This work proposes the design of an off-axis null-screen that is displayed on an LCD screen and allows characterizing the surface quality of a sliding seismic isolator. For this purpose, we design a null-screen with a pattern of quasi-elliptical dots drawn on it, so that its image, which is formed by reflection on the concave surface, becomes a precise set of circular targets if the surface under test coincides with the designed surface. It is discussed how to integrate the off-axis measurement system to calibrate it by testing a reflecting concave surface, as a result optical parameters are obtained, at the surface vertex, such as radius of curvature, conic constant, and some deformation coefficients necessary for the characterization of the deformations associated to the test surface with respect to the design surface. Finally, based on the preliminary results, the advantages and disadvantages of the proposed test are discussed.
Most corneal topographers are based on the Placido disk, which is consists of a set of concentric rings illuminated in black and white. Each luminous ring is projected onto the corneal surface and its image produced by reflection is captured by a camera. When the corneal surface is symmetrical and aligned with respect to the optical axis of the corneal topographer, the image consists of concentric rings; therefore, displacements occur only in the radial direction. However, if the cornea lacks revolution symmetry, the image suffers deformations in both radial and azimuthal directions; therefore, corneal topography depends not only on the radial direction, but also on the azimuthal direction. This is known as the skew ray error. In this work, we present a numerical analysis on the effects on the corneal topography caused by skew ray error and show the advantages of using illuminated elongated ellipses, which are designed using exact ray tracing, to recover the corneal topography considering a conical corneal topographer.
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.
Elastic lenses have been used in various optical systems, such as cameras, microscopes and vision systems, to name a few. A recently reported technique consists of making the lens's optical design, subsequently manufacturing an aluminum mold with the optical parameters of the design obtained, and finally injecting the polymer mixture into it to generate the lens. Where the lens surfaces take the shape of the mold surfaces, it is necessary to verify the finish of the mold surfaces so that the manufactured lenses meet the design requirements. In this work, the null screen technique is presented to evaluate the finish of these surfaces. An analysis of the results obtained and their conclusions is offered.
We present an iterative procedure to retrieve the wavefront using a Shack–Hartmann sensor. Traditionally, a uniform array of microlens is used as a domain to reconstruct the wavefront under test; however, this properly works if the wavefront differs slightly from a plane. But generally in optical tests, astronomy, and ophthalmology the wavefronts under test can have appreciable deviations with respect to a plane wavefront. The proposed method considers the reconstruction of the wavefront deformations with respect to a known reference wavefront. At each iteration, the wavefront deformation is used to find a reference wavefront closer to the wavefront under test and a domain closer to the actual domain. When the values of the wavefront deformations are small enough, we can take the reference as the wavefront under test. In addition, we simulate the centroid positions of the spot pattern used to retrieve the wavefront under test using the proposed method. We compare our results with those obtained by three other different approaching methods described in the literature (Modal, Trapezoidal Rule, and Southwell). For the simulations used in this work, our method retrieves wavefronts closer to the real wavefront than the other methods. Also, we apply the proposed method to an experimental case to reconstruct the wavefront under test using a Shack–Hartmann sensor.
We propose the design of a conical null-screen with quasi-elliptical targets drawn on it so that its image, which is formed by reflection on a biconical convex surface, becomes a precise radial set of circular targets if the surface under test is perfect. This null-screen avoids alignment difficulties of the test system due to the contour of the face (eyebrows, nose or eyelids). In addition, the proposed method prevents the targets from overlapping and touching each other. We discuss how to integrate the system to calibrate it by testing a spherical and a biconical surface on which we obtain geometrical parameters such as radius of curvature and conic constant, as well as elevation, and sagittal and meridional curvature maps with a smartphone-based corneal topographer.
In this work, we show the design of a conical null-screen for evaluating non-symmetric convex surfaces, such as toroidal and biconical convex surfaces. We propose a customized evaluation algorithm to compute the shape of the surface. The data obtained by our algorithm are fitted to a customized non-symmetric shape surface, considering orthogonal polynomials, to obtain the geometrical parameters such as the radius of curvature and the conic constant. The advantages and disadvantages of applying this algorithm to the quantitative test results are also presented.
In this work, we use a null-screen corneal topographer with a semiradial spot pattern by using a mobile device’s camera to obtain images of the reflected pattern with the main aim of obtaining the corneal topography. First, we discuss how to integrate the system to calibrate it by testing a reference surface where we obtain optical parameters such as the radius of curvature and the conic constant, as well as elevation, sagittal curves, and meridional curvature maps with this method. Finally, we show some prelaminar measurements of the topography of some human corneas.
