Common-path heterodyne interferometers (COPHIs) have been proposed for measuring small variations in the heights of surfaces. A COPHI could be used, for example, to measure the deviation of the surface of a mirror or other optical component from nominal flatness or nominal sphericity. Like phase-shifting interferometers that have been used previously for the same purpose, a COPHI would generate an optical-phase map equivalent to a topographical map of the surface under test. The advantages of the COPHI over a phase-shifting interferometer would be (1) greater resolution in phase and thus in surface height and (2) shorter measurement time.

The figure depicts a COPHI for measuring the deviation of a mirror from flatness. The light from a laser would be split into two coherent beams, denoted 1 and 2. By use of an acousto-optical modulator, beam 1 would be modulated at a radio frequency f1. In the same manner, beam 2 would be modulated at frequency f2, which would differ from f1 by a convenient amount, e.g., 10 kHz. Half of beam 1 would pass through beam splitter 1. The mirror under test would be positioned to retro-reflect beam 1. After reflecting off beam splitter 1, beam 1 would combine with beam 2 at beam splitter 2 to an form interference fringe.

A Common-Path Heterodyne Interferometer could generate a high-resolution surface-height map of a mirror surface under test. A multichannel version would be capable of sampling the surface under test in a relatively short time.

The interference fringe would then be split into two identical sets with beam splitter 3. One set of fringe would pass through a large iris 1, which would sample the entire portion of the mirror surface. The light would be coupled into and through an optical fiber to photodiode 1; consequently, the phase of the |f1 - f2| frequency heterodyne output of photodiode 1 would amount to an average over the entire mirror surface. This heterodyne output would be used as a reference signal (REF). The other set of fringe would then pass through a much smaller iris 2, which would select a small spot on the mirror for measurement. After passing through iris 2, the light would be coupled into and through a second fiber to photodiode 2. This heterodyne output would be used as measurement signal (UNK). The phase of the |f1 - f2| frequency heterodyne output of photodiode 2 would thus correspond to the surface height at the measurement spot.

A high-resolution phase meter would measure the phase difference between UNK and REF, thus providing a measurement of the deviation of the measurement-spot surface height from the average surface height of the mirror. Because of the common path nature of REF and UNK signals, many error sources such as vibration would become common-mode error in the measurement. This interferometer configuration would allow much higher resolution than phase-shifting interferometers.

A surface-height map of the test surface could be generated from phase readings acquired in a mechanical scan of iris 2. Of course, such a scan would take some time. To eliminate the need for mechanical scanning, one could construct a multichannel version of the COPHI: Iris 2 would be replaced by a 2-D array of lenslets registered with input ends of many optical fibers. Each optical fiber would define a pixel in the interference image of the test surface. The output ends of the optical fibers would be connected via an optoelectronic switch to a smaller number of photodiodes. By a combination of electronic and optoelectronic switching, the outputs of the photodiodes would be fed sequentially to the phase meter to generate a sequence of phase readings, each corresponding to one pixel.

This work was done by Feng Zhao of Caltech for NASA's Jet Propulsion Laboratory.


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Common-Path Heterodyne Interferometers

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