A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

The fact that light carries both linear and angular momentum is well-known to physicists. One application of the linear momentum of light is for optical tweezers, in which the refraction of a laser beam through a particle provides a reaction force that draws the particle towards the centre of the beam. The angular momentum of light can also be transfered to particles, causing them to spin. In fact, the angular momentum of light has two components that act through different mechanisms on various types of particle. This Review covers the creation of such beams and how their unusual intensity, polarization and phase structure has been put to use in the field of optical manipulation.

Tweezers with a twist

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

Fringe projection techniques: Whither we are?

Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

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Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

The invention discloses a method and a system for correcting the circle center deviation of round mark points during camera projection transformation. The method for correcting comprises the following steps of: step A, arranging the round mark points which have colors different with a background and have concentric ring shapes; step B, shooting the round mark points by utilizing a camera, carrying out sub-pixel positioning on the edges of the shot image of the round mark points, and fitting a large ellipse and a small ellipse according to the positioned sub-pixel edges; and step C, according to the radiuses r1 and r2 of a large circle and a small circle which are concentric and are obtained in the step A and the center coordinates C1 (muB1, vB1) and C2 (muB2, vB2) of the large ellipse and the small ellipse which are obtained in the step B, correcting the image coordinates of the practical projective points of the circle centers of the round mark points on an image plane after the camera projection transformation. A concentric ring method is adopted, and the linear combination of the large ellipse and the small ellipse is ingeniously utilized to correct the real positions of the circle centers of the manual round mark points on the image plane.

Method and system for correcting circle center deviation of round mark points during camera projection transformation

An acoustic-optics heterodyne fringe interferometry coupled with a three-camera system is developed for dynamic 3D imaging. In this system, first-order beams with a slight frequency difference diffracted from two acousto-optic deflectors (AODs) form a beat intensity fringe pattern. Setting the frequency of the trigger signal for the CCD cameras into four times the beat frequency, four-step phase-shifting fringe patterns can be obtained, and the wrapped phase map (WPM) can be calculated. Under the epipolar constraint among three cameras, the homologous points can be determined unambiguously with the assistant of a WPM; thus the 3D shape can be reconstructed while skipping the phase unwrapping step. Experimental results are presented to validate this approach.

Dynamic 3D imaging based on acousto-optic heterodyne fringe interferometry

Enhancement of optical image encryption based on radial shearing interference

To enhance the non-diffracting distance of propagation-invariant beams, fabrication of an axicon with large aperture diameter and height is essential. It is noted, however, that fabrication of continuous surface profile micro-optical elements with a large physical height (thick resist) is prone to various fabrication constraints and errors. We employ the kinoform technique to alleviate such problems in the fabrication of axicons. In this paper kinoform micro-axicons and kinoform micro-double-axicons are designed and fabricated employing electron beam lithography techniques to generate a Bessel beam and a self-imaged bottle beam with long non-diffracting distance. Furthermore, a detailed study of power conversion efficiency of kinoform structures is discussed.

https://iopscience.iop.org/article/10.1088/1464-4258/9/4/004/pdf

Direct electron beam writing of kinoform micro-axicon for generation of propagation-invariant beams with long non-diffracting distance

This Letter reports an approach to single-shot three-dimensional (3D) imaging that is combining structured illumination and light-field imaging. The sinusoidal distribution of the radiance in the structured-light field can be processed and transformed to compute the angular variance of the local radiance difference. The angular variance across the depth range exhibits a single-peak distribution trend that can be used to obtain the unambiguous depth. The phase computation that generally requires the acquisition of multi-frame phase-shifting images is no longer mandatory, thus enabling single-shot structured-light-field 3D imaging. The proposed approach was experimentally demonstrated through a dynamic scene.

Xiang Peng

Papers

Method and system for correcting circle center deviation of round mark points during camera projection transformation

Dynamic 3D imaging based on acousto-optic heterodyne fringe interferometry

Enhancement of optical image encryption based on radial shearing interference

Direct electron beam writing of kinoform micro-axicon for generation of propagation-invariant beams with long non-diffracting distance

Single-shot structured-light-field three-dimensional imaging.