Nowadays, optical systems commonly use either aspheric or free-form surfaces to improve their performance; however, to ensure that the manufactured surfaces become successful in concordance with to the nominal design, some geometrical parameters such as radius of curvature, conic constant, aspheric coefficients, etc., must be measured, including the surface shape under test. In this work, we propose a simple method to evaluate the optical quality of a plano-convex aspheric lens, where the convex face is modeled as an aspheric or free-form surface. We design a non-uniform pattern on the plane face of the plano-convex lens, to obtain a uniform pattern on a predefined detection plane by using the law of refraction in vector form. Additionally, implementing numerical simulations, we calculate the synthetic images produced through a predefined optical surface that we will use as if they were obtained from an experimental test. Finally, we apply an iterative method to retrieve the shape of the surface by using the normal vector field to demonstrate the feasibility of our proposal.
We present experimental results for testing concave optical surfaces by the Shack–Hartmann (S–H) test, where a set of microholes is used instead of the array of lenses employed in the original (S–H) plate.
In recent years, with technological advances, head-mounted display systems (HMDs) for virtual reality (VR) and augmented reality (AR) have been adopted for their applications in the military, government, education, training, medical visualization, aerospace, entertainment industries, and tourism. For this reason, a compact and light HMD but without sacrificing their performance is necessary. In this paper, the optical design of a lightweight and compact head-mounted display (HMD) system is proposed. We use an off-axis three-mirror system (OTS) with freeform surfaces for the correction of the aberrations and obtain a wide field of view (FOV), a compact structure with an exit pupil size over 7 mm and eye relief of 25 mm.
New hydrodynamic improvements have been developed in order to enable pulsed polishing with the HyDRa system. The operational parameters of the tool are not affected by these modifications, i.e., tool bias and the tool’s floating capability are not lost, and a linear erosion function is produced. The minimum removal is no longer ruled by maximum computer numerical control speed, allowing for high-precision removal that can be taken from zero to the maximum attainable of the tool, in minimum increments of 3.5 nm / ms. This modification also improves the convergence rate of the polishing process toward the desired surface. This development guarantees a high-speed, pulsed operation that enables the tool to be used in a variety of polishing modes, ranging from discrete pixel to continuous pulse width modulation (PWM) polishing. This new capability opens a wide range of applications that can now be tackled with the system, such as zonal and tessellated polishing. PWM capability also allows for simultaneous, multi-head polishing of large optical surfaces.
We present a new optical design of an off-axis three-mirror system (OTS) that is corrected for spherical, coma, astigmatism, and field curvature aberrations. Our design methodology begins using paraxial theory and continues with the third-order approach for a coaxial three-mirror system (CTS) with a wide field of view and high resolution. We propose to use only two optical elements because the primary and tertiary mirrors will be integrated in a single optical element, the secondary mirror will be the other optical element. For our final design, we will use only off-axis surfaces. Thus it will be possible to obtain a compact, light, easy-to-align optical system with high stability. However, when the CTS is transformed into an OTS, new aberrations are generated. The last step in our methodology is to use freeform surfaces to compensate for new aberrations. With this methodology, a limited diffraction system is obtained.
This paper proposes the design of an anastigmatic three-mirror telescope using freeform surfaces for the correction of spherical aberration, coma, astigmatism, and field curvature, allowing a wide field of view (FOV) and high resolution. For the structure of this telescope, it is proposed to use only two optical elements where the primary and tertiary mirrors are integrated into an only optical element and the secondary mirror in the other, thus achieving a considerable reduction in the difficulty of alignment and assembly. To achieve a high performance of the telescope, the system was decentered (offaxis design), avoiding the loss of energy due to the obscuration of the M2 in the on-axis system. In addition, to solve the difficult access to the focus.
