In this work we describe how to perform virtual experiments by deforming our ideal device with translations and rotations of each component, then we determine which are the minimal deformations that can be detected (sensibility) and how much does they affect the results of the measurement (sensitivity), a necessary endeavor since systematic errors due to misalignment of the components may lead to poor performance of optical systems, especially those used to measure optical components. The simulation of the passage of light is computed using a system of equations obtained from the vector reflection law.
In this work we report the design of a conical corneal null-screen compact topographer, which uses a mobile device to capture null-screen reflection produced by the posterior corneal surface. The instrument features a head holder like those of virtual reality headset with the aim of align the topographer. For corneal topography the device is calibrated by testing a reference surface where the geometrical parameters such as the radius of curvature and the conic constant, are obtained. We present examples of surface topography measurements on some human corneas.
One of the problems that have manufacturers of aspheric and freeform surfaces is the local measurement of the shape, in order to ensure the performance of the surface. In this paper we present an alternative method to measure local radii of curvature of systems with symmetry revolution, using the Point Diffraction Interferometer technique (PDI). To implement this proposal a certified plane wavefront is used as reference light source, and the PDI as sensor element for measuring the local radii of curvature. We proposed to use a PDI due to its high sensitivity because is a common path interferometer and generate interference only when there is an only point a single convergence which is produced from an annular region of the surface, and the annular region is associated to each local curvature center. Experimental results are shown for one aspherical surface with different rates of change in their slopes for each region of the surface, showing the versatility of the proposal and its possible use, including free-form surfaces without symmetry of revolution.
In this work we report the design of a null-screen for corneal topography. Here we assume that the corneal surface is an ellipsoid with a diameter of 12 mm and a radius of curvature of 7.8 mm. To avoid difficulties in the alignment of the test system due to the face contour (eyebrows, nose, or eyelids), we designed a compact conical null-screen with spots drawn in such a way that its image, which is formed by reflection on the test surface, it becomes an exact semi-radial array of circular spots if the surface is perfect. To validate our proposal, we perform topography measurements of a reference surface and some human corneas using a probabilistic algorithm. The results obtained with our algorithm were consistent and we can recover the shape of the surface with accuracy.
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.
WEAVE is the new wide field multi-object and integral field survey facility for the prime focus of the 4.2 m William Herschel Telescope. WEAVE fiber-fed spectrograph offers two resolutions, R ~ 5000 and 20,000. The dual-beam spectrograph has two cameras: the blue one optimized for the wavelength interval of 366 - 606 nm and the red one for 579 - 959 nm. Each camera is formed by eight lenses, one aspherical and seven spherical. The lenses of the red camera are identical to the lenses of the blue camera only differentiated by the anti-reflection coating wavelength range. The diameter of the largest surface is 320 mm while of the smallest is 195 mm. INAOE, as a member of the collaboration is responsible of the manufacturing of the 14 spherical lenses and the collimator mirror. Here, we describe the main characteristics of WEAVE high precision cameras lenses, the manufacturing challenges giving the combination of OHARA glasses properties, dimensions and specifications. We discuss the solutions developed to achieve the very demanding specifications.
In this work, the topography of human corneas is evaluated with a conical corneal topographer based on the null-screen method. Geometrical parameters such as the radius of curvature and the conic constant, are obtained. Additionally, elevation, sagittal curvatures and meridional curvature maps can be calculated with the proposed method. Here, it is assumed that the shape of the cornea surface is an aspherical surface. To validate our proposal, we compare the results with those obtained by a commercial corneal topographer.
We extend the principles of the null-screen method for testing fast aspheric surfaces with polynomial expansion. We
present the formulae to design the null-screen in such a way that the image on the CCD is a perfect array circular points;
the departures of the surface from a perfect shape are observed as deformations of the array in the image. For the testing
of fast aspherics with polynomial expansion, we propose some geometrical configurations. In addition, we perform an
analysis of the deformations of the image of the null-screen reflected by the testing surface due to the slop defects of the
surface. Experimental results for the testing fast aspherics are shown. The main advantages and the limitations of the
method will be discussed.
MEGARA is the new IFU and multiobject spectrograph for Gran Telescopio Canarias. The spectograph will offer spectral resolution Rfwhm~ 6,000, 12,000 and 18,700. Except for the optical fibers and microlenses, the complete MEGARA optical system has been manufactured in Mexico. This includes a field lens, a 5-lenses collimator, a 7-lenses camera and a complete set of volume phase holographic gratings with 36 flat windows and 24 prisms. All these elements are very large and complex, with very efficient antireflection coatings. Here the optical performance of MEGARA collimator and camera lenses and the field lens is presented.
