High-sensitivity Diffraction-compensated Moiré Deflectometry

Abstract

The spatial resolution and angular sensitivity of conventional moiré deflectometry are known to obey a conjugate relationship reminiscent of the uncertainty principle so that one cannot be improved without deteriorating the other. This paper looks at the origin of this relationship and suggests ways by which this ‘uncertainty principle’ can be violated. It is shown that a ‘projection’ of the grating which is free from diffraction effects and which, at the same time, contains the deflection information amplified by the ‘optical lever’ distance D between the gratings can be formed if the diffracted beams of order + 1 and ? 1 are separated from other orders and are recombined in certain ways. As a result, the angular sensitivity, which depends on the ratio of the pitch d of the grating to the distance D between the two gratings, can be improved without losing the spatial resolution by multiple diffraction orders. One of the diffraction compensation schemes is experimentally illustrated. It is shown that the ‘uncertainty product’ is improved by more than two orders of magnitude.     

Photopolarimeter based on two gratings recorded in thin organic films

A photopolarimeter based on two different kinds of diffraction gratings (a two-grating photopolarimeter) has been developed for real-time measurements of the four elements of the Stokes vector. The main elements of the device are a pure polarization grating and an ordinary transmission grating, both recorded by means of holographic techniques in thin films of organic materials. The first one consists of a diffraction grating recorded by two interfering opposite circularly polarized beams in a Langmuir-Blodgett film of an azo-compound material. The second component is a grating recorded by two interfering parallel circularly polarized beams in a thin film of a photosensitive polymer. Both gratings offer long time stability and good diffraction efficiency. Four photodiodes collect the first-order diffracted beams from these gratings, the output signals of which are read through an analog-to-digital converter by a PC. The optical alignment of the device is easy and the calibration is realized in a one-step procedure.     

Optics for Neutral Atomic Beams: Reflection and Diffraction of Sodium Atoms by Evanescent Laser Light Fields

Abstract

Realization of the analogues of optical components for the manipulation of atomic de Broglie waves has recently become possible through the use of laser-based techniques. The strong fields generated by laser light have already been used to reflect atoms using travelling evanescent waves, and to diffract atomic beams through small angles using transmission gratings formed by a standing laser light wave in vacuo. Present experiments aim to combine these techniques to produce a reflection diffraction grating formed by a standing evanescent laser-light field, and to exploit the larger diffraction angles made possible theoretically by such a scheme.     

Optical properties of disperse-red-1-doped nematic liquid crystal

We report on the optical properties of nematic liquid crystal cells containing the commercially available liquid crystal E7 doped with the azo dye Disperse Red 1 at concentrations ranging from 0.3% to 1.0%. From polarized absorption measurements an order parameter of S=0.569 was obtained, thus showing that the dye molecules align themselves very well with the liquid crystal's director axis. Optical index gratings were written in the material by overlapping two coherent laser beams at 532 nm. Self-diffraction of the writing beams and diffraction of a probe beam at 670 nm were measured. First-order self-diffraction efficiencies and rise times were found to be linearly dependent upon the dye concentration with a maximum efficiency of 3.29% and a minimum rise time of 10.6 ms. The non-linear index coefficient, n ₂, was calculated to be 7.6 × 10^-3cm²W^-1. The data are consistent with a grating formation based on trans–cis photoisomerism of the dye molecules that leads to a reorientation of the liquid crystal phase. These photonic devices are functional without the application of any external field, they are easily prepared, and have lifetimes in excess of two years without any indication of degradation when stored at ambient temperature.     

