Spotlight Processing of Wide-Beam Stripmap SAR Data Using the Frequency Scaling Algorithm Josef Mittermayer*, Alberto Moreira* and Otmar Loffeld** *DeutschesZentrum fur Luft- und Raumfahrt (DLR) Institut f i r Hochfrequenztechnik 82234 Oberpfaffenhofen, Germany T +49-8153-28-2360, E-Mail: joSef.mittermayer@dlr.de **Universitiit-GH-Siegen Institut fur Nachrichtenverarbeitung, 57068 Siegen, Germany Abstract- This paper presents a new processing algorithm for spotlight SAR data processing. The Frequency Scaling Algo- rithm (FS) allows the processing of dechirped raw data [l]. Due to the use of frequency scaling and SPECAN combined with azimuth scaling, the whole processing is performed without interpolations. A very useful formulation for dechir- ped SAR signals in the range Doppler domain is presented. The analytical modelling is presented in this paper. A more demonstrative explanation of the algorithm, including sub- aperture approach, frequency and azimuth scaling, can be found in [ 21. A spotlight image is presented, which has been processed from stripmap raw data of the E-SAR system of DLR by using the FS algorithm. I. INTRODUCTION The spotlight mode provides a very high geometric resolution in azimuth direction. A very good overview is given in [ 1 1. During the formation of the synthetic aperture, the antenna is constantly steered to scene center direction, which results in a long spotlight aperture which means high bandwidth azimuth signals for a high geometric resolution in azimuth. In order to obtain a similar high geometric resolution in range, a high bandwidth chirp signal is transmitted. Due to the small range extension of a spotlight scene, dechirp on receive is used to reduce the signal bandwidth before A/D conversion. Dechirp on receive means to multiply the received echoes by a chirp signal with inverted modulation rate, centered at scene center range rref. The resulting bandwidth is reduced if the range dimension of the imaged scene is smaller than the range chirp length. 11. SIGNAL IN RANGE-DOPPLER DOMAIN The spotlight SAR signal of a point target after dechirp on receive, down-conversion and AID-conversion can be ex- pressed by: frequency are denoted by fa and fe The distance between antenna and a point target at closest approach is r,, while r is the azimuth dependent distance to the point target: r(t.;rJ= .,/m (2) The first exponential term in ( 1 ) is the range signal, which consists of sinusoidal signalls. The second exponential term is the residual video phase, which describes a range dependent range time shift arising during the dechirp operation. The last exponential term is the aziImuth modulation. After some cal- culations and by using the a.pproximation: exp-j- =1 (3) [ k . 4 which is valid for a high time-bandwidth-product, the signal of a point target can be expiressed in range-Doppler domain: In the equation, * is the convolution operator. The signal representation in ( 4 ) with the unwanted residual video phase term being convoluted wilb the wanted part of the signal is the key for the derivation of the frequency scaling. The square root expression can be approximated in a way similar to the approximation in the derivation of 'the chirp scaling algorithm and becomes: In ( 1 ), h is the wavelength, and te is azimuth and range where P is defined by: time, k, is the chirp modulation rate, c, is velocity of light gram and pulse envelope. In the following, azimuth and range and C is a complex constant, including azimuth antenna dia- 0-7803-4403-0/98/$10.00 0 1998 IEEE 1177