Author: JOSE ZACARIAS MALACARA HERNANDEZ
"Convex aspherical optical surface testing, has inherently several difficulties. They are considered as the most challenging to perform. Recent failures in achieving high performance telescopes like the Hubble Space telescope, have made a deep concern about the difficulties and importance of the tests. The importance in testing aspherical optical testing is evident from the constantly increasing papers in specialized journals around this subject. This document is built around three main subjects in three chapters. Chapter 1: Convex Surface Testing; Chapter 2: Projection of the Pupil in Non-Null Tests and Chapter 3: Digitization of Interferograms of Aspheric Wavefronts."
A least-squares procedure to find the tilts, curvature, astigmatism, coma, and triangular astigmatism by means of measurements of the transverse aberrations using a Hartmann or Shack–Hartmann test is described. The sampling points are distributed in a ring centered on the pupil of the optical system. The properties and characteristics of rings with three, four, five, six, or more sampling points are analyzed with more detail and better mathematical analysis than in previous publications.
The measurement of astigmatic lenses, optical surfaces or wavefronts are a highly studied problem and many different instruments have been commercially fabricated to perform this task. Many of them use a Hartmann arrangement to obtain the result. In this paper, we analyze with detail the algorithms that can be used to make the necessary calculations and propose several alternatives with different advantages and disadvantages. Different mathematical algorithms that are involved in the calculation process have been given whereas any description of the instrument itself is not proposed, but only the different mathematical algorithms that are involved in the calculation process.
Instead of measuring the wavefront deformations, Hartmann and Shack–Hartmann tests measure wavefront slopes, which are equivalent to ray transverse aberrations. Numerous integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., modal and zonal. Frequently, a least squares fit of the transverse aberrations in the 𝑥 direction and a least squares fit of the transverse aberrations in the 𝑦 direction is performed to obtain the wavefront. In this work, we briefly describe a modal method to integrate Hartmann and Shack–Hartmann patterns by means of a single least squares fit of the transverse aberrations simultaneously instead of the traditional 𝑥–𝑦 separate method. The proposed method uses monomial calculation instead of using Zernike polynomials, to simplify numerical calculations. Later, a method is proposed to convert from monomials to Zernike polynomials. An important obtained result is that if polar coordinates are used, angular transverse aberrations are not actually needed to obtain all wavefront coefficients.
Instead of measuring the wavefront deformations directly, Hartmann and Shack–Hartmann tests measure the wavefront slopes, which are equivalent to the ray transverse aberrations. Numerous different integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., modal and zonal. In this work we describe a modal method to integrate Hartmann and Shack–Hartmann patterns using orthogonal wavefront slope aberration polynomials, instead of the commonly used Zernike polynomials for the wavefront deformations.