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Timestamp: 2016-07-29 18:41:06
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Patent US7126698 - Measurement of complex surface shapes using a spherical wavefront - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign inPatentsConical surfaces (and other complex surface shapes) can be interferometrically characterized using a locally spherical measurement wavefront (e.g., spherical and aspherical wavefronts). In particular, complex surface shapes are measured relative to a measurement point datum. This is achieved by varying...http://www.google.com/patents/US7126698?utm_source=gb-gplus-sharePatent US7126698 - Measurement of complex surface shapes using a spherical wavefrontAdvanced Patent SearchPublication numberUS7126698 B2Publication typeGrantApplication numberUS 11/329,304Publication dateOct 24, 2006Filing dateJan 10, 2006Priority dateOct 16, 2001Fee statusPaidAlso published asDE02773388T1, DE60236811D1, EP1436570A1, EP1436570A4, EP1436570B1, US6714307, US7030996, US20030011784, US20040239947, US20060114475, WO2003033994A1, WO2003033994B1Publication number11329304, 329304, US 7126698 B2, US 7126698B2, US-B2-7126698, US7126698 B2, US7126698B2InventorsPeter J De Groot, Xavier Colonna de LegaOriginal AssigneeZygo CorporationExport CitationBiBTeX, EndNote, RefManPatent Citations (24), Non-Patent Citations (10), Referenced by (3), Classifications (18), Legal Events (3) External Links: USPTO, USPTO Assignment, EspacenetMeasurement of complex surface shapes using a spherical wavefront
US 7126698 B2Abstract
1. An interferometry method for measuring conical surfaces, the method comprising:
directing a measurement wavefront to reflect from a conical portion of a measurement surface and subsequently overlap with a reference wavefront to form an interference pattern,
wherein the measurement and reference wavefronts are derived from a common light source and paths for the measurement and reference wavefronts define an optical measurement surface corresponding to a theoretical test surface that would reflect the measurement wavefront to produce a zero optical path length difference between the measurement and reference wavefronts across the interference pattern;
translating a spherical portion of the optical measurement surface relative to the conical portion of the measurement surface; and
determining information about the conical portion of the measurement surface based on the interference pattern.
2. The method of claim 1, wherein the translation comprises translating an interferometer used to form the interference pattern relative to the conical portion of the measurement surface along an optical axis of the interferometer.
3. The method of claim 2, wherein a z-stage is used to translate the interferometer relative to the measurement surface.
4. The method of claim 1, further comprising varying the radius of curvature of the spherical portion of the optical measurement surface over the conical portion of the measurement surface, and detecting the interference pattern as a function of the radius of curvature to determine the information about the measurement surface.
5. The method of claim 1, wherein the interference pattern is imaged onto an electronic detector to measure the interference pattern.
6. The method of claim 1, further comprising directing the reference wavefront to reflect from a spherically shaped reference surface prior to overlapping it with the measurement wavefront, wherein the spherically shaped reference surface causes the optical measurement surface to have the spherical portion.
7. The method of claim 6, further comprising focusing the measurement wavefront in a direction of a measurement datum point before it reflects from the conical portion of the measurement surface.
8. The method of claim 7, wherein the measurement and reference wavefronts are directed along different directions before being overlapped to form the interference pattern.
9. The method of claim 1, wherein a Linnik interferometer is used to form the interference pattern.
10. The method of claim 1, wherein determining information about the conical portion of the measurement surface comprises mapping points on the interference pattern to corresponding points on the measurement surface, wherein a distance between a point in the interference pattern and a common reference point in the interference pattern is related to a chief ray angle at the optical measurement surface.
11. The method of claim 1, wherein determining information about the conical portion of the measurement object comprises generating a radial height profile.
12. The method of claim 11, wherein the radial height profile corresponds to the distance between the measurement surface and the optical measurement surface at a particular radius of curvature along a normal to the optical measurement surface at the particular radius of curvature.
13. The method of claim 11, wherein determining information about the conical portion of the measurement surface further comprises reconstructing the measurement surface in Cartesian coordinates based on the radial height profile.
