Reflective grating interferometer in a noncollimated configuration

A third-order aberration analysis for a reflective grating interferometer (RGI) is developed for a noncollimated configuration. In such a configuration the RGI is still a folded and reversing interferometer that is sensitive only to coma aberration, as it is in the collimated configuration. However, for an unaberrated input beam converging on a plane grating, the reflective grating of the interferometer introduces self-aberrations. Consequently, a nonnull fringe pattern is obtained. Nevertheless, a RGI in the noncollimated configuration has the potential to be applied for isolating and measuring coma, and a possible configuration for this application is proposed. As an example of the application, the coma of a large mirror could be isolated and measured by use of a converged configuration to avoid the main limitation in using the RGI in a configuration with a nearly collimated beam.     

Reflective grating interferometer: a folded reversal wave-front interferometer

We present a new, folded reversal interferometer. It is based on the reflective grating interferometer and can be applied for optical isolation and testing of coma aberration. The interferometer has several advantages in respect to other existing optical reversal configurations. A carrier can be easily added for phase retrieval in interferometric fringe patterns for mapping coma aberration. Furthermore, in an asymmetric optical configuration a lateral shear can also be added, transforming it in a reversal shearing interferometer. The principle of operation of the interferometer is described, and the application for measuring the coma aberration of a parabolic mirror used off axis is demonstrated.     

Aberration compensation in a grating interferometer

The transfer function of a grating interferometer with aberrated gratings is discussed. A geometrical configuration is developed that minimizes the aberrations of the output fringes in the interferometer, which is constructed with three hyperbolic gratings. Theoretical and experimental investigations show that it is possible to compensate for first-order aberrations of the interferometer and obtain straight output fringes if a suitable geometric configuration is used for both the recording of the grating components and the interferometer itself.     

Testing of refractive silicon microlenses by use of a lateral shearing interferometer in transmission

Wave aberrations of refractive photoresist microlenses and silicon microlenses were measured with a lateral shearing interferometer. Because of the silicon elements, a near-infrared working wavelength (lambda = 1.32 mum) was used. The wave front was evaluated by a phase step technique with four steps. Integration of the phase distributions was performed with a computationally efficient Fourier transformation algorithm. The influence of the detector vidicon nonlinearity on the measured wave front was calculated. The defocusing behavior of the interferometer was investigated by fitting the measured wave fronts with the help of Zernike circle polynomials. It is shown that the reproducibility can be kept below lambda/100 rms. Examples for the measured wave fronts of plano-convex silicon microlenses are discussed in detail.     

Modified double-wedge-plate shearing interferometer for collimation testing

A modified configuration of the double-wedge-plate shearing interferometer for collimation testing is described. Results of the measurements to determine the setting sensitivity with this configuration are presented.     

Continuous lateral shearing interferometer

A simple lateral shearing interferometer based on the use of gratings is discussed, which facilitates the display of the spatial complex degree of coherence (CDC). A first version consisting of two identical gratings inclined relative to each other was used to demonstrate the working principle. For this purpose partially coherent light was used which was generated by imaging different object distributions on a rotating scatterer (e.g., double-slit or linear grid patterns). Furthermore, an achromatic lateral shearing interferometer based on the use of three gratings in a series arrangement is discussed and a theoretical proof for the achromatism of this arrangement is given.     

Vectorial shearing interferometer

The vectorial shearing interferometer is based on the Mach-Zehnder configuration; it incorporates a displacement shearing system composed of a pair of wedge prisms that modify the optical path difference and the tilt of the sheared wave front with respect to that of the reference wave front. Variable shear and tilt can be implemented along any direction by choice of displacements Dx and Dy. The number of fringes and their orientation can be controlled with the vectorial shear. Knowledge of the prescribed displacements in the x and the y directions permits one to obtain a phase gradient in any direction.     

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.     

