Gently Undulating Topography

The next example is of slightly more complicated topography quite close to the same airfield, with a central area consisting of a mixture of ploughed (light areas) and unploughed fields, with some interesting topographic features at the sides, particularly the wooded area at the right-hand side (Fig. 2.34). It can be deduced from the interferogram (Fig. 2.35) that the fields have no more than gentle variations in terrain slopes, but these are unknown.

F i g . 2 . 3 4 : SAR image of gently undulating topography. Aircraft height

=1100m, slant range 1708-1544m, resolution = 2.1 m in range, 1 m in azimuth. The aircraft track follows the top of the image, from left to right.

By visual inspection of the interferogram, the characteristic near-range to far-range repetitive pattern of roll induced phase errors seems to be apparent, and small features with height are easily picked out, especially in the final unwrapped phase image (Fig. 2.37). However, due to the unknown topography, it is difficult even by eye to separate the ripples in the fringe lines due to aircraft-roll from those generated by the gently rolling English countryside.

Fig.2.35: interferogram corresponding to SAR image of Fig.2.34.

Consider the following examples: looking at the wooded area in the mid-right hand side of the SAR image, this has some of the repetitive features of aircraft roll, but is easily identifiable as a real topographic feature as it does not extend right across the image. Besides, it can also be identified from contextual information in the SAR image, and the feature is also surrounded by a discontinuity, particularly visible in the flat ground compensated interferogram shown in Fig. 2.36, rather than having the continuously variable phase consistent with aircraft roll.

However, if it were a longer feature, devoid of discontinuities or other contextual information in the SAR image, such as for instance the fields in the central portion of the image which may possibly be gently undulating and sloping, it would not be possible to unambiguously deconvolve the real topography from the artefacts of aircraft roll without a- priori knowledge - any attempt to do so, such as suggested in [39], runs the risk of flattening any real topographic variations happening to have the same characteristics as aircraft roll, leaving behind residual variations of smaller spatial extent. This is particularly apparent by looking at the phase banding in the unwrapped phase image of Fig. 2.37. Should the central banding be attributed solely to aircraft roll, undulating topography, or a combination of both? There is no information in the processed interferogram to resolve this dilemma.

Fig.2.37: Unwrapped phase of interferogram after flat ground phase removal.

The solution to the data-driven roll compensation problem lies not in the interferogram, but in the SAR imaging process used to generate the high resolution images for interferometry, which up to this point has been avoided for clarity, but has interesting properties in the presence of motion errors.

2.6 References

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Synthetic Aperture Radar