Properties of light scattered by a diffuse object under dynamic speckle illumination and their application to the roughness distribution measurement

The properties of the scattered light which depends on the surface roughness of the diffuse object under a dynamic speckle illumination have been investigated. From these properties, a new method to measure the spatial roughness distribution by means of the dynamic speckle illumination is proposed.     

A contrast variation of image speckle intensity under illumination of partially coherent light

Speckle patterns are formed by completely and partially coherent light at the image plane of a diffusing object. The general formula is derived for the contrast variation of the image speckle intensity distribution as a function of the spatial coherence of the illuminating light, the amplitude point-spread function of the optical imaging system and the statistical characteristic of the diffusing object. The effect of spatial coherence of the illuminating light on the contrast variations of the image speckle intensity distribution is theoretically evaluated under various statistical conditions of the diffusing object. The theoretical results are confirmed experimentally.     

Comparing roughness dependent contrasts of polychromatic speckle patterns in light of different spectral densities

An exact solution is obtained for the roughness dependent speckle contrast in the case of a rectangular spectrum. This is compared to the simple formula previously obtained for a gaussian spectrum. The agreement is shown to be good if the formulas are fitted to the same asymptotic dependence in the incoherent limit. From this we conclude that the simple gaussian formula may be a useful approximation even for other non-gaussian spectra, and a fitting procedure is indicated.     

Surface roughness measurement using spatial-average analysis of objective speckle pattern in specular direction

The speckle contrast method (SCM) and the light scattering method (LSM) are two of the most promising optical techniques for on-line surface roughness measurement of slightly-rough surface. However, due to the lack of capability in eliminating the influence from the diffuse component of scattered light, SCM and LSM are both sensitive to the variations of surface correlation length. Additionally, for LSM, the presence of speckle noise leads to fluctuations in the measuring results. To solve these problems, an approach based on the spatial-average analysis of the objective speckle pattern in the specular direction, simply called spatial-average method (SAM), is proposed. The SAM establishes the quantitative relationship between a new characteristic parameter extracted from the recorded speckle image and the rms surface roughness, eliminates to a large extent the influence of diffuse light component on the measuring results, and immunizes itself from the speckle noise. The theoretical foundation of SAM is given in details. A computer simulation is then performed to make comparisons among these three methods. Finally an experiment is presented.     

Whole field surface roughness measurement by laser speckle correlation technique

This paper describes a speckle correlation technique for the determination of surface roughness, ranging from 1.6 to 50 μm. Instead of moving the laser beam, the specimen is rotated to achieve angular speckle correlation (ASC) in the far-field plane. The technique is simple and requires minimum optical alignment. The experimental results show a good agreement with the standard specimen of known roughness. An error analysis on the experiment has been carried out. Together with the theoretical curves, the roughness values can be easily related to the change of incidence angle at a particular visibility of the correlation fringes between two speckle patterns.     

Statistical properties of speckle intensity variations in the diffraction field under illumination of coherent light

The statistical properties of speckle intensity variations produced by coherent light in the diffraction field of diffusely transmitting objects are investigated experimentally with intimate relation to their surface roughness. The probability distribution and the average contrast of intensity variations in speckle patterns are studied as a function of the surface roughness of the objects and the receiving plane in the diffraction field.     

Verification of speckle contrast measurement interrelation with observation distance

The speckle contrasts of two types of laser projectors were measured at various observation distances and observation lens pinhole diameters using a quantitative measurement technique. We found that the speckle contrast as a function of the observation numerical aperture varies with the projection architecture. In a full-frame projector, it is proportional to the numerical aperture, but it is proportional to its square root in a raster-scanned projector. The difference in speckle contrast as a function of the numerical aperture was analyzed based on Goodman’s speckle theory. The obtained results were found to be very useful and applicable for speckle evaluation and display qualifications in an arbitrary observer’s position.     

Stereophotogrammetric 3D shape measurement by holographic methods using structured speckle illumination combined with interferometry

We present a unique combination of the numerical three-dimensional (3D) reconstruction of the shape of an object with interferometric deformation measurements. Two cameras record several holograms of an object that is illuminated by structured illumination. This illumination is realized by speckle patterns. To improve the image quality, an inplace speckle reduction technique is combined with the structured illumination to reduce the effect of disturbing subjective speckles which appear in the reconstructed images. Stereophotogrammetric methods are applied to extract the 3D surface information of the object out of the reconstructed images. Since the recording is done by holography and because stereophotogrammetry enables a pointwise correlation between the two views, it is possible to combine other holographic techniques with the reconstructed 3D shape. This is demonstrated by an interferometric deformation measurement of an object cooling down. The resulting interferometric fringes are mapped onto the reconstructed 3D surface. Hence, the proposed method enables automatic and dense matching of interferometric fringe-maps recorded by spatially separated holograms onto the surface of the object, which has not yet been realized by existing techniques.     

Optical surface profile measurement using phase retrieval by tuning the illumination wavelength

In this paper, we present a method for measuring the surface profile of an object by using diffraction intensity patterns recorded at different illumination wavelengths. The main advantages of this technique are: simple optical set-up, high immunity to noise and environmental disturbance, since no reference beam (like in holography) or additional moving parts are needed. Two iterative calculations are synchronously performed using two sequences of diffraction intensity patterns, producing fast convergence to the expected result. The effects of different parameters on the accuracy and efficiency of the method are investigated. Simulation and experimental results are presented.     

