The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part BI. Beijing 2008 
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Compute the distance /^between the image center and 
the earth’s center with the data of incidence angle (j and 
length of slant range r N/2 at the image central point. 
Compute Q by use of r according to Equ.9 
r] +H 2 - R. 
ß / = arccos(- 
2 Hr. 
-) 
(9) 
5. Compute the flat ground phase difference between column 
j and the central column N/2 in Equ.10 
■ _ 2xBcos(6 N!2 -a) 2nB 2 Ar j AkB{H 2 -R h 2 )cos(<9 v/2 - or) 
AH sin 0 NI1 1 Arf 2 2AHrf 2 sin0 NI2 
(10) 
6. After some practical revision of Equ. 10, flat ground phase 
of every point at the coordinate of (i, j) can be presented 
in Equ. 11 
,/./ 2nBcos(0 NI2 -a) 2 kB 2 4kB(H 2 -R h 2 )cos(d Nn -a) +KxAr) 
R AH sin0 NI2 Arf 2 2AHrf 2 s\n0 N/2 
(11) 
However, it can not be directly applied to compute elevation 
because the phase recorded on intergerogram is only a part of 
its real value called major value with a range of(-^,^]. The 
real value of a phase is equal to its major value plus integral 
multiple of2;r, in a process call phase unwrapping [3]. After 
establishing the relation between the real phase difference 
A^and the elevation Az as shown in Equ. 11, interferogram can 
be used to produce DEM by elevation computation. 
4*3cos(11) 
Ar 0 H sin 9 0 
2.3.2 Algorithm for Elevation Computation 
Based on the geometric information in Fig.2 and algebraic 
relation in Equ.ll, we proposed an algorithm for elevation 
computation shown in Fig.4. This algorithm grounded on Price 
Geometry Model (PGM) brings improved ambiguity of height 
in Equ. 12 compared to those of Approximate Geometry Model 
(AGM) in Equ. 13. While two equations have the same value 
only at image central point, the ambiguity of height rooting in 
PGM which involves curvature of the earth has better precision 
at other points. 
7. To a point P(i,j), the result of flattening phase can be 
attained by phase recorded in a SAR image minus the 
flat ground phase A(f>f , namely ¡f, = 0 iJ - Aff 
8. Observe the output of this step: if unsatisfactory result is 
gained, we should adjust some basic parameters and go 
back to reprocess it; otherwise, we need only store it for 
next steps 
2.3 Algorithm for Elevation Computation 
^ ArH sin 9 
2Bcos(9-a)R h 
(12) 
. Ar sin 9 n 
=— ~ 
2 B L 
(13) 
2.3.1 Principle of Elevation Computation 
With the assumption of no noises, the left information of 
interferogram after flattening phase merely reflects elevation. 
Baseline 
Incidence angle ¡3 at 
image center 
DistanceHbetween satellites 
and the earth’s center 
Slant range r „ n at 
image center 
Distance R 4 between image 
center and earth’s center 
Relative height h, at the point P(i,j) compared to image center 
Relative height jj at the point P(i,j) compared to the earth’s 
I 
Store output 
Slant range at column 
j and its resolution 
estimation 
Length 2? of baseline and 
Angle 9 Mn of slant range 
V 
Angle of si 
' 
ant range 
angle a. 
at image center 
at colu 
inn J 
Fig.2 flow chart of algorithm for elevation computation 
2.4 Algorithm for Baseline Estimation 
As shown in Fig. 4, there are five vector points on the master 
track including P mX P m2 P m} P m4 P m5 which are separately 
corresponding to its UTM timef mi t m2 t mi t mA t m5 ■ Similarly,