14. The method of claim 11, wherein determining information about the conical portion of the measurement surface further comprises determining a deviation of the measurement surface from an ideal conical surface.
15. The method of claim 1, wherein the information about the conical portion of the measurement surface is determined using a computer processor coupled to an electronic detector positioned to detect the interference pattern.
16. The method of claim 1, wherein the common source is a broadband source.
17. The method of claim 16, wherein the broadband source has a coherence length, and wherein the relative translation of the optical measurement surface is over a range larger than the coherence length.
18. The method of claim 1, further comprising imaging the spherical portion of the optical measurement surface to an intermediate image plane.
19. The method of claim 18, further comprising imaging the intermediate image plane to an electronic detector.
an interferometer configured to direct a measurement wavefront to reflect from a measurement surface and subsequently overlap with a reference wavefront to form an interference pattern, the measurement and reference wavefronts being derived from a common source,
wherein the interferometer comprises a beam splitter positioned to direct the measurement and reference wavefronts along different directions and subsequently recombine them, and a spherically shaped reference surface positioned to reflect the reference wavefront back toward the beam splitter,
wherein paths for the measurement and reference wavefronts define an optical measurement surface corresponding to a theoretical test surface that would reflect the measurement wavefront to produce a zero optical path length difference between the measurement and reference wavefronts across the interference pattern, and
wherein the spherically shaped reference surface causes the optical measurement surface to have a spherical portion,
wherein the interferometer further comprises optics to image the spherical portion of the optical measurement surface to an intermediate image plane; and
the apparatus further comprising a translation stage configured to translate the optical measurement surface relative to the measurement surface.
21. The apparatus of claim 20, wherein the optics to image the spherical portion of the optical measurement surface to an intermediate image plane comprise a first optic positioned to focus the measurement wavefront toward a measurement datum point and a second optic positioned at the measurement datum point.
22. The apparatus of claim 21, wherein the first optic is an objective lens.
23. The apparatus of claim 21, wherein the second optic is a collimating lens.
24. The apparatus of claim 21, wherein the second optic is an aperture stop.
25. The apparatus of claim 20, further comprising an electronic detector and wherein the interferometer further comprises relay optics to image the intermediate image plane to the detector.
26. The apparatus of claim 20, wherein the translation stage comprises a z-stage is used to translate the interferometer relative to the measurement surface.
27. The apparatus of claim 26, wherein the interferometer comprises a second translation stage configured to vary the radius of curvature of the spherical portion of the optical measurement surface.
28. The apparatus of claim 27, further comprising an electronic detector configured to measure interference pattern.
29. The apparatus of claim 28, wherein the interferometer further comprises relay optic to image the interference pattern to the electronic detector.
30. The apparatus of claim 29, further comprising an electronic processor coupled to the electronic detector and the second translation stage and configured to process the measured interference pattern as a function of the variation of the radius of curvature to determine the information about the measurement surface.
31. The apparatus of claim 20, wherein the interferometer further comprises a spherically shaped reference surface positioned to reflect the reference wavefront prior to overlapping it with the measurement wavefront, and
wherein the spherically shaped reference surface causes the optical measurement surface to have the spherical portion.
32. The apparatus of claim 20, wherein the interferometer is a Linnik interferometer.
33. The apparatus of claim 20, further comprising an electronic detector configured to measure the interference pattern.
34. The apparatus of claim 33, further comprising an electronic processor coupled to the electronic detector, wherein the electronic processor is configured to determine information about the measurement surface based on the interference pattern.
35. The apparatus of claim 34, wherein the electronic processor is configured to determine information about the measurement surface by mapping points on the interference pattern to corresponding points on the measurement surface, wherein a distance between a point in the interference pattern and a common reference point in the interference pattern is related to a chief ray angle at the optical measurement surface.
36. The apparatus of claim 34, wherein the electronic processor is configured to determine information about the measurement surface by generating a radial height profile.
37. The apparatus of claim 36, wherein the radial height profile corresponds to the distance between the measurement surface and the optical measurement surface at a particular radius of curvature along a normal to the optical measurement surface at the particular radius of curvature.
