By correlating bi-Ronchigram images, surface errors without any supposed symmetry are evaluated. No approximation and interference orders are needed. First, only one experimental bi-Ronchigram (Ronchigram with a square grid) image was recorded. Second, given a surface parameter set (curvature radius, conic constant, and/or symmetric and asymmetric deformation coefficients), a bi-Ronchigram image is simulated and correlated with the bi-Ronchigram experimental image. Third, genetic algorithms are used to find the parameters for which the correlation coefficient reaches its maximum value. Finally, the parameters of the experimental surface are estimated. Evaluations of curvature radius, conic constant, and error functions for reflecting surfaces will be shown.
Nowadays, there is a demand for more efficient opto-mechanical mounts which allow for the implementation of robust optical arrays in a quick and simple fashion. That is to say, mounts are needed which facilitate alignment of the optical components in order to perform the desired movements of each component. Optical testing systems available in the market today are costly, heavy and sometimes require multiple kits depending on the dimensions of the optical components. In this paper, we present the design and analysis of a mechanical system with some interchangeable basic mounts which allow for the application of both Ronchi and Fizeau tests for the evaluation of concave reflective surfaces with a diameter of 2 to 10 cm. The mechanical system design is done using the methodology of product design process, while the analysis is performed using the commercial software SolidWorks.
In this paper, we propose the design of a robotic system to semi-automatically align components in the Ronchi test; the robotic system will align the Ronchi tester with the surface being tested. In this work, we present the control system design of a rail system with two degrees of freedom, which allows semiautomatic alignment of the Ronchi tester with the surface in production. Informative visual markings (IVM) are used to achieve this [1]. The IVM help locate the system coordinates of the optical surface with respect to the basic system coordinates of the rail system. Quantification of the alignment is performed using the value of non-integer interference order, which is calculated to generate the simulated ronchigram which more closely resembles the experimental ronchigram [2].
To estimate qualitatively the surface errors with Ronchi test, the experimental and simulated ronchigrams are
compared. Recently surface errors have been obtained quantitatively matching the intersection point coordinates of
ronchigrama fringes with x-axis . In this case, gaussian fit must be done for each fringe, and interference orders are used
in Malacara algorithm for the simulations. In order to evaluate surface errors, we added an error function in simulations,
described with cubic splines, to the sagitta function of the ideal surface. We used the vectorial transversal aberration
formula and a ruling with cosinusoidal transmittance, because these rulings reproduce better experimental
ronchigram fringe profiles. Several error functions are tried until the whole experimental ronchigrama image is
reproduced. The optimization process was done using genetic algorithms.
It is well known that astigmatic surfaces are obtained when surfaces are polished in commercial polishing machines,
which are designed to produce surfaces of revolution. The authors of this paper do not know an explanation for this
result.
In order to understand why the wear is a function of the angular position on the glass, we measured the dragging force
applied from a rotating glass to a small fixed tool of Teflon®. These experiments were done for several tool radial
positions by using a table travel X-Y.
With the aid of a force sensor dragging force as a function of the time was measured. We found that dragging force is a
periodic function with fundamental frequency equal to the angular velocity of the glass, indicating that there is more
wear on one glass angular position than another. We also found that this result is independent of the radial position of the
tool. We used a polisher concentration of 20 degrees Baumé which is recommended by the supplier. And the amount of
polisher per time and area units, dragged by the tool, remained constant for each one of the radial positions of the tool.
In the manufacturing process of an optical surface with rotational symmetry the ideal ronchigram is simulated and
compared with the experimental ronchigram. From this comparison the technician, based on your experience, estimated
the error on the surface. Quantitatively, the error on the surface can be described by a polynomial e(ρ2) and the
coefficients can be estimated from data of the ronchigrams (real and ideal) to solve a system of nonlinear differential
equations which are related to the Malacara formula of the transversal aberration. To avoid the problems inherent in the
use of polynomials it proposed to describe the errors on the surface by means of cubic splines. The coefficients of each
spline are estimated from a discrete set of errors (ρi,ei) and these are evaluated by means of genetic algorithms to
reproduce the experimental ronchigrama starting from the ideal.
Wear profiles obtained with tools that oscillate in one direction and simultaneously displace perpendicularly in another are classified and analyzed. Profiles are obtained for different-shape tools and oscillation amplitudes. Analytical and numerical calculations of wear were made with known rectangular, elliptical, and diamond tool shapes. In the test, both sets of calculations turned out to be equal. A generalized equation was used to describe and speed up numerical calculations of the inner points of both known and other asymmetrical tools. The wear profiles obtained are of great help in enabling us to determine the shape, size, and oscillation amplitude of a tool to achieve a desired wear. Experimental results show that these simulated profiles can be obtained in practice using square, circular, and diamond tool shapes.
Alberto Cordero-Dávila, Leonardo Téllez-Arriaga, Jorge González-Garcia, Carlos Ignacio Robledo-Sánchez, Jorge Cuautle-Cortéz, José de Jesús Díaz-Anzures, Luis Alberto Martinez-Medina
An adaptive lens can be made from plastic and elastic material, its focal distance can be changed by appling radial forces at the lens border ring. To make these kind of lenses it is necessary to figure molds. However, these molds can not be figured by using rigid tools for rapid surfaces. Then we are developing a new technique based in a linear array of independent sub-tools. A linear tool consists of subtools, the pressures of each one can be regulated according to the measured surface errors. The pressures are given by weights put over each sub-tool. By using genetic algorithms the pressure values of each subtool have been calculated in order to obtain the optimal wear. They are shown numerical and experimental results for several axisymmetrical surfaces.
