Showing papers on "Zernike polynomials published in 1977"

The circle polynomials of Zernike and their application in optics

Abstract: The Zernike polynomials are orthogonal functions defined on the unit circle, which have been used primarily in the diffraction theory of optical aberrations. A summary of their principal properties is given. It is shown that the polynomials, which are closely related to the general spherical harmonics, are especially useful in numerical calculations. In particular, by using the polynomials as a basis to represent the commonly encountered functions of optical theory, it is often possible to avoid numerical quadrature and computations are reduced to the simple manipulation of expansion coefficients.

Zernike test. 1: Analytical aspects.

Abstract: The Zernike test is extensively interpreted from an interferometric point of view. The discussion includes the optimization of the Zernike disk parameters (radius, phase, and transmittance) for low-order aberrations, and a method is provided for choosing the disk parameters so as to optimize test performance for maximum sensitivity and linear range. A signal-to-noise analysis predicts test sensitivity to be better than λ/100.

Zernike test. 2: Experimental aspects.

Abstract: A step-by-step procedure for the manufacture of Zernike disks and the design and fabrication of a laboratory Zernike test instrument are described. A laboratory wavefront error simulator is used to evaluate the low-order aberration measurement sensitivity of the Zernike test instrument. Measurement sensitivities were found to be better than λ/100 for all the low-order aberration types.

Multi-Wavelength Interferometric Testing

Abstract: We have built a modified Twyman-Green interferometer illuminated with a krypton laser. The configuration allows for center of curvature or autocollimation testing at various selected wavelengths. Software data reduction uses a Zernike polynomial fit to the wavefront. The interferograms are all made without moving the source, so the effects of axial color, lateral color, and chromatic variation of aberrations will exhibit themselves in a straightforward fashion in terms of the coefficients of the Zernike polynomials. Also, a scheme for using this information in the calculation of a polychromatic optical transfer function (OTF) has been developed. Requirements for the interferometer's optics are examined, and interferometer calibration discussed.