Prerequisites & Notation

Prerequisites for This Chapter

This chapter develops Synthetic Aperture Imaging — the art of creating high-resolution images by coherently combining radar returns collected along a synthetic aperture. It builds on Part II's forward model and shows that SAR, ISAR, and TomoSAR are all special cases of $\mathbf{y} = \mathbf{A}\mathbf{c} + \mathbf{w}$ .

Electromagnetic scattering and the Born approximation(Review ch06)
Self-check: Can you write the Born approximation for a point scatterer?
Radar matched filtering and range-Doppler processing(Review ch07)
Self-check: Can you derive the range resolution $\Delta R = c/(2B)$ from a chirp waveform?
Sensing matrix construction and Kronecker structure(Review ch08)
Self-check: Can you explain how rows of $\mathbf{A}$ encode Tx-Rx-frequency triples?
MIMO radar virtual aperture(Review ch11)
Self-check: Can you describe how $N_t + N_r$ elements create $N_t N_r$ virtual elements?

Notation for This Chapter

Symbols introduced or heavily used in this chapter. See also the global notation table in the front matter.

Symbol	Meaning	Introduced
$L_{\text{sa}}$	Synthetic aperture length (m)	s01
$v_p$	Platform velocity (m/s)	s01
$T_{\text{sa}}$	Synthetic aperture time ( $L_{\text{sa}}/v_p$ )	s01
$R_0$	Closest approach range (broadside)	s01
$\Delta R$	Range resolution ( $c/(2B)$ )	s01
$\Delta x$	Cross-range (azimuth) resolution	s01
$\tau$	Fast time (range time)	s01
$\eta$	Slow time (azimuth time)	s01
$K_r$	Chirp rate ( $B/T_p$ )	s02
$K_a$	Azimuth FM rate ( $-2v_p^2/(\lambda R_0)$ )	s02
$\phi_e(\eta)$	Phase error function (autofocus)	s02
$\omega$	Target rotation rate (ISAR)	s03
$\Delta\theta$	Total rotation angle (ISAR)	s03
$b_m$	Baseline position for $m$ -th pass (TomoSAR)	s04

← Ch 11 SAR Geometry and Resolution