Lars Benckert

Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy

Replacing photographic recording by electronic processing has some obvious advantages. An algorithm used for electronic speckle pattern photography is presented, and the reliability and accuracy is analyzed by using computer-generated speckle patterns. The algorithm is based on a two-dimensional discrete cross correlation between subimages from different images. Subpixel accuracy is obtained by a Fourier series expansion of the discrete correlation surface. The accuracy of the algorithm was found to vary in proportion to sigma/n(1 - delta)(2), where sigma is the speckle size, n is the subimage size, and delta is the amount of decorrelation, with negligible systematic errors. For typical values the uncertainty in the displacement is approximately 0.05 pixels. The uncertainty is found to increase with increased displacement gradients.

Systematic and random errors in electronic speckle photography

Electronic speckle photography offers a simple and fast technique for measuring in-plane displacement fields in solid and fluid mechanics. Errors from undersampling, illumination divergence, and displacement magnitude have been analyzed and measured. The nature of the systematic error is such that a drift toward the closest integral pixel value is introduced. Because of the finite extent of the sensor area, considerable undersampling is tolerable before systematic errors occur. The random errors are mainly dependent on the effective ƒ-number of the imaging system and speckle decorrelation introduced by object displacement. When sampling at a rate of ~ 70% of the Nyquist frequency, we avoided systematic errors and minimized random errors.

Improving the quality of phase maps in phase object digital holographic interferometry by finding the right reconstruction distance

Improved quality of phase maps in pulsed digital holographic interferometry is demonstrated by finding the right reconstruction distance. The objective is to improve the optical phase information when the object under study is a phase object and when it is out of focus, leading to low contrast fringes in the phase map. A numerical refocusing is performed by introducing an ideal lens as a multiplication by a phase field in the Fourier domain, and then a region of maximum speckle correlation is found by comparing undisturbed and disturbed subimages in different refocused imaging planes. After finding the right reconstruction distance, a phase map of high visibility is constructed. By this technique a 30% reduction of the phase error for a flow of helium gas and a 50% reduction of the phase error for a weak thin lens were obtained, which resulted in a significant improvement of the visual appearance of the phase maps.

Speckle interferometry: noise reduction by correlation fringe averaging.

A method for noise reduction in double-exposure speckle interferometry is proposed, based on averaging independent spatially filtered correlation fringe patterns.

Phase object data obtained from defocused laser speckle displacement

An optical technique that is based on defocused digital speckle photography is proposed for the evaluation of phase objects. Phase objects are different kinds of transparent or semi-transparent media that allow light to be transmitted. A phase object inserted in a laser speckle field introduces speckle displacement, from which information about the object may be extracted. It is shown that one may use speckle displacements to determine both the phase gradients and the positions of phase objects. As an illustration the positions and focal lengths of two weak lenses have been derived from defocused laser speckle displacement.

Measurement of dynamic crack tip displacement field by speckle photography and interferometry

Abstract Speckle interferometry has been used to measure the transient displacement field around a crack due to stress wave loading. Double exposure interferograms are recorded with a pulsed ruby laser, and correlation fringes formed by spatial filtering of the developed film. A new technique is presented for reducing the noise level in spatially filtered speckle interferograms. Independent fringe patterns, obtained from one interferogram but with the filtering aperture sampling different regions of the Fourier transform plane, are digitised by a CCD camera and combined numerically. It is demonstrated that accurate analysis of fringe patterns by the Fourier transform method can be carried out, even if no carrier fringes are present. The measurements are compared with those obtained by speckle photography. Least-squares fitting of the theoretical displacement field is used to calculate the stress intensity factor at the crack tip as a function of time.

Parallel processing system for rapid analysis of speckle-photography and particle-image-velocimetry data.

An automated system has been constructed to process double-exposure speckle-photography and particle-image-velocimetry images. A 3 × 3 array of laser beams probes the photograph, forming nine fringe patterns in parallel; these are then analyzed sequentially by digital computer and the use of a two-dimensional Fourier-transform method. Results are presented showing that the random errors in the measured displacements from such a system approach the expected speckle-noise-limited performance, with a total analysis time per displacement vector of 160 ms.

Measuring True In-Plane Displacements Of A Surface By Stereoscopic White-Light Speckle Photography

When in-plane surface deformations are measured using white-light speckle photography, errors arise if an out-of-plane displacement is present. Stereoscopic photography resolves this problem and makes possible the measurement of true in-plane displacements. A rigid-body translation is introduced to determine unambiguously the direction of the displacement.

Phase object data obtained by pulsed TV holography and defocused laser speckle displacement

Transient events in optically transparent media occur in many engineering applications. Using pulsed TV holography to capture a laser speckle field propagated through an optical disturbance makes it possible to obtain both the position and the phase gradients of the disturbance. The technique depends on the fact that speckles transmitted through an optical disturbance will be displaced by an amount that depends on the relation of the defocus to the object. First the speckle field is captured holographically, without and with disturbance present. Then the recorded fields are numerically refocused in a computer to a number of different focal planes. With a cross-correlation technique a number of speckle displacement fields are obtained, and from them the data about the disturbance are obtained. So far the technique has been shown to work for thin objects.

Fresnel diffraction of a Gaussian laser beam by polished metal cylinders

A laser beam touching the periphery of a polished cylinder is subjected to both diffraction and reflection. In the area where diffracted light and reflected light interact the resulting intensity distribution differs from the pattern predicted by diffraction theory for a sharp edge. The difference increases with cylinder radius. In this paper it is shown that a good description of the resulting intensity pattern is obtained by adding the reflected light amplitude to the diffracted amplitude as predicted by the Fresnel-Kirchhoff theory for a sharp edge.