Coherent detection in 3D FMCW flash LIDAR with large FOV: part I - speckle size in the image plane

Part I of this two-part paper presents a detailed theoretical, numerical, and experimental study of the angular dependence of speckle grain size in a 3D flash FMCW LIDAR imaging system. Following both empirical hypotheses and rigorous mathematical derivations, we demonstrate that the speckle grain size scales differently along two principal orthogonal directions in the image sensor plane. Specifically, the lateral speckle size along the direction of observation increases with the inverse cube of the cosine of the observation angle, while the perpendicular direction scales linearly with the inverse of the cosine. Numerical simulations based on the Rayleigh-Sommerfeld-Smythe solution of Maxwell's equations and experimental results using a microscope-based magnification strategy validate the theoretical predictions. The magnification approach enables accurate speckle size measurements across observation angles up to 35°. These findings provide important insights into speckle behavior affecting the heterodyne efficiency in 3D flash FMCW LIDAR systems that will be addressed in Part II.