We propose a method to design the null-screen on a cylindrical surface when the surface under test is a freeform, this implies that the surface is described by a complex analytical expression. Also, the method avoids overlapping objects in the image plane this assures the appropriate correlation between the object and the image points. The surface under study was designed using Zernike polynomials and it was built through a 3D printer and CNC machine. To retrieve the surface sagitta, in previous work, we obtained the best-fitting surface using a probabilistic algorithm. In this work, we propose to measure the slopes of the test surface in the x and y directions, and by integration, we calculated the sagitta of the test surface. We present a comparison between both methods to show which of them recovers the shape of the surface more accurately.
We use the null-screen method to evaluate in a qualitative and quantitative way the shape of a parabolic trough solar collector. When a parabolic trough solar collector is fabricated can occur that the manufacturing errors are large. In some cases, when using the null screen method, the objects in the image plane are overlapped. This problem is solved adequately by placing the CMOS sensor and LCD null-screen in off-axis positions. Also, we propose to display a suitable null-screen on the LCD screen. In the first evaluation the null screen is composed of few object points, in the next evaluation, we change the distribution of objects that compose the null screen with the aim of increasing the measurement points. Finally, the data corresponding to each evaluation is merged in only one set of evaluation data to calculate the surface sagitta from slope measurements of the test surface in the x and y directions.
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.
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.
An experimental arrangement is proposed to measure the wavefront aberration associated with a plane-convex lens of PDMS. The wavefront is obtained by numerically solving the transport intensity equation (TIE) using intensity measurements in different planes. In addition, the Zernike polynomials will be used to show the contribution of each optical aberration on the wavefront.
In this work we proposed a flat null-screen method to test parabolic trough solar collectors (PTSC). The null-screen testing method measures the slope of the test surface and by a numerical integration procedure the shape of the test surface can be obtained. In this work, we show that the test can be sensitive to small surface deformations, such as those caused by sinusoidal deformations with different amplitudes and spatial periods introduced on the PTSC surface. These calculations also show that the attainable theoretical slope accuracy in the rms sense is about 0.34 mrad. This value was obtained under the assumption that is possible to achieve a 1-pixel resolution on the measurement of the position departures of the centroids of the targets of the null-screen.
In this work we develop an algorithm to determinate the accuracy of the Null-Screen Method, used for the testing of flat heliostats used as solar concentrators in a central tower configuration. We simulate the image obtained on a CCD camera when an orderly distribution of points are displayed on a Null-Screen perpendicular to the heliostat under test. The deformations present in the heliostat are represented as a cosine function of the position with different periods and amplitudes. As a resolution criterion, a deformation on the mirror can be detected when the differences in position between the spots on the image plane for the deformed surface as compared with those obtained for an ideally flat heliostat are equal to one pixel. For 6.4μm pixel size and 18mm focal length, the minimum deformation we can measure in the heliostat, correspond to amplitude equal a 122μm for a period equal to 1m; this is equivalent to 0.8mrad in slope. This result depends on the particular configuration used during the test and the size of the heliostat.
The null-screen method has been used to test aspheric surfaces, among them the surface of a parabolic trough solar collector (PTSC). This geometrical method measures the slope of the test surface and by a numerical integration procedure the shape of the test surface can be obtained. In this work, through some numerical simulations sinusoidal deformations with different amplitudes and spatial periods are introduced on PTSC surfaces. Then, an analysis of the deformations of the reflected images of a null-screen by the PTSC surface due to defects on the surface is performed. This procedure allows to validate the kind and magnitude of the surface deformations that can be measured with the proposed method. Also, an analysis of the advantages and limitations of the null-screen testing method will be discussed.
In this work we report the design of a null-screen for corneal topography. To avoid the difficulties in the alignment of the test system due to the face contour (eyebrows, nose, or eyelids), we design a conical null-screen with a novel radial points distribution drawn on it in such a way that its image, which is formed by reflection on the test surface, becomes an exact array of circular spots if the surface is perfect. Additionally, an algorithm to compute the sagittal and meridional radii of curvature for the corneal surface is presented. The sagittal radius is obtained from the surface normal, and the meridional radius is calculated from a function fitted to the derivative of the sagittal curvature by using the surfacenormals raw data. Experimental results for the testing a calibration spherical surface are shown. Also, we perform some corneal topography measurements.
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