This study presents results obtained from the exact tracing of rays of an adaptive lens, that is, a liquid lens with transparent elastic surfaces. Because the elastics surfaces are deformed by a liquid, they acquire different curvatures depending on the difference in pressures of the liquid and of the environment. Images generated by this type of lens are simulated with a ray-tracing computer program, considering that each surface can be modeled with concentric spherical rings with different curvatures; this is because the elastic coefficients of the plastic materials used are non-linear.
The wear produced by free-pinned tools is difficult calculate, since their angular movement is not entirely predictable. First, we analyze the wear produced with free-pinned ring tools using both simulations and experiments. We conclude that the wear of an incomplete ring is directly proportional to its angular size, independently from the mean radius of the ring. Second, we present an algorithm for the calculation of the wear produced by free-pinned petal tools, since they can be considered as a linear combination of incomplete free-pinned ring tools. Finally, we apply this result to the enhancement of a defective flat surface and to aspherate a concave spherical surface.
The objective of this paper was to generate Sidel polynomials using a LCD in a Fourier processor. Our proposal was to use this PCL, due to the fact that it is a small device that does not consume too much energy, with several active elements, and we verified the speed with which it is possible to work with optical processing by changing the images on the screen. Since this system is easy to construct, stable and accessible, we want to use it in the future as a corrector system, due to the fact that it can evaluate the system using a program and with the LCD to try to correct the aberrations that it has.
The objective of this paper was to generate Sidel polynomials using a LCD in a Fourier processor. Our proposal was to use this LCD, due to the fact that it is a small device that does not consume too much energy, with several active elements, and we verified the speed with which it is possible to work with optical processing by changing the images on the screen. Since this system is easy to construct, stable and accessible, we want to use it in the future as a corrector system, due to the fact that it can evaluate the system using a program and with the LCD to try to correct the aberrations that it has.
We obtained novel analytic expressions which permit us to realize the optical design of any thick lens, this analysis include both first and exact order design. We employ the conic constant of the first surface to correct the marginal spherical aberration. We analyzed both finite and infinite conjugates cases. Examples done with our methodology also show good agreement with commercial optical design programs.
In optical workshops, Ronchi test is used to determine the optical quality of any concave surface while the surface is in the polishing process its quality is verified based on the technician experience. We describe a method based on digital image superposition between a real Ronchigram with an ideal obtained by a computer simulation program. The real Ronchigram image is processed by an erosion algorithm to obtain its skeleton. We supposed a linear relationship between the separation of each fringe for both experimental and ideal fringes, to obtain in this way the desired surface. Such method allows us to compute in a direct way the transversal aberration of the surface under test.
In order to overcome classic polishing techniques, a novel hydrodynamic radial polishing tool (HyDRa) is presented; it is useful for the corrective lapping and fine polishing of diverse materials by means of a low-cost abrasive flux and a hydrostatic suspension system that avoids contact of the tool with the working surface. This tool enables the work on flat or curved surfaces of currently up to two and a half meters in diameter. It has the advantage of avoiding fallen edges during the polishing process as well as reducing tool wear out and deformation. The functioning principle is based on the generation of a high-velocity, high-pressure, abrasive emulsion flux with radial geometry. The polishing process is repeatable by means of the control of the tool operational parameters, achieving high degrees of precision and accuracy on optical and semiconductor surfaces, with removal rates of up to 9 mm3/hour and promising excellent surface polishing qualities. An additional advantage of this new tool is the possibility to perform interferometric measurements during the polishing process without the need of dismounting the working surface. A series of advantages of this method, numerical simulations and experimental results are described.
In the polishing process, the wear tends to be greater when the tool extends beyond the edge of the workpiece. A linear pressure distribution (between the tool and the workpiece) has been used to explain this effect, however, this model also can predict negative pressures. This could mean that material is deposited instead of being removed. We present a new pressure distribution proposal, which presents like a skin effect. This means that the pressure is significantly higher at the border points than at internal points of the glass. With this model the material removal at the border points is increased considerably since, according to Preston, the wear is proportional to the pressure. This pressure distribution model is applied to calculate the wear produced by a square tool on a glass border moving along straight lines.
We report experimental results and analysis about a new hydrodynamic radial tool (HyDra, patent pending), which expels a suspension of water and polishing particles radially on glass. With this method it is possible to locally shape optical surfaces. The depth of material removed by HyDra grows linearly with the time. The removal rate is independent of the velocity between the tool and the glass element. The HyDra has been used to fabricate successfully an optical flat and Schmidt surface.
Optical testing of the 2.1-m telescope in San Pedro Martir, Observatorio Astronomico Nacional de Mexico, by the methods of wavefront curvature sensing and bi-Ronchi analysis, has shown that the telescope suffered of large amounts of astigmatism. We identified these as due to improper primary mirror support and developed an active control system to correct for it. The number and position of the actuators were decided in accordance to the flexural modes that needed to be corrected, resulting in a system of 18 pressure controlled pneumatic actuators, with an outer loop that verifies the load at three hard points. A PID algorithm and matrix inversion are fundamental parts of this outer loop, that guarantees that the M1 mirror is tilted as a rigid body to maintain it properly aligned. The successful performance of the system to correct low order aberrations is reported.
We propose to construct an arrangement of several spheres of Hindle, used like element optic assistants in order to prove mirrors convex hyperbolic of several characteristics, like that, their dimension is reduced.
It is analyzed the two mirrors conic constants of a reflecting telescope design for which the spherical aberration is exactly corrected. This condition is reached by means of a formula for a secondary mirror conic constant, as function of other telescope parameters.
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