Showing papers on "Interferometry published in 1998"

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Abstract: A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Radar interferometry and its application to changes in the Earth's surface

Abstract: Geophysical applications of radar interferometry to measure changes in the Earth's surface have exploded in the early 1990s. This new geodetic technique calculates the interference pattern caused by the difference in phase between two images acquired by a spaceborne synthetic aperture radar at two distinct times. The resulting interferogram is a contour map of the change in distance between the ground and the radar instrument. These maps provide an unsurpassed spatial sampling density (∼100 pixels km−2), a competitive precision (∼1 cm), and a useful observation cadence (1 pass month−1). They record movements in the crust, perturbations in the atmosphere, dielectric modifications in the soil, and relief in the topography. They are also sensitive to technical effects, such as relative variations in the radar's trajectory or variations in its frequency standard. We describe how all these phenomena contribute to an interferogram. Then a practical summary explains the techniques for calculating and manipulating interferograms from various radar instruments, including the four satellites currently in orbit: ERS-1, ERS-2, JERS-1, and RADARSAT. The next chapter suggests some guidelines for interpreting an interferogram as a geophysical measurement: respecting the limits of the technique, assessing its uncertainty, recognizing artifacts, and discriminating different types of signal. We then review the geophysical applications published to date, most of which study deformation related to earthquakes, volcanoes, and glaciers using ERS-1 data. We also show examples of monitoring natural hazards and environmental alterations related to landslides, subsidence, and agriculture. In addition, we consider subtler geophysical signals such as postseismic relaxation, tidal loading of coastal areas, and interseismic strain accumulation. We conclude with our perspectives on the future of radar interferometry. The objective of the review is for the reader to develop the physical understanding necessary to calculate an interferogram and the geophysical intuition necessary to interpret it.

Synthetic aperture radar interferometry

Abstract: Synthetic aperture radar (SAR) is a coherent active microwave imaging method. In remote sensing it is used for mapping the scattering properties of the Earth's surface in the respective wavelength domain. Many physical and geometric parameters of the imaged scene contribute to the grey value of a SAR image pixel. Scene inversion suffers from this high ambiguity and requires SAR data taken at different wavelength, polarization, time, incidence angle, etc. Interferometric SAR (InSAR) exploits the phase differences of at least two complex-valued SAR images acquired from different orbit positions and/or at different times. The information derived from these interferometric data sets can be used to measure several geophysical quantities, such as topography, deformations (volcanoes, earthquakes, ice fields), glacier flows, ocean currents, vegetation properties, etc. This paper reviews the technology and the signal theoretical aspects of InSAR. Emphasis is given to mathematical imaging models and the statistical properties of the involved quantities. Coherence is shown to be a useful concept for system description and for interferogram quality assessment. As a key step in InSAR signal processing two-dimensional phase unwrapping is discussed in detail. Several interferometric configurations are described and illustrated by real-world examples. A compilation of past, current and future InSAR systems concludes the paper.

Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses.

Abstract: We present a novel, self-referencing interferometric technique for measuring the amplitude and the phase of ultrashort optical pulses The apparatus uses a collinear geometry that requires no moving components The phase-retrieval procedure is noniterative and rapid and uses only two one-dimensional Fourier transforms We apply the technique to characterize ultrashort pulses from a mode-locked Ti:sapphire oscillator

Polarimetric SAR interferometry

Abstract: The authors examine the role of polarimetry in synthetic aperture radar (SAR) interferometry. They first propose a general formulation for vector wave interferometry that includes conventional scalar interferometry as a special case. Then, they show how polarimetric basis transformations can be introduced into SAR interferometry and applied to form interferograms between all possible linear combinations of polarization states. This allows them to reveal the strong polarization dependency of the interferometric coherence. They then solve the coherence optimization problem involving maximization of interferometric coherence and formulate a new coherent decomposition for polarimetric SAR interferometry that allows the separation of the effective phase centers of different scattering mechanisms. A simplified stochastic scattering model for an elevated forest canopy is introduced to demonstrate the effectiveness of the proposed algorithms. In this way, they demonstrate the importance of wave polarization for the physical interpretation of SAR interferograms. They investigate the potential of polarimetric SAR interferometry using results from the evaluation of fully polarimetric interferometric shuttle imaging radar (SIR)-C/X-SAR data collected during October 8-9, 1994, over the SE Baikal Lake Selenga delta region of Buriatia, Southeast Siberia, Russia.

