Copyright 2000 Society of Photo-Optical Instrumentation Engineers. This paper was published in Optical Engineering and is made available as an electronic reprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.
Geometrically desensitized interferometry for shape measurement of flat surfaces and 3-D structures Peter de Groot, MEMBER SPIE Xavier Colonna de Lega Dave Stephenson Zygo Corporation Laurel Brook Road Middlefield, Connecticut 06455 E-mail:
[email protected]
Abstract. We construct an interferometer for flatness testing of precision-engineered objects such as rigid disk drive platters, pump parts, and fuel injectors. A pair of phase diffraction gratings illuminate an object simultaneously at two different angles of incidence, resulting in an equivalent wavelength of 12.5 m. This system operates in standard phase-shifting mode for a height resolution of 0.01 m with up to 150 m of surface departure. The ⬍1 s measurement speed, 96-mm viewing aperture, simple mechanical part alignment, and 50-mm working distance are consistent with high-volume production testing. A recently developed coherence scanning mode accommodates even larger departures and discontinuous regions such as step heights. © 2000 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(00)01001-1]
Subject terms: interferometry; interferometers; optical testing; flatness testing; grating. Paper SM-10 received May 10, 1999; revised manuscript received Aug. 20, 1999; accepted for publication Aug. 20, 1999.
1
Introduction
Interferometry is the most successful and widespread technique for shape measurement of precision optics. Conventional optical interferometers take on many forms, a familiar one for nonmicroscopic surfaces is the laser-based Fizeau. This instrument is highly precise, given that the fundamental unit of measure is typically half of the 633-nm wavelength of a HeNe laser. There is presently a convergence of opinion that interferometry will find important applications in precision engineering and manufacturing environments outside of the optics lab. This view reflects the ever tighter tolerances of machined, ground, or molded components together with the imposition of international standards for manufacturing processes. Unfortunately, the high precision of interferometry is actually a barrier for many nonoptical or ‘‘technical’’ surfaces, because of high fringe density, surface roughness, and sensitive part alignment. Several means have been developed for extending interferometry to technical surfaces: the most straightforward is the use of longer wavelengths. Common IR wavelengths for interferometry are 1.06, 1.55, 3.39, and 10.6 m, corresponding to YAG, laser diode, HeNe, and CO2 laser sources, respectively.1–3 An alternative approach is grazing incidence interferometry, for which the most well known instrument is the Abramson prism interferometer developed4 in the 1960s. Grazing incidence interferometry operates at a long equivalent wavelength, typically 2 to 12 m for a visible wavelength source and a measurement beam incident at 72 and 87 deg, respectively. We propose here another option for long-equivalentwavelength shape measurement employing an unusual in86
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terferometer geometry. Geometrically desensitized interferometry 共GDI兲 is a two-beam technique in which both beams reflect from the object surface at different angles of incidence. There is no reference beam; rather there are two measurement beams that have slightly different sensitivities because of their incident angles. The resulting vernier effect provides large equivalent wavelengths at moderate angles of incidence, typically less than 25 deg. Earlier we reported on a form of GDI employing transparent diffraction gratings to separate, direct, and recombine the measurement beams.5 Our approach was the first to provide full-field GDI with a large working distance to facilitate automated part placement. Since that time, we have refined the instrument to accommodate 96-mm-diam objects at a 50-mm working distance, using a 12.5-m equivalent wavelength. We also developed fixtures and techniques for automated alignment of sample parts. Most recently, we expored a technique for profiling 3-D structures using a combination of GDI with coherence scanning.
2
Dual-Grating GDI
Although there are many ways to make a GDI instrument,6 diffractive optics are particularly attractive for largeaperture systems. The different incident angles are a natural consequence of multiple diffraction orders. If the object surface is smooth on the scale of visible light, it is sufficient to place a linear phase grating in near contact with the object surface to observe GDI fringes. Barus7 observed this effect almost a century ago, and Ja¨risch and Makosch8 constructed a wafer metrology system in the 1970s using es-
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de Groot, de Lega, and Stephenson: Geometrically desensitized interferometry for shape measurement . . .
terference pattern having an equivalent wavelength ⌳ given by
⌳⬇
Fig. 1 GDI for flatness testing. The coarse grating (e.g., 250 lines/ mm) diffracts the source light into two beams and the fine grating (e.g., 500 lines/mm) brings them back together again at the object surface. The 6.25 m/fringe sensitivity of the interferometer to surface topography is caused by the difference in the incident angles of the two beams on the object surface.
