Principles of Modern Radar - Volume 2 1891121537

7.1 Introduction 263u = along-track location of platform (m)x = along-track (crossrange) location of scatterer (m)r = cross-track (downrange) location of scatterer (m)r 0 = reference cross-track (downrange) to imaged swath (m)r = differential cross-track (downrange) with respect to reference (m)R = slant-range from platform to scatterer (m)t = time-delay into data (s)x S = crossrange half-extent of scene (m)y = cross-track (downrange) location of pixel in image (m)g(x,r) = reflectivity of scene (complex RCS, m)d(u,t) = recorded data (complex RCS, m)d Dechirp (u,t) = data after azimuth dechirp (complex RCS, m)d RMC (u,t) = data after range migration compensation (complex RCS, m)D(k u ,t) = along-track Fourier transform of data (complex RCS, m)D(k u ,ω) = 2-D Fourier transform of data (complex RCS, m)D RMC (k u ,ω) = 2-D Fourier transform of data after RMC (complex RCS, m)f (x,r) = SAR image (complex RCS, m)δ D (t) = Dirac delta functionh(u,t; x,r) = PSR (complex RCS, m)h(u,t; r) = reference PSR (complex RCS, m)h(u,t; r 0 ) = reference PSR at r 0 (complex RCS, m)ACR = area coverage rate (m 2 /s)T Swath = pulse time over swath (s)L Swath = length of swath on the ground (m)L Swath,BW = length of elevation-beamwidth-limited L Swath (m)U SAR = SAR system utility (m/s)t = time-delay progression due to platform motion (s)t 0 = reference time delay for reference range r 0 (s)t Shift = time shift for support of PSR in (k u ,t) (s)t Dif = differential time shift with respect to reference PSR (s)ψ = phase progression due to platform motion (radians)ψ QT = quadratic term in phase progression (radians)ψ Mig = phase progression due to range migration (radians)ψ PSR = 2-D frequency phase function for PSR (radians)ψ PSR ′ψ PSR ′′= 1st approximation to phase function for PSR (radians)= 2nd approximation to phase function for PSR (radians)d(t) = generic 1-D data record (complex voltage)h(t) = generic 1-D filter impulse response (complex voltage)h 0 (t) = generic 1-D matched filter impulse response (complex voltage)s(t) = generic 1-D signal (complex voltage)y(t) = generic 1-D filter output (complex voltage)D(ω) = generic 1-D data frequency response (complex voltage)H(ω) = generic 1-D filter frequency response (complex voltage)