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Because many models of Graham Interferometers provide a fixed reference flat as an integral part of the instrument, it is relatively easy to measure the sphericity and radius of spherical surfaces using any "good" converging lens.  For example, the operator may select a high quality camera lens of appropriate aperture and focal length.

This offers a distinct cost advantage and for many applications is more than sufficient. First let us consider the measurement of a concave surface.

First let us consider the measurement of a concave surface. The plane wavefront leaving the reference surface is converted to a spherical wavefront by the converging lens and is directed to the focal point after which it diverges -- still a spherical wavefront.  Unlike a Transmission sphere, this system does not require a spherical reference surface.  Instead, after striking the test surface, the beam is reflected back through the lens.  If the test surface is spherical, and positioned at either the Focus of the lens, or with its center of curvature coincident with the focus of the lens (Confocal Position) the reflected wave front will be converted back to a plane wave front by the lens, and then compared to the reference flat of the interferometer. 

Thus, a properly aligned spherical surface will show straight interference fringes.  Any deviation from spherical will result in distortion of the interference fringes.  Any variation in axial position of the test piece will result in closed (circular) fringes -- just the same as when using standard techniques with a transmission sphere. There is no limit on the radius of curvature that can be measured on a concave test piece, but the maximum diameter that can be measured is limited by the F/# of the converging lens -- just as with a transmission sphere.

Just as with a transmission sphere, the distance between the "Cat's Eye" Position and the Confocal Position is the radius of curvature.

Now, when measuring a Convex Surface, the maximum radius of curvature is limited by the focal length of the converging lens and, of course, the maximum diameter of the test piece is limited by the F/# of the converging lens.  Again this is no different from the limitation imposed by a transmission sphere.  However, since the converging lens is most likely a quality camera lens, the relative low cost permits the purchase of a selection of lenses with a range of focal lengths. 

The setups for convex lenses, illustrated below, are exactly the same as would be employed when using a Transmission sphere.  As when measuring a concave test piece, the distance from the "Cat's Eye" position to the null fringe position is the radius of curvature.


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This page last updated April 23, 2013