38. The apparatus of claim 37, wherein the electronic processor is configured to determine information about the measurement surface by further reconstructing the measurement surface in Cartesian coordinates based on the radial height profile.
39. The apparatus of claim 20, further comprising the common source is a broadband source.
40. The apparatus of claim 39, wherein the broadband source has a coherence length, and wherein the translation stage is configured to translate the optical measurement surface over a range larger than the coherence length.
41. The apparatus of claim 20, wherein the interferometer is a Twyman-Green interferometer.
42. The method of claim 1, wherein a Twyman-Green interferometer is used to form the interference pattern.
Pursuant to 35 U.S.C. � 120, this application is a continuation of prior U.S. application Ser. No. 10/806,496, filed Mar. 22, 2004 now U.S. Pat. No. 7,030,996, which is a continuation of and claims the benefit of prior U.S. application Ser. No. 10/190,353, filed Jul. 3, 2002 and issued as U.S. Pat. No. 6,714,307, which claims priority under 35 U.S.C. � 119(e) to Provisional Patent Application No. 60/329,627, filed Oct. 16, 2001. The contents of the prior applications are incorporated herein by reference in their entirety.
A common challenge for manufacturers is precise measurement of surface topography. Examples of manufactured items requiring metrology are engine parts, components for magnetic storage devices, flat-panel displays, molded and textured plastic surfaces, mechanical pump surfaces and seals, and minted coins. In these and other. Industrial Markets, there is a significant and growing need for fast, accurate metrology of parts having non-flat prismatic surfaces. These parts include three-dimensional (3D) cones, cylinders, and spheres, often having surfaces as small as 2 mm in diameter and 75 mm deep with 3D form tolerances of as low as 0.5 μm. An important example is fuel system valves, which are fundamental building blocks in engines, pumps and other hydraulic systems. Manufacturing the conical form of these parts within tolerance specifications is a high priority. For instance, the roundness of valve seats is important to valve function as it relates closely to leakage—a valve seat not conforming to specified roundness would likely yield a leaky valve. Additionally, many of these surfaces are deeply recessed within narrow cylindrical holes, making precise metrology even more challenging.
In general, in a first aspect, the invention features an interferometry method. The method includes directing a measurement wavefront to reflect from a measurement surface and a reference wavefront to reflect from a reference surface, where the measurement and reference wavefronts are derived from a common light source and directing the reflected measurement and reference wavefronts to overlap with one another and form an interference pattern. Paths for the measurement and reference wavefronts define an optical measurement surface corresponding,to a theoretical test surface that would reflect the measurement wavefront to produce a constant optical path length difference between the measurement and reference wavefronts. The method also includes varying the radius of curvature of a locally spherical portion of the optical measurement surface to contact a conical portion of the measurement surface, and detecting the interference pattern as a function of the radius of curvature.
In a further aspect, the invention features an interferometry method that includes directing a measurement wavefront to reflect from a measurement surface and a reference wavefront to reflect from a reference surface, where the measurement and reference wavefronts being are from a common light source, and directing the reflected measurement and reference wavefronts to overlap with one another and form an interference pattern. Paths for the measurement and reference wavefronts define an optical measurement surface corresponding to a theoretical test surface that would reflect the measurement wavefront to produce a constant optical path length difference between the measurement and reference wavefronts. The method also includes varying the radius of curvature of a locally spherical portion of the optical measurement surface to contact the measurement surface, detecting the interference pattern as a function of the radius of curvature and generating a radial height profile. The radial height profile corresponds to the distance between the measurement surface and the optical measurement surface at a particular radius of curvature along a normal to the optical measurement surface at the particular radius of curvature.
In yet a further aspect, the invention features a method for calibrating an interferometric system using a calibration artifact having a known shape. The method includes directing a measurement wavefront to reflect from the calibration artifact and a reference wavefront to reflect from a reference surface, where the measurement and reference wavefronts are derived from a common light source, and directing the reflected measurement and reference wavefronts to overlap with one another and form an interference pattern. Paths for the measurement and reference wavefronts define an optical measurement surface corresponding to a theoretical test surface that would reflect the measurement wavefront to produce a constant optical path length difference between the measurement and reference wavefronts. The method further includes varying the radius of curvature of a locally spherical portion of the optical measurement surface to contact the calibration artifact, detecting the interference pattern as a function of the radius of curvature, and generating a radial height profile. The radial height profile corresponds to the distance between the calibration artifact and the optical measurement surface at a particular radius of curvature along a normal to the optical measurement surface at the particular radius of curvature. The interferometry system is calibrated based on the radial height profile.
