, £ (see 
Figure 2 (right)): 
RR s A 
Ç = --^-AR = —-$- — (/> 
B, 
B ± An 
(5) 
Solving for (/) and projecting into the vertical direction Z yields 
AnB L z 
A R sin 0 
(6) 
Equation (6) is the basis to calculate the so-called phase-to- 
height sensitivity: 
d(f) _ An B ± 
dz A R sin# 
Figure 2: Geometric layout of across-track interferometry (left) and 
definition of local co-ordinate system on ground, C, , (right). 
Figure 3 illustrates the influence of varying incidence angle and 
baseline length on the phase-to-height-sensitivity. As can be 
seen, the interferometric measurement gets more and more 
sensitive the longer the baseline and the smaller (steeper) the 
incidence angle is. 
Figure 3: Influence of incidence angle and baseline on phase-to-height- 
sensitivity