Polarimetric SAR interferometry

Abstract: In this paper, we examine the role of polarimetry in synthetic aperture radar (SAR) interferometry. We first propose a general formulation for vector wave interferometry that includes conventional scalar interferometry as a special case. Then, we show how polarimetric basis transformations can be introduced into SAR interferometry and applied to form interferograms between all possible linear combinations of polarization states. This allows us to reveal the strong polarization dependency of the interferometric coherence. We then solve the coherence optimization problem involving maximization of interferometric coherence and formulate a new coherent decomposition for polarimetric SAR interferometry that allows the separation of the effective phase centers of different scattering mechanisms. A simplified stochastic scattering model for an elevated forest canopy is introduced to demonstrate the effectiveness of the proposed algorithms. In this way, we demonstrate the importance of wave polarization for the physical interpretation of SAR interferograms. We investigate the potential of polarimetric SAR interferometry using results from the evaluation of fully polarimetric interferometric shuttle imaging radar (SIR)-C/X-SAR data collected during October 8-9, 1994, over the SE Baikal Lake Selenga delta region of Buriatia, Southeast Siberia, Russia.

"Coherence radar" and "spectral radar"-new tools for dermatological diagnosis.

Abstract: "Coherence radar," an optical 3-D sensor based on short coherence interferometry, is used to measure skin surface topology. This method is called optical coherence profilometry (OCP) and it may be a useful tool for medical diagnosis in dermatology because different medical conditions show distinct alterations of the skin surface. The measuring uncertainty is less than 2 μm. The measuring time is about 4 s. in vivo 3-D mapping of naked skin was performed without preparation. For clinical application, a fiber optical implementation was introduced. Spectral radar is an optical sensor for the acquisition of skin morphology based on OCT techniques. The scattering amplitude a(z) along one vertical axis from the surface into the bulk can be measured within one exposure. No reference arm scanning is necessary. The theory of the sensor, including the dynamic range, is discussed and in vivo measurements of human skin by a fiber optical implementation of the sensor are demonstrated. © 1998 Society of Photo-Optical Instrumentation Engineers.

Interference model for back-focal-plane displacement detection in optical tweezers.

Abstract: The lateral position of an optically trapped object in a microscope can be monitored with a quadrant photodiode to within nanometers or better by measurement of intensity shifts in the back focal plane of the lens that is collimating the outgoing laser light. This detection is largely independent of the position of the trap in the field of view. We provide a model for the essential mechanism of this type of detection, giving a simple, closed-form analytic solution with simplifying assumptions. We identify intensity shifts as first-order far-field interference between the outgoing laser beam and scattered light from the trapped particle, where the latter is phase advanced owing to the Gouy phase anomaly. This interference also reflects momentum transfer to the particle, giving the spring constant of the trap. Our response formula is compared with the results of experiments.

In vivo video rate optical coherence tomography.

Abstract: An optical coherence tomography system is described which can image up to video rate. The system utilizes a high power broadband source and real time image acquisition hardware and features a high speed scanning delay line in the reference arm based on Fourier-transform pulse shaping technology. The theory of low coherence interferometry with a dispersive delay line, and the operation of the delay line are detailed and the design equations of the system are presented. Real time imaging is demonstrated in vivo in tissues relevant to early human disease diagnosis (skin, eye) and in an important model in developmental biology (Xenopus laevis).

