Abstract:
A scanning interferometer employs dual interferometer modules at different wavelengths to expand a dynamic range of measurement, a compound probe for measuring multiple surfaces, and a confocal optical system for distinguishing between the surfaces measured by the compound probe. Within the compound probe, miniature optics divide a test beam into two sub-test beams that are focused normal to different test surfaces. Both sub-test beams contain the different wavelengths. A separate interferometer monitors movements of the compound probe for producing absolute measures of the test surfaces.

Description:
TECHNICAL FIELD 
     Interferometric measuring systems with optical probes as can be arranged for the practice of our invention provide for measuring localized surface features, geometric surface forms, and overall dimensions. The invention is particularly applicable to the measurement of cylindrical, conical, and flat surfaces whose roughness approaches tolerances for geometric form as well as to the measurement of test pieces having multiple surfaces requiring individual or comparative measurements. 
     BACKGROUND 
     Tolerances for many precision manufactured components continue to go beyond the capabilities of conventional contact measuring techniques. Optical measuring techniques, particularly those using interferometric mechanisms, provide for measuring with much greater precision. However, the roughness of the surfaces under test often exceeds one-half of the wavelengths used in conventional interferometers (i.e., wavelengths in the visible or near-infrared range). Surface features larger than one-half the measuring wavelength cannot be unambiguously measured with conventional interferometers. Longer wavelengths can be used, but lasers for producing such longer wavelengths are less common and more expensive than those available for producing wavelengths in the visible or near-infrared range. 
     Manufactured components that include multiple surfaces can require measurements of their individual surface forms (e.g., roundness and straightness) as well as measurements of relationships between their surfaces (e.g., runout and perpendicularity). Measuring each of the surfaces individually with setups or recalibrations between the different measurements is time consuming and can make comparisons difficult. 
     SUMMARY OF THE INVENTION 
     Our interferometer in one or more of its preferred embodiments provides for measuring multiple surfaces with a compound optical probe. Sub-test beams emitted from the probe separately measure the multiple surfaces. A confocal optical system distinguishes the measurements between the surfaces. Each of the sub-test beams can be composed of two fundamental wavelengths of light from different interferometers. Combined, the two interferometers greatly increase the dynamic range of measurement for measuring rough surfaces with conventional lasers. 
     An exemplary interferometer for measuring multiple surfaces of a test piece in accordance with our invention includes a test arm and a reference arm that convey test and reference beams along different but ultimately interconnected paths. A beamsplitter within the test arm separates the test beam into first and second sub-test beams. A focusing optic of the confocal optical system within the test arm focuses the first and second sub-test beams to different points of focus. A compound probe also within the test arm conveys the first and second sub-test beams to the different points of focus. 
     Preferably, each of the sub-test beams is intended for measuring a different surface of the test piece at normal incidence. As such, the principal axes of the sub-test beams are oriented normal to their incident test surfaces, which can be oriented in different directions. Directional optics within the probe direct the sub-test beams to their points of focus at their intended orientation. Additional sub-test beams can be split from the test beam within the test arm for measuring more than two surfaces of the test piece, each being directed to a point of focus at normal incidence to a different test surface. 
     The test surfaces are preferably measured individually in succession. An actuator relatively moves the probe with respect to the test piece between two or more measuring positions. In a preferred embodiment, the actuator is movable between two positions for measuring two surfaces of a test piece. At a first of the positions, the point of focus of the first sub-test beam is positioned on the first surface of the test piece and the point of focus of the second sub-test beam is positioned off both the first and second surfaces of the test piece. At a second of the positions, the point of focus of the second sub-test beam is positioned on the second surface of the test piece and the point of focus of the first sub-test beam is positioned off both the first and second surfaces of the test piece. Similarly, at a third or higher measuring position, the additional points of focus are positioned in turn on other of the test piece surfaces while the remaining points of focus are positioned off of all the test surfaces. 
