High-accuracy thickness measurement of a transparent plate with the heterodyne central fringe identification technique

In a modified Twyman-Green interferometer, the optical path variation is measured with the heterodyne central fringe identification technique, as the light beam is focused by a displaced microscopic objective on the front/rear surface of the test transparent plate. The optical path length variation is then measured similarly after the test plate is removed. The geometrical thickness of the test plate can be calculated under the consideration of dispersion effect. This method has a wide measurable range and a high accuracy in the measurable range.     

Surface profilometry with laser-diode optical feedback interferometer outside optical benches

A simple and robust interferometer with a laser diode subject to optical feedback from the interferometer is presented for surface testing of a spherical mirror. The fringe phase can be locked by the optical feedback within less than 0.2pi (peak-to-valley value) even when the interferometer is placed on a wooden table. The fringe locking is caused by the change of lasing wavelength that suppresses the net phase change to be much less than 2pi. The locked fringe pattern with spatial carriers can be analyzed by a fringe analyzer at a video rate, and the measurement results of the spherical mirror showed the same result as on an optical bench.     

Precise interferometric AO method for SAW velocity measurements inan anisotropic solid

We suggest an original method utilizing a two beam optical interferometer for the accurate SAW velocity measurements in an anisotropic solid. Namely, two parallel and spatially separated optical beams are diffracted from different points along the path of SAW propagation. Then at the output of the interferometer light beams of different orders (0, ±1) reflecting from the surface with SAW are combined in pairs to create the interference patterns. Measurement of the interference pattern's intensity oscillations versus the SAW frequency gives all needed information to determine the phase and the group SAW velocities and their dispersion. Experimental software includes: statistical data accumulation with auto correction of the interferometer phase change caused by a change of the external conditions, and Fourier analysis of interferometer signal spectrum with the use of generalized variables taking into account the SAW dispersion. The experimental error depends on the experimental peculiarities and is about 0.5 m/s for the phase velocity and 3 m/s for the group velocity. The method is tested by SAW velocity measurements on ST-quartz with a thin film of Al     

Multipass Michelson interferometer with the use of a wavelength-modulated laser diode

An improved multipass Michelson interferometer is implemented. This technique uses the fact that the wavelength of a laser diode varies in proportion to the diode's injection current. With this method the sensitivity augmentation is accomplished by inserting a beam splitter into one arm of the interferometer, resulting in multiple reflections between the end mirror and the beam splitter. In addition, the interference of laser beams reflected from two arms can be accomplished with unequal arms in the condition of a short coherence length. The sensitivity increase of interference fringes and the compensation of the short coherence length have been demonstrated in experiments.     

A Multiple-beam Interferometer Coherence Analyser

A laser coherence analyser is described which yields simultaneous temporal and spatial coherence analysis of laser beams. It is of particular application to high power pulsed laser systems, for high speed holography and non-linear optics, where the short duration of the pulse (often less than 50 nsec) excludes the use of photoelectric spectrometers, employing time variation scanning of the optical path length. The instrument consists of two high quality spherical mirrors, having dielectric multilayer coatings of reflectivity typically 0.95 to 0.97, separated by a cylindrical invar spacer of adjustable length. In use, the spacer is normally set so that the pole separation of the plates is a few hundred micrometres less than their common radius of curvature (typically 10 cm). The resulting defocusing term combines with spherical aberration to yield a multiple beam interferogram having an annular region of nearly linear dispersion. Spectral resolving powers in the range 10⁷ to 10⁸ are readily obtainable. When the input beam possesses a high degree of spatial coherence, the fringes of the concentric rings interference pattern are alternately of high and low intensity, the visibility of the alternation being a direct measure of the spatial coherence. This alternation effect may be eliminated by obstructing one-half of the input aperture. Any spatial, spectral or intensity variations across the laser beam are superposed on the fringe pattern, since the spherical interferometer is not translationally invariant in a parallel beam. This is in contrast to the behaviour of a plane Fabry-Pérot etalon. The experimental characteristics of the instrument, and its properties, as predicted by numerical computation, are examined both for C.W. and pulsed lasers. The effect of the finite response time is described. This is particularly important when the coherence analyser is employed in conjunction with an image tube streak camera to obtain time-resolved spectra of pulsed systems. Both time-integrated and time-resolved fringe profiles are considered for various types of laser pulse. The effect of plate defects on fringe profiles is also considered in outline. In addition to providing quasi-linear dispersion and information on coherence and other spatial properties of the input, the instrument described has the advantages of providing high illumination, and of being easy to use in practice, the plates remaining permanently in alignment.     

