Conic that best fits an off-axis conic section.
TL;DR: This method is based on the method of continuum least squares to obtain the vertex’s curvature and conic Constant of the fitted conic on-axis, given the curvature at the vertex and the conic constant of the parent conic from where the authors want the section and the size of that section.
Abstract: To help in the fabrication of off-axis conic sections, we present a method to approximate this off-axis section by an on-axis conic centered on the portion desired. This method is based on the method of continuum least squares to obtain the vertex’s curvature and conic constant of the fitted conic on-axis, given the curvature at the vertex and the conic constant of the parent conic from where we want the section and the size of that section. Simple analytic expressions for the curvature and conic constant are derived in terms of the parameters of the off-axis section.
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TL;DR: The feasibility of using null screens for testing the segments of a parabolic segmented telescope mirror for the Large Millimeter Telescope (LMT) is analyzed and an algorithm for designing the null screen forTesting the off-axis segments of conic surfaces is described.
Abstract: The feasibility of using null screens for testing the segments of a
parabolic segmented telescope mirror for the Large Millimeter Telescope
(LMT) is analyzed. An algorithm for designing the null screen
for testing the off-axis segments of conic surfaces is
described. Actual screen designs for the different classes of
segments of the LMT are presented. The sensitivity of the test and
the required accuracies for the fabrication and positioning of the
screen are analyzed. A measuring accuracy of ∼12 µm in
surface sagitta is within the reach of the technique.
42 citations
TL;DR: A common mathematical model is established for the Ronchi and Hartmann tests and for interpretation of the Ronchigrams as level curves of the components of the transversal aberrations.
Abstract: A common mathematical model is established for the Ronchi and Hartmann tests and for interpretation of the Ronchigrams as level curves of the components of the transversal aberrations. With the same point of view, a Hartmanngram is regarded as two 90° crossed null Ronchi gratings. A simple and direct method is also developed for calculating Ronchigrams for the cases of centered and off-axis conic sections with the point light source at any location.
37 citations
TL;DR: Here a tilted null screen with drop shaped spots drawn on it is designed in such a way that its image, which is formed by reflection on the test surface, becomes an exact square array of circular spots if the surface is perfect.
Abstract: We report the testing of a fast off-axis surface based on the null screen principles. Here we design a tilted null screen with drop shaped spots drawn on it in such a way that 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. Here the whole surface is tested at once. The test surface has a radius of curvature of r = 20.4 mm (F/0.206). The surface departures from the best surface fit are shown; in addition, we show that the errors in the surface shape are below 0.4 μm when the errors in the determination of the coordinates of the centroids of the reflected images are less than 1 pixel, and the errors in the coordinates of the spots of the null screen are less than 0.5 mm.
34 citations
TL;DR: This work employs the direction cosines of the principal ray to compute the wave-front aberration function of a beam reflected by an off-axis paraboloid, and calculates by exact ray-trace equations the modified wave- front aberration and expresses it in power series.
Abstract: When an off-axis paraboloidal mirror focuses a parallel beam, the image is formed on one side of the optical axis. For a tilted beam focused by an off-axis paraboloidal mirror, the focus is no longer pointlike (not considering the diffraction effect); rather, it is a distorted spot. This is due to the inherent aberrations of the surface. In addition, there is a change in the focus position. We calculate by exact ray-trace equations the modified wave-front aberration and express it in power series. Our formulation uses the optical path variation along a defined principal ray that we relate to the parameters that describe the surface and the beam angle of incidence. We designate this ray as that reflected by the center of the entrance pupil and field of view. We employ the direction cosines of the principal ray to compute the wave-front aberration function of a beam reflected by an off-axis paraboloid.
25 citations
TL;DR: In this article, the outer mirror segment for the European extremely large telescope is taken as a case-study, assuming a rigid tool size of 150 mm and a simple independent approximation validates the calculation.
Abstract: Rigid tools can confer advantages at certain stages of manufacturing off-axis mirror segments, but the misfit due to surface asphericity and asymmetry poses constraints on their application. Types of misfit are classified and, using least squares, the best-fit tool forms with different distances from the pole of the parent asphere are calculated. The outer mirror segment for the European extremely large telescope is taken as a case-study, assuming a rigid tool size of 150 mm. A simple independent approximation validates the calculation. A close parallel is wavefront misfit in subaperture interferometry, which is also considered.
21 citations
References
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TL;DR: In this paper, the theoretical basis for a technique to fabricate nonaxisymmetric mirrors is developed for a mirror blank that would have the effect of elastically deforming a desired surface into a sphere, and upon release of the applied stress, the spherical surface deforms into the desired one.
Abstract: The theoretical basis is developed for a technique to fabricate nonaxisymmetric mirrors. Stresses are applied to a mirror blank that would have the effect of elastically deforming a desired surface into a sphere. A sphere is then polished into the blank, and upon release of the applied stress, the spherical surface deforms into the desired one. The method can be applied iteratively, so arbitrary accuracy should be possible. Calculations of the stresses and deformations are carried out in detail for an off-axis section of a paraboloid. For a very general class of surfaces, it is sufficient to only impose appropriate stresses at the edge of the blank plus a uniform pressure on the back.
126 citations
TL;DR: In this paper, a new method of obtaining aspherical surfaces from elasticity is applied to the wavefront function and the primary aberrations with arbitrary amplitude are considered in detail.
Abstract: A new method of obtaining aspherical surfaces from elasticity is applied to the wave-front function. The primary aberrations with arbitrary amplitude are considered in detail. It is shown with respect to conventional criteria concerning a given value of the normalized intensity at the diffraction focus, that three simple loads and associate thickness configurations of the plates can be found in the case of primary spherical aberration. One configuration for simple loads and thickness is found in each case for primary coma and primary astigmatism.
12 citations