An interferometer incorporating phase-diffraction gratings brings optical accuracy to flatness testing of high slope regions. The gratings divide the output from a single source into two beams, recombining them at the surface under test. The interference pattern created by the reflected beams is equivalent to that which would be created by a source with wavelength ten times the size of the actual source, introducing the notion of the system "equivalent wavelength."
The equivalent wavelength of the grating interferometer is greater than visible wavelengths so the system can characterize a surface with higher slope and peak-to-valley departures than those accessible by conventional methods. The grating interferometer provides a bridge between high-precision Fizeau interferometers that can assess only surfaces with low rms variation and geometric-optics-based systems such as triangulation and moiré interferometry that are suitable for low-precision metrology.
In the grating interferometer, a pair of diffraction gratings are placed in front of and parallel to the object under test (see figure). The ruling frequency of the first grating is one-half that of the second. Collimated output from a white-light source is incident on grating 1. The element diffracts the incident light into two beams that diverge from one another. When the beams pass through grating 2, the diffraction process redirects them to converge on the same object point at different angles of incidence. The beams reflect from the object and pass through grating 2, converging at the surface of grating 1 and generating an interference pattern that is captured for subsequent analysis by a charge-coupled-device (CCD) array camera.
The angles of incidence of the two beams at the object plane drive the equivalent wavelength of the interference pattern. Depending on system particulars and beam alignment, the grating-interferometer equivalent wavelength can range between 4 and 40 µm.
Peter de Groot of Zygo Corp. (Middlefield, CT) developed the equivalent-wavelength approach, expanding on single-grating work performed previously. He has demonstrated a two-grating system with an equivalent wavelength of 8 µm. The 75-mm gratings are ruled with a frequency of 300 grooves/ mm. The system acquired data on a 30-mm-diameter sample of brush-finished aluminum with an rms surface roughness of 0.4 µm; the source beam incident angle was 11.6°. Using phase-shifting interferometry techniques in which the system detector registers data during a linear phase shift caused by mechanical translation of the sample on the order of the equivalent wavelength, de Groot obtained repeatabilities on the order of 1% of the equivalent wavelength.
The two-grating method involves diffraction, so it is complicated by tight grating tolerances and by the need to suppress transmission of the zero diffractive order. On the other hand, the approach offers the advantages of a large working distance, less-stringent source requirements, and high-contrast fringe patterns. In addition, a grating interferometer is vibrationally insensitive compared to conventional interferometers. Notes de Groot, "The equivalent wavelength is a good compromise between measurement range and the increasing demands of precision metrology in manufacturing."