The optical measurement surface can be a spherical or aspherical optical measurement surface. The radius of curvature can be varied relative to a fixed measurement a datum point.
The methods and/or systems can generate a radial height profile based on thee interference patterns, wherein the radial height profile corresponds to the distance between the measurement surface and the optical measurement surface at a particular radius of curvature along a normal to the optical measurement surface at the particular radius of curvature. The methods and/or systems can reconstruct the measurement surface in Cartesian coordinates based on the radial height profile, and can determine a deviation of the measurement surface from an ideal conical surface.
FIG. 2( a) shows detail of the measurement optics of the sensor shown in FIG. 1 FIG. 2( b) shows alternative measurement optics for the sensor shown in FIG. 1 FIG. 3 is a schematic diagram of an interferometry system including the sensor of FIG. 1 and x,y,z staging;
FIG. 17( a) shows a shallow cone measurement with an interferometry system;
FIG. 17( b) shows a steep cone measurement with the interferometry system of FIG. 17( a);
FIG. 18( a) shows a conical surface measurement with an interferometry system;
FIG. 18( b) shows a cylindrical surface measurement with the interferometry system of FIG. 18( a);
FIG. 19( a) shows referencing an interferometry system to a horizontal flat datum for height measurements;
FIG. 19( b) shows measuring a conical surface with the interferometry system of FIG. 19( a);
FIG. 2( b) shows an alternative arrangement for measurement optics 140 without a collimating lens positioned at measurement datum point 150. Here, measurement optics 140 includes objective lens 141, which focuses chief rays 211B and 213B to measurement point datum 150—in other words, measurement datum point 150 is located at the focal plane of objective lens 141. An aperture stop 244 is positioned at measurement datum point 150. Objective lens 141 focuses marginal rays 212B and 214B reflected from measurement surface 202 back to substantially flat intermediate real image 262B.
FIG. 5 is a further detail drawing of the measurement geometry, showing the angles and lengths of a specific chief ray 451 similar to chief rays 321 and 322 shown in FIG. 4. We define the inclination or chief ray angle θ, the azimuthal angle φ, the ray length r from measurement datum point 150 to optical measurement surface 152, and the Cartesian coordinates x, y, z. When measurement surface 152 is substantially spherical, ray length r is the same as the radius of the corresponding virtual sphere; FIG. 6 shows how the chief ray angle, θ, and azimuthal angle, φ, maps onto a flat-field image 560 on a camera area 562. The mapping typically involves a coordinate transformation that may for example be
In the low coherence interferometry approach, the measurement process is similar to that used with a scanning white light interferometer (SWLI). An example data set acquired for a single camera pixel using a SWLI process is shown in FIG. 7. The localization of an interference intensity signal 613 around the zero OPD position is characteristic of interferometry assuming that source 110 (see FIG. 1) is spectrally broadband, e.g., has a spectral bandwidth of 100 nm centered at 600 nm. The fringe localization provides a means for determining the precise moment when the optical measurement surface intersects the object point corresponding to the image pixel. The scan motion is precisely controlled, so that knowledge of when a given object point is at zero OPD can be directly translated into a ray length r. One can apply any of a variety of techniques for determining surface height using low-coherence sources. Suppose for example interference data for a first pixel looks as in FIG. 7, with a peak 612 in the fringe contrast 611 at a scan position of 0 μm. A second pixel might have a different fringe contrast peak at a different scan position, for example 10 μm. The difference in radius r between the two object points corresponding to these image pixels would therefore be 10 μm. The data processing involves, e.g., coherence envelope detection or frequency domain analysis, as described by T. Dresel, et al. in Applied Optics Vol. 31, pp. 919–925 (1992) and U.S. Pat. No. 5,398,113, respectively.
