Image Formation for Coherent Diffuse Objects: Statistical Properties

Reduction of speckle in digital holography by discrete Fourier filtering

“…The first being the power spectrum of the image itself, and the second being the power spectrum of the speckle, which we want to reduce. The autocorrelation of f͑r͒ can be written 15 R ff ͑r 1 ,r 2 ͒ = ͗f͑r 1 ͒f * ͑r 2 ͒͘ = ͗t͑r 1 ͒d͑r 1 ͒t * ͑r 2 ͒d * ͑r 2 ͒͘, ͑2͒…”

“…From this equation, Lowenthal and Arsenault 15 have shown that the manner in which the speckle spatial frequencies are distributed does not depend on the signal t͑r͒, but only on the coherent transfer function of the system. Only the total signal power ͉R tt ͑0͉͒ 2 effects the power spectrum of the speckle.…”

“…(12) is rewritten with u replacing u 1 and u 2 to obtain the average power spectrum of the speckle, ⌫͑u 1 , u 2 ͒ becomes the average power spectrum of the object amplitude, which has been shown to be a constant and is equal to the total power in the signal. 15 The power spectrum of the speckle is rewritten as…”

“…However, using basic Fourier theory, one may deduce that the bandwidth of the reconstruction intensity is twice the extent of the rect function. For a more thorough analysis of the optical system, please refer to Lowenthal and Arsenault 15 and Hariharan and Hegedus. 10 Figure 1(b) shows the DFF technique for reducing speckle.…”

Speckle and fringe dynamics in imaging-speckle-pattern interferometry for spatial-filtering velocimetry

“…In [15] it has been shown that a scattering surface, which in a free-space-propagation system can produce fields with circular symmetric complex Gaussian and ergodic random variables, will produce fields of the same statistics in an imagingconfiguration system. Therefore, the first term, containing the product of four scattered fields, can be expressed in terms of mutual second-order field correlations [12]:…”