Abstract:
A non-contact method for measuring the composition-dependent phase change on reflection that occurs using profile measuring interferometry. A profile measuring interference microscope utilizing an extended, narrow bandwidth illumination source is used to generate a two-beam interference intensity pattern at a given field position on a detector array. A reference surface of known surface characteristics and an unknown test surface being profiled are axially translated relative to each other while the interference intensity pattern impinging on the detector array is sampled, digitized, stored and then utilized to produce a digitized two-beam interference intensity pattern, the shape of which is characteristic of the particular interferometer configuration. The axial position of maximum interference contrast and the phase of the digitized two-beam interference intensity pattern at this position of maximum interference contrast are determined by mathematical analysis of the intensity data. The phase at the maximum interference contrast position is divided by an analytically-derived constant to determine the phase change on reflection from the test surface, without regard to the compositional characteristics of the test surface material. The ability to measure and quantify the phase change on reflection for materials with complex indices of refraction notably improves the accuracy of heretofore-known profile measuring interferometric techniques when profiling test surfaces formed of two or more dissimilar materials with at least one having a complex index of refraction.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This is a continuation-in-part of U.S. patent application Ser. No. 893,324, filed Jun. 3, 1992, now abandoned. 
    
    
     FIELD OF THE INVENTION 
     The invention relates generally to precision optical metrology instrumentation, specifically to profile measuring interferometers and, more particularly, to increasing the accuracy of profile measuring interference microscopes used in measuring the topography of test surfaces whose index of refraction and hence phase change on reflection may vary significantly as a function of field position. 
     BACKGROUND OF THE INVENTION 
     When using profile measuring interference microscopy to measure the phase of a heterogeneous test surface comprised of two or more dissimilar materials, at least one of which has a complex index of refraction, measurement errors result because the amount of phase change on reflection varies with each individual material forming the test surface. Materials with complex indices of refraction produce a phase change on reflection that, in general, varies from material to material as well as from a dielectric&#39;s phase change on reflection which is either 0 or π. For example, conventional profile measuring interferometric techniques cannot distinguish, on the one hand, a phase difference between two points of different height on a test surface and, on the other, a phase difference between two points on a test surface of the same height but composed of dissimilar or composite materials with at least one having a complex index of refraction. 
     Use of the technique of profile measuring interferometry with an interference microscope to measure the profile of a test surface is known. Such use is described, for example, in Biegen, J. F. and Smythe, R. A., &#34;High-Resolution Profile Measuring Laser Interferometric Microscope for Engineering Surface Metrology&#34;, presented at the Fourth International Conference on Metrology and Properties of Engineering Surfaces at the National Bureau of Standards, Washington, D.C., Apr. 13-15, 1988. As applied to interference microscopes, the profile measuring interferometric technique provides effective and accurate test surface profile measurements so long as the test surface is homogeneous, i.e. comprised of a singular material having either a complex or a non-complex index of refraction. The phase change on reflection from a homogeneous test surface is constant as a function of field position and, therefore, does not affect the accuracy of the test surface profile measurement. When, however, the test surface to be profiled is heterogeneous and the phase change on reflection accordingly varies significantly as a function of field position, the phase map produced by profile measuring interferometry no longer represents an accurate geometrical profile of the test surface. In conventional profile measuring interferometry there is no way to extract the phase change on reflection component induced by reflection of the illumination beam off the test surface from the total phase that is measured. This has been a fundamental limitation in the utility and practice of conventional profile measuring interferometry. 
     Also known is the technique of using values of n and k--the real and imaginary parts of a material&#39;s complex index of refraction--previously measured using instrumentation other than profile measuring interferometers, to correct subsequent profile measuring interferometry measurements. This prior art technique, however, has serious limitations. The n and k measurements are usually made on representative materials, rather than on the actual test surface, and even minor differences in material composition between the representative material and the test surface material can introduce large errors in the phase correction. Moreover, when correcting phase measurements carried out with a moderate to high numerical aperture microscope interferometer objective, both the quantities n and k and a measure of the average illumination beam angle of incidence to the test surface are needed. The average illumination beam angle, which is a function of the numerical aperture and of the illumination beam intensity distribution at the entrance pupil of the microscope interferometer objective, can only be found through empirical means with this technique and, as such, introduces a source of potentially significant measurement error in the test surface profile. 
