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Unobscured Laser-Beam-Expander Pointing System with Tilted Spherical Mirrors W. B. King Hughes Aircraft Company, Electro-Optical Division, Culver City, California 90230. Received 24 August 1973. In designing unobscured high-power-laser beam-expand- ers, the power density of the laser beam precludes the use of any refractive elements in the beam-expander optics. The design solution usually consists of an off-axis, all- reflective system with two or more mirrors, at least one of which is an off-axis, conic reflector. Because of a lack of rotational symmetry, such an off-axis, conic mirror is very costly and difficult to manufacture, and this is particular- ly true if the mirror diameter is large. A design exercise has therefore been carried out to find a possible alterna- tive solution for the all-reflective beam-expander in which good performance may still be achieved with only spheri- cal mirrors. Buchroeder 1.2 has discussed a number of design exam- ples of tilted-component telescope using only spherical mirrors. In the tilted-component system, each compo- nent is tilted so that the light path is unobstructed, and it is centered on its vertex. Detailed study of the design ex- amples has confirmed the fact that only certain particular tilt configurations can produce successful designs; other configurations can only lead to poor design performance and should be avoided. The initial study also indicated that a new design configuration had to be found for the tilted-component beam-expander; those successful config- urations for the telescope design fail to perform for the beam-expander. For the laser beam-expander, it is found that three tilted spherical mirrors are required to provide a 3.5 × beam expansion ratio in the tangential section of the sys- tem, with the input beam diameter equal to 20 cm. The system configuration (see Fig. 1) constitutes a convex mir- ror facing the input beam, followed by two concave mir- rors. The first and last mirrors are located, respectively, to the left and the right of the axis of the second mirror. The system has bilateral symmetry about its tangential section. Because of the tilt geometry, the exit pupil of this beam-expander is anamorphic; the effective beam ex- pansion ratio in the sagittal section is 2.85×. The com- putation of third- and fifth-order aberrations shows that the field aberrations of each component offset those of the other components, giving a corrected pointing axis to the beam-expander. The included angle between the input and output beams is 92.3332°. The system specifications of the tilted-component beam- expander are presented in Table I. Theoretical perfor- Fig. 1. An unobscured laser beam-expander with tilted, spheri- cal mirrors. Table I. System Specifications of the 3.5 × Tilted-Component Laser Beam-Expander with 20-cm Diam Input mance of greater than 90% Strehl ratio 3 has been achieved on axis at 2 km and 5 km for 10.6-μm wavelength. Focus- ing is carried out by adjusting the secondary mirror along its mechanical axis. It is useful to point out that the sys- tem has been optimized by maximizing its Strehl ratio. In evaluating the system, the Strehl ratio is computed at the diffraction focus. For the particular case correspond- ing to axial input and 5-km range, the diffraction focus has longitudinal and transverse focal shifts of 23 m and 3.265 cm, respectively. One drawback of the tilted-component beam-expander is that the spherical mirrors generally have large ƒ-num- bers, and consequently the system is rather cumbersome. For the particular 3.5× beam-expander given in Table I, the ƒ-numbers of mirrors 1, 2, and 3 are 6.8, 12.5, and 15.4, respectively. The maximum separation between the mirrors is 250 cm at 5-km range, and for comparison, an equivalent off-axis beam-expander with an ƒ/3 ellipsoidal primary and a paraboloidal secondary would have a sepa- ration of approximately 157.9 cm. It is of interest to point out that aspherizing any one of the three spherical mirrors of this tilted-component beam- expander produced almost negligible improvement in 'the final performance of the system, unless the aspheric sur- face equation is asymmetric in the plane of tilt. January 1974 / Vol. 13, No. 1 / APPLIED OPTICS 21