     A detection system detects an interference signal between the reference beam and the first sub-test beam when the probe is located at the first position and detects an interference signal between the reference beam and the second or higher sub-test beam when the probe is located at the second or higher position. The detection system is preferably arranged in conjunction with a confocal optical system that excludes from detection light that is not focused on one of the test surfaces. An imaging optic of the confocal optical system can be used to refocus the sub-test beams conjugate to their points of focus of the focusing optic. A limited aperture size near the focus of the imaging optic limits a depth of focus through which light is effectively collected by a detector at the end of the confocal optical system. If any of the test surfaces are located out of focus (e.g., by as few as 10 to 100 microns), little of the reflected light reaches the detector. The aperture size can be limited by locating a stop near the conjugate focal point or by locating a detector of limited dimension near the same point of focus. 
     For measuring rough surfaces or surfaces with significant discontinuities, such as surfaces with an average roughness approaching one-half of wavelengths in the near-infrared range, our invention provides laser sources that produce two beams having different fundamental wavelengths of light. Beamsplitters divide each of the different wavelength beams into test and reference beams. Another beamsplitter combines the two different wavelength test beams into a common test beam composed of the two different wavelengths. It is the common test beam that is divided into the multiple sub-test beams, resulting in each of the sub-test beams being composed of the two wavelengths. 
     Each of the different wavelength reference beams preferably propagates along respective reference delay lines of the reference arm for controlling the optical path lengths traversed by the two reference beams. Preferably, the two reference delay lines have adjustable optical path lengths to equate optical path lengths between the test and reference arms of the interferometer. The optical path lengths of the test and reference arms can also be equated by incorporating similar path-length adjustments within the test arms. 
     The detection system preferably includes first and second arrays of detectors for separately detecting interference between each of the two pairs of test and reference beams. The detectors within each of the first and second arrays are preferably relatively phase shifted for simultaneously detecting a plurality of phase-shifted measurements within each of the first and second pairs of test and reference beams. The simultaneous phase-shifted measurements allow for discerning more accurate phase differences between the test and reference beams at each fundamental wavelength. 
     Although accurate, the two individual wavelength measurements produce ambiguous results for surface discontinuities greater than one-half the fundamental wavelengths. Our invention, however, provides a controller that combines information from the first and second arrays of detectors to produce aggregate interference measurements having a sensitivity equated to an effective wavelength significantly longer than either of the two different fundamental wavelengths. The aggregate measurements are useful for measuring surfaces with a roughness exceeding one-half the two fundamental wavelengths. 
     The actuator is preferably a part of a relative motion system between the probe and the test piece for measuring a plurality of points on each of the two surfaces of the test piece. Preferably, both the test arm and the reference arm are relatively movable together with the probe with respect to the test piece. The detection system is also preferably mounted together with the test and reference arms and the probe on a multi-axis stage assembly for relative motion with respect to the test piece. A base preferably supports both the test piece and the multi-axis stage assembly for relating motions between the probe and the test piece. A displacement-measuring interferometer preferably measures movements between the multi-axis stage assembly and the base. Information from the displacement-measuring interferometer can be combined with interferometric measurements taken through the probe to compensate for any motion errors of the relative motion system or to resolve remaining phase ambiguities required to obtain absolute measurements. 
     Our preferred method of measuring multiple surfaces of a test piece with a scanning interferometer follows the basic interferometric practice of dividing a beam of light into test and reference beams but further divides the test beam into multiple sub-test beams. The multiple sub-test beams are focused to different points for separately measuring different surfaces of the test piece. For measuring a first test piece surface, the point of focus of a first sub-test beam is positioned on the first surface of the test piece while the point of focus of a second or higher sub-test beam is positioned off of their respective measuring surfaces of the test piece. For measuring a second or higher test piece surface, the point of focus of the second or higher sub-test beam is positioned on the second or higher surface of the test piece while the point of focus of the first or other lower sub-test beams is positioned off of their respective measuring surfaces of the test piece. Relative motion between the probe and the test piece is used both (a) to move the points of focus across the test surfaces for measuring a plurality of points on each of the test surfaces and (b) to move the points of focus between the sequential measuring positions. 
     At their respective measuring positions, the sub-test beams are retroreflected from their points of focus on the surfaces of the test piece. The retroreflected sub-test beams are preferably refocused together with the reference beam proximate to a detector. Interference signals between each of the sub-test beams and the reference beam are detected separately according to which of the sub-test beams is positioned in focus on one of surfaces of the test piece. 
