Design And Tolerance Analysis Of Null Lens For Testing Hyperboloid Concave Mirror

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Design and tolerance analysis of null lens for testing hyperboloid concave mirrorK. K. Saxena, D. V. B. Rao, N. J. Babu and T. K. AlexSensor Systems Division, ISRO Satellite Centre, Bangalore-560017AbstractA null lens is described to test the hyperboloid primary mirror of Very High Resolution Radiometer (VHRR) telescope. It can be used to test a variety of optical systems or components. Conies and higher order aspheric mirrors can be tested with the same null lens if it can zoom the amount of spherical aberration introduced. It is a triplet lens with all spherical surfaces. The output F/No. and image position remains fixed during the zoom.The performance of this device has been analysed for hyperboloid mirror of diameter of 208 mm which works at F/2.0. The performance has been characterised by RMS wave front deformations. Test set up has been analysed for centered and decentered tolerances, irregularity in surfaces, single surface decenter and displacements and a group decentering tolerances. Final tolerance parameters for null lens have been tabulated.IntroductionThe application of conic aspheric surfaces is one of the classical developments in geometrical optics. Conies in reflection are used for aberration free imagery in cases where large aperture is desired. A reflecting conic surface can be thought of as a spherical base surface which provides the optical convergent or divergent power necessary to form an image in a desired location or with a specified magnification, but with higher order aspheric deformation to compensate for the spherical aberration introduced by the spherical surface to a specified degree. But surface testing of an aspheric is somewhat more complicated because the surface does not have a null characteristic when examined at the center of curvature. A convenient method for testing conic surfaces is to use additional optics in the test set up such that the result of the test, where the aspheric attained shows no error indicated on the surface - the null lens. This device has most often been used in the testing of telescope mirrors and similar large reflectors. ' 3 The VHRR is of Ritchey Chretien (R-C) type telescope comprising of hyperboloid primary mirror and hyperboloid secondary mirror. A null lens has been worked out to test the hyperboloid concave mirror. The obscuration in optical path, due to null lens itself, is to be minimized. In VHRR, the primary mirror has a central hole of diameter of 65 mm, therefore, the null lens diameter including housing does not exceed the same.Design DescriptionA wavefront is passed through an aberrating lens (the null lens), and reflected off the surface to be tested. Then the wavefront proceeds to a flat mirror and it retraces its optical path after getting reflected. If the surface being tested is perfect, the resulting wave front will exactly match the input wavefront. For a single pass test, with small residual errors, any irregularities in the reflecting surfaces will appear in the resulting wavefront as the deviations from the plane wavefront. If the input wavefront after reflection interferes with the resulting wavefront, the interference fringes of equal optical path difference (OPD) formed yield errors which are proportional to the residual wave front errors.An aspheric section can be described by the classical wave front aberrration. The difference between general aspheric and paraxial sphere can be expressed as a linear combination of classical wavefront aberration terms. Since the wavefront coefficients are normalized at the edge of aperture, the coefficients represent the amount of particular aberration present on the surface. In this respect, the coefficients are useful for finding the starting values of the various aberrations, the null lens will need to null the surface.The null lens shown in the figure 1, has been optimized to test the concave hyperboloid mirror at its focus. The design parameters are tabulated in Table 1. These design parameters can be scaled down or up for testing the different aspheric surfaces having same F/No.1 The test set up is shown in the figure 2 and optimized design parameters for the test arrangement have been tabulated in table II.