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

The reduction mechanism of speckles appearing in laser-microscope images is studied theoretically and experimentally when an object is illuminated by laser light through a rotating multimode optical fiber. The principle of the speckle reduction is based on independent addition of microscope images with boiling-like speckles as a result of the rotational motion of the optical fiber used for illumination. Especially, the speckle reduction is evaluated from first-order statistics of the speckle intensity in which its saturation effect is taken into consideration.

Mechanism of speckle reduction in laser-microscope images using a rotating optical fiber

Velocity measurement of the diffuse object based on time-differentiated speckle intensity fluctuations

The autocorrelation function of the spatially integrated speckle intensity fluctuation is investigated theoretically and experimentally by using both the circular hard aperture and the circular gaussian soft aperture for detection This investigation shows that the use of the circular gaussian soft aperture simplifies an evaluation of the autocorrelation function of the spatially integrated speckle intensity fluctuation and that the resultant autocorrelation functions obtained using the circular gaussian soft aperture sufficiently approximate to the ones obtained using the circular hard aperture which is usually employed in real situations The autocorrelation function of the speckle intensity fluctuation integrated spatially by an elliptic detecting aperture is also studied theoretically and experimentally as an extension of the circular hard and gaussian soft detecting apertures

The Autocorrelation Function of the Speckle Intensity Fluctuation Integrated Spatially by a Detecting Aperture of Finite Size

Characteristics of the phase of Gaussian speckles are studied theoretically in both image and diffraction fields. The general analysis for these studies is given by introducing an "optical system function," and the results are applied to the analysis of the speckle phases in both fields. The speckle phase distributions are evaluated by a phase angle defined as the extent of the equiprobability density ellipse stretched from the origin in the complex plane of the speckle amplitude. In addition, several peculiar properties of the equiprobability density ellipse are summarized.

N. Takai

Papers

Mechanism of speckle reduction in laser-microscope images using a rotating optical fiber

Velocity measurement of the diffuse object based on time-differentiated speckle intensity fluctuations

The Autocorrelation Function of the Speckle Intensity Fluctuation Integrated Spatially by a Detecting Aperture of Finite Size

Statistical Properties Of The Speckle Phase In Image And Diffraction Fields

Relation between statistical properties of surface roughness and the averaged speckle intensity in the diffraction field