Optical design of off-axis Cassegrain telescope using freeform surface at the secondary mirror

Abstract

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...

Construct freeform surface directly in an initial layout of an off-axis reflective image system by seed curve extension and simulated annealing algorithm

“…The specifications of the freeform two-mirror system are listed in Table 1, which is given in Ref. [1]. In the initial layout of the off-axis two-mirror system, the primary mirror M 1 is a freeform surface, and the secondary mirror M 2 is a planar mirror as shown in Fig.…”

“…A base conic surface and 11 added polynomial aspheric terms up to fifth order are used. The surface sag is of the form [1,7]:…”

“…Off-axis reflective optical systems are widely used in telescopes [1], hyperspectral imaging spectrometers [2], ultrashort throw ratio projection optics [3] and so on because of compact structure, having no blocking, absence of chromatic aberrations etc. [4]..…”

Design method of off-axis extreme ultraviolet lithographic objective system with a direct tilt process

“…6 To solve these problems, the freeform offaxis objective for EUV lithography is proposed. 9,10 Hence, as the fabrication and test technology of freeform optical surfaces develop, the freeform off-axis objective for EUV lithography has become a trend for the future. 9,10 Hence, as the fabrication and test technology of freeform optical surfaces develop, the freeform off-axis objective for EUV lithography has become a trend for the future.…”

Combining freeform optics and curved detectors for wide field imaging: a polynomial approach over squared aperture

“…In the considered examples a few mathematical descriptions of the freeform surfaces are applied: ordinary XY-polynomials [1][2][3][4][5][6][7], Zernike polynomials [8,9], non-uniform rational Bsplines (NURBS) [10][11][12] and a few other types of equations, used in [13][14][15][16][17]. Among the latter it is reasonable to note Bernstein polynomials [13] and Legendre/Q-Legendre polynomials [14].…”