The computation of the average speckle size from the point spread function for triangular apertures (original) (raw)
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Optics and Photonics Journal, 2013
In this paper, we present an elongated speckle images produced from diffusers using sharp elliptical apertures. The orientation of the elliptic aperture is recognized from the direction of the elongation in the speckle images. The aperture tilting out of the plane is investigated. Three models of elliptical apertures are considered and the corresponding speckle images are obtained. The 1st model is composed of two orthogonal ellipses or plus symbol pupil; the 2nd has four symmetric ellipses with an angle of 45˚ between each of them or in the form of a snow flake pupil and the 3rd model looks like an airplane. Also, the autocorrelation profiles of the speckle images corresponding to the diffused airplane are obtained from which the average speckle size is computed. Finally, the reconstructed images of the described elliptical models and its autocorrelation images, making use of Mat lab code, are obtained.
Optics and Photonics Journal, 2011
A computer generated quadratic and higher order apertures are constructed and the corresponding numerical speckle images are obtained. Secondly, the numerical images of the autocorrelation intensity of the randomly distributed object modulated by the apertures and the corresponding profiles are obtained. Finally, the point spread function (PSF) is computed for the described modulated apertures in order to improve the resolution.
Properties of speckle patterns generated through multiaperture pupils
Optics Communications, 2001
The characteristics of the image speckles obtained through multiple aperture pupils are theoretically analyzed in terms of the parameters de®ning the pupils. The possibility of interpreting and synthesizing the image speckle distribution in terms of rather elementary structures is considered, based on the Fourier optics analysis. Then, ®rst and second order statistical properties of the speckle patterns are studied by evaluating both the mutual intensity and the auto-correlation intensity of speckle distributions obtained by means of pupils consisting of identical apertures. Experimental results are presented to con®rm the analysis. Ó 2001 Published by Elsevier Science B.V.
Fringe visibility analysis with different scale apertures in speckle photography
Journal of Modern Optics, 2001
The use of different scale aperture pupils for image recording in speckle photography is analysed. In particular a double-exposure specklegram is considered. The ensemble-average intensity in the Fourier plane is analytically derived and fringe visibility is investigated. The theoretical results are verified by in-plane displacement translation experiments.
Statistics of spatially integrated speckle intensity difference
Journal of the Optical Society of America A, 2009
We consider the statistics of the spatially integrated speckle intensity difference obtained from two separated finite collecting apertures. For fully developed speckle, closed-form analytic solutions for both the probability density function and the cumulative distribution function are derived here for both arbitrary values of the mean number of speckles contained within an aperture and the degree of coherence of the optical field. Additionally, closed-form expressions are obtained for the corresponding nth statistical moments.
Effect of the Illuminating Point Spread Function and Roughness on the Speckle Correlation Field
Optics and Photonics Journal, 2019
Under conditions differing from those subjected for central limit theorem, the spatial autocorrelation function of speckle pattern resulting from illuminated rough surface is investigated. Its dependence on different illuminating apertures and the average of the roughness heights is presented theoretically and experimentally. The experiments were carried out using a set of circular and square apertures having different sizes. The results indicate that, increasing the size of the illuminating aperture leads to a decrease in the width of the main lobe of the spatial autocorrelation function.
Influence of geometry on polychromatic speckle contrast
Journal of the Optical Society of America A, 2007
Understanding speckle behavior is very important in speckle metrology application. The contrast of a polychromatic speckle depends not only on surface roughness and the coherence length of a light source, as shown in previous works, but also on optical geometry. We applied the Fresnel approach of diffraction theory for the free-space geometry and derived a simple analytical relationship between contrast, coherence length, size of illuminated spot, and distances between source, object, and observation plane. The effect of contrast reduction is found to be significant for low-coherence light sources.
Double-exposure specklegrams obtained by using scaled aperture pupils
4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications, 2001
In speckle photography the pupil aperture is usually not modified between exposures. In our work, the change of the pupil aperture scale between exposures is analysed on the basis of double-exposed image speckle, before and after a diffuser inplane displacement is done. The apertures have the same shape but its scale is modified between exposures. Note that the relative position of the aperture is maintained. In particular, we analyse a simple case that uses a circular aperture whose diameter is modified for recording each image. The intensities in the image plane and the fringe visibility are evaluated, in terms ofthe geometric characteristics ofthe pupils.
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SPIE Proceedings, 2006
The basic convolution integral, h Uo Uf ⊗ = , where Uo is a random object complex amplitude and h the impulse response of the system under consideration, serves to model the observed speckle field Uf. Depending on the choice of h, the simulated field is an objective or a subjective speckle pattern. The computation makes use of two consecutive Fast Fourier Transforms. In the reported examples, the object function represents a pure phase diffuser ruled by a uniform distribution. The probability density functions (PDF) of the simulated intensity and phase patterns fit very well with their analytical counterparts obtained under the classical Gaussian hypotheses. Phase maps exhibit the awaited singularities. Moreover, elements of second order statistics, as the autocorrelation functions, are in very good agreement too. Furthermore, subtle effects, as the dip of contrast in the focused image plane of partially developed speckle patterns, are also suitably disclosed. The linear model thus appears, all together, as conceptually easy, very flexible, computationally simple, very accurate for a wide range of experiments, and endowed with excellent predictive and speculative potentials.
Nonparaxial, three-dimensional, and fractal speckle
Optical Engineering, 2013
Speckle can be modeled by analysis of the statistics of the image of a phase object such as a rough surface. The image can be calculated using the coherent transfer function of the imaging system and the angular spectrum representation. This approach gives a three-dimensional image, and includes the effects of high numerical aperture and the finite depth of the structure. Different correlation coefficients can be assumed, including fractal distributions, such as exponential correlation, as well as Gaussian correlation.