Autodyne interferometry for range-finding under laser radiation wavelength modulation

The results of solution of the inverse problem of determining the distance to the reflector in the case of current modulation of the laser radiation wavelength are presented. It is shown that current modulation of the autodyne signal amplitude can reduce the inverse problem of finding the distance to the reflector to a state of affairs characteristic only of phase modulation. The technique that we propose provides a higher range-finding accuracy than does direct analysis of the autodyne signal.     

Dual-wavelength slightly off-axis digital holographic microscopy

We propose dual-wavelength digital holographic microscopy with a slightly off-axis configuration. The axial measurement range without phase ambiguity is extended to the micrometer range by synthesizing a beat wavelength between the two wavelengths with separation of 157 nm. Real-time measurement of the specimen is made possible by virtue of the high wavelength selectivity of the Bayer mosaic filtered color CCD camera. The principle of the method is exposed, and the practicability of the proposed configuration is demonstrated by the experimental results on a vortex phase plate and a rectangular phase step.     

Speckle decorrelation in surface profilometry by wavelength scanning interferometry

The accuracy and the measurement range of surface profilometry by wavelength scanning interferometry applied to diffusely reflecting surfaces are investigated. The influences of surface roughness and the imaging system in the interferometer are theoretically analyzed by derivation of the autocorrelation function of interferograms arising from wavelength scanning. By using a dye laser with a tuning range of 4.2 nm to a yield resolution of 39.1 mum, we have observed interferograms and their Fourier transforms and autocorrelations to study effects of defocusing and the size ratio of speckle to the CCD pixel for a plane diffuse object positioned normal to the incident beam.     

Trace methane gas detection by wavelength modulated off-axis integrated cavity output spectroscopy

An instrument based on wavelength modulation off-axis integrated cavity output spectroscopy (WM-OA-ICOS) was developed for detection of trace methane (CH₄) gas. The wavelength modulation technique was employed to obtain the second harmonic of the CH₄ absorption signal. The modulation parameters were optimized to obtain a maximum second harmonic signal. A noise-equivalent absorption sensitivity of 9.4 × 10^?11 cm^?1 Hz^?1/2 (corresponding to a detection limit of 28.9 ppbv for CH₄ at this wavelength) was achieved using 2f detection. Compared with the traditional off-axis integrated cavity output spectroscopy (OA-ICOS) technique, WM-OA-ICOS provided an 8-fold improvement in detection sensitivity. CH4 concentration measurements were also achieved by normalization of second harmonic signal to first harmonic signal (2f/1f). The dynamic range and linearity of WM-OA-ICOS for both 2f method and 2f/1f method were investigated. The result showed that the 2f/1f method exhibited better linearity than 2f method.     

Digital holographic microscopy with sequential off-axis illumination directions based on spatial light modulator

Digital holographic microscopy (DHM) with time-sequential off-axis illumination directions can synthesize a large aperture, and thus have a higher spatial resolution than the one with on-axis illumination. In this paper, time-sequential off-axis illumination directions are generated by a spatial light modulator (SLM) in DHM, and the residual phases along different illumination directions are suppressed by using the phase compensation technique, as such the image with resolution enhancement is reconstructed. The usage of SLM enables shifting the illumination for different orientations and phase shifts without mechanical motion. The experiments have been conducted to verify the feasibility of this method on the residual phase suppression.     

Radio frequency controlled synthetic wavelength sweep for absolute distance measurement by optical interferometry

We present a new technique applied to the variable optical synthetic wavelength generation in optical interferometry. It consists of a chain of optical injection locking among three lasers: first a distributed-feedback laser is used as a master to injection lock an intensity-modulated laser that is directly modulated around 15 GHz by a radio frequency generator on a sideband. A second distributed-feedback laser is injection locked on another sideband of the intensity-modulated laser. The variable synthetic wavelength for absolute distance measurement is simply generated by sweeping the radio frequency over a range of several hundred megahertz, which corresponds to the locking range of the two slave lasers. In this condition, the uncertainty of the variable synthetic wavelength is equivalent to the radio frequency uncertainty. This latter has a relative accuracy of 10(-7) or better, resulting in a resolution of +/-25 microm for distances exceeding tens of meters. The radio frequency generator produces a linear frequency sweep of 1 ms duration (i.e., exactly equal to one absolute distance measurement acquisition time), with frequency steps of about 1 MHz. Finally, results of absolute distance measurements for ranges up to 10 m are presented.     

Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography

Two basic types of interferometer, a point diffraction interferometer (PDI) and a lateral shearing interferometer (LSI) suitable for operation in the extreme-ultraviolet (EUV) wavelength region, are described. To address the challenges of wavefront measurement with an accuracy of 0.1 nm rms, we present a calibration method for the PDI that places a mask with two large windows at the image plane of the illumination point light source and a general approach to deriving the phase-shift algorithm series that eliminates the undesired zeroth-order effect in the LSI. These approaches to improving the measurement accuracy were experimentally verified by the wavefront measurements of a Schwarzschild-type EUV projection lens.     

Compensation of wavelength dependent image shifts in imaging optical interferometry

In modern interferometers for absolute length measurements, when applying phase stepping interferometry, several different wavelengths are used as light sources, and the interferogram is projected to a CCD-camera array. Such interferometers are equipped with wedged optical components as windows and beam splitters, to prevent additional interferences. The wedged optics causes the position of a test piece within the interferogram related to the camera pixel coordinates to be dependent on the wavelength used. This effect depends on the wedge angles and the thicknesses of optical components as well as on their distances within the interferometer's optical pathway. We give a quantitative analysis and suggest a compensation of this dispersion effect by an additional wedge plate outside the interferometer.     

Estimation of wavelength difference using scale adjustment in two-wavelength digital holographic interferometry

We propose a method for an estimation of wavelength difference using scale adjustment in two-wavelength digital holographic interferometry. To estimate wavelength difference, two holograms recorded with different wavelengths are reconstructed on the basis of the Fresnel diffraction integral, and pixel sizes in the reconstruction plane, which depend on the wavelength in recording hologram, are analyzed. In the analysis, a zero-padding method and an intensity correlation function are used to adjust pixel sizes in the reconstruction plane and then obtain a wavelength difference given by a difference between the pixel sizes. Theoretical predictions and experimental results are shown to indicate the usefulness of the proposed method in this paper.     

Scanning holographic microscopy with resolution exceeding the Rayleigh limit of the objective by superposition of off-axis holograms

We present what we believe to be a new application of scanning holographic microscopy to superresolution. Spatial resolution exceeding the Rayleigh limit of the objective is obtained by digital coherent addition of the reconstructions of several off-axis Fresnel holograms. Superresolution by holographic superposition and synthetic aperture has a long history, which is briefly reviewed. The method is demonstrated experimentally by combining three off-axis holograms of fluorescent beads showing a transverse resolution gain of nearly a factor of 2.     

Interferometric testing for off-axis aspherical mirrors with computer-generated holograms

The interferometers with computer generated holograms (CGHs) have been used to measure off-axis aspherical mirrors. However, the conventional CGH interferometer could not produce a high lateral resolution because of the blur and the distortion of the interferogram of the test mirror caused by the nonzero order diffraction of the CGH. We further develop the application of CGHs concerning interferometers in order to improve the lateral resolution of the interferogram. In particular, we change the application of the CGH in such a way that the returned test beam passes through the CGH with zeroth order diffraction and demonstrates the performance of the CGH interferometer when used for the measurement of the primary mirror of the Okayama Astrophysical Observatory 3.8 m telescope project. As a result, our CGH interferometer produces a good interferogram with high resolution of 2.8 mm for the off-axis aspherical mirror with a size of 1.2 m. With improved usage of the CGH, we successfully demonstrated a high lateral resolution interferometer.     