To measure the quality of optical surfaces, one of the most used methods is the deflectometry. To implement this technique, a screen is used to choose some incident rays on the surface under test. Subsequently, the intersection of the rays is measured, after having passed through the surface, in a detection plane perpendicular to the optical axis. With the coordinates of the points in the detection plane, the normal vectors are determined in each point of the surface under test. The process is simple if the incident rays are chosen in a configuration called null, that is, in the detection plane the measured points will be distributed in a uniform configuration, rectangular, circular, radial, etc. In this work we present the numerical simulations, considering an incident spherical wavefront in the null screen that is placed at an arbitrary position between the source and the flat surface of an aspheric lens that was used in the experimental arrangement. In the simulations it is expected to obtain a uniformly distributed arrangement of spots, which will be compared with the experimental results.
The design of a two-mirror telescope using a free-form surface for the primary mirror, to obtain a compensation of the spherical and coma aberrations, in the entire pupil of the telescope is proposed. In this design, the conic constant (𝑘1 ) of the primary mirror is a function of the heights, measure from the center to the edge of primary mirror. In this method, we use the exact ray tracing to find the optical path length (OPL) for each ray that intersect the primary mirror at different distances measured from the center of the primary mirror. The OPL is calculated with the sum of the distances that each ray travels until reaching the plane of the image, and the sum of the distances for a paraxial axial ray. From the optical path difference (OPD) of a set of rays, we obtain a set of values of the conic constant that guarantees that the OPD has a value of zero for each incident ray height. With the set of values of the conic constant it is possible to obtain the shape of the surface of the primary mirror.
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.
The tendency in the manufacture of large telescopes that working in visible light, has improve the manufacture of large mirrors by the use off-axis segments, which must be aligned with very high precision in order of fractions of wavelength for the optimal operation. In this paper we present a new method for alignment segments of a big telescope, where the positions of the images produced by each off-axis segment, of a point source placed at center of curvature, the primary mirror. These positions can be known by exact rays tracing, considering the aberrations produce in each off-axis segment. Consequently, each point source is not on the optical axis of the system. Some numerical simulations are shown to establish the accuracy achieved with the proposed method.
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.
One of the most used methods to measure the quality of optical surfaces by light transmission is the de ectometry. To implement this technique, an arbitrary ray selector is used to choose some incident rays. Measuring the intersection of the rays refracted by the surface, in a posterior detection plane perpendicular to the optical axis, the normal at the surface under test, it is determined. Whith measurement points, the shape of the surface is determined by their integration. The process is simple if the incident rays are chosen in a called null configuration, since it is expected that all refracted rays will strike a predetermined ordered array in the detection plane. To numerical calculation we using an ideal surface on this test. In order to full measuare of the surface on simulation, we used vector form of exact ray tracing. To carry out the necessary numerical simulations for a null screen, we considering a point light source and the selector placed in arbitrary position between the point source lens of the test. Some numerical simulations are shown and are compared with experimental results.
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.
When an optical surface has local deformations, it is not practical to measure the entire surface at one time, because an average of the entire surface is obtained, ignoring the local deformations. In a previous work we used the principle of the Chelmer’s test, for analyzing just local defects of an optical surface, the technique uses a reflective spatial light modulator (RSLM), which allows the screen to remain at a fixed position, and only two apertures are used at a time. Our proposed method measures only obtain the local or zonal defects in the wavefront. The use of an RSLM provides a very flexible way of selecting a particular zone to be tested. The advantage of the proposed dynamic Chelmer’s test is that using an RSLM it is possible to select a pair of holes in real time, for any zone, and with different sizes and orientation of the holes. In this work, we compare the results obtained previously, with three different techniques: the first one is the traditional analysis of fringes used in Chelmer’s experiment. The deviations of the interference fringes from a straight line were calculate, according to the equation of Guenther. The second is an analysis by computer, where we developed a computer program to analyze an interferogram produced by a commercial interferometer (ZYGO), with the computer program is possible to know the position of the dark fringes. The ideal separation the dark fringes are obtained by analyzing an area of the interferogram that has no deformations. Finally we analyze the profile of the interference fringes corresponding to the local areas using the commercial program “Durango Interferometry Software”[1].
