Interferometric test method for testing convex aspheric mirror surfaces
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1 Interferometric test method for testing convex aspheric mirror surfaces T. Stewart McKechnie McKechnie Optics Research, Paganica Way NE, Albuquerque, NM 87111, USA Keywords: Interferometry, interferometric testing, convex aspheric surfaces, surface shape measurement Abstract An interferometric null Test Method is described for testing convex aspheric surfaces, such as found in secondary mirrors of Cassegrain telescopes or variations thereof such as Mersenne and Ritchey-Chrétien. A family of test designs is described covering a wide range of mirror diameters, radii of curvature, and aspheric shapes as described by conic constants and/or polynomials. The Test Method has been used successfully for testing the convex hyperboloid surface of the 244-mm diameter secondary mirror of the NASA 3-meter IRTF telescope. The Test Method is currently being used to test the 120-mm diameter, convex paraboloid secondary mirrors of the Magdalena Ridge Observatory Interferometer (MROI). Test designs exist on paper for both Keck secondary mirrors (0.53-m and 1.4-m diameter), the HST secondary (0.3-meter diameter), and secondary mirrors of some of the extremely large telescopes of the future, such as the TMT secondary (3.2-m diameter). In typical test embodiments, the simplicity of the Test enables rapid implementation at a fraction of the cost of comparable Hindle-Sphere or Hindle-Simpson tests. 1. Introduction Large reflector telescopes are generally Cassegrain or variations thereof such as Mersenne and Ritchey-Chrétien. All share the property of having convex aspheric secondary mirrors: hyperboloid for the Classic Cassegrain and Ritchey- Chrétien, paraboloid for the Mersenne. A widely-used interferometric test for convex aspheric secondary mirrors, including those just mentioned, is the Hindle-Sphere test. Figure 1 shows an improved version of the Hindle-Sphere test, the Hindle-Simpson test 1. This test uses two ancillary optical components. Both have spherical surfaces. One is a meniscus component the Hindle sphere the other a concave calibration mirror. The surfaces of the ancillary optics are figured to high precision. The diameters have to be larger than the diameter of the convex mirror under test. Hindle-Simpson null tests are carried out at the conjugate distances used by the telescope. For large telescope secondaries, these distances can be correspondingly large. A shortening lens is sometimes used (Figure 2) to reduce test track length. The surfaces of the shortening lens must also be figured to high precision; lens diameter again has to be larger than the diameter of the convex mirror under test. The Test Method described in this paper offers an alternative to Hindle-Sphere tests. An embodiment is shown in Figure 3. While the Test Method cannot be used with opaque mirror substrates, the Method has a number of advantages over comparable Hindle-Sphere tests when used with transmissive substrate materials, such as fused silica, Zerodur, Clearceram-Z, and other optical glass types. Experience gained thus far indicates that Test Method embodiments can be built and implemented more rapidly and at a fraction of the cost of comparable Hindle-Sphere tests. To test a medium-sized secondary mirror (say 250-mm diameter) using a Hindle-Sphere test could mean outlays of several-thousand dollars for suitable-sized ancillary optic substrates figured to suitable optical specifications. In comparison, substrate and fabrication costs for the smaller ancillary optics used by the Test Method may amount to just a few hundred dollars. The small size and simple shapes of the ancillary optics (often plano-convex) enable low cost Test setups that are capable of high measurement accuracy. In typical Test implementations, residual null test wavefront error is about λ/100 (HeNe).
2 Figure 1: Hindle-Simpson test - a standard test for surface figure quality of convex aspheric mirrors. Carried out at the optical conjugates of the telescope, the test constitutes a perfect null test. Figure 2: Shortened Hindle-Simpson test, another standard test for convex aspheric mirrors. Figure 3: Test Method embodiment used for testing the 244-mm diameter NASA secondary mirror.
