Abstract:
Flatness and thickness variation information concerning transmissive plane-parallel test plates is obtained from a grazing incidence interferometer modified to distinguish between superimposed interference patterns containing both types of information. The grazing angle of the interferometer is varied, and unique modulation frequencies of local fringe intensities within the superimposed interference patterns are identified. The local fringe intensities attributable to the different interference patterns are distinguished by their respective modulation frequencies.

Description:
TECHNICAL FIELD  
         [0001]    Flatness and thickness variation of test pieces can be measured optically by evaluating interference patterns produced between paired surfaces. The flatness of a surface is compared to a reference surface. Thickness variation is compared between two surfaces of a test piece. Grazing incidence interferometry, where at least one of the paired surfaces is illuminated at non-normal angles of incidence, provides for enhancing specular reflectivity and for adjusting the sensitivity of the measurements.  
         BACKGROUND  
         [0002]    Interferometric measurements of thin transmissive test pieces present special problems, because opposite surfaces of the transmissive test pieces can participate in forming multiple interference patterns. For example, interference patterns can be formed between each of the opposite surfaces and a common reference surface as well as between the opposite surfaces themselves. Each of the interference patterns contains information about the test piece, but the information is obscured when the interference patterns overlie each other.  
           [0003]    In the grazing incidence interferometer of co-assigned U.S. Pat. No. 4,325,637 to Moore, which is hereby incorporated by reference, spatial coherence of the illuminating beam is limited to exclude interference patterns between surfaces separated beyond a coherence limit. Collimated light reflected from the surfaces laterally shears as a function of the separation between the surfaces. A rotating diffuser interrupts the illuminating beam and reduces spatial coherence so that interference fringes do not form between surfaces separated by more than the distance between intended test and reference surfaces.  
           [0004]    However, reduced spatial coherence does not preclude interference fringes from forming between the opposite surfaces of thin transmissive test pieces, whose opposite surfaces are separated by amounts comparable to the separation between the transmissive optic and a reference surface. A first interference pattern measuring flatness is formed between the reference surface and the closest of the opposite test surfaces of the test piece. A second overlying interference pattern measuring thickness (and index) variation is formed between the opposite surfaces of the test piece. A third overlying interference pattern also measuring flatness can be formed (if also within the coherence limit) between the reference surface and the more remote of the opposite surfaces of the test piece. The overlying interference patterns obscure the different flatness or thickness variation information contained within each pattern.  
         SUMMARY OF INVENTION  
         [0005]    Our invention provides for distinguishing among superimposed interference patterns that are formed by a grazing incidence interferometer between paired combinations of a reference surface and two nominally parallel surfaces of a thin transmissive test piece. The grazing angle of the illuminating beam, which is incident upon both the test piece and the reference surface, is varied in a stepwise manner to elicit distinguishing responses from the superimposed interference patterns. The distinguishing responses enable the evaluation of individual interference patterns.  
           [0006]    An exemplary method of measuring a transmissive plane parallel test piece with a grazing incidence interferometer includes reflecting a beam of light at a non-normal grazing angle from both a reference surface and two nominally parallel surfaces of the transmissive test piece. A first interference pattern formed between the reference surface and one of the two nominally parallel surfaces of the test piece is superimposed upon a second interference pattern formed between the two nominally parallel surfaces of the test piece. To distinguish between the first and second interference patterns, the non-normal grazing angle of the beam is varied through a range of angles at which local fringe intensities of each of the superimposed interference patterns shift through at least one cycle. A modulation frequency at which the local fringe intensities shift within one of the superimposed interference patterns is determined. The local fringe intensities varying at the modulation frequency are evaluated to extract phase information from the one interference pattern.  
           [0007]    For measuring the flatness of one of the nominally parallel surfaces of the test piece, the determined modulation frequency is the modulation frequency at which the local fringe intensities shift within the first interference pattern. For measuring thickness variation between two nominally parallel surfaces of the test piece, the modulation frequency is the modulation frequency at which the local fringe intensities shift within the second interference pattern. The modulation frequencies of both the first and second interference patterns can be determined to evaluate both the flatness and the thickness variation of the test piece surfaces.  
