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

Fringe projection 3D microscopy (FP-3DM) plays an important role in micro-machining and micro-fabrication. FP-3DM may be realized with quite different arrangements and principles, which make people confused to select an appropriate one for their specific application. This paper introduces the ray-based general imaging model to describe the FP-3DM, which has the potential to get a unified expression for different system arrangements. Meanwhile the dedicated calibration procedure is also presented to realize quantitative 3D imaging. The validity and accuracy of proposed calibration approach is demonstrated with experiments.

Ray-based calibration for the micro optical metrology system

The temporal phase unwrapping will become unstable, if fewer numbers of fringe patterns with different spatial
frequencies are used. In this paper, we present a modified phase unwrapping method based on the phase filtering, which
can be used to achieve correct phase-unwrapping with use of fewer numbers of fringe frequencies. An adaptive phase
filter is designed according to the phase-jumping characteristics to eliminate the phase noise. The window size of the
filter is adaptively determined according to the local noise levels. After filtering operation, we are able to obtain the
approximate phase value with filtering errors. In order to further eliminate the filtering residual errors, we take
unwrapping operation again to get the correct phase value. The simulation experimental results are also presented to
validate our proposed approach.

A modified phase unwrapping algorithm based on phase filtering

The speckle correlation technique is applied to ciphertext-only attack (COA) on optical cryptosystem based on double random phase encoding. According to the inherent merits of speckle correlation, we have revealed a fact that the ciphertext’s autocorrelation is essentially identical to the plaintext’s own autocorrelation. Then, a plaintext image can be directly reconstructed from the autocorrelation of its corresponding ciphertext by employing a iterate phase-retrieval algorithm. This could then lead to a potential security flaw because an unauthorized user could directly retrieve the plaintext from an intercepted ciphertext by performing proposed COA approach. Meanwhile, a series of numerical simulations will also be provided to verify the validity and feasibility of our proposed COA method.

Speckle-correlation-based ciphertext-only attack on the double random phase encoding scheme

Fourier ptychography (FP) provides an alternative scheme for improving the spatial bandwidth product with limited device. However, an angle-variation illumination is necessary to realize scanning imaging in the Fourier plane, which dramatically restricts the imaging speed and detection efficiency. In this paper, we propose a multiplexing and compressible FP scheme based on the structured illuminations and compressive sensing technique. Half of the LEDs are lighted together to reduce the exposure time; meanwhile, a learned dictionary is employed to reduce the sampling times. In addition, spectral independent illumination is proposed to retrieve color information from monochrome samplings. We experimentally verify that the proposed method can effectively reduce the sampling time with limited resolution loss.

Dictionary-based compressive Fourier ptychography.

The invention relates to a sub secret key generation method and decryption or authentication method for optical threshold coding. The generation method that is used for generating three sub secret keys in pure phase distribution for plaintext image information or authentication image information and using any two sub secret keys for recovering the plaintext image information or realizing successful authentication comprises: plaintext information or authentication image information is coded by using a phase retrieval algorithm to an initial first sub secret key, second sub secret key, and third sub secret key; and phase updating is carried out on the initial first sub secret key, second sub secret key, and third sub secret key by using a sub secret key authentication image for verifying sub secret key legality, thereby obtaining a final first sub secret key, second sub secret key, and third sub secret key that include the sub secret key authentication image information. Therefore, sub secret key counterfeiting can be prevented. The methods can be realized by using the simple optical system, so that realization becomes simple.

Xiang Peng

Papers

Ray-based calibration for the micro optical metrology system

A modified phase unwrapping algorithm based on phase filtering

Speckle-correlation-based ciphertext-only attack on the double random phase encoding scheme

Dictionary-based compressive Fourier ptychography.

Sub secret key generation method and decryption or authentication method for optical threshold coding