Using, e.g., a nonlinear least-squares fit, a best-fit theoretical surface 851 is fit to 3D representation 850. Several parameters are extracted from best-fit theoretical surface, including cone angle, decenter of the cone with respect to the instrument optical axis, axis orientation (i.e., tilt) with respect to the instrument optical axis, and location of a specific diameter, e.g. a valve seat diameter, with respect to the 3D representation 850. Referring to FIG. 10, a residual profile r is also calculated with respect to the best-fit theoretical cone 951 corresponding to a 3D data set 950. The residual profile is the deviation of measured part surface 202 from best-fit theoretical surface 851.
For calibration of the overall shape of the optical measurement surface, it is useful to have an appropriate calibrated artifact. For example, a spherical artifact of known radius facilitates these calibrations for a spherical optical measurement surface. FIG. 14 illustrates such a calibration procedure involving a spherical artifact 1400 carried by an artifact fixture 1422 for system 300. Note that artifact fixture 1422 is positioned using x, y stage 1220. x, y stage 1220, support both part fixture 1222 and artifact fixture 1422, for easy switching between surface calibration and measurement. Because spherical artifact 1400 has a known radius of curvature, this calibration provides an absolute radius reference, allowing sensor 100 to measure absolute part diameters accurately, rather than simply deviations, e.g., from roundness. FIG. 15 is a flowchart summarizing a measurement datum point location calibration cycle, including an iterative alignment procedure.
For determining the exact location of measurement datum point 150 with respect to sensor 100, it may be preferable to use a conical artifact instead of, or in addition to, spherical artifact 1400. FIG. 16 summarizes such a procedure. The initial measurement sequence is analogous to the measurement sequence described above for a part surface (see, e.g., FIG. 13), however, as the cone shape is already known there is no need to determine a best-fit surface to the 3D Cartesian coordinate data. Instead, the computer calculates the position of the known surface with respect to the measurement datum point. Once the artifact is sufficiently aligned, the system decenters the artifact with respect to the measurement datum point and acquires a new set of data for the decentered artifact. This is repeated for four times, corresponding to decentering by incremental amounts δx, −δx, δy, and −δy. For each data set, the computer fits the known cone shape to the data for multiple locations of center point 650 and selects the location corresponding to the smallest deviation of the cone reconstructed in Cartesian space with respect to the known cone shape. Hence, each data set yields an optimum position for point 650. The mean of these optimum positions is used as a best estimate of the true projection of the optical axis onto the detector. Of course, this process,can be performed using fewer (or more) than four measurements. Multiple measurements help to compensate for any anomalies or defects in the shape of the conical artifact.
FIGS. 17( a) and 17(b) illustrates the flexibility of the measurement geometry with respect to cone angle. FIG. 17( a) shows a part 2000 with a shallow conical surface 2002 (e.g., cone angle greater than 90�) positioned relative to optical measurement surface 2052. A chief ray 2011 travels down at normal incidence to the shallow part surface 2002 and reflects back through measurement optics 140 to a nominally flat intermediate real image 2062. FIG. 17(b) shows a part 2005 with a steep conical surface 2006 (e.g., cone angle less than 90�) positioned relative optical measurement surface 2052. A chief ray 2012 passes through measurement optics 140 and reflects back to intermediate real image 2062, but at a different location corresponding to a different image radius ρ to shallow conical surface 2002.
