<p>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 (<i>a</i>) the distance of the object from the reference axis, (<i>b</i>) the magnification of the reflecting and refracting surfaces involved and (<i>c</i>) 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.</p><p>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.</p>

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