FREE-FORM OPTICAL COMPONENTS IN SOME EARLY COMMERCIAL PRODUCTS William T. Plummer President, WTP Optics, Inc. Sometime Senior Director of Optical Engineering, Polaroid Corp. The Polaroid SX-70 folding Single Lens Reflex camera was introduced in 1972. Because of its peculiar off-axis viewing optical system, we used two free-form optical components in its optical design. One large free-form surface, deployed on the eye lens, corrected for field tilt and localized apparent power and astigmatic errors across the viewed scene, relayed from a textured Fresnel field mirror focus screen. The other free-form surface, a small corrector plate located just at the real aperture stop, mainly corrected the net coma and spherical aberration common to all of the field. These two surfaces were optimized along with an off-axis aspheric concave mirror to provide a well-corrected system. The eyelens free-form surface functioned much like a familiar progressive-power spectacle lens, or smeared-out bifocal lens. The concept for such a lens goes back about a century, but the optical requirements for designing a good one were laid out by C. W. Kanolt in a 1959 US Patent. The eyelens surface used by Polaroid was different from Kanolt's in several important ways; one difference was the use of a single 6th-order analytic polynomial expression for the entire surface, giving the depth Z as a function of both X and Y across the area. All such free-form surfaces require special means for fabrication. Even with a CNC grinding machine of sufficient precision, the tool path required has to be developed mathematically in three dimensions to allow for the finite size and actual shape of the grinding tool. The tool path can be constructed in various ways, as may be most suitable for the machine to be used, but all depend on the fact that every element of the optical surface will be tangent to the grinding tool at some time in the generation process. There is then an option of making each cutting path a planar curve, if that is more suitable for the machine, or alternatively of spacing the cuts equally on the work surface with a more complicated tool motion. After it is polished with a soft lap, the free-form shape must be measured against a relevant functional tolerance before it is placed in volume production. We evaluated the eyelens surface for local dioptric errors, calculated in an array of eye-sized regions across the surface, simply by applying Kanolt's equations to our 3D profilometry data. For system tooling qualification the assembled camera system was evaluated in much the same way, but with a visual technique applied successively to a 2D array of bright points in the subject plane. Profilometry measurements were made with special machines designed and built by our group. Initially our free-form molded optics were controlled in production by the use of interferometry or contact test plates on the flat or spherical side of each piece, but this method did not perfectly define the parts. By 1980 Steve Fantone had developed a means of using holographic interferometry to test our molded free-form lenses. We had considered that we could use a computer-plotted hologram for this purpose, or could make a hologram photographically from a single near-perfect optical part -- but Fantone realized that the test hologram could also be made more easily from a near-perfect mold cavity, if we just selected the proper diffractive order when we used it. His method is described in US Patent #4,396,289. This test provided a simple and familiar way to check the quality of manufactured free-form product.   The familiar large-format Polaroid cameras typically had f/8 to f/10 taking lenses.  We once manufactured three-element and four-element designs lens to correct the aberrations and provide compact and convenient front-element focus adjustment.  But these designs are quite sensitive to accurate centering of the inner negative elements, at the risk of significant field tilt, or differential focus, across the area of the film.  We realized that a simpler aspheric meniscus landscape lens would perform nearly as well, except for loss of the focus adjustment benefit.  Such a lens was introduced in the 1977 OneStep camera, a fixed focus model, and has been used since then in newer camera models.  In 1981 we provided sonar automatic focus by adding a four-zone rotating turret lens at the aperture stop. In 1986 Polaroid introduced the "Spectra" camera.  As contrasted with the earlier instant cameras, the film area was larger, the focal length was longer, the corners were kept brighter, and distortion was better corrected.  The longer focal length required more zones of focus.  There was no space for a larger zone turret, so we combined the aspheric-meniscus scheme with a close pair of unique free-form optical surfaces, called "Quintics", capable of a compactcontinuous focus adjustment from 60cm to infinity.   The concept behind this free-form focus design dates to a 1926 British patent awarded to a Kyoto physician, Isao Kitajima.  This same idea was rediscovered or elaborated in various ways by Birchall in 1935, by Lewis in 1941, by Alvarez in 1967 and in 1970, and by Baker in 1971, 1984, and 1987.  