Interferogram analysis for optical testing

Abstract: (condensed). Review and Comparison of the Main Interferometric Systems: Two-Wave Interferometers and Configurations Used in Optical Testing. Twyman-Green Interferometer. Fizeau Interferometers. Typical Interferograms in Twyman-Green and Fizeau Interferometers. Lateral Shear Interferometers. Ronchi Test. Hartmann Test. Fringe Projection. Talbot Interferometry and Moire Deflectometry. Common Light Sources Used in Interferometry. Aspherical Compensators and Aspheric Wavefronts. Imaging of the Pupil on the Observation Plane. Multiple-Wavelength Interferometry. Fourier Theory Review: Introduction. Fourier Series. Fourier Transforms. The Convolution of Two Functions. The Cross-Correlation of Two Functions. Sampling Theorem. Sampling of a Periodical Function. Sampling of a Periodical Function with Interval Averaging. Fast Fourier Transform. Digital Image Processing: Introduction. Histogram and Gray-Scale Transformations. Space and Frequency Domain of Interferograms. Digital Processing of Images. Some Useful Spatial Filters. Square Window Filter. Hamming and Hanning Window Filters. Cosinusoidal and Sinusoidal Window Filters. Extrapolation of Fringes Outside of the Pupil. Light Detectors Used To Digitize Images. Fringe Contouring and Polynomial Fitting: Fringe Detection Using Manual Digitizers. Fringe Tracking and Fringe Skeletonizing. Global Polynomial Interpolation. Local Interpolation by Segments. Wavefront Representation by an Array of Gaussians.References. Periodic Signal Phase Detection and Algorithms Analysis: Least Squares Phase Detection of a Sinusoidal Signal. Quadrature Phase Detection of a Sinusoidal Signal. Discrete Low-Pass Filtering Functions. Fourier Description of Synchronous Phase Detection. Synchronous Detection Using a Few Sampling Points. Signal Amplitude Measurement. Characteristic Polynomial of a Sampling Algorithm. General Error Analysis of Synchronous Phase-Detection Algorithms. Some Sources of Phase Error. Shifting Algorithms with Respect to the Phase Origin. Optimization of Phase-Detection Algorithms. Influence of Window Function of Sampling Algorithms. Conclusions. Appendix: Derivative of the Amplitude of the Fourier Transform of the Reference Sampling Functions. References. Phase-Detection Algorithms: General Properties of Synchronous Phase-Detection Algorithms. Three-Step Algorithms To Measure the Phase. Four-Step Algorithms To Measure the Phase. Five-Step Algorithm. Algorithms with Symmetrical N +1 Phase Steps. Combined Algorithms in Quadrature. Detuning-Insensitive Algorithms for Distorted Signals. Algorithms Corrected for Nonlinear Phase-Shifting Error. Continuous Sampling in a Finite Interval. Asynchronous Phase-Detection Algorithms. Algorithm Summary. References. Phase-Shifting Interferometry: Phase-Shifting Basic Principles. An Introduction to Phase Shifting. Phase-Shifting Schemes and Phase Measurement. Heterodyne Interferometry. Phase-lock Detection. Sinusoidal Phase Oscillation Detection. Practical Sources of Phase Error. Selection of the Reference Sphere in Phase-Shifting Interferometry. Paraxial Focus. Best Focus. Marginal Focus. Optimum Tilt and Defocusing in Phase-Shifting Interferometry. References. Spatial Linear and Circular Carrier Analysis: Spatial Linear Carrier Analysis. Space-Domain Phase Demodulation with a Linear Carrier. Basic Space-Domain Phase Demodulation Theory. Circular Spatial Carrier Analysis. Phase Demodulation with a Circular Carrier. Fourier Transform Phase Demodulation with a Linear Carrier. Fourier Transform Phase Demodulation with a Circular Carrier. References. Interferogram Analysis with Moire Methods: Moire Techniques. Moire Formed by Two Interferograms with a Linear Carrier. Moire Formed by Two Interferograms with a Circular Carrier. Summary of Moire Effects. Holographic Interpretation of Moire Patterns. Conclusion. References. Interferogram Analysis without a Carrier: Introduction. Mathematical Model of the Fringes. The Phase Tracker. The N-Dimensional Quadrature Transform. Conclusion. References. Phase Unwrapping: The Phase Unwrapping Problem. Unwrapping Consistent Phase Maps Unwrapping Noisy Phase Maps. Unwrapping Subsampled Phase Maps. Conclusions. References. Wavefront Curvature Sensing: Wavefront Determination by Slope Sensing. Wavefront Curvature Sensing. Wavefront Determination with Defocused Images. Conclusions. References. Index. Short TOC