Recording of holographic diffraction gratings in photopolymers: Theoretical modelling and real-time monitoring of grating growth

Abstract

Recording of holographic volume diffraction gratings in Du Pont's photopolymer HRS-150 is studied theoretically and experimentally. Particular attention is paid to the dynamics of the recording process. The temporal evolution of holographic gratings is monitored for a range of illumination intensities in two ways: (i) by means of a multiple-exposure approach when intensity profiles of recording beams are uniform, many holographic exposures are necessary and each exposure is carried out for a particular value of the total illumination intensity; (ii) by means of a single-exposure approach when intensity profiles of recording beams are strongly Gaussian and a volume grating with spatially distributed diffraction efficiency arises, depending on a local (average) value of the total illumination intensity. The second approach proves to be a useful tool providing us very quickly with qualitative information about the dynamics of the recording process while the first one, which is much more time-consuming, is more reliable for quantitative evaluations. The grating evolution is analysed theoretically by means of the well known photopolymerization-diffusion model. Discrepancies are found between the model and experimental results for low illumination intensities while qualitative agreement is found for higher intensities. For a given grating period, the discrepancies are interpreted in terms of insufficient change of the refractive index due to photopolymerization for low illumination intensities.     

Computer Reconstruction of a Random Rough Surface in the Presence of Higher Diffraction Orders

Abstract

The profile of a random rough surface (RRS), whose mean roughness R_a is greater than the light wavelength, is visualized by computer processing. The surface is presented as a sum of sinusoidal gratings. The light diffracted from this surface field is registered by a photodiode array. The second and third diffraction orders from each grating are taken into account in computer processing of the diffracted field and the mixing field–the field obtained at the mixing of the reference and the diffraction fields. The criterion for taking into account higher diffraction orders is the asymmetry of the diffraction pattern to the left and to the right relative to the central peak (the field of zero diffraction orders obtained from each grating) The number of the diffraction orders higher than the first is defined from the average intensity distribution between the central peak and the diffraction orders to the left and to the right at arbitrary light wavelength. The surface profile is reconstructed by a computer program and the mean roughness R_a is calculated. The obtained value of R_a is in satisfactory agreement with that measured by the contact pin method.     

The Diffraction Efficiency of Double-grating Holographic Fan-out Elements

Abstract

An analytical expression is derived for the diffraction efficiency of a holographic fan-out element containing two superimposed gratings separated by a small angle. In addition to the usual zero and first orders an infinite set of the significant spurious waves is considered. In deriving the expression all these spurious waves are assumed to satisfy the Bragg condition exactly. The results are compared with a direct numerical solution and give very good agreement for angles up to 1°. Furthermore the analysis provides useful information for angles up to 5°. An analogy is drawn with a hybrid hologram consisting of a thick ‘carrier’ grating and a thin ‘modulation’ grating. Using this model the diffraction efficiencies can be calculated using the standard grating formulae. For fan-out applications the spurious waves around the first orders are considered the most important. From this analysis it can be seen that they can be made negligibly small but at the cost of a reduction in total diffraction efficiency.     

Optics for modulating multiple beams using an asymmetric multilevel phase grating and a multichannel acousto-optic modulator

Asymmetric multilevel phase gratings for generating even numbered beams have been designed, assuming that their phase patterns are formed by overlapping plural binary-phase patterns, each of which has an arbitrary phase height. The grating for four beams, which produces uniform and high intense diffraction orders of the minus first to the plus second order, is fabricated. The efficiency is 75.5%, although the theoretical efficiency is 79.9%. It is also demonstrated that the optics in which the beams from the grating are fed into a multichannel acousto-optic modulator through a Fourier-transform lens makes their successful modulation possible for pulse signals of 20-ns pulse duration.     

Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings

Expressions describing the vortex beams that are generated by the process of Fresnel diffraction of a Gaussian beam incident out of waist on fork-shaped gratings of arbitrary integer charge p, and vortex spots in the case of Fraunhofer diffraction by these gratings, are deduced. The common general transmission function of the gratings is defined and specialized for the cases of amplitude holograms, binary amplitude gratings, and their phase versions. Optical vortex beams, or carriers of phase singularity with charges mp and -mp, are the higher negative and positive diffraction-order beams. The radial part of their wave amplitudes is described by the product of the mpth-order Gauss-doughnut function and a Kummer function, or by the first-order Gauss-doughnut function and the difference of two modified Bessel functions whose orders do not match the singularity charge value. The wave amplitude and the intensity distributions are discussed for the near and far fields in the focal plane of a convergent lens, as well as the specialization of the results when the grating charge p=0; i.e., the grating turns from forked into rectilinear. The analytical expressions for the vortex radii are also discussed.     

