Spatial Poincaré Plots as Descriptors of Speckle Pattern Second-Order Statistics

Abstract

Abstract. It is demonstrated herein that the use of spatial Poincaré plots provides an efficient means to describe short and long-range correlations in the spatial structure of the measured intensity distribution of scattered coherent fields. The intensity distribution over a row of pixels in single frames of speckle fields with varying speckle sizes was considered. Statistical descriptors from the spatial Poincaré plots for these intensity data with variable lags were used to estimate the short and long-term variations in the measured intensities, and from these descriptors, the minimum speckle size in the speckle patterns was estimated. This approach yielded similar results for speckle size estimates as the more standard method of calculating the power spectral density of the intensity pattern and simultaneously provided information on the relative contributions of short-term and long-term variations in the measured intensity to the spatial structure of the scattered fields.

High speed determination of laser wavelength using Poincaré descriptors of speckle

“…A change in wavelength on a scale below the speckle correlation limit causes only grain-scale changes to the speckle pattern. Recently, a technique involving Poincaré descriptors was developed to investigate the size of speckle grains [19,20]. Here we show that the grain-scale variations of speckle patterns that are induced by changes of the wavelength λ are also captured by a Poincaré descriptor.…”

“…This Poincaré descriptor is otherwise known as the standard deviation of lag-k differences, related to the standard deviation of successive differences [21], which is widely used in areas such as heart rate variability analysis [22,23]. It was recently demonstrated that this met-arXiv:1909.00665v1 [physics.optics] 2 Sep 2019 ric can probe short-range correlations in the spatial and temporal structure of speckle [19,20]. In order to track grain-scale changes of speckle patterns, we set the parameter k to the size of a typical speckle in the image, determined using the methods outlined in [19].…”

“…It was recently demonstrated that this met-arXiv:1909.00665v1 [physics.optics] 2 Sep 2019 ric can probe short-range correlations in the spatial and temporal structure of speckle [19,20]. In order to track grain-scale changes of speckle patterns, we set the parameter k to the size of a typical speckle in the image, determined using the methods outlined in [19]. The variation with wavelength must be determined empirically, via a training phase which extracts a scaling law between P k and λ.…”

Laser Speckle Modeling and Simulation for Biophysical Dynamics: Influence of Sample Statistics

“…Either approach yields the same information as the autocorrelation function and the PWD constitute a Fourier transform pair. An alternative approach of using spatial Poincaré plots with variable lag lengths was recently presented by Majumdar and Kirkpatrick [15]. This approach reduces some of the uncertainties associated with the approaches discussed above, particularly as the speckle size gets large and also provides a more physical connection with speckle size and the correlation length of the intensity pattern.…”

“…When the speckle size equaled 2 pixels, the spatial Nyquist criteria was met [13]. This process for generating synthetic speckle patterns has been used extensively in the past [2,6,12,[13][14][15]. Using these speckle patterns, the effects of the neighborhood size over which speckle contrast was calculated was investigated as a function of speckle size and the results compared to those obtained when the sampled intensities were statistically independent from each other.…”