Sphericity and radius of curvature measurements

Each interferometer setup example shows a MiniFIZ laser interferometer mainframe, a part being tested, and the optical accessories required to make the interferometry setup work. The accompanying text explains how the setup is used.

Transmission Sphere Selection

Transmission spheres of various f/numbers are available as standard items, and others may be obtained on special order. If the speed (R/number) of the surface under test does not match the f/number of the transmission sphere being used, one of two situations will occur. If the R/number is smaller than the f/number, the interferogram will not fully cover the entire aperture of the surface under test. If the R/number is larger, the interferogram will be smaller than full size. However, the Mainframe’s f/number zoom can be used to bring the image on the viewscreen to full size over a 6X range in the latter situation. In order to select the optimum transmission sphere f/number to fill the aperture of a concave or convex surface, the R/number of the surface to be measured is calculated using the following formula:

R/Number= Radius of curvature of surface under test/ Clear aperture of surface under test

Suggested Accessories: Phase Shifting Interferometer; Transmission flat, 4%; Mount, 3-axis; Self-centering element holder.

Concave Surface Figure - Sphericity

A transmission sphere transforms the Mainframe output beam into a precise spherical wavefront for the evaluation of spherical surfaces and lenses. A concave spherical surface is examined for surface figure and irregularity, i.e., the deviation from the best-fitting sphere, by placing its center of curvature coincident with the focus of the transmission sphere. Adjustment of the surface under test is typically provided by a 3-axis mount.

Suggested Accessories: Phase Shifting Interferometer; Transmission sphere; Mount, 3-axis (tip-tilt); Self-centering element holder.

Sphericity of Convex Surface Figure

Convex spherical surface are examined for surface figure and irregularity using the setup shown. In order to select the optimum transmission sphere, two criteria must be met. Firstly, the radius of curvature of the convex surface under test must be less than the back focal length of the transmission sphere; and secondly, the radius of curvature of the surface under test divided by the clear aperture, i.e., the R/number, should be approximately equal to the f/number of the transmission sphere. Six–inch diameter transmission spheres are available for this application. Adjustment of the surface under test is typically provided by a 3-axis mount.

Suggested Accessories: Phase Shifting Interferometer ;Transmission sphere, diverger; Mount, 3-axis; Self-centering element holder.

Radius of Curvature

Non-Contacting Spherometer Radius and Figure

In addition to surface figure and irregularity, the radius of curvature of either a concave or convex spherical surface can be measured. The center of curvature of the test surface is interferometrically made to coincide with the focus of the spherical wave emanating from the transmission sphere. This is the location shown in the animation, in which the lens is farthest from the interferometer mainframe. Note that a concave test surface would invert the motion in this animation. In this arrangement, the fringe pattern provides information not only about the figure and irregularity of the surface under test, but also about the precise location of the center of curvature of the test surface with respect to the focus of that transmission sphere. The surface under test is then translated along the optical axis of the interferometer until the surface under test coincides with the focus of the spherical wave from the transmission sphere, as shown in the animation, when the hand introduces a card into the lightpath. This is known as the “cat’s eye” position. The fringe pattern again provides a very sensitive indicator of the point where the surface coincides with the focus. The distance that the surface under test is translated, Rx, is equal to the radius of curvature of that surface. The digital radius slide provides a convenient readout of this distance. This technique is typically accurate to 10microns or 0.1% whichever is larger, but precision is subject to the accuracy of the linear gauge. Contact customer support for a list of gauges compatible with ADE Phase Shift interferometers. For cases where extreme accuracy is required (1 micron or 0.001%) an Interferometric Radius Slide is available that inputs distance measurements directly to the interferometer’s processor and is corrected for focus errors.

The equivalent surface figure and irregularity and radius of curvature of a high quality spherical or cylindrical surface can be determined is a function of:

Suggested Accessories: Phase Shifting Interferometer; Transmission sphere; Mount, 3-axis; Self-centering element holder; Linear gauge and slide mounting assembly.

Choosing an Aperture Diameter

Unlike plano surfaces, concave surface of any size can be examined in their entirety without depending upon the interferometer aperture diameter. This is accomplished by generating a diverging measurement wavefront of an f/number equal to, or somewhat faster than, the R/number of the test surface.

Convex surfaces, which must be placed in a converging measurement beam, may require a larger interferometer aperture. For convex surfaces of large size and/or long radius, it may be necessary to begin with a larger aperture converging beam produced by the appropriate transmission sphere.

ADE Phase Shift offers fizeau interferometers with apertures of 300mm, 150mm, 100mm, 50mm and 12.5mm to accommodate nearly any aperture requirement.

Aperture Converters

ADE Phase Shift offers a 4inch to 6inch (100mm to 150mm) aperture converter. The converter accepts standard 150mm elements. The converter permits full resolution measurement of 150mm flats, and greater flexibility in measuring convex surfaces.

Interferometer Measurements

Using MiniFIZ Laser Fizeau Interferometer

Sphericity and radius of curvature metrology