     The refocused light of the sub-test beams is refocused conjugate to their points of focus. A limiting aperture near the conjugate plane excludes light from the sub-test beam that is not focused on one of the surfaces of the test piece. A detector for detecting the refocused light is preferably positioned behind the limiting aperture and arranged to collect only the light that passes through the limiting aperture. Alternatively, a detector with a small active area can be located near the conjugate focal plane to function as a similarly limiting aperture excluding light that focuses before or after the focal plane. The retroreflected test beams could also be refocused through a limiting aperture prior to their recombination with the reference beam remote from the detector. 
     While confocal optical techniques can be used to distinguish one surface from another, two-wavelength interferometry is preferably used for extending the range of dynamic measurement to accommodate rough surfaces or surfaces with significant discontinuities. Two beams of coherent light having different fundamental wavelengths are each divided into test and reference beams. The different wavelength test beams are combined in advance of the step of dividing the test beam into multiple sub-test beams so that each of the multiple sub-test beams includes the two different fundamental wavelengths. 
     Along the path of retroreflection, the two fundamental wavelengths are re-separated for simultaneously measuring optical path differences between the test and reference beam portions of each of the fundamental wavelengths. The optical path differences expressed by the mechanism of interference provide overlapping measurements of individual points on one or the other of the test surfaces that is in focus. Relative motion (i.e., scanning) of the point of focus across the test surface allows for the accumulation of information describing the surface. Interference information detected from both fundamental wavelengths can be combined to reveal unambiguous measurements over a much wider range extending to one-half of an effective wavelength that is significantly longer than either of the two fundamental wavelengths. 
     In addition, the remaining ambiguities of the combined interferometric measurements in two wavelengths can be resolved by measuring from a known point of reference the movements required for positioning the points of focus of the sub-test beams on the surfaces of the test piece. For example, the displacement-measuring interferometer can be calibrated to a master test piece and used to track the further motions required to move the probe into the measuring positions. With the positions of the probe known and the positions of the test surfaces known with respect to the probe, absolute measures of the test surfaces can be made. 
    
    
     DRAWINGS 
     FIG. 1 is a diagram of an exemplary scanning interferometer system in accordance with our invention. 
     FIG. 2 is another diagram showing the layout of one of two different wavelength interferometers that are combined within the scanning interferometer system to increase the range of measurement. 
     FIG. 3 is a greatly enlarged cross-sectional view of a probe in a first position for conveying a first of two focused sub-test beams to one of two internal surfaces of a test piece at normal incidence. 
     FIG. 4 is a greatly enlarged cross-sectional view of the same probe in a second position for conveying a second of two focused sub-test beams to the other of two internal surfaces of a test piece at normal incidence. 
    
    
     DETAILED DESCRIPTION 
     An exemplary scanning interferometer system  10  shown in FIG. 1 includes a compound probe  12  for measuring a test piece  14  having multiple internal surfaces. The compound probe  12  is mounted on a multi-axis stage assembly  16 , and the test piece  14  is mounted on a rotary chuck  18 . A base  20  supports both the multi-axis stage assembly  16  and the rotary chuck  18  for relating relative motions between the compound probe  12  and the test piece  14 . 
     The multi-axis stage assembly  16  is preferably translatable in two orthogonal directions X and Z via mechanical crossed roller bearing stages  16 ′ and  16 ″ driven by respective motor actuators  22  and  24 . Both of the motor actuators  22  and  24  are preferably brushless, slotless DC motors with integral encoders. The compound probe  12  is moved by the multi-axis stage assembly  16  along a desired motion profile by conventional control electronics  26  for the motor actuators  22  and  24  under the programmable direction of a microcomputer  28 . 
     Since the stage motion is neither perfectly smooth nor straight, a three-axis displacement-measuring interferometer  30  is used to monitor the motion. Three measurement arms  32 ,  33 , and  34  of the displacement-measuring interferometer  30  are shown for monitoring translational motions in the two orthogonal directions of stage motion X and Z and a rotational motion about an axis extending in a third orthogonal direction. The two translational motions are measured by the measurement arms  32  and  33  or  34 . The rotational motion is measured by differential measures between the measurement arms  33  and  34 . The measurement arms  32 ,  33 , and  34  are preferably connected to the stage assembly  16  by mirrors  36 ,  37 , and  38  constructed from a low-expansion glass. The light source for the displacement-measuring interferometer  30  is preferably a frequency-stabilized helium-neon laser (not shown). The displacement-measuring interferometer  30  measures errors in straightness and yaw in addition to displacement errors of the stage motions. This error data is recorded to remove stage motion errors from probe profile measurements. 
