High-precision analysis of a lateral shearing interferogram by use of the integration method and polynomials

Abstract

Interferograms obtained with ordinary interferometers, such as the Fizeau interferometer or the Twyman-Green interferometer, show the contour maps of a wave front under test. On the other hand, lateral shearing interferograms show the difference between a wave front under test and a sheared wave front, that is, the inclination of the wave front. Therefore the shape of the wave front under test is reconstructed by means of analyzing the difference. To reconstruct the wave front, many methods have been proposed. An integration method is usually used to reconstruct the wave front under test rapidly. However, this method has two disadvantages: The analysis accuracy of the method is low, and part of the wave front cannot be measured. To overcome these two problems, a new, to our knowledge, integration method, improved by use of polynomials, is proposed. The validity of the proposed method is evaluated by computer simulations. In the simulations the analysis accuracy achieved by the proposed method is compared with the analysis accuracy of the ordinary integration method and that of the method proposed by Rimmer and Wyant. The results of the simulations show that the analysis accuracy of the newly proposed method is better than that of the integration method and that of the Rimmer-Wyant method.

Ultra-large field-of-view two-photon microscopy

“…4(a)) and had negligible spherical or higher order aberration. Note that as a general tool, the shearing interferogram also contains information about coma, astigmatism, and higher order Zernike polynomials [23]. In order to measure the pulse duration at the sample, an interferometric autocorrelation was performed by utilizing a Michelson delay line prior to the scanning setup.…”

Low cost plane parallel plate lateral shearing interferometer for infrared laser beam diagnostics

“…6 Alternatively, one can take a more rigorous approach and write a numerical routine to fit Zernike polynomials to the wavefront. 7 To see how static image analysis of a sheared interferogram can be used to measure wave front aberrations, we must examine the expression for spherical aberration plus tilt, and its sheared equivalent with some wedge in the direction orthogonal to shear: In the region near the x-axis (y is very small), and if the amount of shear, S, is also kept small the last expression above can be simplified to: 8 131 040 11 3 040 4 0 4 ) ,…”

Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror

“…One of these is a shearing method. [15][16][17][18] In this method, the real figure of the test optic can be reconstructed from the difference of the measured data before and after displacing. By subtracting the measured data after displacing from that before displacing, the system error is calculated and the finite-difference equation of the test figure is derived.…”