Fourier-transform Lens Research Articles

Polarization-filterless polarization-sensitive polarization-multiplexed phase-shifting self-reference digital holography

I propose a phase-shifting self-reference digital holography technique in which both three-dimensional (3D) and polarization information is simultaneously obtained without any polarization filters. A Fourier-transform lens, a polarization beam splitter, and two phase-only spatial light modulators are used to simultaneously generate self-reference holograms with orthogonal polarization directions. 3D and polarization information is multiplexed in the recorded phase-shifted digital holograms and retrieved by applying polarization-selective phase-shifting interferometry and numerical refocusing. The validity of the proposed technique is experimentally demonstrated.

Gouy phase of Bessel-Gaussian beams: theory vs. experiment.

It is well-known that the wave of a freely propagating Gaussian beam experiences an additional π phase shift compared to a plane wave. This phase shift, known as the Gouy phase, has significant consequences in, e.g., nonlinear optics, since the nonlinear processes require high peak intensity and phase matching of the focused beams. Hence, determining and controlling the Gouy phase is crucial in many fields of modern optics and photonics. Here, we develop an analytical model for the Gouy phase of long-range Bessel-Gaussian beams obtained by annihilating highly charged optical vortices. The model accounts for the influence of the relevant experimental parameters (topological charge, radius-to-width ratio of the initial ring-shaped beam, and focal length of the Fourier-transforming lens). We find an evolution of the Gouy phase varying nearly linearly with propagation distance and confirm this result experimentally.

Autofocusing Airy beams generated by all-dielectric metasurface for visible light.

Conventional method to generate autofocusing Airy (AFA) beam involves the optical Fourier transform (FT) system, which has a fairly long working distance due to the focal length of FT lens, presence of spatial light modulator (SLM) and auxiliary total reflection mirrors. Here, we propose an extremely compact design to generate high-efficiency AFA beam at visible frequency by using metasurface which is composed of a single layer array of amorphous titanium dioxide (TiO2) elliptical nanofins sitting on the fused-silica substrate. Numerical simulations show that the designed structures are capable of precisely controlling the deflection of Airy beam and tuning the focal length of AFA beam. We further numerically demonstrate that the phase modulation of AFA beam could combine with the concept of vortex light field to produce vortical AFA beam. We anticipate that such device can be useful in the ultra-compact integrated optic system, biomedical nanosurgery and optical trapping applications.

Surface Fourier-transform lens using a metasurface

We propose a surface (or 2D) Fourier-transform lens using a gradient refractive index (GRIN) metasurface in the microwave band, which is composed of sub-wavelength quasi-periodical metallic patches on a grounded dielectric substrate. Such a metasurface supports the transverse magnetic (TM) modes of surface waves. To gradually change the size of textures, we obtain different surface refractive indices, which can be tailored to fit the required refractive-index profile of a surface Fourier-transform lens. According to the theory of spatial Fourier transformation, we make use of the proposed lens to realize surface plane-wave scanning under different feeding locations. The simulation and experimental results jointly confirm the validity of the surface Fourier-transform lens. The proposed method can also be extended to the terahertz frequency.

光刻机照明光瞳测量用傅里叶变换物镜光学设计

光刻机照明光瞳测量用傅里叶变换物镜光学设计

Исследование влияния аберраций фурье-преобразующей системы на восстановленное изображение символа в системах сокрытия информации

Исследование влияния аберраций фурье-преобразующей системы на восстановленное изображение символа в системах сокрытия информации

Fourier-space generation of abruptly autofocusing beams and optical bottle beams

We demonstrate analytically and experimentally that a circular abruptly autofocusing (AAF) Airy beam can be generated by Fourier-transforming an appropriately apodized Bessel beam whose radial oscillations are chirped by a cubic phase term. Depending on the relation between the chirp rate and the focal distance of the Fourier-transforming lens, it is possible to generate AAF beams with one or two foci, the latter case leading to the formation of an elegant paraboloid optical bottle.

Measurement of residual wedge angle of a high optical quality transparent parallel plate with a multipass optical configuration

A new technique of wedge angle measurement of a transparent nearly parallel plate (PP) is presented. In this technique, the single-pass angular deviation suffered by a pair of mutually parallel, laterally separated pencil beams is enhanced by using a multipass cavity formed with two right-angle prisms. The resultant angular deflection is converted to linear deviation by means of a Fourier transform lens (FTL), which focuses the pencil beams on to its focal plane. A two-dimensional CCD detector array placed at the focal plane of the FTL measures the linear shift of the intensity centroid (IC) of the resulting Young's fringes formed due to the superposition of the laterally separated pencil beams. The wedge angle is determined from the measured value of the linear shift of the IC due to the PP.

