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

Security analysis is important and necessary for a new cryptosystem. In this paper, we evaluate the security risk of the optical cryptosystem with spatially incoherent illumination from the view of imaging through scattering medium and then demonstrate that it is vulnerable to ciphertext-only attack. The proposed ciphertext-only attack method relies on the optical memory effect for speckle correlations, which reveals a fact that the ciphertext's autocorrelation is essentially identical to the plaintext's own autocorrelation. Furthermore, by employing of an improved dynamic hybrid input-output phase-retrieval algorithm, we show that a plaintext image can be directly reconstructed from the autocorrelation of its corresponding ciphertext without any prior knowledge about the plaintext or the phase keys. Meanwhile, the theory analysis and experiment results will also be provided to verify the validity and feasibility of our proposed ciphertext-only attack method. To the best of our knowledge, this is the first time to report optical cryptanalysis from the point of view of imaging through scattering medium and we believe this contribution will open up an avenue to deepen the investigation of optical cryptosystems.

/pdf/ciphertext-only-attack-on-optical-cryptosystem-with-1rr824kv2y.pdf

Ciphertext-only attack on optical cryptosystem with spatially incoherent illumination: from the view of imaging through scattering medium.

Secret shared multiple-image encryption based on row scanning compressive ghost imaging and phase retrieval in the Fresnel domain

We propose a method to achieve the purpose of hierarchical authentication on the basis of two beams’ interference and the one-way hash function. For this security protection system, only if the “phase key” and the password-controlled “phase lock” of a user are verified simultaneously can one obtain a permission to visit the confidential resources of the system. Moreover, this scheme can not only check the legality of the users but also verify their identity levels so as to grant them corresponding hierarchical access permissions. The authentication process is straightforward; the phase key and the password-controlled phase lock of one user are loading on two spatial light modulators in advance, by which two coherent beams are modulated and then interfere with each other at the output plane leading to an output image. By comparing the output image with all the standard certification images in the database, the system can thus verify the user’s identity. However, the system designing process involves an iterative modified phase retrieval algorithm. For an authorized user, a phase lock is first created based on a “digital fingerprint,” which is the result of a hash function on a preselected user password. The corresponding phase key can then be determined by use of the phase lock and a designated standard certification image. Theoretical analysis and computer simulations both validate the effectiveness of our method.

Optical hierarchical authentication based on interference and hash function

In previous work, we presented a structured light field (SLF) method combining light field imaging with structured illumination to perform multi-view depth measurement. However, the previous work just accomplishes depth rather than 3D reconstruction. In this paper, we propose a novel active method involving ray calibration and phase mapping, to achieve SLF 3D reconstruction. We performed the ray calibration for the first time to determine each light field ray with metric spatio-angular parameters, making the SLF realize multi-view 3D reconstruction. Based on the ray parametric equation, we further derived the phase mapping in the SLF that spatial coordinates can be directly mapped from phase. A flexible calibration strategy was correspondently designed to determine mapping coefficients for each light field ray, achieving high-efficiency SLF 3D reconstruction. Experimental results demonstrated that the proposed method was suitable for high-efficiency multi-view 3D reconstruction in the SLF.

Ray calibration and phase mapping for structured-light-field 3D reconstruction.

A system of asymmetric cryptography based on wavefront sensing (ACWS) is proposed for the first time to our knowledge. One of the most significant features of the asymmetric cryptography is that a trapdoor one-way function is required and constructed by analogy to wavefront sensing, in which the public key may be derived from optical parameters, such as the wavelength or the focal length, while the private key may be obtained from a kind of regular point array. The ciphertext is generated by the encoded wavefront and represented with an irregular array. In such an ACWS system, the encryption key is not identical to the decryption key, which is another important feature of an asymmetric cryptographic system. The processes of asymmetric encryption and decryption are formulized mathematically and demonstrated with a set of numerical experiments.

Xiang Peng

Papers

Ciphertext-only attack on optical cryptosystem with spatially incoherent illumination: from the view of imaging through scattering medium.

Secret shared multiple-image encryption based on row scanning compressive ghost imaging and phase retrieval in the Fresnel domain

Optical hierarchical authentication based on interference and hash function

Ray calibration and phase mapping for structured-light-field 3D reconstruction.

Asymmetric cryptography based on wavefront sensing