<title>Migration processing of spotlight SAR data</title>

Abstract

Migration processing exactly accounts for the wavefront curvature over the imaged scene. Migration processing is therefore capable of forming high resolution SAR images when the data is acquired over a large synthetic aperture collection angle. Because migration processing requires phase compensation to a line corresponding to the nominal SAR flight path, the phase history is chirped ever a very large bandwidth, requiring a very high sample rate to prevent aliasing in the frequency spectrum. The sample rate is determined by the size of the synthetic aperture collection angle. When migration processing is applied to a spotlight-mode SAR, this sampling rate ca be much higher than that required for normal spotlight-mode processing. In this latter case, the phase history is motion cornpnsated to scene center and the sample rate is determined by the spot size. Higher sampling rates result in larger FVFs and may cause range ambiguity problems. ERIM has pursued the development of a variation on migration processing, which we call the Frequency domain Replication and Downsampling (FReD) algorithm, which enables the acquisition of data at normal spotlight-mode rates and which does not require the computation of FFTs any larger than those required for normal spotlight-mode processing. The FReD algorithm is based on the fact that when a discrete, aliased spectrum is replicated a sufficient number of times, the resultant spectrum will contain the desired signal spectrum. What we call the FReD algorithm is discussed in two articles by Prati, et 12 Subsequent processing steps extract the desired portion of the spectrum to form an image. This paper will review migration processing, discuss the FReD algorithm and present expressions for the number of operations required for its implementation. Migration-processed, spotlight-mode SAR imagery derived from airborne collected data and demonstrating the utility of FReD are presented. MIGRATION PROCESSING .1 Migration processing of continuous dataIn this section we will review each of the steps used in migration processing, assuming that the available signal is from a SAR using a stepped FM signal. The migration processor obtains the 2-dimensional Fourier transform of the scene reflectivity function by motion-compensating the phase history to a line, computing the along-track Fourier transform of the data, and performing a coordinate transformation (often called a Stolt interpolation 3)• Subsequent steps include shifting the desired scene center to zero spatial frequency and interpolating to obtain evenly spaced samples of the Fourier transform for subsequent use of efficient FF1 algorithms. When a modulated (e.g., chirped) signal is transmitted by the SAR, the form of the complex function used to shift the scene center to lower spatial frequency changes, as discussed by Cafforio, et al We begin by writing the signal received by the sensor from a reflectivity distribution (x, p) , when the sensor radiates at a fixed frequency f. In this formulation the reflectivity distribution is mod...

<title>Space-variant filtering for correction of wavefront curvature effects in spotlight-mode SAR imagery formed via polar formatting</title>

“…These algorithms are the RMA (range migration algorithm) described in [2] , and the FReD (Frequency Domain Replication and Downsampling) algorithm, described in [3]. Both algorithms are based upon the original work of Prati, Rocca, et.…”

General formulation for wavefront curvature correction in polar-formatted spotlight-mode SAR images using space-variant post-filtering

“…The algorithms used for comparison are the range migration algorithm (RMA) [6], and a modified, more computationally efficient version of RMA known as FReD [7]. One of the drawbacks of the RMA algorithm is that it requires the phase history data to be upsampled in the along-track dimension at a rate that depends upon the collection geme try.^ For some imaging scenarios, such as those involving significant squint angles, the time to compute the upsampled data may be quite large.…”