     The probe  12  is preferably mounted in a kinematic bracket  13  with a magnetic preload that allows the probe  12  to be removed and reinserted or replaced while maintaining the original alignment. The rotary chuck  18  mounting the test piece  14  is preferably a hydraulic expansion chuck rotatable on an air bearing spindle  40  powered by a direct-drive brushless DC motor  42  with an integral high-resolution encoder. Quadrature signals from the spindle encoder are used to clock data acquisition including data from the displacement-measuring interferometer during measurement. Residual tilt and decenter mounting errors can be removed by software analysis of probe measurements. 
     The base  20  supporting both the multi-axis stage assembly  16  for the probe  12  and the rotary chuck  18  for the test piece  14  is preferably made of granite and includes a riser (not shown) on which the multi-axis stage assembly  16  is supported. The rotary chuck  18  is mounted in a hole through the base  20 . The granite structure of the base  20  is integrated into a cradle (not shown) supported by a pneumatic isolation frame (also not shown) for increased immunity from external vibration sources. 
     Two interferometer modules  50  and  52  are carried by the multi-axis stage assembly  16 . The two interferometer modules  50  and  52  are preferably identical except as required to accommodate different fundamental wavelengths of largely coherent light. Both fundamental wavelengths are preferably within the near-infrared range. For example, the interferometer module  50  can be operated at a wavelength λ 1  of 1550 nanometers (nm), and the interferometer module  52  can be operated at a wavelength λ 2  of 1310 nanometers (nm). Both interferometer modules  50  and  52  are independently capable of measuring smooth parts; but when analyzed together, a combined interference pattern is generated at a much longer effective wavelength λ e  capable of measuring rougher surfaces with greater dynamic ranges. The effective wavelength λ e  is given as follows:                λ   e     =         λ   1     *     λ   2                λ   1     -     λ   2                                                       
     Substituting the fundamental wavelengths of 1310 nm and 1550 nm yields an effective wavelength λ e  of 8460 nm or approximately 8.5 microns (μm). Surfaces with a roughness Rz (comparing five highest peaks to five lowest troughs) in the order of 2 microns (μm) can easily be measured at the effective wavelength λ e  of approximately 8.5 microns (μm). 
     Although only the interferometer module  50  is illustrated (see FIG.  2 ), the depicted features are common to both interferometer modules  50  and  52  varying only to accommodate the different fundamental wavelengths λ 1  and λ 2 . For example, both interferometer modules  50  and  52  preferably include a distributed feedback (DFB) solid-state laser  54  as a source of coherent linearly polarized light. The emitted light beam  56  is collimated by lens assembly  58  and reflected by folding mirror  60  on a path through a half-wave retardation plate  62  to a first polarizing beamsplitter cube  64 . Linearly polarized at 45 degrees, part of the light beam  56  passes directly through both the beamsplitter cube  64  and an attached quarter-wave retardation plate  66  as a first reference beam  68 . The remaining part of the light beam  56  is reflected by the beamsplitter cube  64  through another quarter-wave retardation plate  70  as a first test beam  72 , which passes through a shuttered aperture  74  of the interference module  50 . 
     A second test beam  76  differing only in fundamental wavelength emerges from the interferometer module  52 . Three folding mirrors  78 ,  80 , and  82  orient the two test beams  72  and  76  relative to a dichroic beamsplitter  84  that merges the two test beams  72  and  76  into a combined test beam  86  en route to the compound probe  12 . 