Grating based phase control optical delay line

Abstract: An apparatus for performing high speed scanning of an optical delay and its application for performing optical interferometry, ranging, and imaging, including cross sectional imaging using optical coherence tomography, is disclosed. The apparatus achieves optical delay scanning by using diffractive optical elements in conjunction with imaging optics. In one embodiment a diffraction grating disperses an optical beam into different spectral frequency or wavelength components which are collimated by a lens. A mirror is placed one focal length away from the lens and the alteration of the grating groove density, the grating input angle, the grating output angle, and/or the mirror tilt produce a change in optical group and phase delay. This apparatus permits the optical group and phase delay to be scanned by scanning the angle of the mirror. In other embodiments, this device permits optical delay scanning without the use of moving parts.

Astrometry and geodesy with radio interferometry: experiments, models, results

Abstract: Interferometry at radio frequencies between Earth-based receivers separated by intercontinental distances has made significant contributions to astrometry and geophysics during the past three decades. Analyses of such very long baseline interferometric (VLBI) experiments now permit measurements of relative positions of points on the Earth's surface and of angles between celestial objects at levels of better than one cm and one nanoradian, respectively. The relative angular positions of extragalactic radio sources inferred from this technique presently form the best realization of an inertial reference frame. This review summarizes the current status of radio interferometric measurements for astrometric and geodetic applications. It emphasizes the theoretical models that are required to extract results from the VLBI observables at present accuracy levels. An unusually broad cross section of physics contributes to the required modeling. Both special and general relativity need to be considered in properly formulating the geometric part of the propagation delay. While high-altitude atmospheric charged-particle (ionospheric) effects are easily calibrated for measurements employing two well-separated frequencies, the contribution of the neutral atmosphere at lower altitudes is more difficult to remove. In fact, mismodeling of the troposphere remains the dominant error source. Plate tectonic motions of the observing stations need to be taken into account, as well as the nonpointlike intensity distributions of many sources. Numerous small periodic and quasiperiodic tidal effects also make important contributions to space geodetic observables at the centimeter level, and some of these are just beginning to be characterized. Another area of current rapid advances is the specification of the orientation of the Earth's spin axis in inertial space: nutation and precession. Highlights of the achievements of very long baseline interferometry are presented in four areas: reference frames, Earth orientation, atmospheric effects on microwave propagation, and relativity. The order-of-magnitude improvement of accuracy that was achieved during the last decade has provided essential input to geophysical models of the Earth's internal structure. Most aspects of VLBI modeling are also directly applicable to interpretation of other space geodetic measurements, such as active and passive ranging to Earth-orbiting satellites, interplanetary spacecraft, and the Moon.

Image enhancement in optical coherence tomography using deconvolution

Abstract: The present invention provides an improved optical coherence tomography system and involves estimating the impulse response (which is indicative of the actual reflecting and scattering sites within a tissue sample) from the output interferometric signal of an interferometer according to the following steps: (a) acquiring auto-correlation data from the interferometer system; (b) acquiring cross-correlation data from the interferometer system having the biological tissue sample in the sample arm; and (c) processing the auto-correlation data and the cross correlation data to produce an optical impulse response of the tissue The impulse response may be obtained from the cross-correlation and auto-correlation data by: (d) obtaining an auto-power spectrum from the auto-correlation data by performing a Fourier transform on the auto-correlation data; (e) obtaining a cross-power spectrum from the cross-correlation data by performing a Fourier transform on the cross-correlation data; (f) obtaining a transfer function of the LSI system by taking a ratio of the cross-power spectrum to the auto-power spectrum; and (g) obtaining the optical impulse response of the LSI system by performing an inverse-Fourier transform on the transfer function Preferably, coherent demodulation is used in combination with the above deconvolution technique to resolve closely-spaced reflecting sites in the sample By utilizing both the magnitude and phase data of the demodulated interferometric signals, the OCT system of the present invention is able to distinguish between closely spaced reflecting sites within the sample

