Showing papers on "Interferometry published in 1990"

Electromagnetic Wave Propagation, Radiation, and Scattering

Abstract: Fundamental field equations waves in homogeneous and layered media waveguides and cavities Green's functions radiation from apertures and beam waves periodic structures and coupled mode theory dispersion and anisotropic media antennas, apertures and arrays scattering of waves by conducting and di-electric objects waves in cylindrical structures, spheres and wedges scattering of complex objects geometric theory of diffraction and low fequency techniques planar layers, strip lines, patches and apertures radiation from a dipole on the conducting earth, inverse scattering radiometry, noise temperature and interferometry numerical techniques.

Laser Ultrasonics Techniques and Applications

Abstract: INTRODUCTION Ultrasonics Lasers Main characteristics of laser light Lasers for ultrasonics ACOUSTO-OPTIC INTERACTIONS The acousto-optic effect The measurement of ultrasonic fields Bragg diffraction Acousto-optic devices Applications of acousto-optic devices The interaction of light with surface waves LASER INTERFEROMETRY Principles of laser interferometry Theory of interference between light beams Reference beam interferometry with rough surfaces Light detection and signal amplification Effects of laser mode structure Signal processing Stabilized interferometers Optical frequency shifting Quadrature interferometers Long path difference and interferometry Fabry-Perot interferometers APPLICATINOS OF LASER INTERFEROMETRY TO ULTRASONIC DISPLACEMENT MEASUREMENT The measurement of acoustic fields Scanned laser interferometry Full field visualisation of surface displacement The measurement of surface waves Calibration of transducers Acoustic emission The measurement of transverse and vector displacement Sensitivity comparison with other ultrasonic detection techniques ULTRASONIC GENERATION BY LASER Absorbtion of electromagnetic radiation Temperature distributions Thermoelastic stresses Other effects Constrained surfaces Ultrasonic wave propagation in unbounded solids Propagation in bounded solids Radiation patterns for laser-ultrasonic sources Ultrasonic bulk waveforms in plates Ultrasonic surface and guided waves Lasers for ultrasonic generation APPLICATIONS USING LASER GENERATION OF ULTRASOUND Applications to flaw detection Applications to materials property measurement APPLICATIONS TO ACOUSTIC MICROSCOPY Calibration Wave propagation studies Medical applications CONCLUSIONS AND FUTURE PROSPECTS FOR LASER TECHNIQUES IN ULTRASONICS Summary and conclusions Future research and development Future prospects for applications REFERENCES INDEX

The VIRGO Project: A wide band antenna for gravitational wave detection

Abstract: The status of advancement of the VIRGO Project is presented: the first-generation results from the Pisa seismic noise super attenuator give an upper limit to the noise transfer function of 2 × 10 −8 at 10 Hz. The upper limit to the absolute noise of the 400 kg test mass at 10 Hz has been measured to be 1.5 × 10 −13 m/√Hz. The scheme and the related problems of the VIRGO interferometer, which is supposed to work down to 10 Hz, are also presented. At the 3rd Pisa Meeting in 1986 we presented the idea of what could be a very efficient seismic noise reduction system able to give a sensitivity h ∼ 10 −25 at 10 Hz, in a 3 km interferometer for 1 year integration time. Now we have two new facts to present: the first is that the attenuation has been built, is working in Pisa, and shows remarkable characteristics. The second is the Italian-French interferometer VIRGO [1,2], a 3 km long antenna for low and high frequency (10–1000 Hz) gravitational wave (GW) detection. These two items will be presented in this article.

Two-photon interference in a Mach-Zehnder interferometer.

Abstract: Pairs of 826.8-nm correlated photons, generated by parametrically down-converting 413.4-nm krypton-ion laser light, are directed into a single Mach-Zehnder interferometer such that each photon of the pair enters a different input port. The rate of coincidence at the two output ports displays oscillations (as the path-length difference is swept) with a spatial period equal to the 413-nm wavelength of the pump photons, and with a visibility of 62% when the path-length difference exceeds the coherence length of the individual photon beams. This unequivocally demonstrates the nonclassical and entangled nature of the two-photon state.

Fourier description of digital phase-measuring interferometry

Abstract: A general description of phase measurement by digital heterodyne techniques is presented in which the heterodyning is explained as a filtering process in the frequency domain Examples of commonly used algorithms are given Special emphasis is given to the analysis of systematic errors Gaussian error propagation is used to derive equations for the random phase errors of common algorithms

Group-delay measurement using the Fourier transform of an interferometric cross correlation generated by white light.

