Point shifting in the optical testing of fast aspheric concave surfaces by a cylindrical screen

Abstract

A method for increasing the precision and sensitivity of the quantitative evaluation of fast aspheric surfaces through the null screen method is presented. This consists of applying small displacements to the cylindrical null screen along the optical axis. These movements allow a scan of the image spots over zones that with the analysis of a single image are more difficult to evaluate. The precision of the test is increased due to a greater density of sampling reducing the numerical errors during the integration. Results of the evaluation of an elliptical concave mirror on axis show that the numerical integration errors can be reduced from 20% for short paths to 80% for larger integration paths.

Deflectometry for specular surfaces: an overview

“…The final stepstone for convenient low-uncertainty evaluation was the introduction of the phase-shifting technique, created for interferometry in the 1970s and immediately adopted for fringe projection after sufficient digital storage and processing means became available [183][184][185]. Surprisingly, phase shifting has spread to deflectometry only around the turn of the millennium [7,158,[186][187][188][189][190][191][192] one reason may be that convenient flat-screen monitors for displaying modulated patterns were starting to become available at that time. As a result, moiré techniques are now largely obsolete in DM, and can in hindsight be interpreted as a complicated way (but necessary at the time) to reduce uncertainties.…”

Surface shape evaluation with a corneal topographer based on a conical null-screen with a novel radial point distribution

“…Second, the number of evaluation points is also increased, as is the evaluation time. Finally, in [33] it is shown that with a higher density of points the numerical errors introduced by the integration algorithm are reduced. The density, however, cannot be increased indefinitely because of the resolution of the laser printer and of the CCD camera.…”

“…The density, however, cannot be increased indefinitely because of the resolution of the laser printer and of the CCD camera. However, it is possible to increase the density of points of evaluation by considering the point shifting procedure by using a dynamic null-screen [33], this nullscreen could be implemented on an LCD monitor [34] and one can use chromatic [35] and/or monochromatic arrays of points [36].…”

Shape Measurement of Solar Collectiors by Null Screens

“…An important problem in the test with a null screen is that the integration method accumulates important numerical errors along the different selected integration paths. It is well known (Moreno-Oliva et al, 2008a) that a bound to the so called truncation error can be written as…”

“…This implies more spots in the design of the null screen; there is, however, a physical limit on the number of spots; if the spot density is too large,the spot images can overlap because of defocus, aberrations or because of diffraction. A method to increase the number of points, thus reducing the average separation between them, is to use the so called point shifting method (Moreno-Oliva et al, 2008a;Moreno-Oliva et al, 2008b). The basic idea is to acquire a total of m pictures, each with different null screen arrangement and containing n spots on the image; the spots will be shifted from their positions in other pictures, making a total of m×n evaluation points, with an average separation of…”