On-ground simulation of optical links for free-space laser communications

A method of on-ground simulation of optical links for free-space communications by Fourier-transform, image magnification and wavefront sampling with limited apertures was proposed. An optical simulator for free-space laser links was designed, which has the range of equivalent links distances from 160,000 km to 25 km. It can be used for the evaluation of communication performances of optical links in space, particularly for measuring the bit error rate under a constant transmission distance or for testing the equivalent transmission distance under a constant bit error rate. System analysis indicates that the wavefront aberrations of Fourier-transform lens have the main influence on the measurement results. But these effects can be corrected only if the RMS value of wavefront aberrations of Fourier-transform lens on the work aperture is known. Simulation experiment further shows that this method will be feasible by providing excellent optical devices and fine calibration accuracy and by overcoming the environmental disturbances.

Design of a short-focal-length double-Fourier-transform-lens system for holographic storage

A short-focal-length double-Fourier-transform-lens system for holographic storage was designed. The system is minimized by propagating signal beam and reference beam along a common optical axis. In order to obtain a compact configuration and high information density, the front and the rear Fourier-transform lens have short focal length (33 and 30 mm, respectively). The multiconfiguration optimization method is adopted to correct aberrations of the object region and meet the requirement of reference beam. The designed system, whose total numerical aperture for signal beam and reference beam is 0.60, achieves diffraction-limited imaging quality.

Analysis of slitless holographic spectrometers implemented by spherical beam volume holograms

The analysis of a slitless volume holographic spectrometer is presented in detail. The spectrometer is based on a spherical beam volume hologram followed by a Fourier-transforming lens and a CCD. It is shown that the spectrometer is not sensitive to the incident angle of the input beam for the practical range of applications. A holographic spectrometer based on the conventional implementation is also analyzed, and the results are used to compare the performance of the proposed method with the conventional one. The experimental results are consistent with the theoretical study. It is also shown that the slitless volume holographic spectrometer lumps three elements (the entrance slit, the collimator, and the diffractive element) of the conventional spectrometer into one spherical beam volume hologram. Based on the unique features of the slitless volume holographic spectrometer, we believe it is a good candidate for portable spectroscopy for environmental and biological applications.

Compact Fourier-transform volume holographic spectrometer for diffuse source spectroscopy

We present a new idea for diffuse source spectroscopy using a Fourier-transform volume holographic spectrometer formed by a Fourier-transform lens, a volume hologram, and a CCD. We show that this spectrometer can operate well under spatially incoherent light illumination. Furthermore, this spectrometer is less bulky, less sensitive to input alignment, and potentially more appropriate for implementation of highly sensitive spectrometers than conventional spectrometers.

Facial recognition by a compact parallel optical correlator

With the progress of information technology, the need for an accurate personalidentification system based on biological characteristics is increasing the demandfor this type of security technology instead of conventional systems usingID cards or pin numbers. Among other features, the face is the mostfamiliar element and is less subject to psychological resistance. As a simpleand compact recognition system satisfying the required performance, weimplemented a hybrid system based on the optical recognition principle usinga multi-level zone plate as a Fourier-transform lens and we report thepreliminary results of their application to face recognition. In this paper, wepresent the design procedure and fabrication process for an improvedversion of a second-generation compact parallel correlator (named COPaCII), the size of which is 20 × 24 × 43 cm3 and weight 6 kg. As a result, weobtained a low error rate of 0% as the false match rate and 0.3% as the falsenon-match rate, thus the COPaC II significant identification security level issufficiently stable. With the aim of further enhancing the throughput androbustness, we conducted performance tests where the system is used as acomputer log-in device and as a pre-screening device for crime investigation.In both experiments, a high rate of successful recognition, such as 90%recognition and 94% rejection rate for log-in, was obtained. Experiments ontwins to check the disguise recognition, and on the effects of changes inbrightness and arbitrary size of images to test its robustness are also included.

Aspect ratio of elongated polychromatic far-field speckles of continuous and discrete spectral distribution with respect to surface roughness characterization.

