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

This paper proposes a new method for measuring the in-plane velocity of a moving diffuse object by using the technique of zero-crossings for the intensity fluctuation of spatially integrated laser speckles The scattered speckle pattern is detected in the diffraction field by a finite-aperture photodetector whose output current is analyzed, after removal of its dc component, by counting zero-crossings The number of zero-crossings per second for the signal is investigated theoretically and found to depend linearly on the object’s velocity The theoretical results are confirmed experimentally for translational speckles detected by the photodetector having circular apertures of various sizes The excellent agreement between theoretical and experimental results shows that the new method allows measurement of the velocity of a moving object in real time with good accuracy

Real-time velocity measurement for a diffuse object using zero-crossings of laser speckle

In this paper we study the statistical properties of both speckle patterns incident upon and emerging from a diffuse object under illumination of the laser light generated from a multimode optical fiber. The speckle field resulting from the modal noise at the exit face of the optical fiber is treated as a quasi-homogeneous monochromatic source that describes the quasi-stationary state within a finite region and, simultaneously, has the correlation coefficient that remains to be strictly stationary. The speckle pattern at the object plane in the Fresnel-diffraction field is first investigated by analyzing the propagation of the correlation function of the optical fields emerging from the source and found also to be quasi-homogeneous. Next, the correlation function of the optical field produced at the observation plane by scattering from a moving diffuse object under illumination of the above speckle pattern is analyzed in connection with the source parameters.

Statistical properties of laser speckles produced under illumination from a multimode optical fiber

A new type of phase shifting interferometer with a common-path arrangement using a polarization technique is proposed and discussed. In the interferometer, the dc (specular) component of an object beam is separated in the Fourier transform plane and used as a reference beam for its ac component. The phase of the dc component used as the reference beam is shifted by using a polarization technique for phase shifting interferometry. The present interferometer is different from a shearing type in that the phase distribution of an object beam is directly analyzed from the acquired intensity variations obtained by a 2-D detector such as a TV camera. Some experiments were conducted to verify the validity of the present phase shifting interferometer. They showed that high stability of the phase measurements is achieved up to λ/200 with an accuracy of λ/40 for wavelength λ light. The interferometer is suitable for obtaining 2-D phase information about the surface structure of small objects.

New common-path phase shifting interferometer using a polarization technique.

The translational and boiling motions of dynamic speckles produced in the Fresnel diffraction field under illumination of a Gaussian beam are investigated in detail. The speckle motion is analyzed from the space–time cross-correlation function of speckle intensity fluctuations detected at the two points in the receiving plane. The correlation distance of time-varying speckles is compared with the translation distance of the spatial speckle pattern. The optical conditions for the translational and boiling motions of dynamic speckles are examined and expressed in a diagram. The characteristics for the correlation distance of time-varying speckle intensity fluctuations are finally verified by several experiments.

Correlation distance of dynamic speckles.

The dynamic statistical properties of laser speckle produced in the far-field diffraction region from a diffuse object moving longitudinally along the optical axis under illumination of a Gaussian beam are investigated theoretically and experimentally. Although the spatial structure of speckle patterns varies in time owing to the longitudinal motion of the object, the time-varying speckle intensity detected at the center of the far-field diffraction plane is found to follow a statistically stationary variation. The autocorrelation function and power spectral density of the speckle intensity variations are studied with relation to the illuminating condition of the Gaussian beam.

N. Takai

Papers

Real-time velocity measurement for a diffuse object using zero-crossings of laser speckle

Statistical properties of laser speckles produced under illumination from a multimode optical fiber

New common-path phase shifting interferometer using a polarization technique.

Correlation distance of dynamic speckles.

Dynamic statistical properties of laser speckle due to longitudinal motion of a diffuse object under Gaussian beam illumination