II. On a cassegrain reflector with corrected field

Abstract

The great advantage enjoyed by the reflecting telescope is its equal treatment of rays of all colours, and the geometrical defects or aberrations of its field are less than those of many of the older refractors. The most serious of these defects is coma, owing to which different zones of the objective do not place the light which they receive from the same object-point symmetrically around any common centre in the image area, but arrange it in a radial fan or flare, the light from the outer zones being most diffused; besides spoiling the image this tends to neutralize, for any except narrow fields, the value of extended aperture in the objective as a light-collector. In the refractor this can be and is now always met by adjusting the curves of the two lenses, for when achromatism, as far as possible, and spherical aberration are allowed for, there still remains one unused datum; in old forms this was often used to make the inner curves contact curves that might be cemented together if it was convenient to do so, but it is properly employed to extinguish coma. But with the reflector the case is different. In the Newtonian form there is only one available surface, and when this is made a paraboloid to cure spherical aberration, nothing is left to adjust. In the Gregorian or Cassegrain forms there are two curved surfaces and, theoretically, these would offer means to correct two faults. An illuminating study of the possibilities of a system of two mirrors has been made by Schwarzschild in his ‘Untersuchungen zur Geometrischen O ptik’; I shall deal with its outcome below. Its general tenor is comprehensive and exploratory rather than detailed, and it remains doubtful whether any of the forms which he indicates for the reflector, at the point at which his research stops, could actually be made successfully upon a scale that would show their advantages. My own purpose in the present paper is essentially a practical one. I have in mind throughout a telescope of large aperture and considerable focal length, and seek to devise a correction for the faults of its field which shall leave its achromatism unimpaired, which can really be made and which shall effect its purpose without employing any curves and angles outside those that are already known to work well. It has been said that “an object-glass cannot be made on paper,’’ but the possibilities of new and somewhat complicated constructions must in all cases first be demonstrated on paper, since practice can never conveniently vary more than a single factor at a time. Study is directed to the Cassegrain because of the great advantage which this design possesses in shortening the tube of the instrument for given focal length, and in placing the observer at the lower, in place of at the upper, end of it. The best introduction to the subsequent work will be in the form of a few remarks upon Schwarzschild’s results. These are not meant as a complete criticism or estimation of it but are merely such as arise naturally in relation to the points with which I deal afterwards. The traditional form of Cassegrain telescope consists of a great concave mirror faced by a small convex one, which is placed between the great mirror and its principal focus, and throws the image out through a hole cut centrally in the great mirror. The small mirror increases the effective focal length in the ratio of its distances respectively from the final principal focus and from the principal focus of the great mirror.