sentially the same phenomenon. Boone and Jacquot invented an ingenious GDI employing a holographic test plate that doubles as a collimating lens.9 In practice, it is highly desirable to maintain at least several millimeters of distance between the object and the nearest optical component of the interferometer. This is not generally feasible with a single diffractive optic placed in near contact with the sample surface, as was done in the past. We employ two linear phase gratings in series with a 1:2 pitch ratio, as shown in Fig. 1. The grating pair directs two beams to the same point on the surface but at different angles of incidence, thereby fulfilling the basic requirement of GDI while maintaining the sample surface at a convenient distance.10 The sensitivity to surface topography in GDI is related to the difference in optical path change for the two angles of incidence. The reflected, recombined beams form an in-
Fig. 2 Interference fringes for a 12.5-m equivalent wavelength on a precision engineered component. The 0.5-m root mean square (rms) surface roughness is too great to be viewed with a conventional visible-wavelength Fizeau interferometer.
1 , 2N sin共 ␥ 兲
共1兲
where ␥ is the angle of incidence of the source light, N is the spatial frequency of first or ‘‘coarse’’ grating, and the second or ‘‘fine’’ grating has twice the pitch as the first.5 We normally select gratings and incident angles for an equivalent wavelength ⌳⫽12.5 m. Interestingly, Eq. 共1兲 does not include the source wavelength. This together with the near equal path geometry means that the wavelength stability of the source is unimportant, and even broadband sources provide excellent fringe contrast. Figure 2 shows the fringe pattern from a rough surface object using this interferometer with a 680-nm multimode laser diode. As we noted previously,5 it is possible to interpret Fig. 1 as an unusual example of projection moire´. From this point of view, the grating pair acts as a high-efficiency fringe projection system, generating a fine-grain pattern by the achromatic interference of two mutually coherent plane waves. The same grating pair on the imaging side serves as a demodulator at a viewing angle of ⫺␥, resulting in a desensitized interference effect. Noting that the spatial frequency of the projected pattern is 2N and the difference between the projection and viewing angles is 2␥, one readily derives a height sensitivity equivalent to Eq. 共1兲. A unique characteristic of the optical design in Fig. 1 is the use of transmission phase diffraction gratings to perform beam directing tasks over a large field of view. We use photolithographically generated gratings having apertures of 100 ⫻150 mm with square profile grating lines to suppress zeroth order in transmission. The gratings are flat and uniform to a fraction of a visible wavelength; however, we find it beneficial to measure and correct for residual system errors using an optical flat as a calibrated reference. Phase shifting is accomplished by a piezoelectric transducer 共PZT兲 actuating a specially designed grating cell, which displaces the coarse grating vertically in Fig. 1 over a range of several micrometers.11 A computer analyzes the data acquired during the phase shift in the usual way to generate surface profile data over 640 ⫻ 480 camera pixels.12 The resolution 共i.e., noise floor兲 for PSI data acquisition on smooth surfaces is ⌳/1000 or 0.01 m rms for a single measurement. The measurement reproducibility, including part removal and replacement, is ⌳/250 or 0.06 m rms for critical surface parameters such as PV flatness.* This corresponds to a 10% repeatability and reproducibility gauge on a 3-m flatness tolerance.† Figures 3 and 4 show typical phase-shifting GDI measurements on precision-engineered components that are inaccessible to conventional visible wavelength interferometry. Both examples have surface roughness greater than 0.5 m rms, *PV flatness is the maximum minus the minimum height values measured over the entire surface, usually encompassing several tens of thousands of pixels. † Gauge R&R is a standard test used in industry. A 10% gauge means that the measurement error due to both user and instrument is less than 10% of a max-min range tolerance with a confidence level of 99.0% 共5.15兲. Optical Engineering, Vol. 39 No. 1, January 2000
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Fig. 3 Oblique surface topography map of the precision-machined metal object shown in Fig. 2.
and the rigid-disk blank in Fig. 4 has the equivalent of 100 HeNe fringes of surface departure. One of the inherent advantages of GDI is that the measurement takes place at nearly normal incidence and is therefore nearly free of the perspective distortion characteristic of grazing incidence interferometry. For a ⌳ ⫽12.5 m equivalent wavelength, the perspective distortion is 95% at grazing incidence and only 1% for GDI. A comparative disadvantage of GDI for the same reason is low light efficiency because of scatter. We use a 100-mW laser diode light source for a rough surface in our GDI, which is an unusual amount of power for an interferometer. The high power overcomes scattered light loss, but results in strong surface reflections and ghost images. To eliminate these unwanted reflections, the grating substrates are polished with a small wedge 共e.g., 1 deg兲 and tilted with respect to the line of symmetry.13 3 Sample Alignment For most purposes, GDI behaves much the same as a true long-wavelength interferometer, fully capable of profiling technical surfaces that are beyond the reach of conventional HeNe interferometers. However, there are important differences. Unlike a Fizeau, GDI requires that the object surface be positioned at a predetermined working distance h ⬘ ⫽50 mm from the fine grating substrate. The distance h ⬘ is approximately equal to the separation of the two grating surfaces. This position corresponds to the optimum metrology plane, for which the two beams reflecting from any individual point on the object surface intersect perfectly on the CCD array. Outside this plane, there is a relative sheer
Fig. 5 Automated part placement fixture for in-line production testing of rigid disk drive platters. A robot arm places the disk in a three-point kinematic mount. Throughput is 350 double-sided disk measurements per hour.
