An autocollimation method has been developed whereby the centering of component surfaces within an optical system may be measured. Paraxial transfer formulas containing a quantity called eccentricity are developed after definitions have been promulgated for certain terms. For a given optical system, the position, with respect to a reference axis, of an image due to reflection from an optical surface within the system depends on (a) the distance of the object from the reference axis, (b) the magnification of the reflecting and refracting surfaces involved and (c) the eccentricities of each surface. If all other factors are known, the eccentricity of each surface may be computed from measurements of the displacement of the autocollimated image.
With equipment commonly available certain optical systems may be examined and with proper instrumentation other systems, including bent systems utilizing reflecting prisms or mirrors, may be inspected. A few possible applications are as follows: 1. adjusting a lens on an edging machine; 2. measuring the eccentricity of lens surfaces with its edge; 3. measuring lens eccentricity on a lathe during mounting; 4. measuring the eccentricities of the various surfaces of a photographic lens; 5. checking the centering of a telescope, binocular or periscope; 6. decentering an optical element by a known amount in order td determine the effect of eccentricity on the performance of the system.
A. L. INGALLS and K. PESTRECOV, "Centering of Optical Systems," J. Opt. Soc. Am. 38, 343-343 (1948)