A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Laser Doppler velocimetry uses the frequency shift produced by the Doppler effect to measure velocity. It can be used to monitor blood flow or other tissue movement in the body. Laser speckle is a random interference effect that gives a grainy appearance to objects illuminated by laser light. If the object consists of individual moving scatterers (such as blood cells), the speckle pattern fluctuates. These fluctuations provide information about the velocity distribution of the scatterers. It can be shown that the speckle and Doppler approaches are different ways of looking at the same phenomenon. Both these techniques measure at a single point. If a map of the velocity distribution is required, some form of scanning must be introduced. This has been done for both time-varying speckle and laser Doppler. However, with the speckle technique it is also possible to devise a full-field technique that gives an instantaneous map of velocities in real time. This review article presents the theory and practice of these techniques using a tutorial approach and compares the relative merits of the scanning and full-field approaches to velocity map imaging. The article concludes with a review of reported applications of these techniques to blood perfusion mapping and imaging.

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Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging

The Doppler technique has traditionally been the method used to extract motion information from ultrasonic echoes reflected by moving tissues. The Doppler technique has been around for a long time, and has been extensively reviewed and analyzed in the literature. Recently, time-domain methodologies for estimating tissue motion have gained in popularity. Time-domain methods have advantages over Doppler methods in many applications, and as of yet have not been comprehensively reviewed. An overview of time-domain techniques that have appeared in the literature over the past few years is presented. Their potential advantages over Doppler are examined, and the individual techniques are compared. >

Current time-domain methods for assessing tissue motion by analysis from reflected ultrasound echoes-a review

An alternative approach to fully automatic speckle-displacement measurement is described. Two speckle patterns of a specimen, one before and one after deformation, are captured by a CCD camera and registered by a frame grabber. Two series of small subimages are obtained by segmenting the two speckle patterns. The corresponding subimage pairs extracted from both series are analyzed pointwise. The interrogation of each subimage pair involves a two-step fast-Fourier transform. While the first-step fast-Fourier transform achieves a complex spectrum characterized by the local displacement information, the second-step one generates a signal peak in the second spectral domain that resolves the local displacement vector. A rough estimate of the displacement vector is achieved by detecting the maximum pixel of the discrete spectrum. A more accurate determination is attained by a subpixel-maximum determination through a biparabolic fitting near the signal peak. The u- and v-displacement fields are deduced by analyzing all subimage pairs. A large rigid-body displacement can be overcome by introducing an artificial rigid shift of the two speckle patterns toward each other before the numerical process. The technique retains all the advantages of optical speckle photography and provides an extended range of measurement. Dynamic incremental deformations can be inspected by registering more speckle patterns at many consecutive deformation stages by using a high-speed CCD camera. The system was applied successfully to the study of crack-tip deformation fields.

Digital speckle-displacement measurement using a complex spectrum method

Multi-point optical measurements of simultaneous vectors in unsteady flow—a review

A method using the speckle contrast for the determination of both the roughness and the correlation length of surface-height variations of a rough-surface object is proposed on the basis of the statistical properties of the Gaussian speckle field in the image region. The expression for the speckle contrast is first theoretically derived in the optical imaging system as a function of the defocus distance and the surface parameters of the object. By solving the equations expressing the speckle contrasts at the image and defocus planes, a unique solution is found to exist for the roughness and the correlation length. In particular, a useful approximate relation that the roughness depends only on the contrast ratio is derived for relatively small values of the roughness. The experiments were performed to confirm the validity of the proposed method. The present method has an advantage of the simplicity in a measuring procedure where the contrasts at only the two points are required to determine the surface parameters.

Roughness and correlation-length determination of rough-surface objects using the speckle contrast

Dynamic statistical properties of laser speckle produced in the diffraction field from an out-of-plane vibrating object are studied theoretically and experimentally. The equations expressing the averaged power spectrum and the autocorrelation function of vibrating laser speckle intensity fluctuations are derived for the first time and evaluated numerically. An analysis of those equations shows that the statistical properties of the averaged power spectrum and the autocorrelation function of vibrating speckle are determined by a product of both the derivative value (vibration slope) of vibrating amplitudes of the object and the laser beam width used for illumination of the object. The correlation length and the power spectrum of vibrating speckle are investigated in detail as a function of the vibration slope of the object and the beam width of illumination. It is shown from numerical evaluation of the equations that the power spectral width of vibrating speckles is linearly dependent on the product of the vibration slope and the beam width except for extremely small values. Experiments confirming the theory were performed and show excellent agreement with the theoretical results.

Dynamic statistical properties of vibrating laser speckle in the diffraction field.

The time correlation function is analyzed of the speckel intensity fluctuation produced in the Fresnel diffraction field from a rotating diffuse object under illumination of a Gaussian laser beam. The dependence of the curvature radius of the rotating diffuse object on the time correlation length of the speckle intensity fluctuation is especially explored by taking into account the size of the detecting aperture. The theoretical results are confirmed experimentally for detecting apertures with various sizes. It is shown that a detecting aperture with an appropriate size is required. It becomes useful for determining the radius of curvature of the rotating diffuse object from measurements of the time correlation length of the speckle intensity fluctuation.

An effect of curvature of rotating diffuse objects on the dynamics of speckles produced in the diffraction field

The dynamic statistical properties of laser speckle produced in the far-field diffraction region by a diffuse object moving in an arbitrary direction of three-dimensional space under illumination of a Gaussian beam are investigated theoretically and experimentally. It is found that the time-varying speckle intensity detected at the center of the far-field diffraction plane is a stationary random process with respect to time. The dependence of the autocorrelation function of the time-varying speckle-intensity fluctuation on both lateral and longitudinal components of the object velocity is studied in some detail by evaluating numerically the resultant equation of the time-varying speckle-intensity correlation. To confirm the theoretical results, an experiment has been performed. Good agreement between the theoretical and experimental results is obtained for the autocorrelation function of the time-varying speckle-intensity fluctuation that is due to three-dimensional translation of the diffuse object.

Dynamic statistical properties of laser speckle produced by a moving diffuse object under illumination of a Gaussian beam

The statistical properties of the speckle phase in the diffraction region are theoretically and experimentally investigated. The statistical parameters describing the equiprobability density ellipse, by which the speckle field is characterized, are first derived for the general case. By using the equiprobability density ellipse, the statistical properties of the speckle phase are next investigated theoretically as a function of the observation point in space and the illumination condition. The speckle phases were experimentally measured by means of a heterodyne interferometer to verify the theoretical results. In particular, when the diffuse object is illuminated by a Gaussian beam around its waist region, the statistical properties of the speckle phase are revealed to be similar to those observed already in the optical imaging system with respect to the defocusing.

N. Takai

Papers

Roughness and correlation-length determination of rough-surface objects using the speckle contrast

Dynamic statistical properties of vibrating laser speckle in the diffraction field.

An effect of curvature of rotating diffuse objects on the dynamics of speckles produced in the diffraction field

Dynamic statistical properties of laser speckle produced by a moving diffuse object under illumination of a Gaussian beam

Statistical properties of the speckle phase in the diffraction region