Precision optics requires testing; otherwise things can and will go wrong. Spheres and flats are routinely tested using commercial Fizeau interferometers. Conic aspheres can also be tested with spherical wavefronts at their conic conjugate points. In contrast, testing a general aspheric surface requires a custom aspheric wavefront. With the notable exception of cylinders, the required wavefront is unique to each asphere. Often, the production of an appropriate null corrector plate can be as difficult as the fabrication of the actual optic.
Figure 1. F/1.5 CGH cylinder null inter-ferogram includes a retro-reflecting annulus for aligning the collimated source and establishing the image scale. Phase-reversed bars (left and right) identify cylinder null axis as horizontal. This cylinder has about 5 fringes of toroidal curvature.
A computer-generated hologram (CGH) null corrector is a diffractive optic written by e-beam or laser lithography that yields a nominally flat or null interferogram (see figure 1). CGH nulls offer several advantages over con- ventional null correctors comprised of multiple refractive and/or reflective spherical elements. CGH nulls do not become more difficult to produce as more aspheric terms are added, and moreover, they can be designed to null an off-axis segment rather than its entire parent. CGH nulls are often simpler to align and easier to certify, although the certification methods may be less familiar.
Engineers tested the Hubble COSTAR aspheres using CGH nulls located inside a modified Twyman-Green interferometer. Because such interferometers are not commercially available, most CGH nulls are instead located external to the interferometer. In this external configuration, the CGH null transforms a spherical, or collimated, wavefront into the appropriate aspheric wavefront. After reflecting from the test asphere, the aspheric wavefront retraces its path and is converted back into a spherical wavefront. To the interferometer, the combination of CGH null and asphere looks like a sphere.
Although they can be used in double pass, external null correctors (CGH or conventional) are most easily designed in single-pass configuration. We model the aspheric surface as a boundary between a fictitious medium of index n = 0 and air. As the source rays meet the air, they refract perpendicular to the aspheric surface, forming the required null wavefront. The design is completed by optimizing the null corrector to bring the null wavefront to a perfect focusthe spherical wavefront. The null corrector design does not require any detailed knowledge of the interferometer optics.
Figure 2. Morphed OPD map corrects cylinder interferogram for test pupil inversion and aspect ratio distortion. Tilt and cylinder focus fringes are artifacts of cylinder misalignment and have been subtracted.
Because aspheric wavefronts change shape as they propagate, and because the CGH null often is not located at an image of the test pupil, the test pupil may be distorted at the camera that captures the resultant interferogram. This distortion must be compensated for if the interferogram will be used to close the loop on a computer-controlled figuring process. Morphing coefficients for undistorting the interferogram are a byproduct of the CGH design (see figure 2).
CGH nulls produce spurious diffraction orders that must be separated to prevent ghost fringes. This is accomplished by introducing focal power or wedge into the CGH null and must be modeled in double-pass.
Alignment is critical to producing accurate results in any kind of interferometry. Because CGH nulls are lithographically produced, they can easily include optical features to aid in the test alignment. Most useful is a grating to retro-reflect the spherical source, yielding a null alignment interferogram when the CGH is correctly positioned; that leaves only the asphere itself to be aligned. For diamond-turned aspheres that include precision flats, a CGH can produce a collimated wavefront for optically aligning tilt and tip. The CGH can produce focused spots at precise locations on or near the asphere for finding centration and spacing. If the null wavefront fills the CGH or interferometer aperture, then such alignment features can be placed on a separate alignment CGH that is interchanged with the CGH null.
For testing of a mirrored aspheric surface, the CGH can be chrome on silica, yielding 10% diffraction efficiency. For testing of lower reflectivity aspheres, a binary pattern etched directly into the silica offers about 35% diffraction efficiency. CGH grating periods are typically in the range of 4 to 40 µm. For an e-beam patterning accuracy of 0.2 µm, this yields a wavefront accuracy of 0.05 to 0.005 wavelengths. oe
Steven Arnold is president of Diffraction International, Minnetonka, MN.