Active millimeter-wave images typically exhibit characteristic speckle noise, due to the coherence of artificial millimeter-wave sources. We study the Hadamard speckle contrast reduction (SCR) technique, which has been successfully used in laser projection systems, in the context of millimeter-wave imaging. We show the impact of Hadamard pattern order and size and of image and pattern resolution on speckle reduction efficiency. Practical limitations of Hadamard pattern implementations and their effect on speckle reduction efficiency are also discussed.

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Abstract-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 difference 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.

Active millimeter wave imaging systems have become a promising candidate for indoor security applications and industrial inspection. However, there is a lack of simulation tools at the system level. We introduce and evaluate two modeling approaches that are applied to active millimeter wave imaging systems. The first approach originates in Fourier optics and concerns the calculation in the spatial frequency domain. The second approach is based on wave propagation and corresponds to calculation in the spatial domain. We compare the two approaches in the case of both rough and smooth objects and point out that the spatial frequency domain calculation may suffer from a large error in amplitude of 50% in the case of rough objects. The comparison demonstrates that the concepts of point-spread function and f-number should be applied with careful consideration in coherent millimeter wave imaging systems. In the case of indoor applications, the near-field effect should be considered, and this is included in the spatial domain calculation.

Abstract-Hadamard speckle contrast reduction (SCR) is considered to be an effective approach to deal with speckle problems in coherent imaging systems. A Hadamard SCR system is divided into two subsystems, which implement phase patterns projection and reflected waves imaging respectively. The performances of both sub-systems are discussed with numerical simulations and linked to certain parameters so as to give more insights of this approach. For generality, both optical and millimeter wave imaging systems are discussed. To distinguish from former literature based on Fourier optics, the simulation is implemented via wave optics, which is more physical and more accurate. Moreover, considering the fact that the Hadamard method originates from statistics, the effectiveness of Hadamard SCR is in the first place linked to the texture of the object's surface. Statistical optics is also adopted during qualitative analysis of the results. It is shown that the ratio between the dimension of a resolution cell and the granular size of the object's randomly rough surface is closely linked to the performance of Hadamard SCR. Differences in the roughness model in imaging cases of optical and millimeter waves are discussed, which would help to evaluate the validity of the Hadamard SCR approach in practice. The purpose of this paper is to clarify the misunderstandings of Hadamard SCR in previous literature and to give a guideline to apply this approach.