ANSI-C program: comb_interfs.c
NAME
comb_interfs - Combine complex interferograms by integer scaling
of the phase.
SYNOPSIS
comb_interfs <int-1> <int-2> <base-1>
<base-2> <factor-1> <factor-2> <width>
<combi_int> <combi_base> [sm]
| <int-1> | (input) complex interferogram 1 (fcomplex) |
| <int-2> | (input) complex interferogram 2 (fcomplex) |
| <base-1> | (input) baseline file 1 |
| <base-2> | (input) baseline file 2 |
| <factor-1> | (input) phase scaling factor 1 (float) |
| <factor-2> | (input) phase scaling factor 2 (float) |
| <width> | (input) width of interferograms |
| <combi_int> | (output) combined interferogram (fcomplex) |
| <combi_base> | (output) baseline file |
| [sm] | magnitude scale factor (default=1.0) |
EXAMPLE
comb_interfs 8560_8059.int 8560_9562.int 8560_8059.base
8560_9562.base 1 -3 3392 a-3b.int a-3b.base
1.0/SAMP>
Creates a complex valued "combined interferogram based on the two input interferograms by scaling the wrapped phases by factors of 1 and -3 for the first and second input interferogram, respectively.
INSTALLATION
Source code comb_interfs.c in ./src. For compilation adjust and
use Makefile: Executable version comb_interfs in ../bin
AVAILABILITY
Uses ISP and DIFF type definition files typedef_ISP.h, typedef_DIFF.h.
DESCRIPTION
comb_interfs combines two registered complex valued
interferograms into a new complex valued interferogram. The phase
of the new combined interferogram is equal to:
(wrapped_ phase_1 * factor_1 + wrapped_phase_2 * factor_2) modulo
2π
. The coherence of the combined interferogram is estimated based
on the assumption that the signal noise is scaled up with the
scaling factors, summed, and divided by the square root of 2 to
account for statistical independence of the two interferograms.
The signal is assumed to be the original signal multiplied by the
user specified signal multiplication factor sm. As default value
sm=1.0 is used standing for unchanged signal as compared to one
of the original interferograms.
As shown by the following considerations only integer valued phase scaling factors seem to be reasonable. The "wrapped" interferometric phase, i.e. the phase information available from an interferogram without phase unwrapping, is defined as the "unwrapped" interferometric phase modulo 2π
When scaling the interferometric phase, which is of interest for example to simulate the interferogram obtained with another baseline, we have to be aware of the fact that in principle the "unwrapped" interferometric phase needs to be scaled. When scaling with a positive or negative integer number the scaling of the "wrapped" phase may be directly scaled as the unknown number i of 2π remains an integer even after the scaling, i.e.
The combination of complex interferograms after scaling of the
"wrapped" interferometric phase with integer numbers may be of
interest for several reasons:
- To do a kind of differential interferometry without phase
unwrapping and geocoding requirement.
- To improve the sensitivity to topography.
In the first case the sensitivity to the topography is reduced as much as possible, in order to have a phase of the combined complex interferogram which is mainly determined by differential effects. The reduction of the sensitivity to topography is achieved by reducing the "simulated" baseline of the combined interferogram to a small value. A perpendicular baseline component of the combined interferogram of only 10m, for example, can be achieved by combination of two interferograms with perpendicular baseline components of 50m and 160m through scaling of the wrapped phases with factors of 3 and -1, respectively. In this example the unwrapped phase of the combined interferogram corresponds to the topographic phase of an interferogram with a 10 m baseline (i.e. a very small sensitivity to topography), plus 3 times the differential phase effects present in the first interferogram minus 1 time the differential phase of effects present in the second interferogram.
In the second case the phase noise and the sensitivity to differential effects is reduced and the sensitivity to topography is increased. The reduction of the sensitivity to differential effects is achieved simply by addition of independent interferograms. Assuming that the unwanted differential effects (I am thinking mainly of atmospheric distortions) of the two interferograms are independent allows to decrease their influence. At the same time the baseline of the combined interferogram may be increased as compared to the initial interferograms. Because the phase noise of the individual interferograms is multiplied with the scaling factors small scaling factors are preferred. The combination of two independent interferograms with comparable perpendicular baseline components (using scaling factors of 1), for example, allows increases the simulated baseline of the combined interferogram to twice that of the individual interferograms with a phase noise of the combined interferogram of only about 1.4 times that of the individual interferograms.
About the same technique but for another purpose was presented by Massonnet D., H. Vadon, and M. Rossi, Reduction of the need for phase unwrapping in radar interferometry, IEEE TGRS, 34-2 pp.489-497, 1996. Their idea was to generate combined interferograms with relatively small baselines in order to reduce the need of phase unwrapping.
As an example of an interferogram with a "combined" perpendicular baseline component of 21m obtained by combining registered complex interferograms of 58m and 95m perpendicular baseline components using phase scale factors of 2 and -1, respectively, for Solothurn, Switzerland.
OPTIONS
Selection of phase scaling factors of 1 and -1 allows to generate
a complex valued interferogram with the phase corresponding to
the difference between the phase of the first and second complex
valued interferograms.
SEE ALSO
typedef_ISP.h, typedef_DIFF.h.
© Copyrights for Documentation, Users Guide and Reference Manual by Gamma Remote Sensing, 2003.
UW, CW, last change 16-May-2003.