Wave-optics simulation of dynamic speckle: II. In an image plane

Abstract

This two-part paper demonstrates the use of wave-optics simulations to model the effects of dynamic speckle. In Part II, we formulate closed-form expressions for the analytical irradiance correlation coefficient, specifically in the image plane of an optical system. These expressions are for square, circular, and Gaussian limiting apertures and four different modes of extended-object motion, including in-plane and out-of-plane translation and rotation. Using a phase-screen approach, we then simulate the equivalent scattering from an optically rough extended object, where we assume that the surface heights are uniformly distributed and delta correlated from grid point to grid point. For comparison to the analytical irradiance correlation coefficient, we also calculate the numerical irradiance correlation coefficient from the dynamic speckle after propagation from the simulated object plane to the simulated image plane. Overall, the analytical and numerical results definitely demonstrate that, relative to theory, the dynamic speckle in the simulated image plane is properly correlated from one frame to the next. Such validated wave-optics simulations provide the framework needed to model more sophisticated setups and obtain accurate results for system-level studies.

Effects of speckle decorrelation on motion-compensated, multi-wavelength, 3D digital holography

“…The first mechanism is well-known and is described in detail for a variety of types of object motion by Burrell et al 10,11 Stationary objects will provide a common speckle pattern across all of the 2D images in U i (u, v; ν n ) such that the linear phase terms that depend on Z d (u, v) are preserved. In contrast, if object motion is severe enough to provide independent speckle patterns for each U i (u, v; ν n ), then a 3D image is impossible to generate.…”

“…We specifically analyzed the effects of speckle decorrelation due to object motion, since that is a specific failure mode of conventional 3D imaging. To simulate this effect, we referred to a study by Burrell et al 11 which simulated speckle decorrelation in an image plane by translating the underlying surface roughness of the object laterally to generate new shifted speckle realizations in the image plane. In that study, the degree of correlation, µ I , between speckle frames was a function of the shift of the underlying surface roughness given by…”

Experimental validation of model-based digital holographic imaging using multi-shot data

“…At optical wavelengths, this decorrelation occurs with rotations of only a few microradians. 9,17,18 When this is true, G is distributed according to…”

“…as the surrogate function for the i th term in Eq. (18). Note that for multi-shot DH, the surrogate function given by Eq.…”

Wave-optics investigation of branch-point density

“…To increase the fidelity of the results, future developments need to include the effects of additive-sensor noise, low signal-to-noise ratios, and subaperture-sampling requirements. [38][39][40][41][42][43][44][45] With this history in mind, reformulating the problem in terms of slope discrepancy, 46,47 especially when accounting for the effects of speckle due to rough-surface scattering, [48][49][50][51] could also inform these future developments.…”