           [0008]    Preferably, the non-normal grazing angle is progressively varied through different size angular increments corresponding to approximately even increments of optical path difference between the surfaces evaluated by the one interference pattern. The resulting modulation frequencies remain constant throughout the range of tilt (i.e., the range of grazing angles) for both the interference patterns. However, the modulation frequencies associated with the first and second interference patterns differ as a function of the separation between the surfaces that form them.  
           [0009]    Differences between the modulation frequencies of the superimposed interference patterns can be enhanced by adjusting the non-normal grazing angle and the separation between the test piece and the reference surface. The modulation frequency is preferably calculated independently of the step of varying the non-normal grazing angle based on an expected relationship between the test piece and the grazing incidence interferometer.  
           [0010]    The beam of light is preferably a temporally coherent beam of spatially coherent-limited light. Shear produced between the various reflections from the reference surface and the two nominally parallel surfaces of the test piece is a function of both the non-normal grazing angle and spacing between the surfaces. A first of the two nominally parallel surfaces of the test piece is oriented adjacent to the reference surface, and a second of the two nominally parallel surfaces is oriented remote from the reference surface. The shear between the reflections from the reference surface and the second of the two nominally parallel surfaces is preferably beyond a spatial coherence limit within which the interference patterns are formed.  
           [0011]    Overall, our preferred method exploits the results of a non-normal grazing angle variation to distinguish among superimposed interference patterns produced between paired combinations of a reference surface and two nominally parallel surfaces of a transmissive test piece. A modulation frequency is calculated for a shift of local fringe intensities of one of the superimposed interference patterns as a function of the variations in the non-normal grazing angle at which a light beam producing the interference patterns reflects from the reference surface and the two nominally parallel surfaces of the transmissive test piece. The non-normal grazing angle of the beam is varied through a range of angles at which local fringe intensities of each of the superimposed interference patterns shift through at least one cycle. A succession of superimposed fringe-shifted forms of the interference patterns is produced throughout the range of angles at which the non-normal grazing angle of the beam is varied. Local fringe intensities that progressively vary through the succession of fringe-shifted forms of the interference patterns at the calculated modulation frequency are distinguished from other local fringe intensities that do not similarly vary at the same modulation frequency.  
           [0012]    The modulation frequency at which the local fringe intensities shift within one of the superimposed interference patterns is preferably calculated in advance of the production of the superimposed interference patterns based on information known about the test piece and its relationship to the grazing incidence interferometer. The calculation preferably identifies modulation frequencies for both of the superimposed interference patterns, and these modulation frequencies distinguish the progressive variations in local fringe intensities between the two superimposed interference patterns.  
           [0013]    Calculating the modulation frequencies in advance of the actual measurements produces more consistent results for measuring similar test pieces by eliminating noise distortions than accompany the actual measurements. The noise distortions can make the true modulation frequencies more difficult to distinguish among other frequencies associated with the noise, especially from a limited number of the fringe-shifted forms of the interference patterns. However, once the modulation frequencies are determined (e.g., by pre-calculation), the progressive variations in the local fringe intensities associated with the different interference patterns can be more easily recognized at the modulation frequencies from a more limited number of the fringe-shifted forms of the interference patterns. 
       
    
    
     DRAWINGS  
       [0014]    [0014]FIG. 1 is a diagram of a grazing incidence interferometer together with a processor for separating overlying interference patterns.  
         [0015]    [0015]FIG. 2 is an enlarged view of a reference prism and test piece showing a division of a central input ray into three output rays reflected from a reference surface of the prism and two nominally parallel surfaces of the test piece.  
         [0016]    FIGS.  3 A- 3 C are images of exemplary interference patterns. FIGS. 3A and 3B represent separate interference patterns between surface pairings, and FIG. 3C represents a combined interference pattern formed by the superposition of the interference patterns of FIGS. 3A and 3B.  