Photocount statistics of gaussian light with analytic spectral profile

The letter derives an explicit expression for the generating function of the photocount distribution corresponding to gaussian light characterized by a triangle-shaped correlation function. The first six moments are compared with those derived from the approximate formula of Rice.     

Surface roughness dependence of the first-order probability density function for integrated speckle

The surface roughness dependence of the first-order probability density function (PDF) of an integrated speckle pattern, produced in the condition of circular detection aperture and gaussian scattering spot, was theoretically investigated. The mutual intensity J_A(x₁, y₁; x₂, y₂) containing two roughness parameters, dispersion of surface height ø² lateral correlation length x_c, was calculated. The exact first-order probability density function was analytically derived and numerically calculated by means of the Karhunen-Loeve expansion and fast Fourier transform (FFT). As a diffuse object became smooth, the first order probability density function was changed from negative exponential to sharp peak gaussian centered around mean intensity.     

Some effects of surface roughness on the appearance of speckle in polychromatic light

A statistical formulation is given explaining the fibrous structure seen in speckle patterns in polychromatic light. It is shown that the appearance of the structure is strongly dependent on the surface roughness of the diffuser. This may be useful as the basis of a determination of surface roughness.     

A novel video-based microsphere localization algorithm for low contrast silica particles under white light illumination

On the basis of a brief review of four common image recognition algorithms for microspheres made of polystyrene or melamine resin, we present a new microsphere localization method for low-contrast silica beads under white light illumination. We compare both the polystyrene and silica procedures with respect to accuracy and precision by means of an optical tweezers setup providing CMOS video microscopy capability. By that we demonstrate that our new silica algorithm achieves a relative position uncertainty of less than ±1 nm for micron-sized microspheres, significantly exceeding the precision of the other silica approaches studied. Second, we present an advancement of our single microsphere tracking method to scenarios where two polystyrene, melamine resin or silica microspheres are in close-to-contact proximity. While the majority of the analysis algorithms studied generate artefacts due to interference effects under these conditions, we show that our new approach yields accurate and precise results.     

Measurement of the spectral distribution of a multi-mode dye laser light by using speckle patterns

A simple method of measuring the wavelength γ₁ and the spectral line spacing Δγ of a multi-mode dye laser light by using the correlated speckle patterns produced at the far-field of a diffuser is proposed. Examples of the obtained values of γ₁ and Δγ are 6.0 × 10³ Å and 3.0 × 10¹ Å, respectively.     

Roughness measurement of metallic surfaces based on the laser speckle contrast method

A method of measuring surface roughness of flat lapped, ground and polished metallic surfaces, by the far-field speckle contrast method is presented in this paper. The laser speckle contrast technique depends on the existence of an approximately linear relationship between the speckle contrast and the roughness of the illuminated surface. Initially it was shown that the linear relationship existed up to 0.1 μm Ra (centre-line average) roughness using Helium–Neon light, after which a saturation effect was observed. The effect of varying the incident angle of illumination was investigated with a view to extending the measurement range. The use of high incident angles of illumination has been found to increase the surface roughness range up to 0.4 μm measurement Ra.     

The spectral profile of light scattered by particles in electrophoretic movement

The electrophoretic movements of polystyrene latex particles suspended in water and in electrolyte solutions have been investigated with an optical beating technique. When two kinds of particles in water move in the presence of an external electric field, it is observed that the laser light scattered by these particles exhibits a shifted spectrum with a single peak profile, even if the electrophoretic mobilities of the two kinds of particles are different to each other. However, when these particles are suspended in an electrolyte solution, two separate spectral lines are observed which correspond to the velocity of each kind of particles.     

Simple method for measurement of surface roughness using spectral interferometry

The phenomenon that correlation between two beams, in a two-beam interferometer, modifies the spectral characteristics of the light field, is used to estimate the average of the roughness of the surfaces. In the case of intensity interferometer, the path difference between the two arms of the interferometer should be less than the coherence length of the light and the light should be quasi-monochromatic. However, the advantage of spectral interferometer is that the light need not be quasi-monochromatic and the path difference could be much more than the coherence length of light. It is found that more the path difference between the two arms of the interferometer, accurate are the measurements of the roughness of the surfaces. This study shows that spectral interferometry enables one to measure average roughness of the surfaces in the subscales of optical wavelengths.     

Designing arbitrary nanoscale patterns by a nanocavity waveguide with omnidirectional illumination

We report one- and two-dimensional arbitrary patterns which are achieved by nanocavity waveguides made of a quasi-metal?Cdielectric-metal heterostructure with omnidirectional illumination. This proposed heterostructure supports the surface plasmon polaritons whose phase and group velocities have opposite sign for given frequency. Negative refraction and reflection in the waveguide result in imaging nanolithography and the omnidirectional property can be well understood by the dispersive relation of the nanocavity waveguide. Numerical results demonstrate that such an omnidirectional nanolithography scheme is feasible for arbitrary 1D gratings and 2D linearly chirped gratings with TM and circular polarized incidence, respectively, at 365?nm.