Determination of the refractive index of a lens using the Murty shearing interferometer

An innovative nondestructive technique for measuring the refractive index of a simple lens is described. The proposed method is superior to existing ones because the focusing error and the spherical aberrations are reduced. Apart from this, the strength parameters (i.e., r1 and r2) of a lens are not required at all since the derived lens-index formula is independent of the lens's physical parameters. The shearing interferometric technique is a sensitive aid for detecting the focal plane of the test lens. A modified criterion for determining the focal length has been used. In this case two miscible liquids or compounds are not necessary. The well-known liquid immersion method is the particular case of this technique. The Murty shearing interferometer has been used as an optical device to observe the defocusing defect in the form of fringes. The amount of defocusing is easily calculated. An equation for this error has been theoretically deduced and experimentally verified. The technique described is quick to perform and easy in handling. The various effects due to the lens's aperture and aberrations, thickness of the glass cell, liquid column, etc. are also discussed. For N liquids, there are N(N - 1)/2 ways of calculating the lens's index. Owing to its nature this is termed the nondestructive nonmiscible-liquid immersion technique for index measurement of a lens.     

Fizeau interferometer for global astrometry in space

We discuss the design and the performance of a Fizeau interferometer with a long focal length and a large field of view that is well suited for a global astrometry space mission. Our work focuses on the geometric optimization and minimization of aberration of such an astrometric interferometer, which is able to observe astronomical targets down to the visual magnitude (mag) mv = 20 mag, with an accuracy in the measurements of 10 micro-arcseconds at mv = 15 mag. We assume a mission profile similar to that of the Global Astrometric Interferometer for Astrophysics mission of the European Space Agency. In this framework, data acquisition is performed by an array of CCDs working in time-delay integration mode. Optical aberrations, particularly distortion and coma, play a crucial role in the efficiency of this technique. We present a design solution that meets the requirements for the best possible exploitation of the time-delay integration mode over a field of view of 0.7 degrees x 0.7 degrees.     

Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise

A simulation study is presented that evaluates the ability of a unit-shear, shearing interferometer to estimate a complex field resulting from propagation through extended turbulence. Performance is defined in terms of the Strehl ratio achieved when the estimate of the complex field obtained from reconstruction is used to correct the distorted wave front presented to the wave-front sensor. A series of evaluations is performed to identify the strengths and weaknesses of the shearing interferometer in the two-dimensional space of the Fried parameter r0 and the Rytov number. The performance of the shearing interferometer is compared with that of a Hartmann sensor in the Fried and Hutchin geometries. Although the effects of additive measurement noise (such as read noise, shot noise, amplifier noise) are neglected, the fundamental characteristics of the measurement process are shown to distinguish the performance of the various wave-front sensors. It is found that the performance of a shearing interferometer is superior to that of a Hartmann sensor when the Rytov number exceeds 0.2.     

Lateral shearing interferometer based on two Ronchi phase gratings in series

Shearing interferometers are very popular and have a growing range of applications, especially in the field of optical testing. We describe a new kind of a lateral shearing interferometer. The lateral shear is produced by two Ronchi phase gratings in series. The phase can be shifted by a lateral movement of one grating relative to the other, and the amount of shear can easily be adjusted by variation of the distance of the gratings. The simplicity of the device is an important advantage, especially in the near IR.     

The design of a triplet with a shape-dependent third-order aberration optimization technique

Abstract

We have derived a series of shape-dependent third-order aberration equations involving lens thickness. These equations are used in a simple and direct method to correct real aberrations and to find the minimum aberration for triple design that has been proposed. These calculated third-order aberrations can exactly meet the target values for each stage by means of the damped least-squares method. The shape of the three elements permits the control of three third-order aberrations: spherical aberration, coma and astigmatism. The spherical aberration is targeted first. The minimal value of the real on-axis aberration is obtained. Similarly, the coma and astigmatism target values are adjusted so as to force the full field angle real off-axis aberrations down to a minimum. Finally, the manual adjustment of the lens thickness and air spacing is used to attain the minimum aberration at the 0.7 field angle. To verify the method, two triplet design examples are presented.     

