Fermín Granados-Agustín

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.

Phase shifting interferometry using a spatial light modulator to measure optical thin films

This work describes a process for measuring thin film steps, using phase shifting interferometry (PSI). The phase shifts are applied only in the region where the thin film steps are located. The phase shift is achieved by displaying different gray levels on a spatial light modulator (SLM Holoeye LC2012) placed in one arm of a Twyman-Green (T-G) interferometer. Before measuring the thin film steps, it was necessary to quantify the phase shifts achieved with this SLM by measuring the fringe shifts in experimental interferograms. The phase shifts observed in the interference patterns were produced by displaying the different gray levels on the SLM one by one, from 0 to 255. The experimental interferograms and the thicknesses of the thin film steps were successfully quantified, proving that this method can be used to measure thin films by applying the PSI method only on the region occupied by them.

Algorithm for Ronchigram recovery with random aberrations coefficients

Abstract. We present the validation for Ronchigram recovery with the random aberrations coefficients (ReRRCA) algorithm. This algorithm was proposed to obtain the wavefront aberrations of synthetic Ronchigrams, using only one Ronchigram without the need for polynomial fits or trapezoidal integrations. The validation is performed by simulating different types of Ronchigrams for on-axis and off-axis surfaces. In order to validate the proposed analysis, the polynomial aberration coefficients that were used to generate the simulated Ronchigrams were retrieved. Therefore, it was verified that the coefficients correspond to the retrieved ones by the algorithm. The results show that the ReRRCA algorithm retrieves the aberration coefficients from the analyzed Ronchigram with a maximum error of 9%.

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.

Ronchi test with variable-frequency rulings

We present a new method for testing an optical surface. It uses the Ronchi test with variable-frequency rulings and a liquid-crystal display. The rulings can be formed by substructuring the spacing of a Ronchi ruling or combining several classical Ronchi rulings in a single variable-frequency ruling. This change allows us to observe smaller de- fects on the surface, because it enlarges the spatial-frequency domain of the ruling, and a larger dynamic range of detection of the Ronchi test can be obtained instead of increasing the resolution of the detection of the Ronchi test by iteratively changing classical Ronchi rulings with higher line density. As a result, we have found that it is possible to measure defects on a optical surface that are of size 57 nm /11.

Classical Hartmann test with scanning

In order to introduce many more evaluation points during the Hartmann test, the scanning of the screen across the pupil is proposed; after each step of the scan a different image of the bright spots is obtained. Basic ideas about how to design radial and square screens for the scanning are presented. Radial screens are scanned by rotation, whereas for square screens a linear inclined scan is enough to introduce many more evaluation points along two independent directions. For square screens it is experimentally shown that the lateral resolution of the test is improved.

Ronchi test with equivalent wavelength

In this work we present an experimental proposal to evaluate optical surfaces with high slopes or with infrared wavelengths based on the Ronchi test as well as on the concept of equivalent wavelength. A spatial modulator is used in the implementation of the Ronchi test, and a white LED with different color filters is employed in order to generate different wavelengths. Two Ronchigrams with incoherent light, each one for a different color, are registered and computationally processed, thus generating a third one with an equivalent wavelength. The results obtained show that it is possible to generate patterns with traditional rulings and substructured sequences of Katyl. Additionally, we discuss some of the limitations of employing different rulings. Finally, we found that appropriate image enhancing algorithms allow us to improve the visibility of the resulting fringes and thus obtain a better analysis.

Building a parabolic solar concentrator prototype

In order to not further degrade the environment, people have been seeking to replace non-renewable natural resources such as fossil fuels by developing technologies that are based on renewable resources. An example of these technologies is solar energy. In this paper, we show the building and test of a solar parabolic concentrator as a prototype for the production of steam that can be coupled to a turbine to generate electricity or a steam engine in any particular industrial process.

Testing a paraboloid mirror using annular subapertures without auxiliary optics.

In an optical shop, during the process of manufacture of optical surfaces, is necessary the testing of the surfaces until to obtain the quality required; there are traditional techniques divided mainly in two groups: the geometric tests (Ronchi, knife, etc.), and inteferometric tests (Newton, Fizeau, etc.). When the surfaces are aspherical, it is difficult to use these techniques, because is required an elaborate experimental arrangement for the surface under test, and is necessary to use an auxiliary optics with the same or superior optical quality them the surface under test. In this work we introduce a new method for testing conic surfaces using a Fizeau interferometer, without auxiliary optics o compensators, in particular we applied this testing to a paraboloidal surface.

Substructured Ronchi gratings from the linear combination of classical gratings

Abstract. Substructured Ronchi gratings are used to sharpen and increase the number of fringes in Ronchigrams, thereby increasing their spatial resolution and allowing greater accuracy in the evaluation of a surface under test. This work presents a simple method for generating substructured Ronchi gratings and for calculating the intensity pattern produced by this type of grating. For this, we propose the generation of this kind of grating from the linear combination of classical gratings; the pattern of irradiance produced by these Ronchi gratings will be a linear combination of the intensity patterns produced by each combined classical grating. A comparison between theoretical and experimental Ronchigrams was obtained by analyzing a parabolic mirror.