We present the numerical simulation of a ray selector with a uniform distribution. This selector shall be used in a deflectometry arrangement and the detection plane of spots necessary in the deflectometry shall be placed at an arbitrary distance from the lens under test. To perform this task, the vector form of the exact ray tracing is used through a lens and from these positions determine the shape of the convex surface of the lens. This program is flexible and can be used on other types of optical surfaces, and different ray distribution, including null distribution. The first preliminary results are shown below.
In this work we present a simulation of the wave-front sensing of the active primary mirror support for the 2.1-m telescope of the San Pedro Mártir's Observatory by Non-Linear Curvature Wave-front Sensing. The active cell is going to be tested by changing its actuator values. In each active cell state, defocused pupil images from both sides of the focal plane will be simulated and phase retrieval will be performed. The algorithm employed to reconstruct the wave-front will be discussed, as well as the sensitivity obtained in our simulation.
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.
A wave-front coded imaging system is an optical-digital method for aberration control. Wave-front coding technology incorporates an aspheric element in the optical system in order to capture a coded image and by digital processing decode it to obtain the final image. The WFC system is very insensitive to defocus-like aberrations and thereby becomes a tool in the aberration balancing for telescope systems. We propose WFC technology to be implemented in a two spherical mirror telescope. In this work we present the design and simulation of the proposed telescope, trade-offs encountered in the design process and aspects of the image restoration.
Some experimental qualitative results are presented with a setup that uses a knife edge for producing partial interferograms, in order to obtain the quality of a lens under test. However, the same method can be extended to test an optical surface. The knife edge is located near the focal point of the lens, covering almost half of the incident laser light beam. The different observed interferograms correspond to the orientation of the knife edge with respect to the optical axis, and its distance to the focus of the lens.
For the testing of components and optical systems, there are diverse methods with different characteristics each one; in the presentation will be done a review of some of them, that can be classified as optical testing techniques, using a self-reference wavefront. Some examples are the lateral shearing interferometers (Bates, Ronchi, Murty), point diffraction interferometer (Linnik), Burch’s scattering interferometer, and the knife edge interferometer. Some advantages of such self-reference methods is the fact that are not necessary optical reference surfaces; and usually the light interfering beams have common paths, that implies that the set up is not affected by environment vibrations and other effects.
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.
In order to obtain a clearer interpretation of the Intensity Transport Equation (ITE), in this work, we propose an algorithm to solve it for some particular wavefronts and its corresponding intensity distributions. By simulating intensity distributions in some planes, the ITE is turns into a Poisson equation with Neumann boundary conditions. The Poisson equation is solved by means of the iterative algorithm SOR (Simultaneous Over-Relaxation).
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%.
This work shows the measurement of the refraction index of a glass plate using a Point Diffraction Interferometer (PDI). The plate of the PDI has a micro-hole and transmittance of less than 10%. The experimental setup consists in a He-Ne laser illuminating a spatial filter, a collimated beam is produced by an achromatic lens, and close to the focal point of a second lens (focusing lens), the plate of the Point Diffraction Interferometer is located. When the laser light pass through the plate of the PDI, it is generated an interference reference pattern, called Ir, which is recorded. As a second step, a glass plate with unknown index refraction is introduced between the focusing lens and the plate of the PDI, obtaining a new modified interference pattern, called It. We use the geometrical of figure of interference fringe for analysis of the interferograms. Value of the refraction index of the glass plate, nt, can be derived, with the previous knowledge of the glass plate thickness. Some experimental results will be shown.
Using the analogy of the double-slit experiment developed by Young and using interferometric technique
developed by Chalmers, we built an interferometric arrangement that can analyze local defects of an optical
surface. With a reflective spatial light modulator (RSLM) controlled by a PC, two apertures are open each
time, and the apertures became as secondary light sources, producing interference pattern for specific zones
for the surface under test. The interference pattern is observed, and storage into a computer by using a CCD
camera. Finally the results are compared with the results obtained using a Fizeau commercial interferometer.