It is feasible for a measurement to include capturing data from other surfaces to serve as datums on the object itself. For example, it may be important to know the location and orientation of the cone with respect to a surrounding cylindrical bore or some other feature, e.g., the runout of the cone with respect to an axial datum established by the cylinder. The data capture can take place simultaneously with the measurement of the cone, or involve a two-step process that includes a precise displacement of the optical point datum between measurements. For example, FIG. 18( a) shows wide-angle measurement probe optics 2140 located relative to a part 2100 having conical and cylindrical portions. Optical measurement surface 2152A contacts part 2100 at conical portion 2101. Wide-angle measurement probe optics 2140 image a reflected chief ray 2111 to an image surface 2199. Varying the OPD allows one to measure the distance of conical portion 2101 from measurement datum point 2182. In FIG. 18( b) optical measurement surface 2152B contacts part 2100 at cylindrical portion 2102. Wide-angle measurement probe optics 2140 also image a chief ray 2112 reflected from portion 2102 to image surface 2199. In this instance, varying the OPD allows one to measure the distance of cylindrical portion 2102 from displaced measurement datum point 2183. Due to an axial aberration, displaced measurement datum point 2183 is shifted from measurement datum point 2182 by an amount Δζ in the z-direction. This displacement can be accommodated for in offline data analysis by replacing z in Eq.2 with z′=z+Δζ. Note that in this case, the resultant wide-angle measurement surface 2152 is not necessarily a perfect sphere and does not necessarily map to a flat intermediate real image 2199, the ray angles being perhaps too severe. The remaining distortion may be corrected by optics elsewhere in the system.
FIGS. 19( a) and 19(b) show another example of datum referencing, this time to a horizontal surface. For this application, precision z-axis and x, y-stages translate measurement optics 140 relative to a measurement part 2200. Referring specifically to FIG. 19( a), the system first measures the location of a datum surface 2202 on a datum-referenced part 2200, using a first measurement point datum 2282. A chief ray 2211 traces an exemplary optical path for this configuration. Referring to FIG. 19( b), after a controlled sensor displacement Δz to provide a second measurement point datum 2283, the system measures a cone surface 2201. A chief ray 2212 shows an optical path for this configuration. The result of both measurements is a measurement of cone surface 2200 referenced in z to datum surface 2202. One can go further and reference the orientation, including tip and tilt, of cone surface 220 by making several z measurements at different locations on datum surface 2202.
Any of the described embodiments can additionally include endoscopic optics for viewing down deep bores. Further-more, chromatic dispersion correction optics in either the measurement or reference legs can improve fringe contrast, and simplify the optical design and data processing.
Although the embodiments described above are with respect to low coherence interferometry, other interferometry techniques can also be used. For example, interferometry methods using a long coherence length light source (e.g., lasers) can also be used. One such technique is phase shifting interferometry (PSI). In PSI, the phase of an detected interference signal is varied by, e.g., varying the wavelength of the light source or dithering the position of a reference surface. The difference in phase of the interference signal as a function of wavelength or reference surface position relates directly to the total optical path difference in the interferometer, which can itself be related to the distance of the surface to the datum point by measuring a calibration sphere of known radius of curvature. In PSI, interference images are acquired according to a phase-shifting algorithm so the each incremental change in interference signal can be related to a known wavelength change of, or OPD change between, reference and measurement wavefronts. Examples of PSI techniques can be found in U.S. Pat. No. 6,359,692, entitled “METHOD AND SYSTEM FOR PROFILING OBJECTS HAVING MULTIPLE REFLECTIVE SURFACES USING WAVELENGTH-TUNING PHASE-SHIFTING INTERFEROMETRY,” to Peter de Groot, U.S. patent application Ser. No. 10/144,527, entitled “APPARATUS AND METHOD FOR PHASE-SHIFTING INTERFEROMETRY,” to Michael Kuchel et al., and U.S. Provisional Application Ser. No. 60/339,214, entitled “FREQUENCY TRANSFORM PHASE-SHIFTING INTERFEROMETRY,” to Leslie L. Deck.
Long wavelength (e.g., infrared, such as 0.75–10μm) interferometry techniques can also be used in the aforementioned methods and systems. By using a longer source wavelength one can also establish a limited measurement volume where there is reduced distance uncertainty to the point datum, again by establishing this volume near a calibration sphere. In this case, a single-phase measurement may be sufficient. Moreover, surfaces that diffusely reflect visible wavelengths or light can appear specular to longer wavelengths. Hence, long wavelength sources can be used to characterize rough surfaces. Of course, for long wavelength interferometry, the system detector and optical components should be selected to perform appropriately at the light source wavelength. Long wavelength interferometry techniques are further described in U.S. Pat. No. 6,195,168, entitled “INFRARED SCANNING INTERFEROMETRY APPARATUS AND METHOD,” to Xavier Colonna de Lega et al.
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