Theoretical Analysis of the Lau Effect with a Sinusoidal Phase Grating

Abstract

By means of both partial coherence theory and diffraction theory, the Lau effect with a sinusoidal phase grating in a double-grating configuration is analysed. The optical intensity distribution at the observation plane is obtained. This distribution is related to the modulation of the phase grating and the separation of the two gratings. The results are somewhat different from the case of double amplitude gratings.     

Suppression of higher diffraction orders in the extreme ultraviolet with a trapezoidal nano-mirror array

ABSTRACT

Higher diffraction orders from a grating introduce harmonic contamination in ‘monochromatic’ output beams processed by grating monochromators at synchrotron radiation facilities, resulting in imprecise calibration of optical elements and detectors. Suppressing these orders can be achieved with a quasi-random nano-hole array, but its fabrication can be a significant limiting factor for implementation. Here, an advanced type of grating is demonstrated that contains a periodic array of several hundred million trapezoidal nano-mirrors with a grazing-incidence reflection geometry that suppresses higher diffraction orders. Moreover, it reduces the difficulty of fabrication to the level of a traditional grating. It has great potential for harmonic suppression in synchrotron radiation, spectral diagnostics of plasmas, and astrophysics.     

Two-channel tunable monochromatic illuminator with a concave diffraction grating and an original scanning system

A two-channel monochromatic illuminator with only one diffraction grating and an original scanning system has been designed for multiple applications. This scanning system consists of two rotational plane mirrors that reflect light diffracted by a concave diffraction grating to the ?1 orders of the spectrum. The light reflected by the mirrors goes to two exit slits that correspond to two channels of the device. The positions of the centers of rotation of the mirrors are selected to produce minimal deviation of the direction of the light reflected during the scanning. The aberration characteristics of some variations in the optical mounting of the device made by use of spherical and toroidal holographic diffraction gratings recorded in stigmatic and astigmatic beams, the possibilities for application of the device for measuring the color sensitivity of the human eye, and the possibilities for measuring the efficiency of concave diffraction gratings, are also discussed.     

Screw Dislocations in Light Wavefronts

Abstract

We discuss screw dislocations of a phase surface as the one type of wavefront of a monochromatic wave. The simple method for construction of the optical wavefronts with an isolated screw dislocation is reported. Laser beams with the dislocations of different orders were experimentally achieved by using diffraction on computer-synthesized gratings.     

Stabilization of volume gratings recorded in polyvinyl alcohol-acrylamide photopolymers with diffraction efficiencies higher than 90%

Abstract

Obtaining holographic volume gratings with high diffraction efficiencies that can be used under white light has been a serious problem for the polyvinyl alcohol-acrylamide-based photopolymers developed by other researchers. In this paper we propose to eliminate the residual monomer in order to stabilize the holographic gratings. The residual dye and residual monomer are the main problems in achieving high diffraction efficiencies stable under white light. In order to polymerize the residual monomer we illuminate the gratings with coherent green light and incoherent white light and we heat the grating at 80°C for different times. We also study the conservation of gratings dried in critical conditions of humidity and temperature. After stabilization the diffraction efficiencies achieved were clearly higher than 90%.     

Amplitude modulation and beam-steering properties of active binary phase gratings with reconfigurable absorption areas

By combining a binary phase grating and materials with a controllable absorption, it is shown theoretically that it is possible to modulate the light in a zero-order diffraction beam and that a high contrast level for the beam modulation can be obtained. The intensity of higher diffraction orders also changes, but it is calculated that high contrasts cannot be achieved for these higher-order beams with the active gratings that we examine. This specific modulator design that we use can be applied both for transmitted and for reflected light. Using the same ideas, one may build a beam-deflection device by varying the period of the grating by selectively changing the absorption levels in the grating. The deflection efficiency of the device can be improved compared with other designs by use of a grating with a reduced intensity of the nondeflected zero-order beam.     

