Parallel-Beam Interferometry With Incoherent Light
It should be possible to achieve resolution beyond the diffraction limit.
NASA's Jet Propulsion Laboratory, Pasadena, California
A technique of parallel-beam interferometry with spatially incoherent light has been proposed to solve two problems that arise in conjunction with using interferometry to measure the shape of a surface. The first problem is how to obtain spatial resolution in excess of the diffraction limit; the second problem is how to measure the variation in the shape of an object with temperature.
Figure 1 illustrates the principle of operation. Spatially incoherent light (e.g., light from an incandescent lamp) would be collimated, then made to pass through beam-splitting-and-combining optics that would split the light into two parallel beams aimed toward the object of interest. These optics would be adjustable to a change the distance between the two beams. The light reflected by the object would pass back through the beam-splitting-and-combining optics which combine the two beams back into a single beam, then through imaging optics into a camera. Objective optics may or may not be used, as explained below.
The technique can be characterized as one that utilizes speckle interferometry with a variable speckle. The splitting of the source incoherent beam into two parallel beams introduces a delta-function spatial coherence that gives rise to a speckle interference in the camera. The speckle pattern is measured as the distance between the two beams is changed. The change in distance changes the location of the delta function in the spatial coherence, and a spatial autocorrelation function is measured. The surface of the object of interest can be determined accurately from the autocorrelation function. Under ideal conditions, resolution beyond the diffraction limit can be achieved.
The solution to the second problem would have to involve utilization of the speckle interferometry in a way that would make it unnecessary to scan the beams. One such way would be to form more than one interference pattern by use of more than two beams, in a generalization of the basic concept that involves several two-beam interferometers working together.
Figure 2 presents an example of a parallel-beam interferometer according to the proposal. A collimated beam of light would pass through an assembly of beam splitters and prisms. The first beam splitter together with the second beam splitter would cause both beams to traverse the same path (and thus the same path length) in opposite directions; this would ensure that white-light fringes would be imaged on the camera. The objective optics may or may not be used, depending on the required numerical aperture, which, in turn, would determine the diffraction-limited imaging resolution. The two beam splitters and the right-angle prism would be moved together to change the distance between the two beams without changing the difference between their optical-path lengths.
In addition to resolution beyond the diffraction limit, the proposed technique would afford several other advantages over prior interferometric imaging techniques:
1. The distance to the object could be set arbitrarily.
2. The alignment of the object with the interferometer would be simplified.
3. Because the two beams would be of the same magnitude, regardless of the reflectivity of the object, the visibility of the fringes would be relatively high.
4. Because the two beams would travel along nearly the same path, effects of variations in the index of refraction of air would be relatively small. Only high-frequency index variations like those associated with turbulence would be problematic.
5. Imaging could be done with very small numerical apertures, so that it would be possible to use working distance longer and optics smaller than those customarily used.
Figure 1. In Parallel-Beam Interferometry, an object would be illuminated with two closely spaced, parallel beams generated by splitting a single input beam. The distance between the parallel beams would be adjustable in any direction in the plane perpendicular to the axis of propagation.
Figure 2. This Optical Layout is one of several candidate layouts for a practical parallel-beam interferometer. The two nonpolarizing beam splitters and the prism would be moved in coordination to adjust the distance between the parallel beams.This work was done by Roman C. Gutierrez of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.nasatech.com under the Physical Sciences category.
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