         [0017]    FIGS.  4 A- 4 B are graphs showing two expected frequency components of normalized intensity variations undergone by individual pixels as a function of a changing grazing angle and distinguishing the intensity contributions of the two superimposed interference patterns.  
         [0018]    [0018]FIG. 5 is an enlarged cut-away diagram showing optical path length differences between interfering beams and their relationship to variables such as the grazing angle. 
     
    
     DESCRIPTION  
       [0019]    An exemplary grazing incidence interferometer  10  as shown in FIG. 1 provides for measuring both flatness and thickness variation of a transmissive test piece  12 , which has the form of a plane parallel plate. A light source  14 , such as a laser diode, emits a beam  18  of temporally coherent light, which a focusing lens  16  sets on an initially converging path.  
         [0020]    A coherence adjuster  20  having a rotating diffuser plate  22  interrupts a narrowed portion of the beam  18  to reduce spatial coherence of the beam  18 . The rotating diffuser plate  22  interrupts the beam  18  and randomly scatters light illuminating a spot  23  on the diffuser plate  22 . The light scattered from the spot  23  emulates an extended light source, whose size is inversely related to the degree of spatial coherence of the beam  18 . The focusing lens  16  is movable in the directions of arrows  24  to change the size of the illuminated spot  23  for adjusting the spatial coherence of the beam  18 .  
         [0021]    An expanding portion of the beam  18  propagates through a tilt mechanism  26  having a reflective surface  28  and a pivot  30  for tilting the reflective surface  28  through a limited range of angles in the directions of arrows  32 . Similar amounts of beam tilt can be achieved by interrupting the beam  18  with a pivotal plane parallel plate. When inclined from normal to the propagating beam  18 , light transmits through the plate from an apparent source that is offset from the extended light source on the diffuser plate  22 .  
         [0022]    A collimating lens  34 , whose focal length is measured from the diffuser plate  22 , converts the expanding beam  18  into a nominally collimated beam  18  that approaches one side  36  of a triangular prism  40  at close to normal incidence. The side  36  is preferably one of two equal length sides  36  and  38  that are inclined to a base  42  at approximately 45-degree angles. Although expanded, residual divergence of the nominally collimated beam  18  is slightly increased by the limited spatial coherence of the beam  18 , and the average incident angle of the collimated beam  18  approaching the prism  20  can depart slightly from normal by the tilt of the beam  18 .  
         [0023]    With reference to FIG. 2, a central ray  48  of the beam  18  propagates through the prism  40  and is partially reflected from the base surface  42  of the prism  40  through a non-normal grazing angle “α” as a reference beam ray  50 . The grazing angle “α” is defined as a non-normal angle inclined from a reflective surface (the base surface  42  of the prism  40 ) within a range of specular reflection. Angles of so-called “grazing incidence” are complementary to these “grazing angles”.  
         [0024]    Another portion of the ray  48  is refracted from the base surface  42  through an air gap  60  before being partially reflected from a first surface  56  of two nominally planar surfaces  56  and  58  of the test piece  12  as a first test beam ray  52 . Yet another portion of the ray  48  refracts at the first surface  56  and propagates through the test piece  12  before being reflected from the second surface  58  of the two nominally planar surfaces  56  and  58  of the test piece  12  as a second test beam ray  54 . The reference beam ray  50  and the two test beam rays  52  and  54  exit the prism  40  through the prism surface  38  relatively sheared but nominally parallel to each other. Preferably, the non-normal grazing angle “α” is at least approximately equal to the complement of a base angle of the prism  40  so that all of the rays  48 ,  50 ,  52 , and  54  enter or leave the prism  40  at close to normal incidence.  
