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To simulate imaging systems, Fourier optics has been applied very successfully to optics for decades. However, when simply moving to indoor millimeter wave imaging systems, some assumptions underlying the Fourier optics may break down, which contribute to the errors by applying Fourier optics. During the review of mathematical derivation of the Fourier optics, we point out how the errors are introduced by making the Fresnel approximation and omitting the phase factors. To distinguish from much literature, we discuss the accuracy of Fresnel approximation rather than plane wave. Moreover, we check the simulation results for millimeter wave imaging systems working in both pixel scanning mode and focal plane array mode and compare them to the results predicted by Fourier optics. It is shown that the difierence can be 28% for the speckle contrast when the object is with certain roughness. The optical routine is that when the lens is four times' larger than the object, the imaging system can be considered as isoplanatic, thus Fourier optics can hold. Our simulation results imply that it may not be valid in indoor millimeter wave imaging systems. The goal of this paper is to draw some attention to the possibly large errors when modeling or designing the indoor millimeter wave imaging systems by Fourier optics directly. The mathematical discussions of the inaccuracies due to some approximations in Fourier optics can serve to understand and deal with aberrations.

LIMITATIONS OF APPROXIMATIONS TOWARDS FOURIER OPTICS FOR INDOOR ACTIVE MILLIMETER WAVE IMAGING SYSTEMS