     Within the compound probe  12  as shown in FIGS. 3 and 4, the combined beam is reshaped by a focusing optic  88  of a confocal optical system before being split by another beamsplitter cube  90  into two sub-test beams  92  and  94 . Each of the sub-test beams  92  and  94  contains both fundamental wavelengths λ 1  and λ 2 . The focusing optic  88  mounted within the compound probe  12  focuses the two sub-test beams  92  and  94  to different points of focus  96  and  98 . (It is this characteristic that makes the probe  12  a compound probe.) Before reaching its point of focus  98 , the sub-test beam  94  is folded by a prism  100  (a directional optic) that angularly orients the sub-test beam  94  with respect to the sub-test beam  92 . The two sub-test beams  92  and  94  are oriented normal to two internal surfaces of revolution  102  and  104  within the test piece  14 . In the illustrations of FIGS. 3 and 4, the test surface  102  has the form of a cylinder, and the test surface  104  has the form of a truncated cone. 
     The two test surfaces  102  and  104  are measured one at a time. A relative motion system, which includes the drive motor actuators  22  and  24  under programmable control, moves the compound probe  12  in the orthogonal directions X and Z to separately trace the expected profiles of the test surfaces  102  and  104 . The drive motor  42  rotates the test piece  14  about a common axis  106  of the internal (test) surfaces of revolution  102  and  104  to provide three-dimensional scans of the surfaces. Although shown angularly related through a particular obtuse angle, the two test surfaces can be relatively oriented through a range of different angles including a right angle where one of the test surfaces is a cylinder and the other is a flat. 
     For separately measuring the two test surfaces  102  and  104 , the compound probe  12  is movable between: 
     a first position at which the point of focus  96  of the sub-test beam  92  is positioned on the test surface  102  and the point of focus  98  of the sub-test beam  94  is positioned off both test surfaces  102  and  104  (see FIG. 3) and 
     a second position at which the point of focus  98  of the sub-test beam  94  is positioned on the test surface  104  and the point of focus  96  of the sub-test beam  92  is positioned off both the test surfaces  102  and  104  (see FIG.  4 ). 
     Within each of the two positions, the compound probe  12  is relatively translated while the test piece  14  is relatively rotated to scan a range of points on one or the other of the test surfaces  102  and  104 . 
     During the course of measurement, light retroreflected from the test surfaces  102  or  104  re-enters the compound probe  12  on return paths to the two interferometer modules  50  and  52 . The entire routes of the two test beams  72  and  76 , the combined test beam  86 , and two sub-test beams  92  and  94  are contained within a test arm of our scanning interferometer  10  between the corresponding beamsplitter cubes  64  (only one shown) in the interferometer modules  50  and  52  and the two points of focus  96  and  98 . Exemplary of both test beams  72  and  76 , the test beam  72  re-encounters the one-quarter wave retardation plate  70  in advance of the beamsplitter cube  64 . The two encounters with the one-quarter wave retardation plate  70  have the effect of rotating polarization so that the returning test beam  72  is transmitted rather than reflected by the beamsplitter cube  64 . 
     Each of the interferometer modules  50  and  52  contains a working reference arm. The reference beam  68  emerging from the beamsplitter cube  64  is reflected by a folding mirror  108  along a reference delay line  110 , which also includes a compound reflecting prism  112  and a reference module  114  that provides for retroreflecting the reference beam on a return path to the beamsplitter cube  64 . The compound reflecting prism  112  is adjustable along an optical axis in opposite directions A R  for matching the optical path length of the reference arm to the optical path length of the test arm. The reference module  114  simulates optics of the compound probe  12  to match the optical experiences of a range of rays surrounding the optical axis between the test and reference arms. 
     The optical path lengths of the test and references arms can also be nominally equated by making path length adjustments to the test arm. For example, the interferometer modules  50  and  52  can be adjusted in position on the multi-axis stage assembly  16  with respect to the folding mirrors  78  and  82  to change the physical path lengths traversed by the first and second test beams  72  and  76 . 
     The returning reference beam  68  re-encounters the one-quarter wave retardation plate  66  and is reflected rather than transmitted through the beamsplitter cube  64  into alignment with the test beam  72 . A combined test and reference beam  118  emerges from the beamsplitter cube  64  through another one-half wave retardation plate  120  as 45 degree linearly polarized light. An interference filter  122 , which removes unwanted wavelengths, and an aperture stop  124 , which removes stray rays, reduce noise in the combined test and reference beam  118 . 