3 2. Test Method Referring again to Figure 3, the Test Method works as follows: Both front and rear surfaces of the convex aspheric secondary mirror under test the Test Optic are polished, thereby transforming the mirror into a lens. The mirror is then tested as if it were a lens by an interferometric null test, prior to applying a reflective coating to the convex mirror surface. Patent applications relating to the Test Method are listed in Section 10. All standard aspheric shapes can be tested using the Test Method, including hyperboloids, paraboloids, and ellipsoids. The Test Method may also be used for testing other more general types of aspheric shape, as described by polynomial equations. The surfaces of the ancillary optics may be either flat or spherical. Test accuracy is matched to requirements. Peak-to-Valley (P-V) wavefront error residuals of the null test are typically about λ/100 (HeNe) but, if needed, can readily be reduced to about λ/1,000 (HeNe). For most purposes, the Test constitutes a perfect null test. 3. Test Method applications In 2009, the convex hyperboloid secondary mirror of the NASA 3-meter Telescope (IRTF, Mauna Kea) was re-figured by Optical Surface Technologies (OST) as part of a telescope optics upgrade program. Secondary mirror surface figure was tested by OST using the Test Method embodiment shown in Figure 3. In its original state, the NASA secondary mirror had P-V surface figure errors of about 1. λ (HeNe) not unusual for telescope optics built in the 1970s. The goal of the secondary mirror upgrade was to reduce this error to λ/8 (HeNe). The Test is currently being used to test the 120-mm diameter convex paraboloid secondary mirrors of the (sixtelescope) Magdalena Ridge Observatory Interferometer. Wider application of the Test Method has been explored through Test designs (on paper) for testing numerous other convex aspheric secondary mirrors. These include both Keck secondaries (0.53-meter and 1.4-meter diameter), the HST secondary (0.3-meter diameter), and the TMT secondary (3.2-meter diameter). In the above applications, the use of uncomplicated in some cases COTS Null Lenses offers the prospect of Test implementations at a fraction of the cost of equivalent Hindle-Sphere tests. The convex surface of the secondary mirror must of course be figured to a precise aspheric shape. There is no similar requirement for the rear surface. This surface may be figured to any convenient shape flat or spherical, convex or concave. Tested as a lens rather than a mirror, the Test Optic introduces significant amounts of spherical aberration, comprising first-order and higher orders. To cancel this aberration, an ancillary lens is used the Null Lens shown in Figure 3. The goal is usually to provide a near-perfect null test, but residual aberrations particularly if only a few waves can be calculated and subtracted, providing a form of null test. There is no obligation to carry out the Test at the optical conjugates used by the telescope. Any convenient conjugate set may be chosen, consistent with providing a practicable Test that delivers required test accuracy. 4. Test Method family An infinite number of Test Method embodiments can be envisaged. The family sub-divides into three main classes, corresponding to the Test geometries shown in Figures 3, 4, and 5. There are many sub-classes and permutations. The different geometries offer a range of measurement sensitivities and choice of Test track lengths. Track length of the Figure 3 embodiment is roughly the same as the focal length, f, of the Test Optic (considered as a lens). For the NASA Zerodur secondary equipped with flat rear surface, f is about 2-meters. Residual null test error for
4 Figure 4: Test embodiment with longer track length (~ 4. f). Residual wavefront error for this type of null test embodiment is usually small (~ λ/1,000). Figure 5: Test embodiment with ultra-short track length. For Test Optic with flat rear surfaces and substrate refractive index ~ 1.5, track length is given roughly by f/3. this Test embodiment corresponds to a P-V surface figure error on the convex mirror surface of about λ/70 (HeNe). Convex mirrors tested as in Figure 4 have Test track lengths of about 4. f, about four times longer than track lengths in Figure 3 embodiments. Generally, increased track length associates with increased test sensitivity. For the NASA secondary tested as in Figure 4, null test residuals correspond to a P-V surface figure error of about λ/2,000 (HeNe). Track lengths in Figure 5 embodiments are generally short, typically about f/3, which means compact Test setups. The Figure 5 arrangement is similar to those proposed in 1983 by Meinel and Meinel 1. For the NASA secondary tested as in Figure 5, null test residuals correspond to a P-V surface figure error of about λ/125 (HeNe). Null Lenses used in the NASA secondary mirror Test embodiments shown in Figures 3, 4, and 5 all have simple plano-convex or planoconcave designs, so that residual surface figure errors, such as the λ/125 just indicated, are useful for cross-comparing test accuracies offered by the different Test geometries. Fold mirrors may be used anywhere in the optical path to shrink Test area footprint. By making the rear surface of the Test Optic convex or concave spherical, Test Optic focal length and hence Test track length can be adjusted. In the Figure 5 Test embodiment, the surface is tested by internal reflection (in contrast to the transmission mode Test embodiments used in Figures 3 and 4). The Figure 5 Test embodiment can provide improved discrimination of surface figure error, the improvement factor being n/(n-1), where n is substrate refractive index. For common substrate materials such as fused silica, Zerodur, and Clearceram-Z, n/(n-1) is about 3. A disadvantage of the Figure 5 Test geometry is that larger amounts of spherical aberration may have to be compensated. To preserve null test accuracy, more complicated Null Lens designs may be necessary, which tends to offset the initial advantage.
