In recent years, the correlation coefficient has been used as a tool for comparison between experimental and synthetic interferograms in algorithms of evaluation, in the areas of optical fabrication and testing. This coefficient has been used with the aim of eliminating the observer criterion during the fabrication process, and in this sense, to make a quantitative test to compare experimental and synthetic interferograms using the correlation as a parameter of evaluation. However, this coefficient is dramatically affected when laboratory conditions are not adequate. Therefore, in this work, we present a detailed analysis of the correlation behavior when interferograms with different values of visibility, Gaussian noise, and background illumination are evaluated/correlated. To analyze the correlation behavior, we simulated different interferograms, where these parameters were varied and examined how they affect the interference patterns. We found that a bad illumination dramatically affects the value of correlation, causing it to decrease to 0.1046, with σ = 0.1.
The present work shows the characterization of a transmissive spatial light modulator (SLM) trademark CRL-Opto and model XGA2L11. This modulator will be used as a variable retarder to generate different polarization states which are produced when the different gray levels from 0 to 250 are displayed in the SLM. So, it is important to determine its response and linear range of work, these parameters were determined experimentally. For this, the SLM was tested with four different wavelengths: red (633 nm), orange (612 nm), violet (405 nm), and green (550 nm). For doing this, the SLM was placed between two linear polarizers aligned first in parallel and then in perpendicular form. The gray levels were varying uniformly from 0 to 250 with increments of 10 in gray levels, and the gray levels were displayed over all the pixels of the SLM. The different intensities for each gray level were measured with a Thorlabs detector model PM100A. Finally, we show the results obtained for each wavelength where we found out that the best linear response was for the green laser with a wavelength of 550 nm.
In this work, we compare two techniques to make point-diffraction interferometers (PDI): microlithography and the mercury drop method to know with which of these the best results can be obtained. For the comparison, we used the wavefront generated by a commercial reference surface of λ/20 analyzing the interference pattern generated by the PDIs, we obtained information from the wavefront generated by the pinhole. Several PDIs were created and analyzed to have a statistical error information of both techniques.
In this work we describe the use of Finite Element Analysis software to simulate the deformations of an optical mirror. We use Finite Element Method software as a tool to simulate the mirror deformations assuming that it is a thin plate that can be mechanically tensed or compressed; the Finite Element Analysis give us information about the displacements of the mirror from an initial position and the tensions that remains in the surface. The information obtained by means of Finite Element Analysis can be easily exported to a coordinate system and processed in a simulation environment. Finally, a ray-tracing subroutine is used in the obtained data giving us information in terms of aberration coefficients. We present some results of the simulations describing the followed procedure.
In this work, we describe the well-known methods of cutting and shaping for optical glass materials. These operations are very important in optical workshops and needs to be well defined at the beginning of the optical fabrication process. In this work we show the first steps to fabricate prism components for the MEGARA instrument that is being developed to work with the GRANTECAN. We present a review of the techniques used at INAOE´s Optical workshop for cutting blanks of optical glasses with an extensive use in optical fabrication; besides that, we present the process of shaping of these optical glasses just before they enter to the grinding and polishing processes. We present some results showing the described processes and some tips for the methods used in the optical workshop including the use of the necessary supplies, tools, and machinery.
In this work, we show a simple device that helps in the use of the sub-aperture stitching method for testing convex surfaces with large diameter and a small f/#. This device was designed at INAOE’s Optical work shop to solve the problem that exists when a Newton Interferometer and the sub-aperture stitching method are used. It is well known that if the f/# of a surface is small, the slopes over the surface increases rapidly and this is critical for points far from the vertex. Therefore, if we use a reference master in the Newton interferometer to test a convex surface with a large diameter and an area far from the vertex, the master tends to slide causing scratches over the surface under test. To solve this problem, a device for mounting the surface under test with two freedom degrees, a rotating axis and a lever to tilt the surface, was designed. As result, the optical axis of the master can be placed in vertical position avoiding undesired movements of the master and making the sub-aperture stitching easier. We describe the proposed design and the results obtained with this device.
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.
In this work we show a new technique for sub-structured Ronchi rulings generation and the calculation of the irradiance profile produced by this ruling. Commonly, these rulings are used to increase the spatial resolution in the Ronchi test and allow us to observe smaller surface defects. To generate the sub-structured Ronchi ruling we propose a combination of several classical Ronchi rulings with different frequency, in order to calculate the irradiance profile generated by the substructured Ronchi ruling, we propose a combination of the irradiance profile generated by each combined classical Ronchi ruling. The comparison of synthetic and experimental Ronchigrams of spherical surfaces are shown. We found that the proposed method can reproduce reliably the experimental irradiance profile.
This work arises based on the idea proposed by Millered et al. in 2004, where they show how to get in one shot interferograms with phase shift using a mask with micro-polarizers, in this work we pretend to obtain phase shift in localized areas of an interferogram using the properties of polarization and the pixelated configuration of a liquid crystal display (LCD) for testing optical surfaces. In this work we describes the process of characterization of a liquid crystal display CRL Opto and XGA2P01 model, which is introduced in one arm of a Twyman Green interferometer. Finally we show the experimental interferograms with phase shifts which are caused by different gray levels displayed in the LCD.
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%.
A method based on a variant of genetic algorithm is proposed to obtain the wavefront aberrations of a real ronchigrams using only one ronchigram without using polynomial fit or trapezoidal integration. The recovery of the aberration coefficients of third order is achieved by assigning random values but controlled in the equation of the optical path difference (OPD) which is given for a lateral shear interferometer. The proposed method retrieves the coefficients of the polynomial of the analyzed Ronchigram in a reliable and accurate way.