     An imaging optic  126  of the confocal optical system in combination with a cluster of three beamsplitter cubes  130 ,  132 , and  134  images the combined test and reference beam  118  onto four detectors  136 ,  138 ,  140 , and  142  having an incremental 90 degree phase shift among them. Respective points of focus of the imaging optic  126  are preferably conjugate to the focal points  96  and  98  of the sub-test beams  92  and  94  and are preferably coincident with the four detectors  136 ,  138 ,  140 , and  142 . Each of the four detectors  136 ,  138 ,  140 , and  142  receives light through a limited aperture size at the focus of the imaging optic  126 . Together, the focusing and imaging optics  88  and  126  function as opposite ends of a confocal optical system that excludes light that does not approach the conjugate points of focus. 
     Either the detectors  136 ,  138 ,  140 , and  142  can be arranged in conjunction with aperture stops of limited size or the detectors  136 ,  138 ,  140 , and  142  themselves can be of limited size (e.g., 10 to 100 microns) to exclude light at different depths of focus (e.g., 10 to 100 microns depths of focus). Since the focus  96  or  98  of just one of the sub-test beams  92  or  94  is located on one of the test surfaces  102  or  104  of the test piece  14  in each of the two measuring positions, the imaging optic  126  allows for the detection of light from just one of the two sub-test beams  92  or  94  at each of the two measuring positions. Thus, each of the two test surfaces  102  and  104  of the test piece  14  can be separately measured with the compound probe  12 . 
     Alternatively, the imaging optic  126  could be located in advance of the beamsplitter cube  64  for refocusing one or the other of the test beams  72  or  76  independently of the reference beam. A limiting aperture, such as a stop, is preferably located near the conjugate focus of the imaging optic  126  for excluding the further propagation of light that is not retroreflected from one of the points of focus  96  or  98  on one of the test surfaces  102  or  104 . 
     The clustered beamsplitter cubes  130 ,  132 , and  134  are separated by retardation plates  146  and  148  to support 90 degree phase shifts among the four detectors  136 ,  138 ,  140 , and  142 . The data acquisition system timed to the incremental rotation of the test piece  14  simultaneously acquires data from all four detectors  136 ,  138 ,  140 , and  142  in each of the two interferometer modules  50  and  52  along with data from the three-axis displacement-measuring interferometer  30  for generating instantaneous measurements at individual points on one or the other of the test surfaces  102  or  104 . The phase-shifted data allows for the more precise identification of phase differences between the combined test and reference beams, and the displacement data relates data points with improved accuracy along the measured profiles of the test surfaces  102  and  104 . Phase data from the two interferometer modules  50  and  52  can be combined to produce measurements having a greater dynamic range for accommodating test surfaces having roughness or other surface discontinuities that would otherwise yield ambiguous results. 
     Both interferometer modules  50  and  52  simultaneously measure the same points on either of the test surfaces  102  and  104 . Accordingly, phase information is directly combinable for producing measures at an effective wavelength λ e  that is longer than the wavelengths λ 1  and λ 2  of the two interferometer modules  50  and  52 . The longer effective wavelength λ e  allows phase information from the two interferometer modules  50  and  52  to be unambiguously resolved over a greater range of surface variation. 
     Although the illustrated probe  12  splits the combined test beam  86  into two sub-test beams  92  and  94 , the probe could be arranged to include other directional optics for splitting the combined test beam into three or more sub-test beams for similarly measuring three or more surfaces of a test piece, such as the cylindrical surface  102 , the truncated conical surface  104 , and a plane surface  103  of the test piece  14 . Instead of mounting the two interferometer modules  50  and  52  on the multi-axis stage assembly  16 , the interferometer modules  50  and  52  could be mounted independently of the stage assembly  16  and connected to the compound probe  12  by a flexible optical connection, such as a single mode optical fiber. 
     Our new method is preferably practiced by producing two beams (e.g., beams  56 ) of substantially coherent light having different fundamental wavelengths. The two fundamental wavelengths are preferably in the near-infrared range, where suitable laser sources are readily available for the field of telecommunications. Shorter wavelengths are subject to more speckle, and longer wavelengths generally require more expensive laser sources. 
