Manuel Campos-García

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 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.

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.

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

In order to measure the shape of fast convex aspherics, such as the corneal surface of the human eye, we propose the design of a conical null-screen with a radial point distribution (spots similar to ellipses) drawn on it in such a way that its image, which is formed by reflection on the test surface, becomes an exact array of circular spots if the surface is perfect. Any departure from this geometry is indicative of defects on the evaluated surface. We present the target array design and the surface evaluation algorithm. The precision of the test is increased by performing an iterative process to calculate the surface normals, reducing the numerical errors during the integration. We show the applicability of the null-screen based topographer by testing a spherical calibration surface of 7.8 mm radius of curvature and 11 mm in diameter. Here we obtain an rms difference in sagitta between the evaluated surface and the best-fitting sphere less than 1 μm.

Design of a single flat null-screen for testing a parabolic trough solar collector

Abstract. We present a null-screen design for testing the shape quality of the reflecting surface of a parabolic trough solar collector (PTSC). This technique is inexpensive, the whole surface is tested at once, and it is easy to implement. For this, we propose the design of a flat null-screen perpendicular to the optical axis of the PTSC in such a way that it allows testing of the full aperture; we compute the caustic associated with the reflected light rays on the desired surface and analyze the parameters that determine the null-screen dimensions. Additionally, we perform a numerical simulation to analyze the accuracy of the method by introducing random displacement errors into the measured data. Accuracies >0.35  mrad were found to evaluate the quality of surfaces with this method. The errors in the determination of the coordinates of the centroids of the reflected images must be measured with an accuracy >0.5  pixels, and the errors in the coordinates of the spots of the null-screen must be <0.5  mm.

Sagittal and meridional radii of curvature for a surface with symmetry of revolution by using a null-screen testing method

An algorithm to compute the sagittal and meridional radii of curvature for a surface of revolution is presented. The sagittal radius is obtained from the surface normal, and the meridional radius is calculated from a function fitted to the derivative of the sagittal curvature by using the surface-normals raw data. A calibration spherical surface is tested by using the null-screen testing method. Experimental results of the spherical surface show that the sagittal and meridional radii of curvature differ by 2.600% and 2.604%, respectively, with respect to the actual radius of the calibration spherical surface.

Improving fast aspheric convex surface tests with dynamic null screens using LCDs.

A method for testing fast aspheric convex surfaces with dynamic null screens using LCDs is shown. A flat null screen is designed and displayed on an LCD monitor with drop-shaped spots in such a way that the image, which is formed by reflection on the test surface, becomes an exactly 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 position of the spots on the LCD can be changed in a dynamic way, to perform point-shifting of the image spots. The proposed procedure improves the dynamic point-shifting method. As has been shown previously, this process reduces the numerical error during the integration procedure, thereby improving the sensitivity of the test. The positioning accuracy for the screen spots is related to the LCDs spatial resolution. Results of the evaluation of a parabolic convex surface with f/#=0.22 are shown.

Measurement of aberrations of a solid elastic lens using a point-diffraction interferometer

There has been a considerable recent increase in the use of variable focal length lenses (VFLLs), especially as microlenses in photographic objectives, endoscopes, microscope objectives, etc. One distinguishing feature of these VFLLs is the presence of a mechanism whereby the shape of the lens and its geometrical parameters can be changed. A new type of variable focal length lens is introduced made from elastic material. It is placed inside a mechanical mount where radial forces can be applied to its perimeter. We also present the optomechanical design and the measurement of wavefront aberrations to the third and fifth order of a solid elastic lens (SEL). A point-diffraction interferometer is used as a wavefront sensor to test changes of the lens. Geometrical changes in the lens produce changes in the aberrations. Finally, the aberrations found in the SEL (without any application of stress) are compared with aberrations obtained by means of numerical ray trace. Some experimental results are also shown.