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Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 05/15/2015 Terms of Use: http://spiedl.org/termsAbstract. Freeform surfaces enable imaginative optics by providing abundant degrees of freedom for an optical designer as compared to spherical surfaces. An off-axis two-mirror-based telescope design is presented, in which the primary mirror is a concave prolate spheroid and the secondary mirror is freeform surface-based. The off-axis configuration is employed here for removing the central obscuration problem which otherwise limits the central maxima in the point spread function. In this proposed design, an extended X − Y polynomial is used as a surface descriptor for the off-axis segment of the secondary mirror. The coefficients of this extended polynomial are directly related to the Seidel aberrations, and are thus optimized here for a better control of asymmetric optical aberrations at various field points. For this design, the aperture stop is located 500 mm before the primary mirror and the entrance pupil diameter is kept as 80 mm. The effective focal length is 439 mm and covers a full field of view of 2 deg. The image quality obtained here is near diffraction limited which can be inferred from metrics such as the spot diagram and modulation transfer function. IntroductionThe primary sources of aberrations in a Cassegrain classical two-mirror imaging system with positive focal length are coma and astigmatism in the extended field of view (FOV) with linear field dependence and quadratic field dependence, respectively. 1,2 Material constraint in refractive systems (i.e., change in the refractive index of a material with wavelength) produces chromatic aberrations as compared to reflective optical systems, and limits the use for a wide spectral range. 3 A two-mirror-based on-axis design (Cassegrain and Gregorian) of a reflective telescope with a large entrance pupil diameter (ENPD) provides a limited FOV and the secondary mirror causes central obscuration, which results in a reduced signal-to-noise ratio. Central obscuration results in a smaller central maxima in the point spread function that limits the modulation transfer function (MTF) resolution. 4 This results in a chance for missing fainter objects close to brighter astronomical objects. Other than decreasing the midspatial frequencies in the optical transfer function, different kinds of secondary mirror support produce astronomical objects such as a diffraction pattern, i.e., spider produced a familiar "star"-like diffraction pattern. 5 In general, the optical designer chooses either tilt with decentration of the optical elements or the off-axis segment of larger elements to achieve nonobscuration in the optical system design. Tilting of the optical elements introduces higher-order coma and astigmatism and other field-dependent aberrations, while an off-axis elements-based system design has better control over aberrations. 6 Unobscured allreflective optical system designs are being considered in several ground-and space-based telescopes fo...