Lens structure for giant refractor telescopes Louis Gold

Biopolis Corporation of America, 2725 39th Street N.W. Washington, D.C. 20007. Received 3 April 1976. Sponsored by Richard E. Swing, U.S. National Bureau of Standards. A novel lens design has been conceived that holds special

significance in the realm of large refractor telescopes. In­troduction of a central channel along the axis of a spherical lens makes possible a reduction of volume or weight while maintaining undiminished light-gathering capacity. Such a structure opens prospects of extending the utility of refractor telescopes where the reflector telescope now holds sway.

The cored lens provides a means for molding blanks that can be cooled and annealed more efficiently. Moreover, the weight reduction itself alleviates the ponderous stresses and the creep of the glass material. The lens structure admits the possibility of a central support to further strengthen the sys­tem.

Before describing the mathematical analysis, which affirms the physical characteristics of volume-weight reduction and undiminished light-gathering quality, several other important features should be noted. One of the serious objections to refractor telescopes, which places reflector types into hege­mony, is the susceptibility to light scattering and absorption; diminution of the volume of active lens material inherently acts to afford a further augmentation of light intensity. Second, the greater rigidity of the lens structure also tends to diminish light losses from inhomogeneities ascribable to ex­cessive mass.

The presence of the central channel should not interfere with viewed observations since the objective lies outside both the focal and accommodation distances of the viewer. Indeed, the presence of the hollow opening in the lens cannot be seen through the eyepiece. It does influence the light-gathering quality; but, as already indicated, by enlarging the over-all diameter of the objective light loss can be compensated while attaining a net weight reduction.

Fig. 1. Design parameters for cored lens structure. Comparison displayed with conventional solid lens diameter 2R\, thickness hi. Cored lens diameter 2A2 with channel diameter 2R0; shell depth d;

h0 thickness of removed segment.

July 1976 / Vol. 15, No. 7 / APPLIED OPTICS 1655

Thus, consider a spherical lens with a diameter 2R and a maximum thickness dimension h\. Its planoconvex area Au is given by

where R is the radius of curvature associated with a prescribed focal length. The volume of the lens is that of the segment and follows from simple solid geometry:

Suppose then that an effective larger segment planoconvex lens also having a radius of curvature R has a diameter 2R2 > 2R 1. Removal of a central channel comprised of a segment having 2R0 < 2R2 yields a resultant curved surface,

The net volume of refracting material becomes

where d is the depth of the cylindrical section removed to­gether with the segment. Elementary geometry requires

These underlying relations permit identification of the volume reduction for prescribed light-gathering levels. The complete analysis becomes involved algebraically, and it is sufficiently revealing to examine the limit where h2=R, which yields for the constraint A1 = A2:

Clearly, the ratio cannot be less than unity; and, in fact, as ho/R → 1, it approaches infinity.

It can be shown that for h2 ≠ R, that as h0/R → 1, the ratio approaches a finite value that grows as h2/R → 1.

Hence, mathematical analysis of the proposed lens structure does indeed admit the prospect of conserving weight and volume of a refractor lens while optimizing its light-gathering quality. Moreover, it is precisely in the realm of large objec­tive lens diameter that the gain becomes significant.

It remains, then, to construct prototypes of the suggested improvement in refractor telescopes to learn what practical limits prevail. The avenue set forth here could open new vistas in observational astronomy.

1656 APPLIED OPTICS / Vol. 15, No. 7 / July 1976