We design two different Hartmann type null screens based on an exact ray trace for testing a fast plano-convex aspherical condenser. The first null screen is designed for testing the external convex surface or periphery area for the condenser by reflection. We have implemented an exact ray trace assuming a point source placed along the optical axis, emitting a bundle of rays, which are reflected by the surface under test, to obtain a non-uniform array of spots, which are printed on paper sheet and wrapped on a plastic cylinder fabricated by using additive manufacture. Subsequently, by reversibility Principle’s after by reflection we obtain a uniform array pattern displayed at the detection plane. Alternatively, to evaluate the whole area for the condenser, the second null screen is designed for testing the central convex area for the condenser by refraction. Thus, we have implemented an exact ray trace assuming an incident plane wavefront, these rays are refracted through the lens under test, to obtain a non-uniform array of drop spots, which are printed on plastic sheet and placed in front of the lens under test. Finally, assuming the reversibility Principle’s after by refraction we obtain a uniform array pattern displayed at the detection plane. For this method, we have called Hartmann type hybrid null screens.
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.
One of the most important components of a wind turbine are the blades, the evaluation of their manufacturing quality and aerodynamic capabilities can be very costly, for this reason a 3D reconstruction by stereo vision is proposed. This technique consists of projecting a laser line in each face of the blade. Using a linear stage, two cameras will scan simultaneously, considering bidirectional disparities and feature correspondences between the two pictures. Two symmetric airfoils of the NACA 0012 family are evaluated. The expected precision is 0.1mm.
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.
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.
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.
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.
In this work, we analyze the advantages and limitations of the systems of low speeds of frames per second (fps) for the estimation of the vibrations measurements in systems where optical techniques are used. The acquisition systems with low fps are interesting because they are not expensive. In this way, the aim of this work is to compute the limit speed to obtain good resolutions in data collection. Laser triangulation technique is implemented to determine the natural frequency of vibration of a system using a cantilever beam, as a standard example. The results are compared, with a commercial accelerometer.
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.
We study the formation of caustic surfaces produced by bi-conic lenses, considering a plane wavefront propagating parallel to the optical axis. We have already seen that the shape of caustic surfaces can represent the monochromatic aberrations that we call image errors, furthermore the shape of the caustic can be modified by changing the parameters of the lens in such a way that if we are able to vanish the caustic, the optical system produces an image without spherical aberration, alternatively caustic surfaces having a large area could be applied to design non-imaging optical systems, such as diffusers of light. The shape of the caustic surface is a function of the indices of refraction involved in the process of refraction, and all the parameters of the bi-conic lens. We provide an analytic equation for the caustic surface in a meridional plane and some examples are presented.
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.
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.
We present a null-screen design for testing the shape quality of the reflecting surface of a parabolic trough solar collector (PTSC). This technique is inexpensive, the whole surface is tested at once, and it is easy to implement. For this, we propose the design of a flat null-screen perpendicular to the optical axis of the PTSC in such a way that it allows testing of the full aperture; we compute the caustic associated with the reflected light rays on the desired surface and analyze the parameters that determine the null-screen dimensions. Additionally, we perform a numerical simulation to analyze the accuracy of the method by introducing random displacement errors into the measured data. Accuracies >0.35 mrad were found to evaluate the quality of surfaces with this method. The errors in the determination of the coordinates of the centroids of the reflected images must be measured with an accuracy >0.5 pixels, and the errors in the coordinates of the spots of the null-screen must be <0.5 mm.
We report the qualitative testing of a spherical concave surface with deformation coefficients based on the null-screen principles. The design of cylindrical null screen with curved grid is described; its image, which is formed by reflection on the test surface, becomes an exact square grid if the surface is perfect. Any departure from this geometry is indicative of defects on the surface. In contrast to others tests, here the whole surface is tested at once. The surface under test is 140 mm in diameter and a radius of curvature of 97 mm. The surface is testing during the manufacturing process; departures from the design surface will be analyzed and discussed.
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).
A method to design Ronchi-Hartmann null screens for improved alignment in the testing of fast concave conic mirrors is presented. The designs of these null screens are based on knowledge of the caustic by reflection.
The null-screen method has been used to test aspheric surfaces. 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. Now, in order to test the
surfaces of a variable focal length lens (VFLL), we propose use a conical null-screen. We present the formulae to design
the null-screen in such a way that the image on the CCD is a perfect array of spots; departures from this geometry are
observed as deformation of the surface. The VFLL is designed in such a way that under conditions of mechanical
equilibrium both surfaces are spherical; however, its shape can be easily modified mechanically changing its radius of
curvature. In order to analyze the shape of the surfaces of the VFLL at different radius of curvature, we evaluate its form
using a conical null-screen. This procedure allows study the deformations of the surface.
The null screen is a geometric method that allows the testing of fast aspherical surfaces, this method measured the
local slope at the surface and by numerical integration the shape of the surface is measured. The usual technique
for the numerical evaluation of the surface is the trapezoidal rule, is well-known fact that the truncation error
increases with the second power of the spacing between spots of the integration path. Those paths are constructed
following spots reflected on the surface and starting in an initial select spot. To reduce the numerical errors in
this work we propose the use of the Dijkstra algorithm.1 This algorithm can find the shortest path from one
spot (or vertex) to another spot in a weighted connex graph. Using a modification of the algorithm it is possible
to find the minimal path from one select spot to all others ones. This automates and simplifies the integration
process in the test with null screens. In this work is shown the efficient proposed evaluating a previously surface
with a traditional process.
In this work we report a method for testing a parabolic trough solar collector (PTSC) based on the null screen
principles. For surfaces with symmetry of revolution a cylindrical null screen is used, now, for testing the PTSC we
use a flat null screen. The design of the null screen with ellipsoidal spots is described; its image, which is formed by
reflection on the test surface, becomes an exact square array of circular spots if the surface is perfect. Any departure
from this geometry is indicative of defects on the surface. The flat null screen design and the surface evaluation
algorithm are presented. Here the surface is tested in sections and the evaluation of the shape of the surface is
performed with stitching method. Results of the evaluation for a square PTSC with 1000 mm by side (F/0.49) are
shown.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.