between the reflected beams that can result in loss of fringe contrast and, potentially, slope-dependent measurement errors.13 Fortunately, the alignment requirements of GDI are sufficiently relaxed that for most production metrology applications, a simple mechanical fixture is sufficient and there is no need for interactive adjustment. Figure 5 shows one of the most successful examples of this approach for in-line testing of platters for computer rigid disk drives. The platter sits a three-point mechanical fixture that locates the sample surface at the optimum metrology plane with the correct tip and tilt for measurement. Adjustment screws are used only once for the initial setup of the instrument. A robotic arm inserts and removes 700 platters/h for single-sided measurements, and 350 platters/h for double-sided measurements. The system measures and categorizes both the rough surface aluminum blanks 共Fig. 4兲 and the finished media for PV flatness. The same concept has been applied to automotive fuel injectors, pump parts, and other machined metals. As an alternative to precise mechanical fixturing, we recently implemented an autofocus version of the instrument that simplifies alignment by means of a narrow fringe contrast envelope. Equation 共1兲 shows that the equivalent wavelength ⌳ is a function of the angle of incidence ␥, thus if we provide a range of incident angles ⌬␥, there will be a range of equivalent wavelengths ⌬⌳: ⌬⌳/⌳⬇⌬ ␥ / ␥ .
Fig. 4 Oblique surface topography map of an unprocessed aluminum platter for a rigid disk drive. The 0.5-m rms surface roughness and 35-m departure are beyond the reach of conventional visiblewavelength Fizeau interferometry. The GDI instrument that generated these data will accommodate up to 150 m of departure. 88
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共2兲
The net effect is an incoherent superposition that localizes the fringes to a narrow range of optical path differences, similar to what occurs in white light interferometry. By designing the instrument so that the peak fringe contrast coincides with the optimum metrology plane, we provide an unambiguous means of determining the ideal object placement. In the autofocus measurement, the metrology plane scans 600 m of focus depth by means of a continuous displacement of the fine grating in Fig. 1. Computer software then selects the data near the coherence peak for phase calculation, thus automatically ensuring that the measurement is at the best focus position.14
de Groot, de Lega, and Stephenson: Geometrically desensitized interferometry for shape measurement . . .
injectors, and other precision-engineered components. Our on-going development efforts are focused on simplifying the part fixturing and alignment and improving the repeatability and accuracy of the instrument. We are also actively working on a 3-D analysis tool that combines GDI with coherence scanning.
Acknowledgments The authors thank Dana Seniff, Mike Majlak, Stan Bieleki, Thom Connolly, Jim Soobitsky, and Jim Biegen for their contributions to this work.
References Fig. 6 Topographical image of an anodized metal base plate commonly used to support posts on an optical bench. The object is approximately 20 ⫻40 mm wide, and has a 300-m step. These data acquired using coherence scanning GDI.
4
Coherence Scanning For 3-D Metrology
Although GDI operates at a long equivalent wavelength, there is nonetheless a fringe-order ambiguity for discontinuous surface features greater than 12.5 m. This ambiguity can be overcome by employing a form of coherence scanning familiar to users of white-light interferometric microscopes.15,16 The idea is to restrict the coherence range of the instrument, just as we have done for the autofocus technique, thus localizing the fringe pattern and making it possible to distinguish one fringe from another. In coherence scanning, the object is scanned perpendicularly with respect to its surface to acquire interference information over a large depth range. For each pixel, one observes data localized by the fringe contrast envelope caused by having an extended source. Analysis of this data using any one of the established coherence-scanning techniques provides surface profile data such as that shown in Fig. 6, which is free of the fringe ambiguity normally associated with interferometry, even in the presence of a discontinuous step in surface height of 300 m.