Our 1987 version used in the Spectra camera differed from the earlier proposals by using a pivoting motion to rotate one free-form optical shape across the aperture, an important mechanical convenience, but a change that removed even the mirror-symmetry common to all the previous designs.  The Spectra cameras offered 10 zones of focus by pivoting a moving lens only 2.5 apertures long.  The companion fixed free-form component not only cancelled the coma that would have been produced by the moving component, but carried a rotationally symmetric asphere superimposed on its surface as well. Although it was mathematically complex, with polynomial terms up through 8th order and some 44 numerical coefficients used to define each of the paired analytic surfaces used for focus, the Spectra camera was refreshingly easy to manufacture.  Unlike the earlier camera lens designs with three and four elements, there was no need to make a final focus adjustment on the system; the parts of the taking lens were literally snapped together as the camera was assembled!  Because the optical correction did not depend upon cancellation of large aberrations among the multiple elements, as in conventional photographic lenses, placement tolerances were also looser.  Even with free-form optics inside it, the completed Spectra taking lens may be tested on a standard nodal-slide optical bench or with MTF equipment just as any other assembled photographic lens is tested, but of course should be tested at more than one focus setting.  Unlike front-element focus or conventional unit focus, achieved by motion of an entire taking lens, the Quintic focus motion actually adds and subtracts refractive power in the system, so the net Petzval curvature changes with focus setting, and may ultimately limit the focus range that will be acceptable. Twelve to sixteen cavities were used for molding each of the lens components.  To avoid having to match components by cavity identification for assembly, parts from all cavities were tested sequentially, replacing one component at a time in a standard complete set, to assure that the molded parts were fully interchangeable.  Where differences in refractive power were found, they were corrected by simple adjustment of power:  by altering the spherical or flat surface on the reverse side of each mold cavity until all the molded parts matched.  Polaroid introduced two more free-form optical components in 1992 in the viewfinder of a small-format folding camera called the "Captiva" in the United States, but "Vision" and "Joycam" in other places.  It used a catadioptric SLR system somewhat like the one in the older SX-70, but without a focus-screen texture on its Fresnel field mirror and without an aperture stop to hold an aspheric corrector.  Instead, the concave mirror and one eyelens surface were made free-form to optimize the design. These six different free-form optical components introduced from 1973 through 1992 were all manufactured in the millions by injection molding from ground and polished stainless steel tools, all made on commercial three-axis CNC machines or on granite, air slide, and interferometric machines specially designed and built for the purpose by our group at Polaroid. Several other free-form components were also made at Polaroid, including a pair of linear-translation aspheres used as part of a Polaroid zoom macro camera, two pairs of semiconductor lenses used in a military infrared zoom camera by Rochester Photonics, and a number of cubic phase masks made for CDM Optics.  The smaller parts and their molding tools were generated by diamond turning on a precision lathe equipped with a synchronized fast-tool servo.  This latter technique even provides a way to make prototype optical parts quickly in plastic without having to build a mold. Early free-form optical components made commercially by others include a few generations of progressive-power spectacles, a convenient eye testing machine based on Bill Humphrey's observation that the "Alvarez" lens could also provide any amount of cylindrical power if its halves were displaced crosswise to their spherical power adjustment, and an interesting lens made by Tinsley Labs to improve the photographic placement of color phosphor patterns on color CRTs by enabling light to follow the same contorted path as the electron beams. The free-form optical work done at Polaroid has been documented in several publications, each of which references some others: Plummer, W.T., "Unusual Optics of the Polaroid SX-70 Land Camera" Appl. Optics 21(2), 196-202 (1982) Plummer, W.T., "The SX-70 Camera: The Optics" Optics & Photonics News 5(10) 44-48 (Oct., 1994) Plummer, W.T., J.J. Mader, J.W. Roblee, and J. Van Tassell, "Precision Engineering at Polaroid" Proc. of the Pre-Conf. Day, pp. 24-29, Precision Engineering in Industry 3 International State of the Art, Eighth Int. Precision Eng. Seminar, Université de Technologie de Compiègne, France; M. Bonis, et al., Ed. (May 15, 1995). (Because this publication may be difficult to locate, it is available in html form on this web site at http://www.WTPOPTICS.com.) Plummer, W.T., J.G. Baker, and J. Van Tassell, "Photographic Optical Systems Using Nonrotational Aspheric Surfaces" Appl. Optics 38(16) 3572-3592 (1999) Fantone, S.D., U.S. Patent #4,396,289, "Method and Apparatus for Holographic Testing of Optical Components", August 2, 1983 VIEW the annotated pictorial slides as HTML