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.
Xochicalco is an archaeological site located in the state of Morelos in central Mexico. It flourished from 600 to 900 a.d. with numerous multicultural elements. There are several underground rooms carved into the hillside In particular, a room with a shaft that has a hole in the roof whose orientation towards the zenith supports its astronomical purpose. Our hypothesis is that the place was used as a tlayohualchieliztli or camera obscura for astronomical observations. This would be the first evidence of a pre-columbian image forming device. To explore the feasibility of this assertion, the conditions required to produce an image were studied. The aperture diameter in the top of the shaft is far too large to be used as a "pinhole" but it may have been covered with a screen containing a smaller bore-hole. We work out the optimum aperture size. The portion of the sky that could be observed due to the orientation of the shaft was also undertaken. The two most intense celestial objects should produce bright enough images thus suggesting that observation of the sun took place during day-time and observation of the moon during night-time. Amate paper or cloth could have been used to directly draw the position of celestial objects.
For the diffraction equations for the exact and convolutions Fourier's integrals, the parameters related with mechanical
stress and heat are introduced into the mathematical function of the transmittance t0(x0,y0). Taking into account the new
transmittance equation, a new set of equations for the exact and convolution Fourier's integrals have been derived. The
only restriction for the analysis done is that for the apertures under study, they are only on a plane. An example af an
experiment where a diffraction aperture suffers of a mechanical stress is shown.
In previous works Korneev, et al. and Cornejo, et. al. Shown the feasibility to produce an interference pattern, by
setting near by the focal point of a lens a razor knife edge. The interference phenomena is produced between the
wavefront coming from the lens, and the wavefront produced by the knife edge. In this work, such technique is applied
for testing a lens. Since partial interferograms are observed, due to the obstruction of the knife edge to the wavefront
coming from the lens; by rotation of the knife edge in several directions, interferograms with different information can
be registered by means of a CCD connected to a PC. Experimental measurements are given after several interferograms
with different number of fringes were analyzed.
It is well known that the Ronchi test can be used to measure the derivative of the optical path difference of a
wavefront [1]. 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 [2]. 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 [3], 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 work we present an efficient proposal to evaluate optical surfaces working at infrared wavelengths based
on the Ronchi test and on the concept of synthetic wavelength. The implementation is performed by using a
spatial modulator (XGA2 SLM) and a white Light Emitting Diode (LED) of 5mm. In order to select distinct
wavelengths, different color filters are employed. Thus, for a given selected wavelength, the surface evaluation
is carried out according to the method of Ronchi, registering two perpendicular interferograms for this color;
the process is repeated for a second wavelength (architecture of this proposal allowed us to test the surface in
more than two wavelengths). Then, an equivalent ronchigram is computationally generated with the registered
data which is then analyzed in order to generate the wavefront for the correspondent synthetic wavelength.
Observations of our results show that with an appropriate LED alignment and high intensity, we avoid an
increase of noise due to the employment of longer wavelengths, as well as the alignment problem, often linked
to the evaluation of infrared (IR) surfaces. The simplicity of the optical setup and low cost materials make this
proposal applicable in the area of optical testing.
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 [1]. 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.
The Ronchi test has been consolidated as one of the most successful and powerful techniques applied to determine
the quality of optical surfaces.5 In recent years, the development and availability of LCD's (Liquid Crystal
Displays) have allowed the incorporation of LCD's instead of the traditional static ruling. The easy change of the
characteristics of the fringes in the ruling, such as frequency, position, and geometrical form, transformed this
technique into a dynamic test.1, 8 Its physical interpretation fully connected with a lateral sheared interferometer 5, 6 and some concepts and results associated with the interferometric concept of equivalent wavelenght have
been applied in this proposal for the evaluation of optical surfaces. The procedure described here to evaluate
an optical surface uses the Ronchi test with the equivalent wavelenght.6, 10 This is achieved by registering and
computing Ronchigrams obtained by employing, separately, two distinct wavelengths. For a particular mirror,
some results are shown in order to demonstrate the enhancement of the test with this proposal.
