The Talbot-Lau arrangement is an optical system using two gratings of different pitches. The gratings are placed parallel
with some distance separated. By illuminating them with a broad incoherent source, we obtain high contrast grating
images formed on a plane at a distance determined by the pitches. The phenomenon is called generalized grating
imaging. It is used, for example, in pattern projection profilometer and as a shearing interferometer for light, X-ray and
matter waves. There are many analyses on the Talbot-Lau arrangement. However, almost all of them are related to onedimensional
gratings. This paper presents a rigorous analysis on the phenomenon with two-dimensional gratings using
wave optics. The analytical result is applied to hexagonal gratings and the contrast is calculated by numerical calculation.
The numerical results agree with experimental results. The analysis can be used to design a Talbot-Lau arrangement with
two-dimensional gratings in broad fields.
A high resolution refractive-index sensor with a guided-mode resonant grating has been proposed. The gratin has a two-dimensionally periodic structured surface, which is covered with liquid to be measured. The resonant wavelength depends on the polarization states of light for oblique incidence. The change in refractive index of the liquid is determined from the difference of reflectance (or transmittance) between the P and S polarized light waves. The lattice structured silica substrate with a period of 380 nm was made. And a hafnium-dioxide thin film was deposited on the substrate. When the grating surface was covered with water, the measured reflectance had resonant peaks at a wavelength of 615 nm for S polarization and 617 nm for P polarization at an incident angle of 0.5°. For a wavelength of 616 nm, the difference of transmittance of P and S polarization was in linear relation to the change in refractive index. The refractive index was detected with a resolution of 4x10-4 in a measurement range of 0.064.
Two shearing X-ray interferometers and reconstruction of refractive index distribution from their data are described. The first interferometer is made of a silicon single crystal consisting of two pairs of blades. It can be used with an incoherent x-ray source such as a usual X-ray tube. Simple experiments are made with the interferometer. An algorithm for reconstructing refractive index distribution from the shearing data is described and refractive index distribution on a section of an acrylic cylinder is reconstructed experimentally with the algorithm. Features of the interferometer are discussed. On the basis of the discussion an grooved grating shearing interferometer that can be used with an ordinary X-ray tube is proposed and its performance is estimated.
Several optical elements with subwavelength structured (SWS) surfaces have been developed. The SWS has optical features of artificial refractive index, form birefringence, resonance and band-gap effects. This paper describes some applications of form birefringent optical elements and a resonant reflection element. A form-birefringent quarter-wave plate was realized by sputtering the high refractive-index thin film on a SWS substrate. The wavelength dispersion of form birefringence restrains the phase retardance from depending on the wavelength of light. An array of form-birefringent wave-plates is useful for the real-time imaging polarimetry. We developed a real-time polarization imaging system for the visible light. A guided-mode resonant grating with a PLZT wave-guide was designed for optical switches. The PLZT is ferroelectric material with an electro-optic (EO) effect. We made a feasibility study on the optical switching by numerical simulations.
We have proposed a new structure of guided-mode resonant grating (GMRG) filter with low sideband reflectance. This GMRG filter consists of a high refractive index thin-film on an antireflection structured (ARS) surface called “moth-eye structure”. This antireflective GMRG filter is valid for reducing reflection of nonresonant light waves in a wide spectral range. This antireflective GMRG filter is valid for reducing reflection of nonresonant light waves in a wide spectral range. The resonant reflection of this new filter was investigated by numerical calculation based on an electromagnetic grating analysis. In the case of an antireflective GMRG filter with aspect ratio 2, the sideband reflectance for nonresonant light waves was lower than 0.5% for TM polarized light in the wide-wavelength range. We have fabricated an antireflective GMRG filter. The triangular grating of fused silica for ARS surface was fabricated by reactive ion etching due to high-density fluorocarbon plasma with resist line patterns and chromium thin-film line patterns as etching masks. The fabricated antireflective GMRG filter was a period of 333 nm and a height of about 666 nm. The thickness of a TiO2 thin-film deposited on the triangular grating was about 100 nm. Resonant peak was detected at wavelength of 680 nm, and peak intensity was 45%. Moreover, it was found that sideband reflectance was less than 4%.
