Wavefront divergence: A source of error in quantified speckle shearing data

Abstract

Divergent laser illumination is commonly used in current designs of commercial electronic speckle pattern shearing interferometry (ESPSI) or shearography, for qualitative non-destructive testing (NDT) of material defects. The growing demand for quantitative out-of-plane (OOP) and more recently in-plane (IP) ESPSI, is determining the quality of optical system design and analysis software. However, little attention is currently being given to understanding, quantifying and compensating for the numerous error sources. Data describing the measurement inaccuracy due to the divergence of the object illumination wavefront for an OOP interferometer is presented. The errors are measured by comparing divergent object illumination with collimated illumination, with respect to illumination angle, lateral shear and shearing direction. Results indicate that the magnitude of the relative error increases by approximately a power function as the distance from the illumination source decreases.     

Deep nulling of visible laser light

Nulling interferometry, a proposed technique for dimming a star relative to its surroundings by destructively interfering the light collected by two individual telescopes [Bracewell, Nature 274, 780-781 (1978); Shao and Colavita, Ann. Rev. Astron. Astrophys. 30, 457-498 (1992)], has the potential to permit the direct detection of nearby extrasolar planets. However, because of the extremely high degree of symmetry required for useful levels of starlight nulling, the technique remains in its infancy. We present results of laboratory experiments with a rotational shearing interferometer that are aimed at demonstrating the feasibility of deep nulling at the levels needed for direct planet detection. Our first results include the successful nulling of red laser light to a part in 10(5) and the stabilization of the null leakage to a part in 10(4).     

Simple multifrequency and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry for three-dimensional profilometry

We propose a simple multifrequency spatial-carrier and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry (LSI). In this system a wedge-shaped plate lateral shearing interferometer is used and, owing to the presence of tilt, a finite number of fringes parallel to the direction of the shear appears; hence a significant spatial-carrier frequency is generated at the focus position. We further enhance the spatial-carrier frequency either by changing the wavelength of the laser light or by slight defocusing. A synthetic interferogram with low spatial-carrier frequency is obtained by use of laser light of two wavelengths simultaneously in the lateral shear interferometer. We obtain the phase-shifted fringe patterns from the same setup by simply moving the wedge plate in an in-plane parallel direction, using a linear translator. The fringe projection system was tested for measurement of the three-dimensional shape of a discontinuous object. The present system has many advantages; e.g., it is a common-path interferometry and hence is insensitive to external vibrations, is compact in size, and is relatively inexpensive.     

Wave-front analysis with high accuracy by use of a double-grating lateral shearing interferometer

A phase-stepped double-grating lateral shearing interferometer to be used for wave-front analysis is presented. The resulting interference patterns are analyzed with a differential Zernike polynomial matrix-inversion method. Possible error sources are analyzed in the design stage, and it is shown that the inaccuracy can be kept within 2-5 mλ rms. The apparatus was tested and evaluated in practice. Comparison with a phase-stepped Twyman-Green interferometer demonstrates that the accuracy of the two methods is comparable. Lateral shearing interferometry scores better on reproducibility, owing to the stability and robustness of the method.     

Statistical Properties of Phase Variation in Shearing Speckle Interferometry and Its Effect on Fringe Visibility

Abstract

The statistical properties of two interfering speckle fields indicate a reduction in phase variation as the coherent correlation between them increases. In this paper, the impact of this phenomenon on fringe visibility in shearing speckle interferometry, where two laterally shifted speckle fields are super-imposed, is studied. Work is also done to correlate fringe visibility with the amount of lateral shear based on the limitations imposed by phase variance statistics.     

Chromatism compensation in wide-band nulling interferometry for exoplanet detection

We introduce the concept of chromatism compensation in nulling interferometry that enables a high rejection ratio in a wide spectral band. Therefore the achromaticity condition considered in most nulling interferometers can be relaxed. We show that this chromatism compensation cannot be applied to a two-beam nulling interferometer, and we make an analysis of the particular case of a three-telescope configuration.     

