Influence of geometry on polychromatic speckle contrast (original) (raw)
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Optics and Photonics Journal, 2013
The paper is devoted to study theoretically, the effects of some parameters on the visibility of the speckle patterns. For this propose, a theoretical model for a periodic rough surface was considered. Using this theoretical model, the effects of grain height, its density, the band width and spectral distribution of the line profile (Gaussian and Lorentzian) illuminating a rough surface on the visibility of speckle pattern are investigated. An experimental setup was constructed to study the effect of surface roughness and coherence of the illuminating light beam on the contrast of speckle pattern. The general behavior of the experimental results, which agree with published data, is compatible with the new theoretical model.
Space and wavelength dependence of speckle intensity
Applied Physics A-materials Science & Processing, 1974
A unified, analysis is presented for the spatial and the spectral sensitivity of speckle (the rapid spatial variations which occur in an image when illumination of narrow spectral width is used) in a space-invariant linear system. In prior work considering speckle size, others have shown that its spatial variation is functionally dependent primarily on the autocorrelation function of the system's impulse response, but effects of varying the wavelength were largely ignored. In the present paper we treat the general problem in which a diffuse object, illuminated by a collimated, monochromatic beam, is imaged by a system whose amplitude impulse response isz(x, η), wherex and η are space and normalized (temporal) frequency coordinates, respectively. An expression is derived for the multidimensional autocorrelation functionR u (Δx,η 1,η 2) of the intensityu(x,η) in the image plane. Functionally, it depends upon a convolution of the system autocorrelation functionR u (Δx,η 1,η 2) with the characteristic function of the distribution function for heights, which is used to model the input object's surface. Examples are presented; and, it is shown that one can infer valuable information about the variation of heights for points on the surface of the input diffuse object, which are separated by much less than the classical resolution limit.
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.
Scatterers shape effect on speckle patterns
Biomedical Applications of Light Scattering IX, 2015
Laser speckle analysis is a very powerful method with various existing applications, including biomedical diagnostics. The majority of the speckle applications are based on analysis of dependence of scattered light intensity distribution from sizes of the scattereres. We propose a numerical model of speckle formation in reflected light in one-dimension which shows that properties of the scattered light are strongly dependent on the form of the scatterers. In particular, the dependence of number of speckles from the size of the scatterers was investigated for the light reflected from the surface with varying roughness; the single roughness on the surface was assumed to have the form of one-dimensional 'pyramid' with the sides having either linear or parabolic descent from the top of the 'pyramid' to the bottom. It was found that for the linear roughness, number of speckles decreased with increase of the roughness size, whereas for the parabolic roughness the number of speckles increased. Results of numerical simulation were compared with experiment investigations of roughness samples (0.5-2.5 μm) made of glass and copper. Due to different production processes, the glass samples are likely to have the parabolic roughness and copper samples are likely to have the linear roughness. Experiments show that the dependences of number of speckles also have different slopes, the same as in numerical simulation. These findings can lead to new analytical methods capable of determining not only the size distribution of roughness (or scatterers) but also the shape.
Optics and Lasers in Engineering, 2010
Quantification of surface roughness greater than a micron is desirable for many industrial and biomedical applications. Polychromatic speckle contrast has been shown theoretically to be able to detect such roughness range using an appropriate light source with a Gaussian spectral shape. In this paper, we extend the theory to arbitrary spectral profile by formulating speckle contrast as a function of spectral profile, surface roughness, and the geometry of speckle formation. Under a far-field set-up, the formulation can be simplified and a calibration curve for contrast and roughness can be calculated. We demonstrated the technique using a blue diode laser with a set of 20 metal surface roughness standards in the range 1-73 mm, and found that the method worked well with both Gaussian and non-Gaussian surfaces.
Speckle size of light scattered from slightly rough cylindrical surfaces
Applied Optics, 2002
This research is an extension of the optical method of quality control presented in a previous paper [Appl. Opt. 39, 5811 (2000)] to the case of slightly rough cylindrical surfaces. Applying the Kirchhoff scalar diffraction theory yields an analytical expression of the autocorrelation function of the intensity scattered from slightly rough cylindrical surfaces. This function, which is related to speckle size and shape, is shown to depend on the surface correlation length, unlike for plane surfaces for which the speckle depends on the illuminated area only. The theoretical expression is compared with that for the speckle produced by the light scattered from a cylindrical bearing and from various high-quality wires, showing that the method allows the correlation lengths of high-quality cylindrical surfaces to be determined.
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.
Applied Optics, 2012
Objective speckles produced by two beams overlapping and interfering on a rough object surface contain information about the angle of incidence of the two beams, and how well they overlap. We obtain the autocovariance function for such a speckle pattern, and demonstrate how the information carried by the objective speckles can be used to probe the distance between the object and the observation plane. From a distance of 75 mm to a distance of 150 mm, and using an angle of 0.3 deg between the two incident beams, we can measure the actual distance with an uncertainty of better than 0.1% of the full range. As long as the beams overlap at the object surface, the proposed method can measure distance with an uncertainty inversely proportional to the spot size at the object.
Controlling speckle using lenses and free space
Optics Letters, 2007
The correlation properties of speckle fields are studied for general paraxial systems. The previous studies on lateral and longitudinal speckle size for the case of free-space propagation (Fresnel transform) are generalized to the case of the linear canonical transform. These results have implications for the control of speckle size, through appropriate design of optical systems, with particular relevance for speckle interferometry.