     Both of the different wavelength beams  56  are divided into test beams  72  and  76  and reference beams  68 . The two test beams  72  and  76  are combined and later divided into first and second sub-test beams  92  and  94 , each including both fundamental wavelengths. A common focusing optic  88  focuses the first and second sub-test beams  92  and  94  to different points of focus  96  and  98  for separately measuring two different surfaces  102  and  104  of the test piece  14 . 
     As shown in FIG. 3, the point of focus  96  of the first sub-test beam  92  is positioned on the surface  102  of the test piece  14  while the point of focus  98  of the second sub-test beam  94  is positioned off of both test surfaces  102  and  104 . Precise positioning of the focus  96  on the test surface  102  can be achieved by monitoring modulation (contrast) or intensity as a function of position within either of the two interferometer modules  50  or  52  and choosing the position of greatest modulation or highest intensity. The focusing and imaging optics  88  and  126  cause both modulation and intensity to rapidly decrease for either point of focus  96  or  98  that departs from one of the test surfaces  102  or  104 . 
     The point of focus  96  of the first sub-test beam  92  is moved across the test surface  102 , while a data acquisition system, which includes the detectors  136 ,  138 ,  140 , and  142 , acquires point-by-point height information about the test surface  102 . Preferably, the data acquisition is timed with the rotation of the test piece  14  while the point of focus  96  is translated along a desired rotational profile of the test surface  102 . Typical speeds for measuring a 3.5 millimeter (mm) diameter internal surface are 600 revolutions per minute of rotation with 4 to 50 microns of translation per revolution. Data points are typically collected in an array of approximately 200-1000×1024, where the rows correspond to the increments of translation and the columns correspond to increments of rotation. Of course, more or less points can be acquired at these or other speeds. 
     As shown in FIG. 4, the other test surface  104  is measured by positioning the point of focus  98  of the second sub-test beam  94  on the test surface  104  while the point of focus  96  of the first sub-test beam  92  is positioned off of both test surfaces  102  and  104 . Similar monitoring techniques can be used to locate the point of focus  98  on the test surface  104 , and a similar combination of relative motions (e.g., rotation and translation) can be used to scan the point of focus  98  across the test surface  104  for acquiring a corresponding array of data. 
     At each of the two measuring positions, light retroreflected from one of the test surfaces  102  or  104  is refocused together with the reference beams  68  onto the detectors  136 ,  138 ,  140 , and  142 . Interference signals (i.e., phase differences) between the reference beams  68  and the first and second sub-test beams  92  and  94  are separately detected according to which of the sub-test beams  92  or  94  is positioned in focus on one of the test surfaces  102  or  104 . Optical path lengths of the reference beams  68  are preferably adjustable to provide nominally equal optical path lengths between the test and reference arms to eliminate phase variations caused by changes in temperature or laser wavelength fluctuations. The optical path lengths of the test and reference arms can also be nominally equated by making similar adjustments to the test arm. 
     The refocusing preferably includes limiting an aperture dimension of the refocused light to exclude from detection light from the sub-test beam  92  or  94  that is not focused onto one of the test surfaces  102  or  104 . The detectors  136 ,  138 ,  140 , and  142 , which can themselves be limited in aperture dimension, are preferably located at points of focus conjugate to the points of focus  96  and  98  of the two sub-test beams  92  and  94 . 
     The detectors  136 ,  138 ,  140 , and  142  are preferably arranged in two groups, each for measuring interference characteristics of one of the two fundamental wavelengths. The detectors within each group are separated in phase for simultaneously detecting phase-shifted interference signals between both of the pairs of test and reference beams having different fundamental wavelengths. Preferably, four detectors  136 ,  138 ,  140 , and  142  are phase shifted within each group through increments of 90 degrees. As few as three or more than four can be used to provide lesser or greater accuracy for discriminating phase information. 
     The phase information from each of the two groups of detectors  136 ,  138 ,  140 , and  142  provides precise information about variations in the test surfaces  102  or  104  over limited ranges corresponding to one-half the fundamental wavelengths λ 1  and λ 2 . However, the simultaneous phase information from the two groups of detectors  136 ,  138 ,  140 , and  142  can be combined to provide additional phase information that resolves phase ambiguities up to one-half of a longer effective wavelength λ e . 