         [0025]    The first test beam ray  52  is sheared with respect to the reference beam ray  50  through distance “a”. The second test beam ray  54  is sheared with respect to the first test beam ray  52  through distance “b”. The second test beam ray  54  is sheared with respect to the reference beam ray  50  through distance “c”. Preferably, the shear distance “c” is beyond the spatial coherence of the beam  18  as set by the coherence adjuster  20 . The amount of the shear “a”, which is one component of the shear “c”, can be adjusted by increasing or decreasing the air gap  60  using different diameter filament mounts  62 . Other ways of adjusting the air gap  60  include supports engaging either surface  56  or  58  of the test piece  12 .  
         [0026]    Within the spatial coherence of the beam  18 , a first interference pattern  64  (see for example FIG. 3A) containing information concerning the flatness of the test piece surface  56  is formed between a first portion of the light beam  18  (including the ray  50 ) reflecting from the reference surface  42  and a second portion of the light beam  18  (including the ray  52 ) reflecting from the first test piece surface  56 . A second interference pattern  66  (see for example FIG. 3B) containing information concerning thickness (and index) variations of the test piece  12  is formed between the second portion of the light beam  18  (including the ray  52 ) reflecting from the first test piece surface  56  and a third portion of the light beam  18  (including the ray  54 ) reflecting from the second test piece surface  58 . Although thickness variations are often the primary source of variation, particularly for homogeneous materials, the interference pattern  66  actually contains information about both thickness variations and index variations of the test piece  12 . We generally refer herein to the thickness variations alone, but both thickness variations and index variations are represented by the interference pattern  66  between the opposite surfaces  56  and  58  of the test piece  12 .  
         [0027]    The two interference patterns  64  and  66  appear as a single combined interference pattern  68  (see for example FIG. 3C) on a diffused viewing screen  70 , which can be made of ground glass or plastic. The diffused viewing screen  70 , which can be rotated or dithered to further randomize the diffusion, fixes an image of the combined interference pattern  68  so than an ordinary zoom lens  72  can project the image onto a recording device  74 , such as a charge-coupled device (CCD) camera. Other image-forming optics and recording devices can be used to capture similar information from the combined interference patterns  68  appearing at other locations.  
         [0028]    The information concerning the flatness and thickness variation of the test piece  12  is obscured by the superposition of the two interference patterns  64  and  66 . Local fringe intensities of the two interference patterns  64  and  66  add together to produce the combined interference pattern  68  within which the information concerning flatness and thickness variation of the test piece  12  is mutually obscured.  
         [0029]    We have found that small changes in the grazing angle “α” shift the local fringe intensities of the two interference patterns through cyclical variations, each such cycle of intensity corresponding to the spacing between adjacent fringes. The local fringe intensities of both interference patterns  64  and  66  shift as a result of the changes of the grazing angle “α”; but even more significantly for purposes of this invention, the frequencies (i.e., modulation frequencies) at which the local intensities of the two interference patterns shift can be arranged to differ between the two interference patterns  64  and  66 .  
         [0030]    Although the local intensities of the two interference patterns vary in predictable ways, the modulation frequencies of the two interference patterns do not remain constant as a function of even incremental variations of the grazing angle “α”. This results in modulation frequencies that are chirped and difficult to identify from or attribute to the individual interference patterns  64  and  66 . However, by varying the non-normal grazing angle “α” through different size angular increments, the local fringe intensities can be varied at more stable modulation frequencies.  
         [0031]    For example, FIGS. 4A and 4B graph expected variations in normalized intensity at individual pixel sensors of the recording device  74  as a function of grazing angle variations. The two depicted modulations  76  and  78  correspond to the different rates of change of normalized intensity within the two interference patterns  64  and  66  associated with the same changes in grazing angle “α”. In FIG. 4A, even incremental changes of the tilt mechanism  26  produce frequency variations in the two modulations  76  and  78 . However, in FIG. 4B, uneven variations in the grazing angle “α” corresponding to even variations of optical path differences (OPDs) between interfering beams reproduce the modulations  76  and  78  in more stable forms (i.e., with constant frequencies).  
