Design of rotationally symmetric four-mirror zoom telescope system is investigated and a zooming method of the system is developed. By the third order aberration theory, the aberration coefficients for the spherical aberration, coma, and astigmatism of the four-spherical-mirror system are derived analytically. By using the Gaussian bracket, the expressions for the aberration coefficients are made to a compact form and the dependence of the aberrations on the system parameters is expressed clearly.
Four-spherical-mirror zoom telescope system has seven parameters, four curvatures of each surface and three distances between the adjacent surfaces, and the three distances are varied in the zooming process. When four curvatures and one distance are given, the other two distances are used to satisfy the aplanatic condition resulting in complete use of the system parameters. By varying one distance of the initial aplanat system with given four curvatures and determining the other two distances to satisfy the aplanatic condition, the four-spherical-mirror zoom telescope system becomes to satisfy continuously the aplanatic condition at every point on the zooming locus.
Among the three types of the four-spherical-mirror aplanat systems, Cassegrainian-Cassegrainian type, Cassegrainian-inverse Cassegrainian type, (Schwarzschild-Couder)-Cassegrainian type, only the systems of Cassegrainian-Cassegrainian type are found to be suitable for the zoom system. The spot diagram analysis of the best zoom system with Cassegrainian-Cassegrainian configuration shows that the performance of the system is close to diffraction limited for the focal length range from 66.67 to 133.33 cm and F-number range from F/4.0 to F/8.0 with half-field angle of 1˚ at the wavelength of 10.6 ㎛ . The half-field angle is limited to 1˚ due to the astigmation.
In order to reduce the astigmatism of the system, the four-mirror systems employing an aspherical surface are examined. The system is made to satisfy the aplanatic condition at every point on the zooming locus and further, the initial starting system is made to satisfy the anastigmatic condition as well as aplanatic condition. The zooming loci, system configurations, and the finite ray aberrations are examined for the four cases in which the system employs a conic surface for the primary surface, for the secondary surface, for the tertiary surface, and for the last surface. It is found that the system employing a conic (ellipsoidal) surface as the primary surface is most efficient in reducing the astigmatism. The performance of the system is close to diffraction limited for the focal length range from 66.67 to 133.33 cm and F-number range from F/4.0 to F/8.0 with the half-feld angel of 2˚ at the wavelength of 10.6 ㎛. The half field angle is increased to 2˚ due to the reduction of the astigmatism by employing the ellipsoidal primary surface compared with the four-spherical-mirror zoom system.