Simultaneous determination of refractive index and thickness of moderately thick plane-parallel transparent glass plates using cyclic path optical configuration setup and a lateral shearing interferometer

We present a simple technique for simultaneous determination of refractive index and thickness of moderately thick plane-parallel transparent glass plates (GPs) using a cyclic path optical configuration (CPOC) setup and a wedge shear plate as lateral shearing interferometer. The CPOC setup is used to simultaneously focus the counterpropagating converging beams at a common point at its hypotenuse arm. The apparent thickness and real thickness of the test GP are determined by observing three retrocollimation positions of the GP surfaces with respect to the common focus point. The RI is obtained by dividing the real thickness with apparent thickness of the GP. Presented in this paper are the results obtained for a test GP with a thickness of 14.983 mm and a RI of 1.515.     

Carousel interferometer

A new type of a swinging interferometer, the carousel interferometer, is presented, and its properties are studied and compared with other swinging interferometers. The new interferometer is built with five plane mirrors. The optical path difference is accomplished by rotation of a system that consists of four mirrors. The modulation is almost independent of the scanning of the interferometer. It is not sensitive to external perturbations such as bending or other deformations of the mount. The construction is very compact. Because of its stability and low cost it is very applicable to small Fourier-transform spectrometers for any wave-number region from the far infrared down to the ultraviolet.     

Improved solution for the cemented doublet

A method is described that permits the calculation of a cemented doublet with a given spherical aberration and coma at the edge of the lens. In particular the aberrations can be set to zero. Given one glass, the equations reported in this paper permit the determination of a second matching glass that minimizes the spherochromatism and coma of the lens. This result is obtained by the introduction, into the third-order thin-lens formulas, the third-order values of the aberration coefficients, as derived from the equation developed by Mossotti which yields zero finite aberrations for the same lens with added thickness. After a brief historical introduction, the third-order equations are developed and tables for the color-correcting glasses and SI and SII (the Seidel third-order coefficients) are given for objects at infinity and at a magnification of - 1, both for flint- and crown-leading cases. The paper closes with a table of corrected doublets.     

Differential wavelength-scanning heterodyne interferometer for measuring large step height

An interferometer based on the differential heterodyne configuration and wavelength-scanning interferometry for measuring large step heights is presented. The proposed interferometer is less sensitive to environmental disturbances than other interferometers and can accurately measure interference phases. A tunable diode laser is utilized to illuminate the interferometer and thus solve the phase ambiguity problem. Counting the interference fringes as the wavelength is scanned through a known change in wavelength directly determines the step height. Three gauge blocks of different lengths, 5, 10, and 50 mm, are individually wrung on a steel plate to simulate large step heights. Comparing the results measured by the proposed interferometer with those by the gauge block interferometer reveals that the accuracy is approximately 100 nm.     

Double lateral shearing interferometer for the quantitative measurement of tear film topography

A lateral shearing interferometer designed and built for the study of the precorneal tear film topography dynamics and its effect on visual performance is presented. Simple data processing algorithms are discussed and tested on data illustrating different tear topography features: postblink tear undulation, tear breakup, eyelid-produced bumps and ridges, bubbles, and rough precontact lens tear surfaces.     

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.     

Dove prism with increased throughput for implementation in a rotational-shearing interferometer

An analytical expression is derived for the tilt introduced into a wave front by a Dove prism with manufacturing errors in the prism's base angles and pyramidal angle. We found that the tilt decreases when the base angles are increased above the values of traditional design. The increase in the length-aperture ratio of a prism is detrimental to the prism's performance. However, a Dove prism with a widened aperture increases throughput and maintains a manageable prism weight for implementation in a rotational shearing interferometer. Thus we propose a Dove prism designed with a widened aperture to increase throughput in a rotational shearing interferometer and with larger base angles to minimize the wave-front tilt introduced by manufacturing errors. Experimental results implemented in a rotational shearing interferometer demonstrate the feasibility of this design.