We propose an optical switch of a guided-mode resonant grating (GMRG) filter with a Kerr medium and simulate optical switching effects by using the nonlinear finite differential time domain (FDTD) method. It is shown that the nonlinear FDTD method is needed for simulating the optical switch effect by analyzing the bistable feature. The doubly periodic structure was used in order to produce the optical Kerr effect efficiently. Because a doubly periodic GMRG filter operates for small beam diameter and grating area, the electric field can be accumulated to the small area. The doubly periodic grating consisted of materials with refractive indices of 1.88 and 1.0, and the material of index 1.88 had a third-order susceptibility of 8.5×10-10esu. The TE polarized plane waves were normally incident on the grating structure as “pump light” and “probe light.” When the intensity of “pump light” increases, the refractive index changes due to the optical Kerr effect, so that the resonant condition of the GMRG filter for the “probe light” also changes. Therefore the transmittance of “probe light” can be controlled by the “pump light.” By changing “pump light” from 0 to 100kW/mm2, the transmittance of “probe light” was controllable from 0 to 0.6.
Profile along a circle on precise mirror can be determined with no standard by measuring spacing between a mirror and another reference mirror. Accuracy of the reference mirror needs not be higher than that of the mirror to be measured. The absolute measurement based on this principle is made with a Fizeau interferometer. The result shows that the profile of a flat mirror can be measured in an accuracy of nm though the accuracy of reference mirror is in the order of μm. In order to extend this measurement to profile on a whole surface, we have to measure profiles along different circles and unify them. This unification does not seem to be done without a linear standard.
In the conventional X-ray imaging such as radiography or computed tomography, we measure intensity distribution of X-rays. It reflects the distribution of absorption coefficient inside the object. However, absorption becomes low for materials of low atomic number and for hard X-rays. An alternative way is to measure distribution of refractive index for X-rays. Spatial variation of refractive index causes spatial variation in the phase of the transmitted X-rays. To detect the phase X-ray interferometers can be used. In this paper we shall describe an X-ray shearing interferometer and discuss the method of reconstructing the refractive index distribution from the obtained phase data with the method of computed tomography. Reconstruction is made from data obtained in a simple experiment with plastics as objects.
We developed the fabrication process of all-plastic cantilever for force controlled atomic force microscope. The force controlled atomic force microscope can prevent damage during the scanning of the soft sample. However it has a drawback in its stability. To stabilize the system the cantilever is required to have small Q factor. The negative photo resist for MEMS (SU-8) has ideal properties, micromachinability and small Q factor, for this purpose. Here we demonstrate the cantilever consists of tip, lever and base with same polyimide. The mold of the probing tip is the pyramidal pit pattern on silicon wafer formed by direct leaser writing and anisotropic etching of silicon. Other elements of the cantilever are formed by contact lithography. The photo mask is also fabricated by direct laser writing. By arranging the dimensions of the cantilever, we can control its spring constant and resonant frequency. For the spring constant of 0.1N/m and the first resonant frequency of 2kHz, the typical dimensions of the cantilever is 1030 x 300 x 7 μm3. The fabrication error in cantilever geometry was 1.5%. The estimated resonant frequency has a good agreement with the designed value.
