A theory of the synthetic aperture radar images of time‐dependent scenes

Abstract

Data from synthetic aperture radars (SAR's) can be used to measure the surface height spectrum of the ocean. Traditionally, only the real SAR image is used; we show, both theoretically and with SAR data, that the complex image contains more information about the ocean scene. We derive an expression for the ambiguity function of the complex image, which is an extension of the concept of a power spectrum, but generalized to phenomena with time‐dependent properties. The ambiguity function of the complex image is derived as an integral of the surface height spectrum; this allows us to calculate the statistics of the complex SAR image directly, without having to generate individual realizations of the surface. In the derivation of the ambiguity function, we find that a simple assumption about the complex reflectivity of the surface leads to a formulation of the SAR imaging process that circumvents many traditional problems. By using ambiguity functions, we can remove some of the smearing that is otherwise seen in the images of time‐dependent scenes. One result of this analysis is that we can explain SAR focusing in a simple way, and extend it to range‐traveling waves as well as azimuth‐traveling waves. Also, we can calculate the correlation length and time of the surface directly from the surface height spectrum. While the correlation length seems to play only a minor role in this theory, the correlation time determines the minimum wavelength for azimuth waves that can be imaged. This paper shows how the ambiguity function of the image is related to the surface height spectrum and presents an example using SAR data.

SAR Imagery for Detecting Sea Surface Slicks: Performance Assessment of Polarization-Dependent Parameters

“…where ρ Scattering denotes the correlation between HH and VV due to scattering mechanism (close to 1 over ocean surface) and ρ Temp and ρ SNR denote temporal decorrelation and decorrelation due to noise, respectively. The decorrelation time of moving sea surface is of the order of 1.10 -2 s at Xband [38] and 1.10 -1 s at L-band [39]. For sensors operating at low pulse repetition interval (PRI), the decorrelation due to time lag between transmitted pulses (alternatively polarized H and V) can be neglected.…”

Global Ocean Wave Measurements Using Complex Synthetic Aperture Radar Data

“…As shown, e.g. in Milman et al [1993] the white process assumption about the complex reflectivity r (compare eq. 4.3) is well satisfied on this spatial scale.…”

“…As the high frequency tail of the wave spectrum wind speed 5 ms −1 10 ms −1 15 ms −1 coherence time τ c 0.1 s 0.052 s 0.034 s Tab. 4.1: Coherence time τ c for different wind speeds assuming C-band and 30 • incidence angle (adapted from Milman et al [1993]) is characterised by a ω −5 decay of energy (compare eq. 2.22), the radar return is increasing with decreasing incidence angles.…”

“…For the temporal correlation of r in the open water we assume coherence times as given by Milman et al [1993] for C-band and 30 • incidence angle, which is close the ERS configuration. The respective values for different wind speed are summarised in table 4.1.…”

“…4.46) depending on coherence time τ s and orbital velocity variance ρ u (0). The dashed lines represent coherence times for different wind speeds as given in Milman et al [1993] for C-band radar. .…”