Integrated satellite interferometry: Tropospheric noise, GPS estimates and implications for interferometric synthetic aperture radar products

Abstract: Interferometric synthetic aperture radar (INSAR), like other astronomic and space geodetic techniques, is limited by the spatially and temporally variable delay of electromagnetic waves propagating through the neutral atmosphere. Statistical analysis of these variations, from a wide variety of instruments, reveals a power law dependence on frequency that is characteristic of elementary (Kolmogorov) turbulence. A statistical model for a major component of the delay fluctuations, the “wet” component, has previously been developed by Treuhaft and Lanyi [1987] for very long baseline interferometry. A continuous Global Positioning System (GPS) network is now in place in southern California that allows estimation of, along with geodetic parameters, the total delay due to the atmosphere above each site on a subhourly basis. These measurements are shown to conform to the Treuhaft and Lanyi (TL) statistical model both temporally and spatially. The TL statistical model is applied to the problem of INSAR and used to produce the covariance between two points separated in time and/or space. The error, due to the atmospheric variations, for SAR products such as topography and surface deformation is calculated via propagation of errors. There are two methods commonly cited to reduce the effect of atmospheric distortion in products from SAR interferometry, stacking and calibration. Stacking involves averaging independent interferograms to reduce the noise. Calibration involves removing part (or all) of the delay using data from an independent source such as total zenith delay estimates from continuous GPS networks. Despite the relatively poor spatial density of surface measurements, calibration can be used to reduce noise if the measurements are sufficiently accurate. Reduction in tropospheric noise increases with increasing number of measurement points and increasing accuracy up to a maximum of √N, where N is the number of points. Stacking and calibration are shown to be complementary and can be used simultaneously to reduce the noise to below that achievable by either method alone.

Integrated optical Mach-Zehnder biosensor

Abstract: We present measurements on biomolecular surface multilayers using an integrated optical sensor based on the Mach-Zehnder interferometer (MZI). The sensor design is unique in that it incorporates a three-waveguide coupler structure at the interferometer output which gives advantages in terms of signal referencing and in establishing and maintaining a sensitive operating point. The sensor performance is characterized with respect to bulk superstrate index and by the formation of multiple protein adlayers using a biotin-avidin-based biochemical system. The detection limit for protein loading is estimated as 5 pg/mm/sup 2/.

Ultrafast heterodyne-detected transient-grating spectroscopy using diffractive optics

Abstract: We present a method for implementing optical heterodyne detection using a diffractive optic for time-resolved transient-grating experiments. This technique does not require active phase locking of pulse pairs to achieve interferometric stability. The phase stability, intrinsic time resolution, and signal amplification are demonstrated experimentally through Raman scattering in carbon disulfide.

