Phase statistics of interferograms with applications to synthetic aperture radar (original) (raw)

Abstract

Interferometric methods are well established in optics and radio astronomy. In recent years, interferometric concepts have been applied successfully to synthetic aperture radar (SAR) and have opened up new possibilities in the area of earth remote sensing. However interferometric SAR applications require thorough phase control through the imaging process. The phase accuracy of SAR images is affected by decorrelation effects between the individual surveys. We analyze quantitatively the influence of decorrelation on the phase statistics of SAR interferograms. In particular, phase aberrations as they occur in typical SAR processors are studied in detail. The dependence of the resulting phase bias and variance on processor parameters is presented in several diagrams.

Figures (10)

Fig. 2. The pdf() of the interferometric phase for ¢9 = 0 and different values of the magnitude of the correlation coefficient |y|. The pdf is constant for |y| = 0 and converges toward a delta function as |y| approaches one. whereas the high coherence approximation is ad- equate only for deterministic, pointlike scatterers. We summarize our results as follows: The mean

Fig. 2. The pdf() of the interferometric phase for ¢9 = 0 and different values of the magnitude of the correlation coefficient |y|. The pdf is constant for |y| = 0 and converges toward a delta function as |y| approaches one. whereas the high coherence approximation is ad- equate only for deterministic, pointlike scatterers. We summarize our results as follows: The mean

Fig. 3. Standard deviation o4 of the interferometric phase versus magnitude of the correlation Coefficient |y|. The standard devia- tion has a maximum value of approximately 104° for completely uncorrelated signals (|| = 0).

Fig. 3. Standard deviation o4 of the interferometric phase versus magnitude of the correlation Coefficient |y|. The standard devia- tion has a maximum value of approximately 104° for completely uncorrelated signals (|| = 0).

Fig. 4. Standard deviation o, of the interferometric phase versus SNR. Only the influence of the thermal receiver noise has been considered. enough that we can expand (u,v) into a Taylor series:

Fig. 4. Standard deviation o, of the interferometric phase versus SNR. Only the influence of the thermal receiver noise has been considered. enough that we can expand (u,v) into a Taylor series:

ifo9 OF Wop, Defocusing in Azimuth and Range

ifo9 OF Wop, Defocusing in Azimuth and Range

Fig. 6. Phase bias ¢p of the interferometric phase versus defocus- ing error. The defocusing error is expressed as the maximum phase error ¥ at the edge of the bandwidth. 9 does not depend on the SNR. Unlike the other aberrations, defocusing is repre- sented by an even phase aberration function and introduces a phase bias. Figures 6 and 7 show do and the phase standard deviation as a function of phase error ¥ at the edge of the bandwidth.

Fig. 6. Phase bias ¢p of the interferometric phase versus defocus- ing error. The defocusing error is expressed as the maximum phase error ¥ at the edge of the bandwidth. 9 does not depend on the SNR. Unlike the other aberrations, defocusing is repre- sented by an even phase aberration function and introduces a phase bias. Figures 6 and 7 show do and the phase standard deviation as a function of phase error ¥ at the edge of the bandwidth.

Fig. 7. Standard deviation o, of the interferometric phase versus defocusingerror. The standard deviation is shown for two different SNR’s.

Fig. 7. Standard deviation o, of the interferometric phase versus defocusingerror. The standard deviation is shown for two different SNR’s.

Even in noise-free and aberration-free cases, signal decorrelation will occur if the envelopes of H, and Hz are shifted relative to each other, i.e., Even in noise-free and aberration-free cases, signal decorrelation will occur if the envelopes of H, and Hz are shifted relative to each other, i.e., Fig. 9. Standard deviation o, of the interferometric phase versus uncompensated quadratic range migration for two SNR’s. The quadratic range migration is expressed in fractions ¢ of a range resolution cell.

Even in noise-free and aberration-free cases, signal decorrelation will occur if the envelopes of H, and Hz are shifted relative to each other, i.e., Even in noise-free and aberration-free cases, signal decorrelation will occur if the envelopes of H, and Hz are shifted relative to each other, i.e., Fig. 9. Standard deviation o, of the interferometric phase versus uncompensated quadratic range migration for two SNR’s. The quadratic range migration is expressed in fractions ¢ of a range resolution cell.

Fig. 8. Standard deviation o, of the interferometric phase versus uncompensated linear range migration for two SNR’s. The linear range migration is expressed in fractions 8 of a range resolution cell.

Fig. 8. Standard deviation o, of the interferometric phase versus uncompensated linear range migration for two SNR’s. The linear range migration is expressed in fractions 8 of a range resolution cell.

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