Wigner function measurement using a lenslet array

Abstract

Geometrical-optical arguments have traditionally been used to explain how a lenslet array measures the distribution of light jointly over space and spatial frequency. Here, we rigorously derive the connection between the intensity measured by a lenslet array and wave-optical representations of such light distributions for partially coherent optical beams by using the Wigner distribution function (WDF). It is shown that the action of the lenslet array is to sample a smoothed version of the beam's WDF (SWDF). We consider the effect of lenslet geometry and coherence properties of the beam on this measurement, and we derive an expression for cross-talk between lenslets that corrupts the measurement. Conditions for a high fidelity measurement of the SWDF and the discrepancies between the measured SWDF and the WDF are investigated for a Schell-model beam.

3D Imaging Based on Depth Measurement Technologies

“…The complete characterization of the 4D coherence function (so-called coherence measurement or coherence retrieval) has always been an active research area. The representative approaches include direct interferometric measurement [ 198 , 199 ], phase-space tomography [ 200 , 201 ], multi-plane coherence retrieval [ 202 , 203 ], and windowed Fourier transform approach [ 204 , 205 ]. All of these techniques require extra measurement dimension (by introducing an astigmatic lens) and much more intensity measurements.…”

3D Imaging based on Depth Measurement Technologies

“…The complete characterization of the 4D coherence function (so-called coherence measurement or coherence retrieval) has always been an active research area. The representative approaches include direct interferometric measurement [195,196], phase-space tomography [197,198], multi-plane coherence retrieval [199,200], are windowed Fourier transform approach [201,202].…”

Computational optical sectioning by phase-space imaging with an incoherent multiscale scattering model

“…Phase-space imaging, by collecting the high-dimensional local variances of the coherence, provides a new imaging framework with digital synthesis of the partiallycoherent light field, which shows strong robustness to scattering and aberrations [14][15][16][17][18] . As a typical example, light-field microscopy (LFM) 19 captures the phase-space measurements within a snapshot by a microlens array 20 , facilitating various applications in biology, such as imaging hemodynamics 21 and large-scale neural activities 14,22 .…”