Abstract: A new method and apparatus for measuring the group delay in optical components and laser cavities are described. Cross-correlational fringes are fully recorded with a Michelson interferometer, in one of whose arms the optics to be measured are inserted. The path difference of the interferometer is calibrated to subwavelength accuracy, and the group delay is calculated from the phase of the Fourier transform of the measured fringe. The group delay for the entire visible-wavelength region is evaluated after a single measurement in approximately 10 min, using white light.

IV Advanced Evaluation Techniques in Interferometry

Abstract: Publisher Summary This chapter describes the advanced evaluation techniques in interferometry The chapter discusses the methods that rely on the adjustment of a fringe pattern The chapter examines the historically older interpolation methods where the phase information is extracted from the positions of the extrema The chapter also discusses more general methods that deliver the phase in a more continuous form A comparison of the different methods for phase evaluations necessitates a consideration of the error sources and limitations These error sources for the case of phase sampling interferometry (PSI) have been discussed The error causes are classified into statistical errors (measuring errors that can be diminished in their influence by averaging) and systematic errors (errors that cannot be quenched) The interferometers used in the assessment of test data are rather complex, thus, there is some necessity for calibration The interferometer aberrations, even with ideal test samples, are caused by deviations of optical elements and to also by the state of adjustment The chapter identifies the types of error sources—namely, environmental errors, errors that are dependent on the method, and errors typically encountered in interferometry

Optical measurement of picometer displacements of transparent microscopic objects.

Abstract: An optical laser differential interferometer, based on a modified differential interference contrast microscope, has been developed to measure the thermal motion of microscopic protrusions (stereocilia) that are the sites of mechanoelectrical transduction in auditory hair cells. The measurement sensitivity was limited at high frequencies mainly by shot noise, at intermediate frequencies by acoustic interference, and at low frequencies by thermal drift. The power spectral density of the instrumental noise was found to be as low as 1 pm/Hz in the shot noise regime. We could, thus, measure the Brownian motion of hair bundles over the frequency range from 1 Hz–100 kHz. Experimental data that test and demonstrate the sensitivity and spatial discrimination of the instrument were found to be in agreement with theoretical estimates.

Fiber-Optic Hydrophone

Abstract: The design and preliminary performance results of a fiber-optic (FO) Michelson interferometric hydrophone are described.

Optical sources of non-linearity in heterodyne interferometers

Abstract: Non-linearity of the two-frequency Michelson interferometer is studied by measurement of the modulation in phase and amplitude of the interference signal at the receiver. An important conclusion is that frequency mixing is not a major cause of non-linearity unless the mixing is asymmetric between the two arms of the interferometer. One source of asymmetry is non-orthogonality of the frequency states produced by the laser. Differential transmission between the reference and measurement paths can cause polarization states that are initially orthogonal to become non-orthogonal at the interferometer output. The influence of beam-splitter leakage, misorientation of the polarization axes of the source, and imperfect waveplates are also considered. It is not widely known that typical retroreflectors cause about a 7° rotation of the polarization state. However, polarization mixing induced by the retroreflectors is small in most, but not all, common configurations of the interferometer.

Method and apparatus for white-light dispersed-fringe interferometric measurement of corneal topography

Abstract: An novel interferometric apparatus and method for measuring the topography of aspheric surfaces, without requiring any form of scanning or phase shifting. The apparatus and method of the present invention utilize a white-light interferometer, such as a white-light Twyman-Green interferometer, combined with a means for dispersing a polychromatic interference pattern, using a fiber-optic bundle and a disperser such as a prism for determining the monochromatic spectral intensities of the polychromatic interference pattern which intensities uniquely define the optical path differences or OPD between the surface under test and a reference surface such as a reference sphere. Consequently, the present invention comprises a "snapshot" approach to measuring aspheric surface topographies such as the human cornea, thereby obviating vibration sensitive scanning which would otherwise reduce the accuracy of the measurement. The invention utilizes a polychromatic interference pattern in the pupil image plane, which is dispersed on a point-wise basis, by using a special area-to-line fiber-optic manifold, onto a CCD or other type detector comprising a plurality of columns of pixels. Each such column is dedicated to a single point of the fringe pattern for enabling determination of the spectral content of the pattern. The auto-correlation of the dispersed spectrum of the fringe pattern is uniquely characteristic of a particular optical path difference between the surface under test and a reference surface.

Optical fringe subdivision with nanometric accuracy

Abstract: Reliable bidirectional optical fringe counting is normally obtained by using two signals derived from the optical outputs of an interferometer varying sinusoidally with path difference and in phase-quadrature. This paper describes a calibration technique that uses these signals to achieve nanometric uncertainties in path length determinations. It discusses some of the limitations to achieving this uncertainty and describes a simple experimental technique for verifying the accuracy of fringe subdivision.