A variable lateral-shearing Sagnac interferometer with high numerical aperture for measuring the complex spatial coherence function of light

Abstract

We combine a telescopic imaging system with a common-path, lateral-shearing interferometer and use phase-shifting interferometry to measure the complex spatial coherence function (or mutual intensity) of a linearly-polarized optical field. Our telescopic design increases the numerical aperture of the system without distorting the shape of the wave front, and therefore without changing the phase difference between lateral positions in the optical field. Our method of generating lateral-sheared images introduces no additional astigmatism. To demonstrate the use of the interferometer we extract the information contained in the complex spatial coherence function to reconstruct the amplitude and phase of a coherent optical field, and we also show how the spatial coherence function evolves from a coherent field to a partially coherent one as light traverses a random multiple-scattering medium.     

Anisotropy of the nonreciprocal linear birefringence in crystals

Results are presented of an experimental investigation of nonreciprocal linear birefringence (a difference between the phase velocities of counterpropagating waves having the same linear polarization) in lithium iodate and potassium dihydrophosphate crystals in a magnetic field. An original double-pass optical measuring system using two linear quarter-wave phase plates (Fresnel rhombs) is used to demonstrate a new method of studying the effect which can give a fairly high sensitivity and avoid accompanying effects. Pis’ma Zh. Tekh. Fiz. 24, 13–18 (February 26, 1998)     

Fast Coherence Scanning Interferometry for Measuring Smooth,Rough and Spherical Surfaces

Abstract

Coherence scanning interferometry is a useful instrument for measuring the geometry of a wide range of surfaces with high resolution. By introducing two objectives with a high numerical aperture in both arms of a Michelson interferometer it is possible to investigate spherical and aspherical surfaces. In addition to classical interferometry, the method can be applied to smooth, rough or separated surfaces.     

Symmetric nulling coronagraph based on a rotational shearing interferometer

We describe a fully symmetric nulling coronagraph for single-aperture telescopes that is based on a rotational shearing interferometer (RSI) and that is intended for the imaging of faint companions to nearby bright stars. In the proposed layout, all asymmetries inherent in previous single-aperture RSI-based nulling coronagraphs have been eliminated, and the bright and dark outputs are both accessible. As a resulty deep, broadband, dual-polarization rejection of on-axis starlight should be possible with this system.     

Real Time Pseudocolour Encoding of Depth Using White Light Processing

Abstract

An interferometer, consisting of a grating and a double exposed speckle pattern, used to perform pseudocolour encoding of depth in real time under white light illumination, is described. A theory of operation based on Fresnel diffraction is also given.     

Characterization of mid-infrared single mode fibers as modal filters

We present a technique for measuring the modal filtering ability of single mode fibers. The ideal modal filter rejects all input field components that have no overlap with the fundamental mode of the filter and does not attenuate the fundamental mode. We define the quality of a nonideal modal filter Q(f) as the ratio of transmittance for the fundamental mode to the transmittance for an input field that has no overlap with the fundamental mode. We demonstrate the technique on a 20 cm long mid-infrared fiber that was produced by the U.S. Naval Research Laboratory. The filter quality Q(f) for this fiber at 10.5 microm wavelength is 1000+/-300. The absorption and scattering losses in the fundamental mode are approximately 8 dB/m. The total transmittance for the fundamental mode, including Fresnel reflections, is 0.428+/-0.002. The application of interest is the search for extrasolar Earthlike planets using nulling interferometry. It requires high rejection ratios to suppress the light of a bright star, so that the faint planet becomes visible. The use of modal filters increases the rejection ratio (or, equivalently, relaxes requirements on the wavefront quality) by reducing the sensitivity to small wavefront errors. We show theoretically that, exclusive of coupling losses, the use of a modal filter leads to the improvement of the rejection ratio in a two-beam interferometer by a factor of Q(f).     

Interferometry Based on the Partially Coherent Effect Lying between the Talbot and Lau Effects

Abstract

Based on the partially coherent effect that lies between the Talbot effect and the Lau effect, a novel type of interferometry is proposed in this paper for a general configuration. The resultant interferogram is characterized by two different grating-like carriers. Such an interferometer becomes a Talbot or a Lau interferometer by adjusting the source slit to one or other of the two extremes of coherence. The partially coherent effect and the performance of the interferometer are analysed in detail in terms of the ambiguity function. Experimental results are shown to be in good agreement with the predicted intensity distributions.     