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 defects 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).
Frequently two-dimensional interferograms are obtained when a point-diffraction interferometer (PDI) is used in optical
testing. The PDI is a simple, convenient and robust tool for optical shop testing. In this paper, we propose the use of the
PDI and placing a slit at the exit pupil to scanning the surface under test. Stitching is then used to generate a phase map
of the test wavefront. The advantage of the proposal is the sharpness of the fringes to obtain high resolution contour of
the test wavefront, we describe the method and some experimental results.
The correction of the wavefront in optical systems implies the use of wavefront sensors, software, and
auxiliary optical systems. We propose evaluated the wavefront using the fact that the wavefront and its intensity are
related in the mathematical expression the irradiance transport equation (ITE)
We present a detailed analysis of the reconstruction of gray-level images using orthogonal moments with respect to the basis sets of Zernike, Fourier-Mellin, Chebyshev-Fourier, and pseudo-Jacobi-Fourier polynomials. As test images, we use Ronchigrams with different numbers of fringes as high-spatial-frequency components. The evaluation of image reconstruction between orthogonal moment sets is made in terms of different metrics. These measurements are the normalized image reconstruction error, the overall activity level in each image with respect to spatial frequency variations, the root-mean-square contrast, the total number of reconstructed fringes, the coordinate transformations of the input image, and the number of moment orders. Moreover, a method of denoising the input image based on the Daubechies wavelet transform is implemented to compute the signal-to-noise ratio. Numerical computations show that, for the Ronchigram reconstructions, the performance of Zernike moments is better than that of the other basis sets of orthogonal moments.
The Irradiance Transport Equation (ITE), found by Teague, had been used in optics with different applications. One of the field where had been used is in optical testing, for example, with the method developed by Takeda. In this paper following the idea of using different optical and mathematical analysis method, theorical and experimental results are presented.
The Ronchi test is a well-known method for the testing of optical components and systems, and can be studied by ray tracing and lateral shearing interferometry. In this paper, the Ronchi test is applied using an LCD, for generating gratings with different periods for the dark and light zones, in order to obtain sharpening of the fringes. Experimental and computer simulations will be presented for parabolic surfaces.
At the present time, some astronomical telescopes exist with segmented primary mirrors, as those located in Mauna Kea, Hawai. The Keck telescopes are a classical example. With the purpose of collecting light of weak stellar objects, it is necessary to control the segments of the primary mirror of the telescope, so that whole mirror works as a monolithic mirror. In this paper, it is proposed the subapertures method for the alignment of the segments of the primary mirror. The subapertures method finds tilt, tip, and pistons effects or longitudinal displacements as the defocus error; all of them are necessary to achieve the fitting of a series of measurements. It is shown the experimental results for a parabolic mirror divided in two segments using the proposed method; for this case, the particular equations were developed as well as the necessary software for the alignment of the two parts. The experimental results were obtained in a controlled situation in the laboratory. The alignment process is achieved in a short time, and furthermore is an interactive process.
In this paper we extend previous studies to further diffraction properties of Ronchi rulings. Our considerations are based on the physical theory of gratings with different strip-widths geometry. Under scope are absorptive gratings, phase gratings and mixed gratings. The case of gratings with diverse structures is also considered. In particular, gratings of phase with absorption (mixed gratings) are considered by means of the observed diffraction properties for absorption rulings as it is described in the work. Ronchigrams resulting for different grating parameters and different values from primary aberrations are shown. Some experimental results of Ronchi rulings for diverse structures are including. This study can be used not only for optical testing, but also for gratings of light for diffraction of atoms or to describe diffraction effects of micro-gratings.