Squeezing of pulses in a nonlinear interferometer

Abstract: A symmetric nonlinear Mach–Zehnder interferometer containing a Kerr medium performs the operation of squeezing. The operation is performed by the interference of cotraveling waves, and the pump wave is removed. This mechanism is broadband. We analyze the operation of the interferometer and determine the degree of shot-noise reduction achieved in a balanced detector. A modification of the interferometer into a fiber ring reflector is described that accomplishes the squeezing and the pump separation.

Embedded fiber-optic Fabry-Perot ultrasound sensor

Abstract: A fiber-optic ultrasound sensor is presented. The sensor consists of a continuous length of single-mode optical fiber with a built-in Fabry-Perot interferometer. The acoustic pressure produces changes in the index of refraction along the interferometer cavity through the strain-optic effect, thus modulating the reflected power of the light propagating in the fiber. The dielectric internal mirrors that form the interferometer are fabricated by joining a fiber coating with a TiO/sub 2/ film at one end to an uncoated fiber by electric arc fusion splicing. Experimental results have been obtained for sensors embedded in plastic and graphite composite materials, using ultrasound waves in the range from 100 kHz to 5 MHz. Values for the optical phase shift amplitude as large as 0.5 rad were obtained at an acoustic frequency of 200 kHz for a 1.1-cm-long interferometer embedded in plastic. >

Millimetre-wave optics, devices, and systems

Abstract: Signal Transmission, Modes, and Gaussian Beams Beam Coupling, Lenses, and Mirrors Multi-Mode Beams and Apertures Antennas and Feed Systems Transmission Lines, Impedance Matching, and Signal Reflections Bolometric Signal Detection Mixers and Heterodyne Detection Filters and Resonators The Martin-Puplett Interferometer (MPI) The Design of Optical Circuits Oscillators and Signal Sources Frequency Control Loops and Diplexers Appendices References Index

An electronic speckle pattern interferometer for complete in-plane displacement measurement

Abstract: Measurement of plane-strain surface displacement with ESPI requires at least two in-plane illumination geometries. For static loading conditions it is acceptable to record these two interferograms sequentially. However, for time-dependent strain fields, it is necessary to use both illumination geometries simultaneously so that a recording is made with identical strain conditions existing for both. The authors describe a new interferometer that has been devised to measure two in-plane interferograms at the same time. The determination of the method of operation and experimental verification of the technique are given.

Sub-micron position measurement and control on precision machine tools with laser interferometry

Abstract: The trend towards tighter part tolerances from precision machine tools is placing increased demands on position transducers on these machines. Improved accuracy, repeatability and resolution from the position transducers is required to match this trend. This paper describes a new performance modelling technique for laser interferometer systems. Each error affecting the measurement accuracy and repeatability is described in detail, along with the method to determine these performance measures. Two products from Hewlett-Packard — wavelength tracking compensation and the high resolution interferometer — are also described that will help meet the future measurement requirements for precision machine tools.

Phase shifting interferometry in the presence of vibration: a new algorithm and system.

Abstract: A modification to the usual phase shifting interferometry algorithm permits measurements to be taken fast enough to essentially freeze out vibrations. Only two interferograms are time critical in this 2 + 1 algorithm; the third is null. The implemented system acquires the two time critical interferograms with a 1-millisecond separation on either side of the interline transfer of a standard CCD video camera, resulting in a reduction in sensitivity to vibration of 1-2 orders of magnitude. The required phase shift is achieved via frequency shifting. Laboratory tests comparing this system with a commercial phase shifting package reveal comparable rms errors when vibrations are low; as expected from an analysis of potential phase errors. However, the 2 + 1 system also succeeded when vibrations were large enough to wash out video rate fringes.

Spatial heterodyne spectroscopy: interferometric performance at any wavelength without scanning

Abstract: Spatial heterodyne spectroscopy (SHS) employing a two-beam dispersive interferometer producing a Fizeau fringe pattern having wavelength-dependent spatial frequencies is presented. The pattern is recorded on an imaging detector and Fourier transformed to recover the input stream. It is pointed out that spectrometers operating on the SHS principle can achieve the theoretical resolution limit of the gratings without scanning, retaining at the same time the large angular input tolerance and multiplexing properties of conventional scanning Fourier-transform spectrometers. Additionally, broad spectral coverages can be achieved, and field widening can be accomplished without moving parts.

Experiment on nonclassical fourth-order interference.