Lamellar Gratings as Polarization Components for Specularly Reflected Beams

Abstract

High spatial frequency lamellar gratings are shown to function as phase compensators, quarter-wave and half-wave retarders, and polarization rotators that operate on specularly reflected (zeroth-order) beams. These gratings are designed using rigorous coupled-wave and modal grating diffraction theories. Controlling the geometrical parameters of these gratings allows for engineering the phase retardation and polarization conversion introduced to a reflected beam. Fabrication and operational tolerances for these elements are discussed. Wavelength and polar angle of incidence variation affect the performance of these elements more strongly than variations in other geometrical and operational parameters.     

Efficient holographic recording in novel azo-containing polymer

We report on periodic structures inscribed through holographic recording by both intensity light patterns and polarization patterns in novel azo-containing polymer poly[oxyethylene({6-[4-(biphenyl-4-azo)phenoxy]hexyl}imino) ethylene-carbonylimino(2-methyl-1,3-phenylene)iminocarbonyl] abbreviated as A-TDI. The kinetic of grating recording and diffraction efficiency of recorded gratings using polarized cw Ar⁺ laser light have been measured for s–s, p–p and s–p polarization configurations. The translation grating technique applied during the light self-diffraction process allowed for investigations of phase and amplitude gratings contributions to light diffraction in the studied polymer. Full reversibility of polarization (s–p) grating recording and observation of a half-period structure development during optical erasure process makes this material a good candidate for further studies as a potential material for dynamic holography purposes.     

Diffraction of a one-dimensional phase grating in the deep Fresnel field

We analyze theoretically the diffraction of phase gratings in the deep Fresnel field on the basis of the theory of scalar diffraction and Green's theorem and present the general formula for the diffraction intensity of a one-dimensional sinusoidal phase grating. The numerical calculations show that in the deep Fresnel region the diffraction distribution can be described by designating three characteristic regions that are influenced by the parameters of the grating. The microlensing effect of the interface of the phase grating provides the corresponding explanation. Moreover, according to the viewpoint that the diffraction intensity distribution is the result of the interference of the diffraction orders of the grating, we find that the diffraction patterns, depending on the carved depth of the phase grating, are determined by the contributing diffraction orders, their relative power, and the quasi-Talbot effect of the phase grating, which results from the second meeting of the diffraction orders carrying most of the power of the total field, as in the case of the amplitude grating.     

Zeroth-order complex-amplitude modulation with dielectric Fourier-type dififractive elements

Abstract

Diffraction by a lamellar grating with slowly modulated groove width and depth is considered. By mathematical design of the diffractive microstructure the zeroth diffraction order of the carrier grating may be modulated in amplitude and phase and thereby split into some specified on-axis far-zone diffraction pattern. The noise, which in diffractive optics normally appears in the immediate neighbourhood of the signal, is shifted angularly into the surroundings of the higher diffraction orders of the carrier grating. Therefore a large frame of virtually zero intensity can be formed around the original signal without brute force optimization. This is of interest in, for example, several space-invariant optical interconnection and photonic switching schemes that employ diffractive beam-splitter elements.     

Pitch-modulated phase grating and its application to displacement encoder

Abstract

A binary phase grating with modulated pitch is investigated for a simple displacement encoder. The grating consists of a binary phase grating to eliminate the zeroth-order diffraction, and the pitch of the grating is modulated to compensate the higher harmonics of the encoder displacement signal. Therefore, an undistorted sinusoidal signal as a function of displacement is obtained by simply superimposing a conventional binary grating on the pitch-modulated phase gratings for any air gap between the gratings. The characteristics of the proposed gratings and the encoder signal are investigated by the Fresnel diffraction theory. The proposed grating has been fabricated lithographically, and the signal was examined experimentally. Considering these results, the proposed technique can suppress interpolation error and will be useful for an encoder in precision machining.