Mechanics of bond and interface shear transfer in optical fiber sensors

Abstract: Optical fiber sensors are emerging as a superior nondestructive means for condition evaluation of civil structures. The ability of an optical fiber sensor to monitor strain distribution in a structural material depends on the bonding characteristics between the material and the optical fiber. The strain field transferred from the structure to the optical fiber sensor generates changes in the characteristics of the light signal transmitted by the glass core of the optical fiber. Transduction of this signal will provide a means for measurement of strain. However, the mechanical properties of the protective coatings employed in conjunction with optical fibers alter the strain transduction capabilities of the sensor. A portion of the strain is absorbed by the protective coating of the optical fiber, and hence, only a segment of structural strain is sensed. In the study reported here, a model is introduced and tested through which it is possible to interpret the actual level of structural strains from the values measured by an optical fiber sensor. A number of realistic assumptions were introduced to simplify the development of the mathematical rigor. It was determined that the strain transfer characteristics of optical fibers depend on the mechanical properties of the glass core, the protective coating, and the gauge length of the optical fiber. Mathematical expressions are developed through which it is possible to describe the level of strain loss within the protective coating, and the amount transferred to the optical fiber core. The theoretical findings were verified through a series of experiments involving white light interferometry. The investigation encompassed repeated experiments with a range of fiber sensor gauge lengths. The experimental program included evaluation of strain transfer capabilities of coated as well as bare fibers.

Stage device and exposure apparatus

Abstract: A stage device suitable for exposure apparatus used to produce semiconductor devices, movable in an area wider than the measurement area of an interferometer for position measurement, and capable of measuring the position with high precision. When a movable stage (WST) moves from the position where the laser beams from laser interferometers (15X1, 15X2, 15Y) are not applied into the measurement area of the laser interferometer, the position of a reference mark (MA) is measured by a wafer alignment sensor, and the measurement value measured by the laser interferometer is corrected based on the results of the mesurement by the wafer alignment sensor. When another movable stage (14) enters the measurement area of the laser interferometer, the position of a reference mark (MB) is similarly measured by a wafer alignment sensor, and the measurement value measured by the laser interferometer is corrected based on the results of the measurement by the wafer alignment sensor.

Atomic quantum non-demolition measurements and squeezing

Abstract: We show that the accuracy of atomic interferometry can be improved by using QND measurements of the atomic populations at the inputs to the interferometer. The accuracy of such a scheme surpasses the standard quantum limit of phase measurement δSQL = 1/√N and could reach the Heisenberg limit δ ~ 1/N. We propose to perform QND measurements of atomic populations with an off-resonant laser field. The conditions necessary for this kind of QND measurement could be fulfilled in a variety of ways with current experimental techniques, including magneto-optical traps and atomic cells.

The Palomar Testbed Interferometer

Abstract: The Palomar Testbed Interferometer (PTI) is a long-baseline infrared interferometer located at Palomar Observatory, California. It was built as a testbed for interferometric techniques applicable to the Keck Interferometer. First fringes were obtained in July 1995. PTI implements a dual-star architecture, tracking two stars simultaneously for phase referencing and narrow-angle astrometry. The three fixed 40-cm apertures can be combined pair-wise to provide baselines to 110 m. The interferometer actively tracks the white-light fringe using an array detector at 2.2 um and active delay lines with a range of +/- 38 m. Laser metrology of the delay lines allows for servo control, and laser metrology of the complete optical path enables narrow-angle astrometric measurements. The instrument is highly automated, using a multiprocessing computer system for instrument control and sequencing.

Birefringence imaging in biological tissue using polarization sensitive optical coherent tomography

Abstract: Employing a low coherence Michelson interferometer, two dimensional images of optical birefringence in turbid samples as a function of depth are measured Polarization sensitive detection of the signal formed by interference of backscattered light from the sample and a mirror or reference plane in the reference arm which defines a reference optical path length, give the optical phase delay between light propagating along the fast and slow axes of the birefringence sample Images showing the change in birefringence in response to irradiation of the sample are produced as an example of the detection apparatus and methodology The technique allow rapid, noncontact investigation of tissue or sample diagnostic imaging for various medical or materials procedures

Differential absorption imaging with optical coherence tomography

Abstract: The spatial variation of the backscattering cross section is the primary source of contrast in present applications of optical coherence tomography (OCT). We introduce and analyze a technique for obtaining OCT images of the local concentration of an absorbing compound in biological tissues and other highly scattering media. A pair of light-emitting diodes, one emitting in a vibrational absorption band of the chemical compound of interest and the other emitting just outside this band, are used as sources at the input of the interferometer. The differential absorption of the probe beam is determined by Fourier transformation and ratiometric processing of the measured interference signals. The ability of the technique to distinguish lipid and water inclusions in a scattering material is demonstrated with an OCT system that uses a pair of light-emitting-diode sources with center wavelengths of 1.3 µm and 1.46 µm.