Abstract: A new fourth-order interference experiment has been carried out and analyzed theoretically in classical and in quantum terms. Two photons produced in the process of parametric down-conversion provide the two inputs to a Mach-Zehnder type of interferometer, while two photodetectors coupled to a coincidence counter measure the output. The coincidence rate, after subtraction of accidentals, exhibits a cosine variation with the optical path difference, in agreement with quantum mechanics, but in disagreement with a classical analysis. By contrast, when two coherent light beams from a He:Ne laser are used as inputs to the interferometer, no fourth-order interference is observed.

Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance

Abstract: We propose a sinusoidal phase modulating laser diode interferometer that is insensitive to vibrations of the optical components and fluctuations in the optical wavelength of the laser diode. These external disturbances cause fluctuations in the phase of the interference signal. After we analyze the sinusoidal phase modulation in a laser diode interferometer, we describe the method of the feedback control of the injection current of the laser diode to eliminate the phase fluctuations of the interference signal. We construct two sinusoidal phase modulating interferometers for movement measurements and surface profile measurements, respectively. The experimental results make it clear that the interferometers work well in mechanically noisy circumstances.

Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry.

Abstract: A phase shifting interferometer using a tunable laser as a light source is proposed for measuring shapes of both surfaces of a glass plate and the distribution of refractive index. To separate the superimposed interferograms generated with many wavefronts reflected from the plate, the phase shift associated with the wavelength shift is applied in the phase shifting interferometer with unequal optical paths in testing and reference beams. A laser diode is used for the tunable light source, and the data processing for obtaining phase distribution is based on the least-squares fitting in interferograms. The rms errors of the measurements are <1/50 wavelength for the surface shape, and 10(-5) of the refractive index for a 5-mm thick optical glass plate.

Contouring by electronic speckle pattern interferometry employing dual beam illumination

Abstract: In this paper we extend and study the method for generating contours of diffuse objects employing a dual beam illumination coupled with electronic speckle pattern interferometry. The sensitivity and the orientation of the contour planes are analyzed. A novel method for tilting the planes of contours and experimental results incorporating phase shifting and fringe analysis are also presented. The theoretical and the experimental results show good agreement.

Integrated optical directional-coupling refractometer apparatus

Abstract: In apparatus useful in immunoassay of a fluid, light is directed to an optical sensor wherein the light is transmitted to a replaceable optical device that is responsive to index of refraction in a sensing region thereof that is exposed to the fluid. One portion of the light is transmitted via a reference path to a first detector. Another portion of the light is transmitted via a sensing path that includes the sensing region to another detector. A ratioing device receives an output from each detector and provides a signal responsive to the ratio of the outputs. The replaceable optical device typically comprises a pair of channel waveguides in directional coupling arrangement, or a pair of channel waveguides in an interferometer arrangement, or a ridge waveguide having a serpentine path.

Analysis of input-polarization-induced phase noise in interferometric fiber-optic sensors and its reduction using polarization scrambling

Abstract: The dependence of the phase shift of an interferometric fiber sensor on the input state of polarization is analyzed, and it is shown that fluctuations in the input polarization to a fiber interferometer can lead to the generation of excess phase noise. The relationship between this effect and the variation in visibility with input polarization is described and theoretically confirmed. The use of depolarized source light to eliminate input-polarization-induced excess phase noise is theoretically and experimentally demonstrated. >

Interferometric stain measurement by arbitrarily configured surface-mounted, optical fibers

Abstract: The phase change of light traveling in a single-mode, arbitrarily configured optical fiber when the fiber is subjected to an arbitrary strain field is described by an integral equation. Assumptions concerning strain transfer from the strained body to a surface mounted optical-fiber sensor are experimentally verified. The general mathematical description is applied to two interferometric optical-fiber strain sensor geometries and is verified by experiment. The lack of precise data about the mechanical and optical material properties of the fiber is circumvented through calibration. Extensions of this model to both embedded fibers and nonlinear fiber response are discussed. >

Fourth-order interference of joint single-photon wave packets in lossless optical systems.

Abstract: We examine the fourth-order interference properties of two photons at a lossless four-port optical device. The photon pair is represented by a joint single-photon wave-packet state with arbitrary spectral composition. We explicitly determine the coincidence probabilities at the output ports of a beam splitter and a Mach-Zehnder interferometer when the incident wave packet is described by a joint Gaussian spectral distribution and the two photons are incident one at each port of the device. For uncorrelated and distinguishable input photons, the fourth-order interference is readily understood in terms of the particle or wave behavior of each photon acting separately. On the other hand, highly correlated photon pairs, such as those generated from spontaneous parametric down-conversion, exhibit fourth-order interference effects at the output of the interferometer that depend expressly on the joint nature of the photon-pair wave packet, and cannot be described by the particle or wave behavior of either photon.