     Previous techniques for the direct measurement of phase change on reflection, as for example described in J. Bennett, &#34;Precise Method for Measuring the Absolute Phase Change on Reflection&#34;, 54 J. Opt. Soc. Am. 612-24 (1964), are difficult, time consuming, limited in use to transparent films and produce results independent of the actual test surface so that even if the measurement results are correct there is no certainty that the result actually represents the material on the test surface. 
     A method of directly measuring the phase change on reflection is discussed in &#34;Measurement of Transducers on Thin Film Sliders for Rigid Disk Drives&#34;, presented at the International Disk Conference in Tokyo, Japan, April, 1992. That article describes a time consuming, two-step process which consists of first measuring the test surface with a profile measuring interference microscope, overcoating the test surface with a homogeneous opaque material, and then remeasuring the test surface again with a profile measuring interference microscope. The two profiles thus obtained are subtracted one from the other, the difference between the profiles being the phase change on reflection. 
     Other profile measuring interference microscope techniques that determine the axial position of maximum fringe contrast for profiling the test surface emphasize the use of broad spectral bandwidth (i.e. white light) as the preferred illumination. See U.S. Pat. No. 4,340,306 to Balasubramanian; M. Davidson et al., &#34;An Application of Interference Microscopy to Integrated Circuit Inspection and Metrology&#34;, 775 SPIE 233-247 (1987); G. S. Kino and S. T. Chim, &#34;Mirau Correlation Microscope&#34;, 29 Applied Optics 3775-83 (1990); and B. S. Lee and T. C. Strand, &#34;Profilometry With a Coherence Scanning Microscope&#34;, 29 Applied Optics 3784- 88 (1990). A broad illumination spectral bandwidth reduces crosstalk between vertically adjacent features, permitting depth slicing as in confocal scanning microscopy. A broad bandwidth also allows for a theoretically unlimited test surface feature measurement range with high vertical resolution. And with a large illumination spectral bandwidth, the axial interference region is small and independent of the objective magnification or numerical aperture so that vertical resolution is constant across the magnification range and is not a function of the objective depth of focus, as it is in confocal scanning microscopy. One disadvantage of broad illumination spectral bandwidth is that the axial position of maximum interference contrast will shift in axial position as a function of the material properties of the test surface. The phase of the interference at this axial position cannot be related to the phase change on reflection without a priori information on the material properties of the test surface. This renders the technique as inaccurate as conventional profile measuring interferometry when measuring heterogeneous test surfaces comprised of two or more dissimilar materials with at least one having a complex index of refraction. 
     In contrast, the herein disclosed method and apparatus of the invention extend and improve the technique of conventional profile measuring interference microscopy by additionally measuring the phase change on reflection from the surface of metals, semi-metals, and dielectrics being profiled, and thereby correct a systematic measurement error that occurs when utilizing conventional profile measuring interference microscopy. 
     OBJECTS OF THE INVENTION 
     Accordingly, it is a principal object of the present invention to increase the accuracy of profile measuring interference microscopy for use with a test surface comprised of two or more disimilar or composite materials, at least one of which has a complex index of refraction. 
     It is a particular object of the invention to accurately profile a test surface comprised of disimilar or composite materials with complex indices of refraction. 
     It is another object of the invention to measure the phase change on reflection from a test surface comprised of disimilar or composite materials with complex indices of refraction. 
     A further object of the invention is to use previously measured phase change on reflection values to correct any subsequent profile measurements of test surfaces in any application of profile measuring interferometry. 
