Developing of a model of spacial resolution evaluation of a synthesized aperture space radar

Mathematica modeling, numerical technique and program complexes


Zanin K. A.

Lavochkin Research and Production Association, NPO Lavochkin, 24, Leningradskay str., Khimki, Moscow region, 141400, Russia



At present, there are contradictions in the formulation of the indicators of resolving power of synthetic aperture radar (SAR). Developers of SAR equipment usually suggest evaluate the resolution through the width of the profile of the scattering functions (hardware function). This definition simplifies the commissioning of the target equipment, but does not take into account the resolution relationship with the radiometric characteristics of the X-ray diffraction pattern, the background signal of the underlying surface, and random synthesizing errors.

The inflated expectations of the consumers of radar information quality come into conflict with the requirements of the design specifications formulated by the developer of the target equipment based on their parochial interests. As a result, to formulate the requirements of the design specifications, it is necessary to develop methods for evaluating the quality of the radar image (SAR) that account for the characteristics of SAR.

The article suggests an improved method for estimating the spatial resolution of a synthesized aperture radar, based on the condition that the modulation amplitude exceeds the signal equivalent to noise. The modulation difference is evaluated with account for attenuation of the spatial frequencies of the complex scattering coefficient on the SAR information path.

To evaluate the resolution, the author suggested to employ two types of test objects with harmonic amplitude and phase modulation. Mathematical relationships determining the resolution equation through the spatial function of amplitude modulation transmission by the radar information path are considered.

Analysis of the image formation specifics in radar complexes compared to optoelectronic ones was carried out. The article shows that the SAR provides spatial resolution about twice as low as the limiting value determined by the half-width of the hardware function.

An improved method for determining the space radar’s resolution capability with account for the synthesized aperture formation specifics and random errors, is suggested. The proposed model of a test object with harmonic change in the complex amplitude or phase of the reflected signal allows relate the resolution capability of the SAR with its radiometric characteristics and reflection from the underlying surface.

The function of modulation transmission of the amplitude and phase of the information path of the PCA for harmonic test objects was obtained. The properties of the amplitude modulation transfer function dependence on the spatial frequency made it possible to explain certain characteristic properties of the radar compared to optical images.

The article shows that the SAR ensures approximately the same spatial resolution for the amplitude and phase harmonic modulation of the object scattering function, which is approximately two times worse than the limiting one. Increasing the contrast of the object to absolute values slightly improves the resolution up to 1.6 times. In case of low-contrast objects, the amplitude modulation is transmitted without distortion; the resolution capability is determined only by the realized signal-to-noise ratio with a resolution of 2.5 times worse. If an object is observed against speckle noise, the resolution of the SAR drops three or more times.


quality indicators, space radar with synthesized aperture, linear ground resolution, radiometric resolution, modulation transfer function, radar image quality


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