Carrier-modulated Object Step-loading Method of Automated Analysis in Digital Speckle Shearing Interferometry

Abstract

An object step-loading method has been recently reported to overcome the problems of phase unwrapping and decorrelation in digital speckle shearing interferometry. In this paper, a carrier modulation procedure is incorporated into the object step-loading method in order to improve the phase derivation accuracy. An added advantage with this approach is that the direction of deformation is also revealed.     

Multiple-beam lateral shear interferometry for optical testing

Lateral shear interferometry is used to obtain the lateral aberrations of a lens. The zeroth-order fringe in an interferogram obtained from a wedge-plate lateral shear interferometer, however, directly displays the lateral aberration curve of a test lens. Nevertheless, the intensity distribution, is cosinusoidal. Multiple-beam interferometry results in sharpened fringes; hence the multiple-beam wedge-plate shear interferometer displays the lateral aberration curve of a lens sharply, provided the shear is small. For large shear, some new artifacts appear in the interferogram, which are also explained.     

White-light interferometry with polarization phase-shifter at the input of the interferometer

Abstract

In white-light interferometry the surface profile is determined by measuring the fringe contrast function of the white-light interferogram. One of the techniques proposed for the measurement of the fringe contrast function is the use of the phase shifting technique with the help of an achromatic phaseshifter. The available phase-shifters employ a rotating polarization component at the output end of the interferometer. Using a rotating polarization component at the input end, rather than at the output end, has certain advantages. In this paper we investigate a rotating half-wave plate phase-shifter at the input end for its applications to a white-light interferometer.     

Phase-shifting interferometry using a two-dimensional regularized phase-tracking technique

Abstract

Phase-shifting interferometry is the most used method whenever the optical stability of the interferometer remain high when several phase-shifted interferograms are taken. In this work we present a two-dimensional regularized phase-tracking (RPT) technique applied to demodulate multiple phase-shifted interferograms. The main advantage of this technique with reference to classical phase-shifting interferometry is its higher signal-to-noise rejection as well as a higher signal′s harmonics rejection. In the RPT technique the unwrapping process is implicit; so it is achieved simultaneously with the phase estimation process; then, no additional unwrapping process is required.     

Interpretation of fringes obtained with coherent gradient sensing

An interference analysis for double-grating shearing interferometry called coherent gradient sensing is presented, and the results are compared with an earlier geometrical optics analysis and a Fourier optics analysis based on the Fresnel approximation. The influence of the order of approximation in these analyses and the equivalence of fringe interpretation in each case are discussed.     

Optical Performance of Large Ground-based Telescopes

Abstract

Images taken with ground-based telescopes are dominated by atmospheric seeing. Analytical expressions of long-exposure optical functions, namely the modulation transfer function, point spread function and encircled energy are established, under the assumption that dome and telescope seeing are brought to negligible values, and that the diameter of the telescope is larger than the atmospheric coherence length. The influence of guiding errors and axisymmetrical telescope aberrations is also assessed, and a definition of optical quality is proposed. The results are generalized and the optical performance of a ground-based telescope is expressed in terms of effective diameter and signal-to-noise ratio.     

TV-shearography for measuring 3D-strains

The shearographic interferometry is employed as a nondestructive full field, optical testing and measuring method without contact. Fringes of constant strain (so called isotase, tasis (Greek)=strain) can he observed in real time on the surface of the investigated machine parts and structures of any material and are represented by the shearogram. Using shearography two states of "deformation are recorded by doubly exposing a Holotesl film in an ordinary camera or stored by an electronic image processing system. In the lens of the camera a shearing element inside or outside the focus is integrated or the lateral Michelson shearing interferometer is used. Rigid body motions of the object are not recorded. Local deformation irregularities caused by a defect under or on the surface of the specimen create, strain concentrations; the homogeneous surrounding is poorly superimposed by an interference pattern. The shearogram shows dark and bright fringes which are the functions of the displacement derivative. The holographic interferometry measures the out of plane deformations directly. Terms of the out of plane strain can be determined by the shearographic method as well as the in plane strain fringes which are described in the following.