An interferometric method for simultaneously determination the phase retardation and fast-axis azimuth angle of a wave plate

In this study, an interferometric method was proposed for the simultaneous measurement of phase retardation and fast-axis azimuth angle of a wave plate by using a Mach–Zehnder interferometer. The wave plate to be tested is placed in one of the light passages in the interferometer, and two analyzers with transmission axes at horizontal and vertical orientations are arranged at the two output regions. When a linearly polarized laser light beam is passed through the interferometer, two interference light beams are simultaneously generated. Through an analysis of the intensities of the two light beams, the phase retardation and fast-axis azimuth angle of the tested wave plate can be simultaneously determined using specially derived equations. The feasibility of the proposed method was demonstrated using measurements of zero-order half-wave and zero-order quarter-wave plates. The proposed method is easy to operate, enables rapid measurement, and has high stability and accuracy.     

Fringe visibility, irradiance, and accuracy in common path interferometers for visualization of phase disturbances

Common-path interferometers have been used to perform phase visualization for over 40 years. A number of techniques have been proposed, including dark central ground, phase contrast (π/2 and π), and field-absorption interferometers. The merits of the interferometers have been judged ad hoc by either tests with a small number of phase objects or by computer simulation. Three standardized criteria, which consolidate the work of others, are proposed to evaluate common-path interferometers: fringe visibility, fringe irradiance, and fringe accuracy. The interferometers can be described as one generic class of Fourier-plane filters and can be analyzed for all input conditions. Closed-form expressions are obtained for visibility and irradiance under the forced condition that little inaccuracy is tolerated. This analysis finds that the π-phase-contrast interferometer is a good choice if the optical phase disturbance is at least 2π; for smaller disturbances, the Π/2 filter selected by Zernike is near optimum. It is shown mathematically that the resulting fringe visibility is highly object dependent, and good results are not ensured. By allowing the optical beam to be 50% larger than the phase object, the interferometer performs well under all conditions. With this approach and a combination π-phase/field-absorption filter, interference fringe visibility is greater than 0.8 for all phase objects.     

Investigation of the influence of spatial coherence of a broad-area laser diode on the interference fringe system of a Mach-Zehnder interferometer for highly spatially resolved velocity measurements

Laser Doppler anemometry is a method for absolute velocity measurements that is based on a Mach-Zehnder interferometer arrangement and usually employs transverse fundamental-mode lasers. We employed inexpensive and powerful broad-area laser diodes and investigated ways in which an interference fringe system is influenced by the spatial coherence properties of a multimode beam. It was demonstrated that, owing to poor spatial coherence of the beam, interference is suppressed in the marginal regions of the intersection volume. Based on these results, a sensor for highly spatially resolved velocity measurements can be built. The inherent astigmatism of the broad-area diode is corrected by an arrangement of two crossed cylindrical lenses. An interference fringe system of length 200 microm and a relative variation in fringe-spacing of only 0.22% were demonstrated with light emitted from a broad-area laser diode with a 100 microm x 1 microm emitter size. Based on this principle a powerful, simple, and robust laser Doppler sensor has been achieved. Highly spatially resolved measurements of a boundary layer flow are presented.     

Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces

A point diffraction interferometer (PDI) with adjustable fringe contrast is presented for the high-precision testing of spherical surfaces. The polarizing components are employed in the PDI to transform the polarization states of the test and reference beams, and a good fringe contrast can be realized by adjusting the relative intensities of interfering waves. The proposed system is compact and simple in structure, and it provides a feasible way for high-precision testing of spherical surfaces with low reflectivity. The theory of the interferometer is introduced in detail, along with the properties of optical components employed in the system, numerical analysis of systematic error, and the corresponding calibration procedure. Compared with the testing results of the ZYGO interferometer, a high accuracy with RMS value about 0.0025λ is achieved with the proposed interferometer. Finally, the error consideration in the experiment is discussed.     

Squeezed States in Non-ideal Interferometers: The Effect of Aberrations

Abstract

We extend a previous study of the usefulness of squeezed states of light for noise reduction in a non-ideal interferometer to the case where fringe visibility that is less than unity is caused by non-absorptive processes such as aberrations or misalignment of the beams. The main differences and similarities between this system and our earlier study of an interferometer with unbalanced losses in both arms are presented and discussed. An expression is given for the minimum detectable phase change in this system, in the presence of squeezing, as a function of fringe visibility.     

Analysis of coherent symmetrical illumination for electronic speckle pattern shearing interferometry

In an effort to find a non-contact technique capable of providing measurements of in-plane strain, a speckle shearing interferometer was designed using symmetrical coherent illumination. This paper presents an analysis of the sensitivity to displacement and strain of this interferometer, together with an analysis of the phase-stepping of the resultant fringe patterns. New notation is introduced alongside this analysis to define the interference components in speckle shearing interferometers using multiple illumination beams. Experimental results show fringe patterns and phase stepping in support of the theoretical analysis.     

Dispersion in stellar interferometry: simultaneous optimization for delay tracking and visibility measurements

In long-baseline optical stellar interferometry, it is necessary to maintain optical path equality between the two arms of an interferometer in order to measure the fringe visibility. There will be errors in matching the optical paths because of a number of factors, and it is desirable to use an automatic system to monitor and correct such path errors. One type of system is a delay tracker, based on imaging of the channeled spectrum. The tracking algorithm is designed to maintain a fixed number of fringes, ideally linearly spaced, across the observed spectral band. This results in a constant optical path difference, which may be incompatible with the requirement of path equality for the measurement of fringe visibility. In a practical interferometer that uses an optical path-length compensator operating in air, there is a complication since air paths introduce differential dispersion. This dispersion can be compensated for by including dispersion correction. By modifying the operation of an appropriately designed dispersion corrector, we show that it is possible to make the optical path difference zero at the measurement wavelength and, at the same time, to produce linearly spaced channel fringes across the tracking band.     

Determining small angles of beam splitter rotation in optical vortex shearing interferometer

It is suggested to use a singular beam of unit topological charge in a scheme of vortex shearing interferometer intended for the observation of isoclinic fringes. In the interference pattern, the regions of fringe splitting determine the localization of wavefront dislocations and exhibit a shift that depends on the beam splitter rotation angel. Using the proposed method, it is possible to evaluate small angles of beam splitter rotation with an accuracy determined by the interference fringe width.     

Self-referenced rectangular path cyclic interferometer with polarization phase shifting

A polarization phase shifting interferometer using a cyclic path configuration for measurement of phase nonuniformities in transparent samples is presented. A cube beam splitter masked by two linear polarizers is used to split the source wavefront into two counter propagating linearly polarized beams that pass through the sample. At the output of the interferometer, the two orthogonally polarized beams are rendered circularly polarized in the opposite sense through the use of a quarter wave plate. Finally, phase shifting is achieved by rotating a linear polarizer before the recording plane. In a rectangular path interferometer, although the two counter propagating wavefronts are laterally folded with respect to each other in the interferometer arms, the beams finally emerge mutually unfolded at the output of the interferometer. This phenomenon is utilized to create a reference if the sample is introduced in one lateral half of the beam in any one of the interferometer arms. The polarization phase shifting technique is used to generate four phase-shifted interferograms, which are utilized to evaluate the phase profile of the phase sample. Experimental results presented validate the proposed technique.     

