The optical problems of the Ritchey-Chretien astronomical telescope

The optical design principles of the two-mirror Ritchey-Chretien telescope objective system are developed systematically, starting from fundamentals. The third-order aberration coefficients of Buchdahl are derived for such a system and based on these coefficients, expressions for the first of the extra-axial curvature coefficients of the mirrors which provide aplanatic condition at the Cassegran focus are derived. numerical example (proposed Anglo-Australian 150-inch telescope) is considered to illustrate the principles. Third-order correction to achieve aplanatism is found to be inadequate when spot diagram analysis is made. The expressions for the fifth-order spherical aberration coefficient, `˜í¬¿_1`, and linear coma coefficients, `˜í¬¿_2`, `˜í¬¿_3`, for the two-mirror system are then derived and are used to achieve aplanatic condition to fifth-order. When this is applied to the numerical example, the performance of the system is found to be extremely good. The profiles of the mirrors of the seventh-order aplanatic system are found to be scarcely distinguishable from those of the fifth-order aplanatic system. The mirrors are then considered as two hyperboloids, based on third-order aberrations, and it is noticed that the curvature coefficients of these mirrors and the performance of such a system is not far removed from that of the fifth-order aplanatic system, justifying the popular view. A consideration of the aberration balance technique has brought the hyperboloid system still closer to the fifth-order system. The design principles of two types of secondary focus correctors to eliminate the residual astigmatism and field curvature of the aplanatic system are outlined. These are an aspheric plate with field flattener and a Rosin type doublet. The principles are successfully adopted to develop these correctors for the numerical example. With the farmer type of corrector, it is noticed that best correction canbe achieved if the Ritchey-Chretien mirror constants are slightly changed Rosin type corrector is associated with colour problems: Expressions for the prime focus aberrations are derived and the design principles of single plate and three-plate correctors to correct these aberrations are discussed: Two-plate correctors provide no practicable arrangement: The single plate corrector provides a small useful field, whereas the three-plate corrector offers more useful field. With these correctors in place, the prime focus largely suffers from higher order aberrations. The conclusions are mostly derived from the numerical example. However, they are valid for a wide range of parameters.