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.

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

An improved partial differential equation algorithm with high validity and accuracy has been proposed to reconstruct a wavefront from its phase differences in lateral shearing interferometry. The algorithm is based on a complete point to point mapping relationship between the wavefront phase and its differences via a least squares principle. A special set of linear equations which relates the phase of the wavefront under test to its bi-direction difference data is derived initially, and then by solving the set of equations the wavefront phase is determined. As the coefficient matrix of the set of equations is sparse and symmetric, it is transformed to a new small matrix to reduce the memory and numerical calculation needs in the solving process. Since the matrix is a positive-definite matrix, the Choleski factorization is adopted to solve the set of equations conveniently. The advantages of the algorithm such as reduction of computer memory needs, high reconstruction accuracy and efficiency are analyzed and discussed. The error propagation analysis and testing shows a good noise suppression ability.

https://iopscience.iop.org/article/10.1088/1464-4258/11/4/045702/pdf

A partial differential equation algorithm for wavefront reconstruction in lateral shearing interferometry

A simple, versatile, sensitive optical interferometer based on diffractive optics is presented. The absence of a need for active stabilization, and a compact common-path design requiring two optical elements, make the interferometer ideal for time-resolved measurements in the picosecond through millisecond regimes. Its performance is characterized quantitatively, and its utility for local detection and scanning as well as spatially resolved imaging of thermoelastically induced strain is demonstrated.

Phase mask based interferometer: Operation principle, performance, and application to thermoelastic phenomena

A new lateral shearing interferometer for precision surface measurement

Double grating interferometer is usually used to achieve phase information from distorted wave front by its temporal phase-shifting characteristic. In this paper, the spatial phase-shifting characteristic of double grating interferometer is presented. The explicit intensity distributions of interferograms produced by double gratings are derived with the scalar diffraction theory, and the stable phase shift is found between plus-first, zero and minus-first order interferograms. Results indicate that the phase shift only depends on the grating period and the distance between two gratings if no phase object exists. If phase object exists, it varies on the interferograms. But the phase shifts are equal at any special point of interferograms. In particular, the triple grating interferometer is presented to generate at least four phase shift interferograms simultaneously with the similar method.

Spatial phase-shifting characteristic of double grating interferometer.

In order to increase the dynamic range of shape measuring interferometry, a double-grating shearing interferometric technique has been developed. The interference takes place between two wavefronts diffracted from two high density sinusoidal gratings. Phase stepping by means of lateral shifting was introduced to obtain automatic fringe analysis. The surface shape is reconstructed from the first derivative of the phase distribution with the assumption of a rotationally symmetric object. This assumption is reasonable for testing diamond-turned surfaces. The measurement accuracy depends upon the surface size and the shear amount. The authors have experimentally measured a spherical diamond-turned mirror shape with an accuracy of lambda /2 ( lambda =0.6328 mu m), and a theoretical dynamic range of hundreds of lambda .

Double grating phase stepping interferometry for testing aspherics

In this paper we propose a concept for a quasi-distributed fiber-optic strainand temperature sensor based on time division multiplexing (TDM) of in-line coupledFabry-Perot interferometers (FPI) with fiber Bragg gratings used as weak reflectors. A"differential" two core fiber is used for separate measurement of strain and temperatureand a dual-wavelength technique is used to perform absolute measurements over anextended dynamic range. Some advantages and limitations of this sensor system are dis- cussed. The system has been primarily designed to be embedded in composite structuresfor aerospace applications.

L. Wosinski

Papers

Double grating phase stepping interferometry for testing aspherics

Quasi-distributed fiber-optic sensor for simultaneous absolute measurement of strain and temperature