Principles of Modern Radar - Volume 2 1891121537

214 CHAPTER 6 Spotlight Synthetic Aperture RadarAcronyms used in this chapterAASR Along track ambiguity to signal ratioADC Analog to digital converterASR Ambiguity to signal ratioCNR Clutter to noise ratioCR Contrast ratioDTCR Distributed target contrast ratioFFT Fast Fourier transformGPS Global positioning systemGSD Ground sampled distanceINS Inertial navigation systemISLR Integrated side lobe ratioLFM Linear frequency modulationMLE Main lobe energyNESZ Noise equivalent sigma zeroNIIRS National image interpretability rating scaleMNR Multiplicative noise ratioPDA Phase difference algorithmPGA Phase gradient algorithmPFA Polar format algorithmPRI Pulse repetition intervalPRF Pulse repetition frequencyPSR Point scatterer responseQNR Quantization noise ratioQPE Quadratic phase errorRASR Range ambiguity to signal ratioRF Radio frequencyRVP Residual video phaseSAR Synthetic aperture radarSLE Side lobe energySNR Signal to noise ratio6.2 MATHEMATICAL BACKGROUNDAnyone with an understanding of basic signal processing ideas [6] is well-equipped toachieve a deep understanding of SAR imaging [7,8]. This section introduces the mostessential mathematical and signal processing theory needed to understand spotlight modeSAR.6.2.1 The Fourier TransformThe fundamental mathematical tool required for this chapter is the Fourier transform [9] inone, two, and three dimensions. The principles in multiple dimensions are essentially thesame as for a single dimension, so we begin there. The one-dimensional Fourier transformand its inverse are defined as:F(ω) =∫ ∞−∞f (t)e − jωt dt (6.1)