There are many systems for measuring precise position of stages or probes. Three-dimensional coordinate measuring machine is an example. These machines, however, do not measure orientation of the stage. In recent years, positioning stages using parallel mechanisms have been developed. To obtain the information of their geometrical motions, we have to measure the orientation in addition to position. In this paper, we shall propose an interferometric system for measuring the position and orientation of such a positioning stage. In this system multiple retro-reflectors such as corner cubes are fixed on the moving stage and multiple interferometers are formed with the corner cubes as reflectors. Light beams are incident on the corner cubes from different incident directions. We have two ways to measure the positions of the corner cubes with interferometers. One is "fringe counting method", measuring the moving distance of the corner cubes in several directions directly, and calculating the position and orientation of the stage from the moving distances. The other is "multi-directional coincidence method", utilizing multiple image sensors to detect the interferograms in several directions. From the interferograms, we obtain fractional fringe orders by image processing, and estimate the integer fringe orders, which conform to the fractional orders for all the interferograms. The simulation results in 2-dimension (2-D) showed that an error within 0. 1 tm in translation and 0.01 degree in rotation are achieved in the measuring ranges of several millimeters with the fringe counting method. Simulation for one-dimensional multi-directional coincidence method showed the potentiality ofthe method.
This paper describes a novel refractive index sensor with a guided-mode resonant grating (GMRG) filter. The GMRG filter is a narrowband wavelength reflection filter. The incident light is reflected at a resonance condition of incident angle and wavelength. When the grating filter is covered by a liquid to be tested, the resonant condition depends upon its refractive index. The refractive index of the liquid can be determined from the resonance angle for a known wavelength. Since a full-half width of incident angle for the resonance is very narrow (less than 0.1 degree(s)), a high resolution is expected. We designed the GMRG filters for the refractive index sensor. And the resonance angle of incidence was investigated experimentally for the mixture of water and ethyl alcohol.
We present the real time polarimeter with a micro retarder array consisting of subwavelength gratings with different directions. A 2x2 form-birefringent micro retarder array was fabricated with an electron-beam lithography method and a reactive ion etching technique. Each retarder was a TiO2 grating with 300-nm period on a silica substrate, and the phase retardance was 0.31 (pi) for 633-nm wavelength light. Using the fabricated retarder array, the real time polarimeter was made. The micro retarder array and a linear polarizer film were stacked up on a 2x2 photo-detector array. Four Stokes parameters were computed at a real time rate from outputs of the detector array. We could measure temporal change in polarization states of light by simple experiments.
A broadband quarter-wave plate of subwavelength lamellar grating has been designed by an optimizing method using the effective medium theory and the rigorous couple wave analysis. The phase retardation can be maintained at 90 degree(s) by strong dispersion of the propagation constant in the periodic structure. Before optimizing the grating profile by the rigorous analysis, the profile is roughly estimated with the effective medium theory. After the rough estimation, the close profile is determined by the steepest descent method using the rigorous analysis. The optimized quarter wave plate keeps the retardation at 90 degree(s) with errors smaller than 1 degree(s) for the +/- 10% change in wavelength from the nominal wavelength. Also tolerances of fabrication errors are discussed.
Interferometers have come to be used in production processes for surface profiling. Common- path interferometers are becoming important because they are insensitive to environmental disturbances such as mechanical vibration, air turbulence, and thermal drift. Among common- path interferometers, those using double-focus lens are promising because they can easily incorporate phase-shifting technique. In this paper, common-path interferometers using double-focus lenses are described and some experimental results are given. Properties of double focus lenses are investigated and their effect on surface profiling is discussed.
Ground state resonance Raman spectroscopy and picosecond transient Raman spectroscopy provide similar information. The former method superimposes excited state structural information on the ground state vibrational spectrum while the latter method is a direct probe of the excited state vibrational spectrum. When the two methods are taken together the resonance Raman spectrum provides a means for correlating vibrational bands in the ground state spectrum with bands observed in the excited state transient spectra. We are using a MHz amplified synchronously pumped dye laser as the source for our experiments. We demonstrate recent improvements in the laser system that increase the power and extend the wavelength coverage. We use the source to study the vibrational spectra of dilute solutions of biological molecules and to study the structure of the excited state of trans-stilbene in several solvents. 1.
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