High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics

Abstract: An advanced displacement measuring interferometer system has been developed to satisfy the needs of semiconductor manufacturing and lithography. The system electronics provides a position resolution of 0.31 nm at velocities up to 2.1 m when the system is used with a double-pass interferometer. Output data rates up to samples per second are available. The data age, which is the delay from the interferometer optics to the measurement sample, can be adjusted to equalize differences between axes to within 1 ns. This low data age uncertainty is necessary for high-resolution, high-speed, multiple-axis measurements.

Reconstruction of three-dimensional refractive index fields from multidirectional interferometric data

Abstract: Numerical and analytical techniques are presented that allow three-dimensional, asymmetric, refractive index fields to be reconstructed from optical pathlength measurements, which can be obtained using multidirectional holographic interferometry. Analytical reconstruction techniques that have been used in radioaptronomy and electron microscopy for a number of years, and recently in interferometry, are presented in the context of interferometric applications in the refractionless limit. These techniques require that optical pathlength data be collected over a 180 degrees angle of view. The required pathlength sampling rate is discussed. An efficient numerical procedure is developed for direct inversion of the data. Several numerical techniques are developed that do not require that data be collected over a full 180 degrees angle of view. All such techniques require redundant data to achieve accurate reconstructions. The required degree of redundancy increases as the angle of view decreases. Numerical simulations using six different reconstruction techniques indicate that with a 180 degrees angle of view, all are capable of providing accurate reconstructions. Four of the techniques were used to analyze simulated interferometric data recorded over an angle of view of less than 180 degrees . Examples of reasonably accurate reconstructions using data with angles of view as low as 45 degrees are presented.

An improved interferometer design for use with meteor radars

Abstract: The measurement of the directions of radio meteors with an interferometric system is beset by two problems: (1) The ambiguity in the measured directions for antennas spaced by more than λ/2 and (2) the effects of mutual impedance when the antennas are spaced at λ/2 and less to avoid these ambiguities. In this paper we discuss the effects of mutual impedance between spaced antennas and describe an interferometer which both minimizes these effects and avoids the ambiguities associated with spacings larger than λ/2. We have modeled a version of this design numerically and show that under ideal conditions an interferometer of total span 4.5λ can yield directions accurate to about 0.3° with a signal-to-noise ratio of 20 dB. Finally, we have tested the design with observations from the 1996 Geminid and 1997 Quadrant meteor showers and find that even without a ground plane, the interferometer provides unambiguous directions to an accuracy of the order of 1.5°.

Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry

Abstract: We propose and demonstrate a novel technique for simultaneous measurement of the phase index, n(p) , the group index, n(g) , and the thickness, t , of transparent plates by use of a low-coherence interferometer. The output light from a superluminescent diode is focused upon the front plane of a transparent plate that is used as the sample. The sample stage is subsequently moved until the light is focused upon the rear plane of the plate. Measurement of the stage movement distance and the corresponding optical path difference allows us to determine both n(p) and n(g) . By placing the sample between two glass plates, we measured n(p) , n(g) , and t simultaneously, with an error of 0.3% or less, for nearly 1-mm-thick transparent plates, including glass and electro-optic crystals.

Interferometer system and lithograph apparatus including an interferometer system

Abstract: A composite interferometer system has a plurality of X and/or Y measuring axes which co-operate with an X and/or Y measuring mirror arranged on an object. The interferometer system also has at least one Z measuring axis, which extends partly in an XY plane and co-operates with Z measuring mirrors arranged on the object and Z reflectors. Thus, a larger number of more accurate and reliable measurements can be performed with the interferometer system.