5 5. Optical homogeneity requirement for Test Optic Refractive index inhomogeneity in Test Optic substrates can affect Test accuracy. Fused silica, Zerodur, and Clearceram-Z are all available in highest-grade (Grade 5) blanks. All three materials make suitable Test Optic substrates. Inhomogeneity may become more of an issue for larger thicker secondary mirrors. By initially flattening and polishing the front and rear surfaces of the Test Optic, inhomogeneities can be characterized, the characterization used later to correct final surface figure data. 6. Null Lens The Null Lens used for testing the NASA secondary mirror (Figure 3) is a custom plano-convex lens made from highest grade Grade 5 fused silica. Null Lens surface figure accuracy is crucial to overall Test accuracy. By oversizing the Null Lens, P-V surface figure errors of less than λ/100 (HeNe) are readily achieved over clear aperture portions. Null Lenses are often plano-convex. Sometimes they are COTS, facilitating rapid Test implementation. For more challenging Test applications, Null Lenses with aspheric surfaces could be used. But a simpler approach is to use a Null Lens design comprising two (or more) conventional lenses. Null Lens diameters are significantly smaller than Test Optic diameters. For example, a Figure 4 Test embodiment designed for testing the 300-mm diameter HST secondary mirror uses a 25-mm diameter COTS Null Lens. Despite the simplicity and low cost of this particular Null Lens, the Test embodiment delivers λ/1,000 (HeNe) residual null test accuracy. 7. Interferometry (and wavefront sensing) The Test may be carried out at any wavelength transmitted by the substrate. Fused silica, Zerodur, and Clearceram-Z are all transmissive at standard visible test wavelengths, such as 633 nm. UV, IR, and other wavelengths can also be used. The interferometer test beam may be collimated, convergent, or divergent, the latter options provided by transmission spheres. For tests involving longer paths, vibration-insensitive interferometers are desirable. Frequency stabilized lasers have coherence lengths of about 100 meters, sufficient for testing very large several meter diameter convex secondary mirrors, such as found in ELTs. The scope of the paper limits the discussion to interferometric applications. However, the Test Method can be used equally with wavefront sensing techniques, with only minor modifications needed to the Test setups. 8. Relaxing figure requirement on rear surface of Test Optic The rear surface of the Test Optic can be made flat or spherical, concave or convex. If multiple copies of the same Test Optic have to be made, having to figure each individual rear surface to high precision could add significantly to overall production costs. The figure requirement on the rear surface can be significantly reduced by index-matching this surface to a Test Window of good optical quality, as shown in Figure 6. Index-matching liquids are commercially available with refractive indices held to about +/ In a typical index-matching enactment, one surface of the Test Window is figured to high precision, perhaps to λ/20 (HeNe) or better. The other surface the left-hand surface in Figure 6 is figured to lower precision, as discussed below. With Test Window and Test Optic index-matched together, figure requirement for the rear surface of the Test
6 Figure 6: Relaxing surface figure requirement on rear surface of Test Optic by index-matching to a precisely fabricated Test Window. With close enough index-matching (+/ ) a ground or generated finish on the rear surface may be adequate. Optic relaxes by a substantial factor perhaps 1000x to about 10. λ (HeNe). A ground or generated surface may satisfy the relaxed requirement. A similar figure relaxation also occurs in the contacting surface of the Test Window. Test Window cost may be amortized over the number of mirrors (Test Optics) produced. 9. NASA 3-meter telescope secondary mirror Test embodiment Figure 3 shows the double-pass Test setup used for testing the NASA secondary mirror. Figure 7 shows final surface figure achieved. By testing the convex aspheric surface in transmission as in Figure 3, surface figure errors appear 1/(n-1) times smaller than had the test been carried out in reflection. When used on the telescope, the Zerodur NASA secondary (n = 1.54) produces wavefront errors about 1.85x larger than those indicated by Figure 7. Figure 8 (Left) shows a theoretical interferogram for a perfectly-figured NASA secondary mirror. Figure 8 (Right) again shows the NASA mirror, but with distorted fringes caused by a significant conic constant error. Figure 9 shows the theoretical double-pass residual null test wavefront error for the (Figure 3) NASA secondary Test embodiment. Residual wavefront error corresponds to a surface figure error on the mirror of about λ/70 (HeNe). Had a more precise null test been required for the NASA secondary, a Figure 4 embodiment type with λ/2,000 (HeNe) residual error could have been used. For the NASA mirror, however, shorter track length was preferred over what was considered unnecessarily high null test precision. Figure 7: Interferogram showing final surface figure achieved by OST on the refurbished, 244-mm diameter hyperboloid NASA secondary mirror. P-V surface figure error λ/8 HeNe).
7 Figure 8: (Left): Fringe appearance at 633-nm for perfectly-figured 244-mm diameter hyperboloid NASA secondary mirror, tested as in Figure 3. (Right): Fringe appearance for same mirror with significant conic constant error ( instead of ). Figure 9: Theoretical residual null test wavefront error, P-V λ/130 (HeNe), for the NASA secondary mirror, tested as in Figure 3. Wavefront corrugations are barely discernible. Vertical plot scale: +/- λ/2 (HeNe). 10. Patents [1] Test Method for Surface Figure of Large Convex Mirrors. Inventor/Applicant Name: Thomas Stewart McKechnie; Filed Dec 24, 2008; Application Number 12/ [2] Test Method for Surface Figure of Large Convex Mirrors, continuation-in-part of pending Application Number 12/ Inventor/Applicant Name: Thomas Stewart McKechnie; Filed May 17, 2009; Application Number References [1] Malacara, D., (Ed.), [Optical Shop Testing], Second edition, John Wiley & Sons, Inc., (1992).
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