Modified white-light Mach-Zehnder interferometer for direct group-delay measurements

A modified white-light Mach-Zehnder interferometer based on a single beam splitter is described for direct group-delay measurements. The arms of the interferometer are folded in such a manner that a single beam splitter can be used to split the incoming beam and combine the outgoing beams. This method offers a twofold advantage: The measuring range of the interferometer is twice as large as that of the Michelson interferometer, and the systematic error that is associated with the beam splitter is minimized because of the configuration. We report the results of measurements on various optical components performed in the 555-630-nm spectral region and propose a scheme for the processing of the experimental data. We present a comparison of the data analyzed by the proposed processing scheme along with the theoretical calculations.     

Quasi-achromatic laser Doppler anemometry systems based on a diffractive beam splitter

We propose a new beam-splitter system that makes it possible to use nonstabilized laser diodes for laser Doppler anemometry (LDA) systems by making the system wavelength independent. The beam splitter consists of two linear diffraction gratings that produce two parallel beams with a beam spacing that is wavelength dependent. This ensures passive wavelength compensation for the fringe spacing in the measurement volume. One can choose the distance between the two parallel beams by changing the distance between the two gratings, whereas the distance to the measurement volume can be designed by choice of a condensing lens with the proper focal length. This means that the system can be designed to have a desired fringe spacing in the measurement volume. The gratings are implemented as surface-relief holograms in photoresist, which makes it possible to mass produce the beam-splitter system at low cost through replication of the structure. The method for passive wavelength compensation for the fringe spacing is demonstrated both theoretically and experimentally.     

An optical self-calibrating technique for the dynamiccharacterization of PZT's

A system suitable for the measurement of linear sinusoidal vibration amplitudes is described. The signal beam of a Michelson interferometer is focused on the vibrating target while a suitable phase noise is applied to the reference arm of the interferometer. Signal processing is based on the null adjustment of the Bessel coefficients J₁ and J₂ derived from the signal provided by a single photodiode placed in the center fringe of the interference pattern. The system has been shown to be self-calibrating and intrinsically immune to mechanical perturbations induced in the interferometer. The technique proposed has been experimentally demonstrated by measuring the vibration amplitude of a PZT device in the amplitude range from 0.4 to 1.7 μm and in the frequency range from 8 to 22 kHz     

Interferometric measurement of laser heating in praseodymium-doped YAG crystal

Temperature measurement is required for many applications but can be difficult in some cases. Laser heating or cooling studies demand accurate measurements of temperature changes. A Michelson interferometer configuration has been used to investigate laser heating in solids. An analytical formula was derived to estimate the temperature change from the fringe count by taking into account the temperature dependence of the sample length and refractive index. When 115?mW of a focused Ar+ laser beam (488?nm) passes through a Pr(3+)-doped YAG sample, its temperature increased by 11.7±1.0?K along the beam path due to nonradiative relaxation. The power dependence of the fringe count/movement was recorded. The temperature change was estimated by the interferometric method and is in agreement with that measured by a thermocouple.     

Fast,common-path,switchable, achromatic phase-shifter for polarization interferometry

Abstract

A fast switchable phase-shifter using a pair of liquid-crystal devices with a switching angle of 60° is described. This phase-shifter can be placed in the common path traversed by the two orthogonally polarized beams emerging from a polarization interference microscope and used for digital phase measurements over a wide range of wavelengths. It can also be used in a stellar interferometer with orthogonally polarized beams for measurements of fringe visibility with white light.     

Collimation testing by use of the Lau effect coupled with moiré readout

We present an easy, simple, and inexpensive technique for checking the quality of the collimation of optical beams using the Lau effect combined with moiré readout. The experimental arrangement consists of a modified Lau-based interferometer in which a white-light incoherent source illuminates a set of two gratings. A collimating lens is placed between the two gratings such that the self-images of the second grating are formed. The third grating is positioned at one of the self-imaging planes forming moiré fringes. The type of the moiré fringe demonstrates the quality of collimation of the optical beam. The necessary theoretical background is presented and the results of our experimental investigation are reported. The technique can also be used for accurate determination of the focal length of a collimating lens using low-cost components.