Wavefront coding sees through aberrations

Jan. 1, 1999
Digital image processing may soon become a way to improve the performance of optical systems, at least if the efforts of CDM Optics Inc. (Boulder, CO) bear fruit.

Digital image processing may soon become a way to improve the performance of optical systems, at least if the efforts of CDM Optics Inc. (Boulder, CO) bear fruit. The company is commercializing a technique in which a specially contoured clear plate is inserted into the pupil plane of any standard optical system to alter the system`s point-spread function (PSF). The plate causes the PSF to remain unchanged in its intensity profile, even when the optics are highly aberrated, thus simplifying image-processing requirements.

The PSF, which is simply the image of a point object, ordinarily changes drastically when aberrations such as defocus or astigmatism are induced. The image of an extended object is made up of an infinite number of PSFs; if the PSF varies across the field, as when, for example, a microscope images an uneven object, then the image itself will vary in sharpness. A field-varying PSF is a problem for traditional image-processing techniques, explains Ed Dowski, vice president at CDM. "In this case, a calculation applied uniformly across the field will not work," he says.

The plate, called a cubic phase mask, can take one of two shapes. One is described in Cartesian coordinates and provides for rectangularly separable image-processing calculations. This version produces an L-shaped PSF (see Fig. 1). Another, described in polar coordinates, has the advantage that when two identical plates are overlapped, one can be rotated relative to the other to adjust the degree of phase alteration. In either case, the resulting spatially invariant PSF lends itself to easy image processing.

The technique, which Dowski calls "wavefront coding," was originally developed at the University of Colorado Imaging Systems Laboratory (Boulder, CO) and is exclusively licensed to CDM. Traditional image processing depends on techniques such as edge sharpening, color interpolation, distortion correction, and image compression, Dowski notes, while wavefront-coding processing--an offspring of radar systems communications theory--is based on linear filtering and one-dimensional (separable) or two-dimensional kernels and is object-independent.

When put to use, wavefront coding can lead to dramatic increases in focal depth (see Fig. 2). "We`ve increased depth of focus by up to ten times," says Dowski. He notes that wavefront coding acts equally well to reduce the effects of spherical aberration, axial color, and other lens aberrations. The only trade-off is an increase in image noise: for example, an image digitized to ten bits will lose two bits to noise.

Dowski is most excited about the potential of using wavefront coding to reduce the cost of optical systems. "The price of digital-signal processing is getting down to pennies per million instructions per second," he says. "Falling electronics prices and constant optics prices will lead to more electronics and less optics." Given an optical system in which the image is captured electronically, he explains, the reduction in cost and complexity of optics can more than offset the cost of adding wavefront coding. He mentions the machine-vision industry as one in which CDM is involved as an OEM. To encourage evaluation of wavefront-coding technology, CDM sells a kit that includes a 0.5-in.-diameter plastic cubic phase mask.

Researchers at CDM are currently working on optimizing wavefront coding for high-numerical-aperture optics such as high-magnification microscope objectives, where depth of field is short, alignment tolerances are tight, and aberrations can vary severely across the field. One possible outcome of the research is a fluorescence microscope free of chromatic aberration and with a large depth of field.

About the Author

John Wallace | Senior Technical Editor (1998-2022)

John Wallace was with Laser Focus World for nearly 25 years, retiring in late June 2022. He obtained a bachelor's degree in mechanical engineering and physics at Rutgers University and a master's in optical engineering at the University of Rochester. Before becoming an editor, John worked as an engineer at RCA, Exxon, Eastman Kodak, and GCA Corporation.

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