     In addition to acquiring information about phase variations from one or the other of the two sub-test beams  92  or  94 , information is also acquired about the relative motions between the points of focus  96  and  98  and the test piece  14 . The additional information, which is collected simultaneously with the information from the sub-test beams  92  or  94 , includes deviations from a desired path of relative motion. The deviations of relative motion combined with the phase variations of the sub-test beams  92  or  94  provide accurate measures of test surface variations from the desired path of relative motion. 
     Conventional data analysis can be applied to these measures by the microprocessor  28  to extract measures of both form and geometry, including roughness, runout, concentricity, and tilt. Errors relating to the mounting and rotating of the test piece  14 , such as decenter and tilt, can be removed by conventional analysis techniques. Relational measurements can also be made between the two surfaces  102  and  104 , such as runout, co-axiality, and perpendicularity. A workstation  44 , an output  46  such as a printer or CRT, and a storage device  48  such as a hard disk or optical disk are connected to the microprocessor  28  to provide a conventional interface. 
     In addition to removing stage motion errors from probe profile measurements, the displacement-measuring interferometer  30  can also be used to resolve modulo  2 π phase ambiguities at the effective wavelength λ e  of the combined measurements of the two interferometer modules  50  and  52  to produce absolute measurements of the test piece  14 . The displacement-measuring interferometer  30  can be calibrated to a master test piece of known dimensions, and the further relative motion required to move a point of focus  96  or  98  from a surface of the master having a known dimension (e.g., diameter) to a position on one of the test surfaces  102  or  104  can be measured. Combining the known dimension of the master with the further relative motion of the probe  12  to a measuring position provides an absolute measure of the test piece  14  within sufficient accuracy to resolve the modulo 2π phase ambiguities at the effective wavelength λ e  of the combined measurements of the two interferometer modules  50  and  52 . 
     As explained earlier, the probe  14  is moved to precise measuring positions by exploiting the confocal nature of the interferometric measurements made through the probe  14 . Both the modulation (contrast) of the interference signal and the intensity of light returning from the probe  14  to the detectors  136 ,  138 ,  140 , and  142  rapidly decrease as either point of focus  96  or  98  departs from one of the test surfaces  102  or  104 . The multi-axis stage assembly  16  can be adjusted to position the probe  14  to the measuring positions at which the highest modulation or intensity is detected, and the displacement-measuring interferometer  30  tracks the absolute location of these measuring positions from which the more precise interferometric measurements are made. 
     Precise absolute measurements of the test surfaces  102  and  104  can be made in stages. The information acquired from the calibrated displacement-measuring interferometer  30  resolves the modulo 2π phase ambiguities at the effective wavelength λ e  of the combined measurements of the two interferometer modules  50  and  52 , and the information acquired from the combined measurements of the two interferometer modules  50  and  52  at the effective wavelength λ e  resolves the modulo  2 π phase ambiguities at either or both of the fundamental wavelengths λ 1  or λ 2  of the two interferometer modules  50  or  52 . Within the dimensions of the fundamental wavelengths λ 1  or λ 2 , conventional phase-shifting techniques, such as those based on the simultaneous detection of phase-shifted measurements by the multiple detectors  136 ,  138 ,  140 , and  142 , can be used to accurately identify the phase of the interference signals for even further extending the precision of the absolute measurements. 
     Although the two interference modules  50  and  52  are shown mounted on the multi-axis stage assembly  16 , the two modules  50  and  52  could also be mounted independent of the multi-axis stage assembly  16  and be connected to the probe  12  through a more flexible optical connection. For example, the two modules  50  and  52  could be connected to the probe  12  through fiber optics. 
     Two separate enclosures (neither shown) are used for environmental regulation. The control electronics are housed within one of the enclosures, and the optical and electromechanical components from the probe  12  to the rotary chuck  18  are housed in the other enclosure. The environmental control system (not shown) can include a solid-state thermoelectric cooler and heater, a blower assembly, and control and monitoring electronics positioned throughout the enclosures. Temperatures within 0.25 degrees Celsius are preferably maintained within the optical and electromechanical component enclosure.