5
Summary
GDI is one of many optical techniques for shape measurement that are finding their way into precision engineering and manufacturing environments. Our approach to GDI is to employ a pair of high-quality diffraction gratings to direct two beams at different angles of incidence to the sample surface and generate an interference pattern having a long equivalent wavelength. The long working distance afforded by our technique has facilitated the introduction of GDI into high-throughput production line applications, such as the inspection of platters for rigid disk drives, as well as the inspection of the surface of pump flanges, fuel
1. P. de Groot, ‘‘Long-wavelength laser diode interferometer for surface flatness measurement,’’ in Optical Measurements and Sensors for the Process Industries, Proc. SPIE 2248, 136–140 共1994兲. 2. C. Ai, ‘‘IR interferometers using modern cameras,’’ Proc. SPIE 3134, 461–464 共1997兲. 3. C. R. Munnerlyn and M. Latta, ‘‘Rough surface interferometry using a CO2 laser source,’’ Appl. Opt. 7共9兲, 1858–1859 共1968兲. 4. N. Abramson, ‘‘The interferoscope: a new type of interferometer with variable fringe separation,’’ Optik (Stuttgart) 30, 56–71 共1969兲. 5. P. de Groot, ‘‘Grating interferometer for flatness testing,’’ Opt. Lett. 21共3兲, 228–230 共1996兲. 6. F. H. Smith, ‘‘Interferometric apparatus,’’ U.S. Patent No. 3958884 共May 25, 1976兲. 7. C. Barus and M. Barus, ‘‘The interface of the reflected-diffracted and the diffracted-reflected rays of a plane transparent grating, and on an interferometer,’’ Carnegie Inst. Wash. Publ. 149, Part 1, Chapt. 11 共1911兲. 8. W. Ja¨risch and G. Makosch, ‘‘Optical contour mapping of surfaces,’’ Appl. Opt. 12共7兲, 1552–1557 共1973兲. 9. P. M. Boone and P. Jacquot, Proc. SPIE 1554A, 512–521 共1991兲. 10. P. de Groot, ‘‘Method and apparatus for profiling surfaces using diffractive optics which impinges the beams at two different incident angles,’’ U.S. Patent No. 5526116 共June 11, 1996兲; additional U.S. and foreign Patents pending. 11. P. Domenicali, ‘‘Tilt free micromotion translator,’’ U.S. Patent No. 5721616 共Feb. 24, 1998兲. 12. J. E. Greivenkamp and J. H. Bruning, ‘‘Phase shifting interferometry,’’ in Chap. 14 Optical Shop Testing, D. Malacara, Ed, 共Wiley, New York 1992兲. 13. X. Colonna de Lega, J. Biegen, D. Stephenson, and P. de Groot, ‘‘Characterization of a geometrically desensitized interferometer for flatness testing,’’ in Three-Dimensional Imaging, Optical Metrology, and Inspection IV, K. G. Harding, Ed. Proc. SPIE 3520, 284–292 共1998兲. 14. X. Colonna de Lega and D. Stephenson, ‘‘Diffraction grating design for a geometrically-desensitized interferometer,’’ U.S. Patent pending. 15. T. Dresel, G. Haeusler, and H. Venzke, ‘‘Three-dimensional sensing of rough surfaces by coherence radar,’’ Appl. Opt. 31共7兲, 919–925 共1992兲. 16. P. de Groot and Leslie Deck, ‘‘Surface profiling by analysis of whitelight interferograms in the spatial frequency domain,’’ J. Mod. Opt. 42共2兲, 389–401 共1995兲. Peter de Groot is senior scientist at Zygo Corporation, Middlefield, Connecticut, which designs, develops, manufactures, and markets high-performance optical measurement instruments and precision optical components. Dr. de Groot has 15 years experience in optical metrology, holds 35 patents, and has published 70 papers in optics, primarily in the field of interferometry and its application to distance measurement and surface profiling. Optical Engineering, Vol. 39 No. 1, January 2000
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de Groot, de Lega, and Stephenson: Geometrically desensitized interferometry for shape measurement . . . Xavier Colonna de Lega is a research scientist with Zygo Corporation. He graduated from the Institute of Optics in Orsay, France, in 1989. He then worked at the University of Arizona on in situ measurement of stress in thin films. In 1991 he joined the Swiss Federal Institute of Technology (EPFL), Lausanne, where he worked on fringe analysis techniques applied to holographic and speckle interferometry. He obtained his PhD in 1997 from EPFL and joined Zygo Corporation in 1998.
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Dave Stephenson manages the optical engineering group at Zygo Corporation. Mr. Stephenson has 18 years experience in the design and fabrication of optical systems, specializing in laser-based systems employing a mixture of refractive and diffractive surfaces.
