Wavefront Reconstruction In Optics Research Articles

3D display based on complete digital optical phase conjugation

Digital optical wavefront reconstruction for 3D display at tens or hundreds centimeters scale with viewing angle over 100° calls for resolutions at sub-wavelength scale. However the pixel pitches of spatial light modulators (SLM) are at micrometer or tens of micrometer scale. When people generated 3D images by digital holography using SLMs they had to make the interference patterns very sparse, resulting in small image size or narrow viewing angle. The paper employed an adiabatic waveguide taper made of quantities of single-mode waveguides to decompose complicated light fields into simpler forms so that complete digital optical phase conjugation (CDOPC) could be performed using low resolution SLMs. Then the paper introduced an optical transforming unit to project the reconstructed small wavefronts over a large volume while maintaining large viewing angle. The paper shows both theoretically and experimentally that 3D display systems based on CDOPC could create large size 3D images with large viewing angle and diffraction limited image quality. Besides, CDOPC might also be widely used for 3D measurement, optical tweezers, high energy laser beam forming, etc.

Accurate optical wavefront reconstruction based on reciprocity of an optical path using low resolution spatial light modulators

A method for high precision optical wavefront reconstruction using low resolution spatial light modulators (SLMs) was proposed. It utilizes an adiabatic waveguide taper consisting of a plurality of single-mode waveguides to decompose an incident light field into simple fundamental modes of the single-mode waveguides. By digital generation of the conjugate fields of those simple fundamental modes a field proportional to the original incident light field might be reconstructed accurately based on reciprocity. Devices based on the method using transparent and reflective SLMs possess no aberration like that of a conventional optic lens and are able to achieve diffraction limited resolution. Specifically on the surface of the narrow end of a taper a resolution much higher than half of the wavelength is attainable. The device may work in linear mode and possesses unlimited theoretical 3D space-bandwidth product (SBP). The SBP of a real device is limited by the accuracy of SLMs. A pair of 8-bit SLMs with 1000 × 1000 = 10 6 pixels could provide a SBP of about 5 × 10 4. The SBP may expand by 16 times if 10-bit SLMs with the same number of pixels are employed or 16 successive frames are used to display one scene. The device might be used as high precision optical tweezers, or employed for continuous or discrete real-time 3D display, 3D measurement, machine vision, etc.

Optical Wavefront Reconstruction: Theory and Numerical Methods

Optical wavefront reconstruction algorithms played a central role in the effort to identify gross manufacturing errors in NASA's Hubble Space Telescope (HST). NASA's success with reconstruction algorithms on the HST has led to an effort to develop software that can aid and in some cases replace complicated, expensive, and error-prone hardware. Among the many applications is HST's replacement, the Next Generation Space Telescope (NGST). indent This work details the theory of optical wavefront reconstruction, reviews some numerical methods for this problem, and presents a novel numerical technique that we call extended least squares. We compare the performance of these numerical methods for potential inclusion in prototype NGST optical wavefront reconstruction software. We begin with a tutorial on Rayleigh--Sommerfeld diffraction theory.

Solution to the shearing problem

Lateral shearing interferometry is a promising reference-free measurement technique for optical wave-front reconstruction. The wave front under study is coherently superposed by a laterally sheared copy of itself, and from the interferogram difference measurements of the wave front are obtained. From these difference measurements the wave front is then reconstructed. Recently, several new and efficient algorithms for evaluating lateral shearing interferograms have been suggested. So far, however, all evaluation methods are somewhat restricted, e.g., assume a priori knowledge of the wave front under study, or assume small shears, and so on. Here a new, to our knowledge, approach for the evaluation of lateral shearing interferograms is presented, which is based on an extension of the difference measurements. This so-called natural extension allows for reconstruction of that part of the underlying wave front whose information is contained in the given difference measurements. The method is not restricted to small shears and allows for high lateral resolution to be achieved. Since the method uses discrete Fourier analysis, the reconstructions can be efficiently calculated. Furthermore, it is shown that, by application of the method to the analysis of two shearing interferograms with suitably chosen shears, exact reconstruction of the underlying wave front at all evaluation points is obtained up to an arbitrary constant. The influence of noise on the results obtained by this reconstruction procedure is investigated in detail, and its stability is shown. Finally, applications to simulated measurements are presented. The results demonstrate high-quality reconstructions for single shearing interferograms and exact reconstructions for two shearing interferograms.

Uniqueness results for the phase-retrieval problem for radial functions

A representation theorem for band-limited functions of several variables whose moduli are radial is stated. The proof of this theorem, which is based on techniques from Fourier analysis and the theory of analytic functions of several variables, is outlined in the Appendix. Several uniqueness results concerning the phase-retrieval problem that follow from the representation theorem are derived. References that relate the phase-retrieval problem to the problem of wave-front reconstruction in optics and image reconstruction in speckle interferometry are cited.

Mapping the Earth with Elastic Wave Holography

Remote sensing of the earth has been carried on for many years by the use of transient elastic waves, as in the seismic method. With the advent of optical holography and the development of high-power sonic sources and electromechanical vibrators, it is now possible to map the subsurface structure of the earth with steady-state coherent waves. This is the process of earth holography, which provides a three-dimensional optical view of the earth's interior. The basic principles of wavefront reconstruction in optics are reviewed and their application to sonic and seismic wave holography discussed. The problems of scaling and field sampling are discussed in connection with the resolution of elastic wave systems. It is shown that the sampling density required is within practical field limits for adequate resolution. Experiments were carried out with a small water tank model using frequencies in the low MHz range and small metal objects. Data were recorded on magnetic tape and subsequently displayed. The resulting holograms and photographs of the reconstructed images are shown. Synthetic holograms and reconstructions are shown and the problems of recording and display are discussed. Possible extensions of this work to large area, deep mapping of the oceans and the earth are outlined.