In this paper we introduce the affine spatial overlap operation defined as a generalization of the two-dimensional convolution and cross-correlation operations. Our attention is focused on the rotational overlap operation and some of its mathematical properties as well as its application to shape description. Based on the auto-rotational overlap operation, a one-dimensional signature is proposed as a shape representation for planar binary objects with bounded support. We provide illustrative examples of its digital computation using different binary objects. In addition, physical realization of the 2-D rotational overlap operation is demonstrated with a hybrid optical-digital system for real time processing. The experimental setup uses a microcomputer controlled high-precision rotatory stage for performing analog rotations at the input plane of an incoherent two lens correlator architecture.
A technique of great help in the optical test is the subaperture method, this method is proposed to align the segments of a primary mirror of telescope, using the ideal form of the primary mirror, which is defined using the sagita z(x, y). When the surface under test is segmented each segment has a sagita zi(xi, yi) that is rotated and displaced with regard to the reference system of all surface, where i = 1, 2, ..., n, with n is the number of segments. Some numerical simulations are shown to align two segments of a mirror using the subapertures method using the least square algorithm to align the segments.
Xiang developed a method for the measurement of radii of curvature of optical surfaces greater than one meter, this method is used for spherical concaves and convexes surfaces, at the vertex; the error is of 0.1%. In this work are carried out some innovations to the method of Xiang, for measurements of local radius of curvature of conical concaves and convexes surfaces. Some results obtained are for a parabolic surface.
We present a new algorithm that applies the correlation functions to phase shifting interferometry to recover the phase of a test surface. In this work we make numerical simulations to test the algorithm and the results are verified with real interferograms. The correlation algorithm recovers the phase value with 5% accuracy.
The star test is conceptually perhaps the most basic and simplest of all methods of testing image-forming optical systems, the irradiance distribution at the image of a point source (such as a star) is give for the Point Spread Function, PSF. The PSF is very sensitive to aberrations. One way to quantify the PSF is measuring the irradiance distribution on the image of the source point. On the other hand, if we know the aberrations introduced by the optical systems and utilizing the diffraction theory then we can calculate the PSF. In this work we propose a method in order to find the wavefront aberrations starting from the PSF, transforming the problem of fitting a polynomial of aberrations in a problem of optimization using Genetic Algorithm. Also, we show that this method is immune to the noise introduced in the register or recording of the image. Results of these methods are shown.
It is necessary to optimize the slit width of a spectrometer in order to obtain the theoretical resolution, the greater amount of energy onto the detector and a better signal to noise ratio. We propose a transformer system of images for spectroscopy, which consists of a plano-convex lens cemented on one side of a parallel-plane glass plate, to transform the image formed in the focal plane of a telescope into an image of rectangular form of a specific size, with the objective that all the light passes the slit of the spectrometer without decreasing the resolution. We present the preliminary simulations and experimental results of the proposed optical system.
In this paper we inspect some further properties of diffraction Ronchi rulings and its effects in Ronchigrams. Our considerations are based on the physical theory of gratings with different strip-widths geometry. Under scope are absorptive gratings, phase gratings and mixed gratings. The presented analysis and respective results are illustrated here with the use of an advanced mathematics software pack. Some possible applications in optical testing, imaging processing and nanolithography are considered.
The primary reflective surface of the Large Millimeter Telescope (LMT), it will be formed by a set of trapezoidal panels. Each panel has a paraboloid off-axis form and it is constructed with carbon fiber. The paraboloid off-axis surfaces is obtained copying by contact to a mold with the required form. One proposal in order to manufacture each mold, is made it of graphitizing steel fused. And after that, it lathing with a numerical control machine for obtain the paraboid off-axis section. But due to the dimensions of the sections, 5x3 meters for the biggest section; the mold of steel will be formed by two small segments. In consequence, it is necessary in the first place, alignment these segments in order to obtain a mold with a surface approximately continuous, with a minimum precision of 5mm. In this work we present a method in order to alignment these two molds' segments, as well as, the results of alignment obtained for the prototype mold.
