Method for Increasing the Accuracy of Interferogram Analysis

If we turn to interferometric works of the recent past, they state as an indisputable fact that the accuracy of analyzing two-beam interferograms cannot, in the best case, exceed a few hundredths of a wavelength. This value proves to be altogether insufficient for the purposes of modern measurement technology. In connection with this, in recent years a number of successful attempts have been undertaken to step beyond this limit and to increase the accuracy of interferometric measurements by somewhat complicating the process of carrying them out. Some of the methods proposed for this have already been described on the pages of our journal. These include methods of multi-beam interferometry, the three-beam interferometer of Chernike, the modulation method of interferometry developed by G. S. Gorelik, photoelectric methods of counting and locating interference fringes, as well as the method of their

photographic contrast enhancement. The author of the paper under review*) proposes, for the same purpose, yet another method, equally suitable for both two-beam and multi-beam interferograms.

The essence of the method, applicable to the investigation of a weakly expressed relief of plane surfaces, consists in replacing the cross of threads usually used to determine the position of interference fringes by a network of the same interference fringes obtained from the same region of the surface, but under somewhat different conditions.

To make it possible to fix with sufficient accuracy the position and orientation of the interference fringes on the surface under investigation, three marks are put on the latter. By an appropriate choice of the inclination of the reference surface of the interferometer, a sufficiently dense network of nearly straight interference fringes is obtained (and photographed), running so that one of the fringes passes through two of the applied marks, while another, differing by 15–20 interference orders, passes through the third mark. Then the inclination of the reference surface is changed to the opposite one, and the former interference pattern is reproduced, with the sole difference that, because of the different direction of inclination, all the distortions and displacements of the interference fringes caused by the relief of the measured surface have the opposite direction.

Then, for example with the aid of a double microscope, the photographic images of both interference patterns are superposed along a certain line (separating the field of view) perpendicular to the direction of the interference fringes, and by relative displacement of the images the most exact possible coincidence of one or another of the fringes is obtained. It is clear that the magnitude of the relative displacement of the images is in this case a direct measure of the local change in the height of the relief (on a doubled scale).

By tracing the changes in relief along a fringe, it is not difficult to construct (with the aid of a pantographic device) a contour map of the region of the surface under consideration. The author asserts that in this way it is possible to attain an accuracy of the order of 0.002 of the wavelength of light.

Another method is also possible for analyzing interferograms obtained in this manner, based on the use of the stereoscopic effect. In fact, since the fringes in the photographs are distorted in opposite directions and the magnitude of the parallax changes from point to point depending on the form of the surface, in stereoscopic viewing of the photographs each fringe directly reproduces the corresponding relief line of the surface, with an increase amounting to approximately a million times. It should be borne in mind, however, that owing to a number of factors there appears a tendency toward differing subjective estimates of the height of ridges running along and across the interference fringes. This difference becomes insignificant in the case when the surface relief is sufficiently smooth. Such a technique is especially convenient, since it makes it possible to obtain a direct representation of the character of the relief.

The stereoscopic effect can also be used for a quantitative measurement of the surface relief. For this purpose both images are projected through different light filters (for example, red and green) onto a screen and are viewed (as is done in stereoscopic cinema) through the corresponding color spectacles. As a result, the irregularities of the relief protrude from the plane of the screen forward or backward, and their height can be measured by direct approach or withdrawal of the screen relative to the projection apparatus.

V. Yur'ev

) J. W. Gates, Brit. Journ. Appl. Phys. 5*, No. 4, 133 (1954).