     SUMMARY OF THE INVENTION 
     Briefly described, the present invention provides an apparatus and technique for measuring the profile and phase change on reflection from test surfaces of materials whose index of refraction is complex. The apparatus comprises a profile measuring interference microscope having an extended, narrow bandwidth illumination source. The microscope interferometer objective is equal path, with a moderate to high numerical aperture. A solid-state camera array having multiple detector pixel sites is located in an image plane of the interference microscope. On the photo-receptive surface of the camera array, in the image plane, the test and reference surfaces are imaged together with the two-beam interference intensity pattern which represents the optical path difference, or phase difference, between the test and reference surface wavefronts. For an equal path two-beam interferometer having an extended, narrow bandwidth illumination source, the interference intensity varies as the geometrical path difference between the test surface and the reference surface is varied axially along the so-called z-axis, generally an imaging axis of the microscope. The resultant intensity function has the form of a cosine wave whose amplitude is modulated by a slowly varying function known as the modulus of the complex degree of coherence, or coherence modulus. The axial extent of the coherence modulus is a function of the diameter of the illumination source and its spectral bandwidth, of the numerical aperture of the microscope interferometer objective, and of the wavelength of the illumination beam. 
     In operation, during an initial macro focusing procedure, the test surface is moved or translated axially along the z-axis, inside focus, until the relative separation between the test and reference surfaces is greater than the axial extent of the coherence modulus, i.e. to a position at which the interference contrast is essentially zero. Then, by means of a piezoelectric transducer (PZT) crystal or other motion transducer, the test surface is linearly translated axially at a constant velocity, or stepped in constant increments, along the z-axis in the direction of increasing interference contrast so as to vary the geometrical path separation between the unknown test surface and the known reference surface until the interference intensity values along the entire axial extent of the coherence modulus have been scanned. For a moderate to high numerical aperture microscope interferometer objective, the coherence modulus axial extent is on the order of a few micrometers. The scanned intensity values received at the detector array are converted to electrical signals, sampled at a predetermined sampling frequency, digitized, and stored sequentially in a computer or processor memory. The stored intensity values obtained at any given pixel site of the detector array represent the two-beam interference intensity pattern of the particular interferometer configuration as a function of the geometrical path separation between the test and reference surfaces at a specific x and y coordinate of the test surface. 
     For an extended, narrow bandwidth illumination source, the axial position of the coherence modulus center--i.e. the position of maximum interference contrast -- is shifted from the position where the geometrical path difference between the test and reference surfaces is zero by an amount that is proportional to the product of the mean wavelength of the illumination source and the composition-dependent phase change on reflection. The composition-dependent phase change on reflection from the non-dielectric test surface also produces a phase shift of the two-beam interference intensity pattern relative to the axial position where the geometrical path difference between the test and reference surfaces is zero. The center position of the coherence modulus and the phase of the two-beam interference intensity pattern at the position of the center of the coherence modulus are determined from the digitized intensity data stored in computer memory for both a dielectric and a non-dielectric test surface. The phase change on reflection from the non-dielectric test surface can then be obtained by subtracting the phase of the two-beam interference intensity pattern determined at the position of the center of the coherence modulus for the non-dielectric test surface from the phase of the two-beam interference intensity pattern determined at the position of the center of the coherence modulus for the dielectric test surface and dividing this quantity by an analytically derived constant that is independent of material. 
     Other objects and features of the present invention will become apparent from the following detailed description considered in conjunction with the accompanying drawings. It is to be understood, however, that the drawings are designed solely for purposes of illustration and not as a definition of the limits of the invention, for which reference should be made to the appended claims. 