Two experimental arrangements for measuring the local radii of curvature of an aspherical surface will be presented, together with a comparison between the experimental and theoretical values obtained. One of this experimental arrangement provides an average value of the radii of curvature in a subaperture with a ring shape. With the other method the measurements are done point by point over on a contour of the surfaces. The theoretical values for the local radii are calculate from the annular subapertures method testing an aspherical surface; also we be shown the advantage and limitations of these proposals.
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.
We propose a method for piston errors detection in a segmented surface by means of the classical ronchi test. This consists in comparing the ronchigram fringes frequency of a reference and piston segment. The comparison is developed for the correlation method of the intensity vs pixels curves of the reference and piston segment. The presence of the piston term in a ronchigram is assured experimentally for the shack interferometer, it is by observing the coincidence rings centered type fizeau in each segment. The proposed method is applied to a segmented spherical surface with a two segment mirrors, and resolutions of piston ⩾63 ηm are experimentally obtained.
We propose one method for the phase alignment of segmented mirrors with piston errors. For this, we use the classical Ronchi test to observe fringes around of curvature center, after we take some lines on the Ronchi image for each segment mirror and obtain its intensity vs. pixels, to do the correlation and approximate the amount of pixels or piston displacement for the phase misalignment. Additionally, we get parabolic fit to find resolutions of sub-pixels. At the same time, we use the Shack Interferometer to observe behavior rings centered for this two segment mirrors to compare with the fringes produced with Ronchi test and to achieve resolutions of piston >= 24 (eta) m.
We present a study of the intensity variations of the joint Fourier spectrum when one of two input objects is rotated while the other remains fixed by determining the average contrast as a function of the angle of rotation. The visibility behavior is explained in a theoretical and experimental way for simple test objects whose fine analog rotations are acquired with an optomechanical system that uses a high precision rotatory stage.
In this work, we present the results obtained in the laboratory when diffraction images are observed, produced by a Ronchi ruling, of a flat circular object, objects with a periodical structure, like for example screws, and masks, with certain regular structure. The diffraction images of these objects are processed by a computer program in order to determine important characteristic of them, for instance: the measurement of the diameter of a hole, the measurements of the profile of a screw, and the periodicity of the structure of square masks.
When optical systems are designed, the final stage corresponds to the optimization of an initial design, and frequently the methods of damped least squares are used. However, some methods, such as the one mentioned, find local minimums and not the global one. Therefore, the solution depends mainly on the initial design. The method proposed in this work, is based in the genetic algorithms that find the global minimum, and besides an initial design is not necessary to begin the optimization process.
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.
Formulae and computer programs were developed for surface contributions to high order aberrations coefficients using the Aldis theorem and Andersen algor ithms for a symmetr ical optical system. 2. THEORY Using the algorithms developed by T. B. Andersent which allow to calculate the high order aberrations coefficients of an optical system. We were able to obtain a set of equations for the contributions of each surface of a centered optical system to such aberration coefficiets by using the equations of Andersen and the so called Aldis theorem 3. COMPUTER PROGRAMS AND EXAMPLES. The study for the case of an object at infinite has been completed and more recently the object to finite distance case has been also finished . The equations have been properly programed for the two above mentioned situations . Some typical designs of optical systems will be presented and some advantages and disadvantages of the developed formulae and method will be discussed. 4. CONCLUSIONS The algorithm developed by Anderson has a compact notation and structure which is suitable for computers. Using those results obtained by Anderson together with the Aldis theorem a set of equations were derived and programmed for the surface contributions of a centered optical system to high order aberrations. 5. REFERENCES 1. T . B. Andersen App 1. Opt. 3800 (1980) 2. A. Cox A system of Optical Design Focal Press 1964 18 / SPIE
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