Rufino Díaz-Uribe

Null-screen testing of fast convex aspheric surfaces

A method for null-testing fast convex aspheric optical surfaces is presented. The method consists of using a cylindrical screen with a set of lines drawn on it in such a way that its image, which is formed by reflection on a perfect surface, yields a perfect square grid. Departures from this geometry are due to imperfections of the surface, allowing one to know if the surface is close to the design shape. Tests conducted with a full hemisphere and with the parabolic surface of a lens show the feasibility of the method. Numerical simulations show that it is possible to detect surface departures as small as 5 microm.

Testing fast aspheric concave surfaces with a cylindrical null screen

A noncontact test procedure to obtain the shape of fast concave surfaces is described. A cylindrical null screen with a curved grid drawn on it in such a way that its image, which is formed by reflection on a perfect concave surface, yields a perfect square grid is proposed. The cylindrical null screen design and the surface evaluation algorithm are presented. Experimental results for the testing of an elliptical mirror of 164 mm in diameter (f/0.232) are shown.

Quantitative evaluation of an off-axis parabolic mirror by using a tilted null screen

We report the testing of a fast off-axis surface based on the null screen principles. Here we design a tilted null screen with drop shaped spots drawn on it in such a way that its image, which is formed by reflection on the test surface, becomes an exact square array of circular spots if the surface is perfect. Any departure from this geometry is indicative of defects on the surface. Here the whole surface is tested at once. The test surface has a radius of curvature of r = 20.4 mm (F/0.206). The surface departures from the best surface fit are shown; in addition, we show that the errors in the surface shape are below 0.4 mum when the errors in the determination of the coordinates of the centroids of the reflected images are less than 1 pixel, and the errors in the coordinates of the spots of the null screen are less than 0.5 mm.

Testing a fast off-axis parabolic mirror by using tilted null screens

We propose the design of tilted null screens for testing off-axis segments of conic surfaces. The tilt allows us to control the size of the screen and the sensitivity of the test. For positive tilt angles the sensitivity is increased while the size of the screen is reduced in the sagittal caustic region and vice versa in the tangential caustic region. Further analysis and preliminary experimental results are presented for a fast off-axis concave parabolic mirror with an elliptical aperture. An offset distance of XC = 25.4 mm yields radius of curvature at the vertex R = 20.4 mm; major axis of the mirror DM = 49.4 mm; and minor axis Dm = 29.5 mm.

Conic that best fits an off-axis conic section

To help in the fabrication of off-axis conic sections, we present a method to approximate this off-axis section by an on-axis conic centered on the portion desired. This method is based on the method of continuum least squares to obtain the vertex’s curvature and conic constant of the fitted conic on-axis, given the curvature at the vertex and the conic constant of the parent conic from where we want the section and the size of that section. Simple analytic expressions for the curvature and conic constant are derived in terms of the parameters of the off-axis section.

Testing fast aspheric convex surfaces with a linear array of sources.

We describe a noncontact test procedure with which to obtain the shapes of fast convex surfaces. For this, an array of sources is positioned in a straight line and separated in such a way that the image by reflection on the surface consists of a set of equally spaced bright spots. By rotating the surface, we test different meridians such that, after 360 degrees, the entire surface is measured. We present the source array design and the surface evaluation algorithm. We found that, to reduce numerical error in the evaluation of the shape of the surface, a numerical integration must be performed by a method that uses parabolic arcs instead of the traditional method that uses trapezoids. Through some numerical simulations we analyzed the accuracy of the method by introducing random displacements into the measured data. We found that to measure the quality of the surface with accuracy better than 5 microm, we have to measure the coordinates of the centroids on the image plane with an accuracy better than 0.5 pixel, and we to have measure the positions of the linear sources with an accuracy better than 0.5 mm. Experimental results for the testing of a carbon fiber convex sphere of 383.6-mm diameter (f/0.398) are shown.

Detection limits of an internal-reflection sensor for the optical beam deflection method

The theoretical detection limit on angle deflection measurement when the quasi-critical internal-reflection method is used is calculated and compared with the more common method of using a bicell position-sensitive detector. Simple formulas for the sensitivity and resolution when the system is shot noise limited are given. It is shown that, even though the bicell detector is potentially much more sensitive for wide and well collimated beams, under typical laboratory restrictions, the internal reflection method may be more sensitive and have better resolution. It is argued that the internal-reflection method may be a tool in developing compact sensors based on the optical beam deflection method.

Caustics caused by refraction in the interface between an isotropic medium and a uniaxial crystal

In general, a caustic by refraction at an arbitrary surface is commonly known as a diacaustic. We study the formation of the diacaustic in a plane interface between an isotropic medium and a uniaxial crystal, for both ordinary and extraordinary rays, when the crystal axis is perpendicular to the plane of incidence and when it lies in the plane of incidence. For the latter case two special positions of the crystal axis with respect to the normal to the refracting surface for the extraordinary rays are treated.

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

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.

Profile testing of spherical surfaces by laser deflectometry

A method for testing the profiles of spherical surfaces is presented. It consists of measuring the transversal deflection of a reflected He-Ne laser beam when the surface is rotated around an axis located near its center of curvature. A set of formulas that enables us to calculate the shape of the profile as well as the decentering of the rotation axis is obtained. By using a simple experimental setup, we found the differences between the experimental profile with respect to the ideal one; the accuracy that was obtained is ~3 µm. The method may be improved and is useful for convex as well as for concave surfaces. With minor modifications it is possible to test large surfaces and weak aspherics.