    
    
     DETAILED DESCRIPTION OF THE DRAWINGS 
     In the drawings, wherein like reference characters denote similar elements throughout the several views: 
     FIG. 1 is a diagrammatic depiction of the basic functional components of a profile measuring interference microscope apparatus constructed in accordance with the present invention and including an extended, narrow bandwidth illumination source; 
     FIG. 2 is an enlarged representation of portions of the interferometer objective of the apparatus of FIG. 1, showing the relation between the reference and test surfaces; 
     FIG. 3 is a graph showing a two-beam interference intensity pattern as a function of axial separation between a dielectric test surface and a dielectric reference surface using an extended, narrow bandwidth illumination source in accordance with the present invention; and 
     FIG. 4 is a graph showing a two-beam interference intensity pattern as a function of axial separation between a non-dielectric test surface and a reference surface using an extended, narrow bandwidth illumination source in accordance with the invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring first to FIG. 1, reference numeral 10 designates an embodiment of a profile measuring interference microscope apparatus constructed in accordance with the present invention. An incandescent, broad bandwidth illumination source 12 emits an illumination beam 13 of spectral bandwidth Δλ that is passed through a narrow bandwidth filter 14 to produce a narrow bandwidth illumination beam 40 of mean wavelength λ 0  such that Δλ/λ 0  &lt;&lt;1, and having the spatial properties of the source 12. Illumination beam 40 is reflected toward the microscope interferometer objective 22 by a beam splitter 20 to define a reflected illumination beam 43. The objective 22 is of the equal path type with a moderate to high numerical aperture (NA). The reflected illumination beam 43 from the beamsplitter 20 is refracted by the objective lens 21 to form the refracted illumination beam 45. 
     The refracted illumination beam 45 from the objective lens 21 impinges a beamsplitter surface 28 that is carried by the objective 22 in fixed positional relation to the lens 21. The beamsplitter surface 28 reflects a portion of the refracted beam and transmits a portion of the refracted beam to thereby split the beam 45 into a partially reflected illumination beam 47 and a partially transmitted illumination beam 49, respectively. The reflected beam 47 impinges on a reference surface 24 of known topography and material characteristics that is carried by the microscope objective 22 intermediately between, in the apparatus 10 herein disclosed, and in fixed positional relation to the lens 21 and beamsplitter surface 28; the resulting reflection of the reflected beam 47 from the reference surface 24 defines the reference surface imaging beam 53 which is directed back to the beamsplitter surface 28. The transmitted beam 49 from the beamsplitter surface 28 is similarly directed into reflective incidence with a test surface 32 of unknown topography and/or material characteristics and the resulting test surface imaging beam 51 reflected from a portion of the test surface impinges on the beamsplitter surface 28 coincident with the reference surface imaging beam 53 to thereby combine the test and reference surface imaging beams and form a reflected imaging beam 55. Thus, the test surface imaging beam 51 is formed by reflection of the image of the extended source 12 from that portion of the test surface 32 to be profiled, and the reference surface imaging beam 53 is formed by reflection of the extended image source from the reference surface 24. The reflected imaging beam 55, representing the interference between the two beams reflected from the test and reference surfaces, is directed from the beamsplitter surface 28 towards the objective lens 21 by which the beam 55 is refracted to form the refracted imaging beam 57. The refracted beam 57 passes through the beamsplitter 20, emerging as the transmitted imaging beam 59 which impinges on a detector array 30 to form the simultaneous image of the extended, narrow bandwidth source 12, of the reference surface 24 and test surface 32, and of the two-beam interference waveform resulting from the combination of the wavefronts reflected from the test and reference surfaces. The detector array 30 may, by way of example, be implemented by a CCD or like solid state camera or detector located in an image plane of the interference microscope. The array 30 thus receives, and converts into an electrical signal, a two-beam interference intensity value which represents the relationship between the interference intensity pattern and the geometrical path difference between the reference surface 24 and test surface 32. 
     A piezoelectric transducer 34, in response to an electrical signal from an electronic or otherwise implemented controller 41, drives the microscope interferometer objective 22--which carries in relatively fixed positional relation the objective lens 21, the reference surface 24 and the beamsplitter surface 28--through an axial translation linearly toward and/or away from the test surface 32, thereby varying the geometrical path difference between the test surface 32 and the reference surface 24 and, correspondingly, producing a two-beam interference intensity pattern formed at the imaging or interference plane 36 of the detector array 30. The axial translation of the microscope objective 22 is preferably at a constant linear rate. Of course, embodiments in which the test surface 32 is axially translated, in lieu of the microscope objective 22, are also within the intended scope of the invention. The analog electrical signal generated by the detector array 30 is sampled and digitized by the controller 40 and sent to a processor or computer 38 for data storage and subsequent analysis, the results of which are displayed on a monitor of the computer 38. The sampling rate should be sufficiently high as to enable suitable reconstruction of the interference intensity pattern; typically, at least two samples per fringe should be collected, although it will be readily recognized that the more samples collected per fringe, the more accurate the achievable reconstruction of the intensity pattern. The intensity pattern at the detector array image/interference plane may also be displayed directly on an image monitor 42. 