MEGARA (Multi-Espectrógrafo en GTC de Alta Resolución para Astronomía) is the new integral-field and multi-object optical spectrograph for the 10.4m Gran Telescopio Canarias.. It will offer RFWHM ~6,000, 12,000 and 18,700 for the low- , mid- and high-resolution, respectively in the wavelength range 3650-9700Å. .The dispersive elements are volume phase holographic (VPH) gratings, sandwiched between two flat Fused Silica windows of high optical precision in large apertures. The design, based in VPHs in combination with Ohara PBM2Y prisms allows to keep the collimator and camera angle fixed. Seventy three optical elements are being built in Mexico at INAOE and CIO. For the low resolution modes, the VPHs windows specifications in irregularity is 1 fringe in 210mm x 170mm and 0.5 fringe in 190mm x 160mm. for a window thickness of 25 mm. For the medium and high resolution modes the irregularity specification is 2 fringes in 220mm x 180mm and 1 fringe in 205mm x 160mm, for a window thickness of 20mm. In this work we present a description of the polishing techniques developed at INAOE optical workshop to fabricate the 36 Fused Silica windows and 24 PBM2Y prisms that allows us to achieve such demanding specifications. We include the processes of mounting, cutting, blocking, polishing and testing.
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.
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.
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.
The preliminary results in the fabrication of off-axis optical surfaces are presented. The propose using the conventional polishing method and with the surface under mechanical stress at its edges. It starts fabricating a spherical surface using ZERODUR® optical glass with the conventional polishing method, the surface is deformed by applying tension and/or compression at the surface edges using a specially designed mechanical mount. To know the necessary deformation, the interferogram of the deformed surface is analyzed in real time with a ZYGO® Mark II Fizeau type interferometer, the mechanical stress is applied until obtain the inverse interferogram associated to the off-axis surface that we need to fabricate. Polishing process is carried out again until obtain a spherical surface, then mechanical stress in the edges are removed and compares the actual interferogram with the theoretical associated to the off-axis surface. To analyze the resulting interferograms of the surface we used the phase shifting analysis method by using a piezoelectric phase-shifter and Durango® interferometry software from Diffraction International™.
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.
It is well known that the Ronchi test can be used to measure the derivative of the optical path difference of a
wavefront . Therefore when the Ronchi test is used to determine the wavefront of the surface under test, two
orthogonal Ronchigrams are required to reconstruct the surface . We present a simple method to recovery the
wavefront with 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 sheared interferometer. Since the Ronchi test can be
seen as a variation of this type of interferometer , namely, the OPD for the Ronchi test is given by the difference
between the original wavefront W(x,y) and the sheared wavefront W(x + Δx,y), resulting in the generation of
various Ronchigrams, which are compared with the Ronchigram under analysis. The generated Ronchigram
with lower RMS (Root Mean Square) must have the highest correlation with the Ronchigram analyzed, since the
RMS is inversely proportional to the correlation. For some simulated Ronchigrams which were generated by
introducing Gaussian noise, some results are shown. The proposed method retrieves in a reliable the coefficients of
the polynomial of the analyzed Ronchigram in a reliable and accurate way.
In this paper, some concepts and results associated with the interferometric concept of effective wavelength have been applied for the evaluation of optical surfaces. This testing technique measures the wavefront slope instead of the contour
of the wavefront, like in the conventional interferometry. Therefore in this paper we present two methods of analysis of
optical surfaces with the Ronchi test. First, we described a procedure to evaluate surfaces employing the effective
wavelength in the Ronchi test . Our results were computationally processed in order to reconstruct the wavefront of a
particular mirror by means of the effective wavelength. A second proposal technique of analysis is based on the change
of the traditional analysis of a ronchigram to a method by a proper scaling of the shearing interferogram, via the
equivalent wavelength. The effective wavelength and equivalent wavelength are distinct concepts and are independent of
the wavelengths used in the image registering process. Comparisons of the Zernike Polynomials for each wavefront with
a reference wavefront show, the differences between both methods. Finally, we discuss some advantages and
disadvantages of each of the proposed analysis and mention the principal factors to improve our results.