Light profile microscopy based on Raman and wavelength resolved luminescence contrast

Light profile microscopy based on contrast from wavelength resolved Raman and luminescence measurements is demonstrated experimentally for the first time. A Raman/multispectral light profile microscope (RMSLPM) has been constructed based on a line profiling geometry in which the sample is irradiated with a tightly focused laser beam (of ten micrometers radius or less) behind a polished view surface and the resulting line image is dispersed over the wavelength using an imaging spectrograph. The instrumentation developed in this laboratory has a spectral resolution approaching 10 cm(-1) and an (actual) depth independent spatial resolution of 6-8 times the Rayleigh diffraction limit, limited at present by optical aberrations and alignment. The technique has the potential to image at approximately twice the Rayleigh diffraction limit. The spectral signatures reconstructed from a variety of common industrial polymers show excellent agreement with reference spectra from the literature, and may be used to identify individual layers in depth images of unknown materials. RMS-LPM image data based on luminescence contrast have also been used to provide concentration depth profiles of additives and degradation products in injection molded samples of high-density poly(ethylene) (HDPE).     

Scattering Matrices for Slightly Non-spherical Particles

Abstract

In this paper the theory of light scattering by slightly non-spherical particles is developed and the forms of the amplitude and Stokes scattering matrices are derived. Forward-scatter and backscatter and the information they give about the shape of the particle are discussed as special cases.     

Generalized Lorenz-Mie theory for a spheroidal particle with off-axis Gaussian-beam illumination

The beam-shape coefficients of arbitrary off-axis Gaussian beams in spheroidal coordinates are evaluated with a generalized Lorenz-Mie theory. The light-scattering properties of absorbing and nonabsorbing homogeneous spheroidal particles, such as the angular distribution of scattered intensity for a wide range of particles sizes and different complex refractive indices versus the magnitude and location of the beam waist, are investigated.     

Synthetic aperture superresolution with multiple off-axis holograms

An optical setup to achieve superresolution in microscopy using holographic recording is presented. The technique is based on off-axis illumination of the object and a simple optical image processing stage after the imaging system for the interferometric recording process. The superresolution effect can be obtained either in one step by combining a spatial multiplexing process and an incoherent addition of different holograms or it can be implemented sequentially. Each hologram holds the information of each different frequency bandpass of the object spectrum. We have optically implemented the approach for a low-numerical-aperture commercial microscope objective. The system is simple and robust because the holographic interferometric recording setup is done after the imaging lens.     

Comparative investigations of the measurement capabilities of atomic-force microscopy and optical interferometry methods

Cross measurements of surface relief of nanometer dimensions using atomic-force microscopy and optical interferometry methods are described. The investigations enable the regions where it is best to use these methods for different kinds of objects to be determined.     

Electron microscopy of second phases in manganese-zinc ferrite crystals

The surface and bulk microstructure of Mn-Zn ferrite single crystals oxidized at 0.7% _{o 2} have been investigated using SEM and TEM methods, assisted by energy- dispersive X-ray micro analysis. In samples heat-treated at 1000° C, haematite formed as an irregular surface layer and as laths which grew throughout the bulk, parallel with the {1 1 1 } planes (where F = ferrite). The haematite laths were related epitaxially to the ferrite host through the relationships (0001)_H | {1 1 1 }_F (where H = haematite) and . However, it was found that the latter parallelism was not exact because the haematite and ferrite lattices were rotated by 1.1 ± 0.2° about the axis perpendicular to the interface between them (i.e. [0001]H, <1 1 1 >_F). The sites for the nucleation of haematite second phase were also observed in highly oxidized ferrite. The formation of small planar defects (< O.1 m in length) in the ferrite, lying parallel to {1 10} planes, is interpreted as the combination of a local shear with the ordering of cation vacancies resulting from the oxidation. Small volumes of other second phases were also recognized, by virtue of both compositional and microstructural differences from the host ferrite.     

Theory for Slightly Doped Antiferromagnetic Mott Insulators

Trial wavefunctions, constructed explicitly from the unique 2-dimensional Mott insulating state with antiferromagnetic order, are proposed to describe the low-energy states of a Mott insulator slightly doped with holes or electrons. With the state behaving like charged quasi-particles with well-defined momenta, a rigid band is observed. These states have much less pairing correlations than previously studied ones. Small Fermi patches obtained are consistent with recent experiments on high T _c cuprates doped lightly with holes or electrons. States showing the incoherent and spin-bag behaviors are also discussed. Using these wavefunctions, a number of results obtained by exact calculations are reproduced.