         [0032]    The different size angular increments of the grazing angle “α” correspond to approximately even increments of optical path difference between the nominally parallel surfaces compared by the interference patterns  64  and  66 . Exact corrections for stabilizing modulation frequency are generally limited to one of the interference patterns  64  and  66 , but the residual chirping of remaining modulation frequency is small. Good results have been obtained by preferentially stabilizing the higher  76  of the two modulation frequencies  76  and  78 .  
         [0033]    A schematic representation of optical path differences (OPDs) and their relationship to the grazing angle “α” is provided by FIG. 5. The optical path differences (OPDs) are shown between test rays “A” and “C” reflecting from the opposite surfaces  56  and  58  of the test surface  12  and interfering reference rays “B” and “D” reflected from the reference surface  42  of the prism  40 . The light beam  18  of the prior illustrations is depicted in FIG. 5 as a nominally planar wavefront  82  approaching the reference surface  48  at the grazing angle “α”.  
         [0034]    An optical path difference (OPD) between reflections from the first test piece surface  56  and the reference surface  42  is apparent as the sum of the two lengths of the rays “A” minus the length of the ray “B” (i.e.,  2 A-B). An optical path difference (OPD) between the second test piece surface  58  and the reference surface  42  is apparent as the sum of the two lengths of the rays “A” and the two lengths of the rays “C” minus the length of the ray “D” (i.e.,  2 A+ 2 C-D). Predicted optical path length differences (OPDs) among the surfaces  56  and  58  of the test piece  12  and the reference surface  42  of the prism can be readily calculated based on the grazing angle “α”, a spacing “S” between the test piece  12  and the reference surface  42 , an average thickness “Tp” of the test piece  12 , and the refractive indices of the test piece  12  and the prism  40 . The effect of changes in the grazing angle “α” on the optical path differences (OPDs) can be similarly predicted for determining the required changes in grazing angle “α” to produce even increments of the optical path differences (OPDs).  
         [0035]    Under the control of a computer processor  80 , Intensity data from the combined interference pattern  68  is collected at the even increments of optical path differences (OPDs) for one or more cycles of the lower  78  of the two pre-calculated modulation frequencies  76  and  78 . For example, 32 to 64 frames of data can be collected over the interval to record progressively changing images of the combined interference pattern  68  in pixel arrays. The pre-calculated modulation frequencies  76  and  78  are applied within a conventional Fourier transform to the collected data to distinguish intensity components of the two interference patterns  64  and  66 . The data for each pixel collected in the data frames undergoes a discreet Fourier transform. Intensity components of the pixels varying at the higher predetermined modulation frequency  76  are attributed to the interference pattern  64  between the first surface  56  of the test piece  12  and the reference surface  42  of the prism  40  (measuring flatness), and the intensity components of the same pixels varying at the lower predetermined modulation frequency  78  are attributed to the other interference pattern  66  between the first and second  56  and  58  surfaces of the test piece  123  (measuring thickness variation).  
         [0036]    Once the intensity data is distinguished between the interference patterns  64  and  66 , the relevant intensity data from the data frames can be used for purposes of phase shifting to more accurately measure intensity (i.e., phase) variations within each of the interference patterns  64  and  66 . The processor can be connected to one or more output devices (not shown) to report the measurement results.  
         [0037]    While it may be possible to derive the two different modulation frequencies  76  and  78  from the successive frames of captured intensity data, system noise can alter or obscure the identification of the modulation frequencies  76  and  78 . The factors that determine the modulation frequencies including the grazing angle “α”, the thickness “Tp” of the test piece  12 , the spacing “S” between the test piece  12  and the prism  40 , and the refractive indices of the traversed mediums are all known in advance. In fact, the variables such as the grazing angle “α” and the spacing “S” can be optimized in advance of the actual measurements to separate the predetermined modulation frequencies  76  and  78 . By calculating the expected modulation frequencies in advance, processing requirements for interpreting the measurements are reduced and the results are more reliable.