Here polychromatic speckle patterns generated either by a polychromatic light source that emits at discrete frequencies or by a light source showing a continuous narrow-band spectral distribution are studied. The purpose here is the application of polychromatic speckle-pattern analysis to an in-process surface roughness characterization. To compare the coherence properties of the different polychromatic light sources, first a modified definition of the coherence length is introduced. Furthermore, the relevant optical phenomena, namely, the speckle elongation caused by the angular dispersion and the roughness-dependent speckle decorrelation, are summarized. It is shown that light sources with a continuous spectral distribution have essential advantages in comparison with discrete wavelength sources. The theoretical results are confirmed by experimental investigations based on a digital algorithm for the evaluation of CCD images of polychromatic speckle patterns, which are recorded in the Fourier plane of a Fourier-transforming lens.

Precision calibration and systematic error reduction in the long trace profiler

The long trace profiler (LTP) has become the instrument of choice for surface figure testing and slope error measurement of mirrors used for synchrotron radiation and x-ray astronomy optics. In order to achieve highly accurate measurements with the LTP, systematic errors need to be reduced by precise angle calibration and accurate focal plane position adjustment. A self-scanning method is presented to adjust the focal plane position of the detector with high precision by use of a pentaprism scanning technique. The focal plane position can be set to better than 0.25 mm for a 1250-mm-focal-length Fourier-transform lens using this technique. The use of a 0.03-arcsec-resolution theodolite combined with the sensitivity of the LTP detector system can be used to calibrate the angular linearity error very precisely. Some suggestions are introduced for reducing the system error. With these precision calibration techniques, accuracy in the measurement of figure and slope error on meter-long mirrors is now at a level of about 1 {mu}rad rms over the whole testing range of the LTP. (c) 2000 Society of Photo-Optical Instrumentation Engineers.

Isotropic and anisotropic intermolecular dynamics of liquids studied by femtosecond position-sensitive Kerr lens spectroscopy

Femtosecond Fourier-transform position-sensitive Kerr lens spectroscopy is shown to be a powerful technique for obtaining the isotropic and anisotropic components of the low-frequency, intermolecular Raman spectra of liquids. The isotropic and anisotropic spectral features are compared for liquids benzene, toluene, and benzonitrile in order to characterize the intermolecular motions in terms of their relative contribution to the different elements of the Raman susceptibility. We observe that the spectral profiles for the isotropic and anisotropic components of the Raman susceptibility tensor of both benzene and toluene are identical within our experimental uncertainty. A frequency-independent depolarization ratio of 0.7±0.1 and 0.75±0.1 are obtained throughout the 0–150 cm−1 region, respectively, for benzene and toluene, respectively. This ratio indicates that the collective intermolecular vibrations can be described as being “depolarized.” On the other hand, we observe that the intermolecular depolarization ratio obtained for benzonitrile is frequency-dependent, gradually decreasing from 0.7 near 0 cm−1 to approximately 0.5 at 150 cm−1. This observation indicates that the intermolecular interactions in benzonitrile become increasingly “polarized” as the frequency is increased. These data are discussed in terms of the distinct molecular properties of each liquid and the differences in their overall intermolecular interaction energies.

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.

Femtosecond time-and-space domain holograms: diffraction on the edge of time

We study the diffraction properties of time-and-space domain holograms stored with femtosecond light pulses with a coherence length much smaller than the lateral geometrical dimension of the hole-burning sample. We show that one can observe diffraction of read out beam on the virtual ‘time edge’ separating the spatial regions where the delay between the reference and the object pulses is either positive or negative. We also demonstrate that by placing a Fourier-transforming lens in the beam diffracted from the ‘time edge’ a spatial intensity pattern proportional to the homogeneous hole-burning spectrum is observed.

Packaged optical interconnection system based on photorefractive correlation

We present an experimental implementation of a packaged free-space optical interconnection system by photorefractive correlation. The system consists of a phase code, a LiNbO(3) crystal, two computergenerated-hologram Fourier-transform lenses, and a detector, all mounted on a glass substrate. We present experimental results with a prototype packaged system showing interconnections between 25 inputs and 25 outputs, and we discuss the possibility of applying this packaging technology to interconnections between larger arrays.

Real-time image processing by degenerate four-wave mixing in polarization sensitive dye-impregnated polymer films

A real-time optical image processing scheme is described using degenerate four-wave mixing in thin films of polymethylmethacrylate thacrylate doped with the azo-based dye disperse red 1. A saturable optical nonlinearity based on the formation of polarization gratings caused by rotation of dye molecules within the polymer matrix is exploited. Selective erasure of spatial frequencies in the back focal plane of a Fourier-transform lens by a high intensity processing beam allows simple optical processing operations to be performed. Edge enhancement and bandpass filtering are demonstrated for amplitude objects, and a technique analogous to darkground illumination in microscopy enhances the visibility of a phase-object.