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 present invention relates to a method and apparatus for obtaining the equivalent key of the random phase coding-based optical encryption system. The apparatus includes a point light source structure, an optical 4f structure, a pure phase space light modulator and a feedback control device. According to the apparatus, the phase modulation parameter of the pure phase space light modulator is adjusted, so that the light intensity of the center of an output surface image can be maximum, and the phase modulation parameter is adopted as the equivalent key of the optical encryption system. According to the method, modulation is completed through the apparatus. With the method and apparatus adopted, the equivalent key of the optical encryption system parameter can be obtained simply, and cost is low.

Method and apparatus for obtaining equivalent key of random phase coding-based optical encryption system

In this paper, we introduced a concept of cascaded phase-truncated Fourier transforms (CPTFTs), which is a nonlinear
iterative operator. Meanwhile, an optical/digital hybrid system was presented to implement the operator of CPTFTs.
Thereafter, by adopting CPTFTs as main processing unit, we have done some research on optical one-way cryptosystem:
an optical Hash function (O-Hash) and a keyed optical Hash function (K-O-Hash) were put forward respectively, which
can be applied to message integrity check and authentication. Both of the O-Hash and K-O-Hash can transform an
arbitrary-length pre-encoded message (without or with a secret key) into a fixed-length output by means of taking a
two-step one-way encryption process. Finally, a set of numerical experiments were carried out to evaluate the performance
of avalanche effect and collision resistance of the O-Hash and K-O-Hash constructed with our approach.

Research on Optical One-way Cryptosystem

A cascaded iterative angular spectrum approach (CIASA) based on the methodology of virtual optics is presented for optical security applications. The technique encodes the target image into two different phase only masks (POM) using a concept of free-space angular spectrum propagation. The two phase-masks are designed and located in any two arbitrary planes interrelated through the free space propagation domain in order to implement the optical encryption or authenticity verification. And both phase masks can serve as enciphered texts. Compared with previous methods, the proposed algorithm employs an improved searching strategy: modifying the phase-distributions of both masks synchronously as well as enlarging the searching space. And with such a scheme, we make use of a high performance floating-point Digital Signal Processor (DSP) to accomplish a design of multiple-locks and multiple-keys optical image encryption system. An evaluation of the system performance is made and it is shown that the algorithm results in much faster convergence and better image quality for the recovered image. And two masks and system parameters can be used to design keys for image encryption, therefore the decrypted image can be obtained only when all these keys are under authorization. This key-assignment strategy may reduce the risk of being intruded and show a high security level. These characters may introduce a high level security that makes the encrypted image more difficult to be decrypted by an unauthorized person.

Optical image encryption based on cascaded iterative angular spectrum algorithm and its implementation with parallel hardware

A improved SPIHT image compression algorithm called symbol-map zero-tree coding algorithm (SMZTC) is proposed
in this paper based on wavelet transform. The SPIHT algorithm is a high efficiency wavelet coefficients coding method
and have good image compressing effect, but it has more complexity and need too much memory. The algorithm
presented in this paper utilizes two small symbol-maps Mark and FC to store the status of coefficients and zero tree sets
during coding procedure so as to reduce the memory requirement. By this strategy, the memory cost is reduced distinctly
as well as the scanning speed of coefficients is improved. Those comparison experiments for 512 by 512 images are done
with some other zerotree coding algorithms, such as SPIHT, NLS method. During the experiments, the biorthogonal 9/7
lifting wavelet transform is used to image transform. The results of coding experiments show that this algorithm speed of
codec is improved significantly, and compression-ratio is almost uniformed with SPIHT algorithm.

A symbol-map wavelet zero-tree image coding algorithm

We present an optical image encryption method based on a modified radial shearing interferometer In our encryption 
process, a plaintext image is first encoded into a phase-only mask (POM), and then modulated by a random phase mask 
(RPM), the result is regarded as the input of the radial shearing interferometer and divided into two coherent lights, one 
of which will be further modulated by a random amplitude mask (RAM) After all, these two coherent lights will 
interfere with each other leading to an interferogram, ie, ciphertext And the ciphertext can be used to retrieve the 
plaintext image with the help of a recursive algorithm and all correct keys The aforementioned encryption procedure can 
be achieved digitally or optically while the decryption process can be analytically accomplished Numerical simulation is 
provided to demonstrate the validity of this method

Xiang Peng

Papers

Method and apparatus for obtaining equivalent key of random phase coding-based optical encryption system

Research on Optical One-way Cryptosystem

Optical image encryption based on cascaded iterative angular spectrum algorithm and its implementation with parallel hardware

A symbol-map wavelet zero-tree image coding algorithm

Optical image encryption based on a modified radial shearing interferometer