     The test surface 32 is preferably positioned relative to the objective 22, during initial focusing, so as to be located just outside of the axial region of interference before the piezoelectric transducer 34 receives an electrical signal from the controller 40 for linearly translating the objective 22. In response to that electrical signal, the piezoelectric transducer 34 expands, and thereby effects movement of the microscope interferometer objective 22 toward the test surface 32. This movement results in a corresponding change or variation in the geometrical path difference as between the test surface 32 and the reference surface 24, which in turn produces a varying interference intensity pattern such, for example, as those depicted in FIGS. 3 and 4. 
     Before describing the use and analysis of the interference intensity pattern data received, sampled and stored in accordance with the invention, it should be pointed out that it is intended, and generally contemplated, that the foregoing procedure for generating the interference intensity pattern be repeated for a plurality of surface locations or areas or portions of the test surface. This will normally be done by predeterminately sampling the detector array 30 at different positions or locations along the &#34;x,y&#34; coordinate axes--i.e. generally perpendicular to the direction of z-axis relative axial movement or translation between the test and reference surfaces--so as to sample another location at which the transmitted beam 49 from the beamsplitter surface 28 reflectingly impinges on the test surface. By repeatedly sampling the detector array 30 along the &#34;x,y&#34; coordinate axes in this manner, the entire test surface portion of interest can be topographically mapped and the material characteristics of that portion may be determined in accordance with the invention. 
     Referring now to FIG. 2, the total phase measured, Φ total  (x, y), by a profile measuring interference microscope such as that herein described and shown in FIG. 1 is the difference between the test surface phase Φ r  (x, y) and the reference surface phase Φ r  (x, y), plus the term 4π[z t  (x,y)-z r  (x,y)]/λ 0  which represents the geometrical phase difference produced as a result of the relative separation between the test surface 32 and the reference surface 24. λ 0  is the mean wavelength of the illumination beam, and is selected so as to accommodate the intended sensitivity of the measurements to be attained in use. The term z t  (x,y) is the test surface geometrical path length from the beamsplitter 28 to the test surface 32 and is proportional to the actual test surface profile H(x,y). The term z r  (x,y) is the reference surface geometrical path length from the beamsplitter 28 to the reference surface 24. In actual practice z r  (x,y), the reference surface geometrical path length, and Φ r  (x,y), the reference surface phase change on reflection, are both assumed to be constant and independent of the x, y coordinate location of the portion of the test surface being profiled, commonly referred to as the field position. Thus, Φ r  (x,y)=Φ r  and z r  (x,y)=z r  and, accordingly, the total phase measured at the detector array 30 may be represented as: 
     
         Φ.sub.total (x,y)=4π[z.sub.t (x,y)-z.sub.r ]/λ.sub.0 +Φ.sub.t (x,y)-Φ.sub.r                            Eq. 2 
    
     Neglecting the constant and linear offset terms introduced by the phase difference term 4 π[z t  (x,y)-z r  ]/λ 0  and the reference surface phase change on reflection term Φ r , the relationship of the total phase measured, Φ total  (x,y), to the actual test surface profile may be written as: 
     
         H(x,y)=λ.sub.0 [Φ.sub.total (x,y)-Φ.sub.t (x,y)]/4πEq. 2 
    
     In order for the test surface phase change on reflection term Φ t  (x,y) to have no effect on the accuracy of the actual test surface profile measurement H(x,y), the term Φ t  (x,y) must either (1) be previously known, so that it can be subtracted out, or (2) be a constant, independent of field position. Only when at least one of these conditions are met will Eq. 2 provide accurate results. 
     Prior art profile measuring interference microscopes determine only the total phase measured, Φ total  (x,y), and neglect the test surface phase change on reflection contribution Φ t  (x,y) because of the difficulty in obtaining accurate, readily achieved measurements of Φ t  (x,y). The consequence is that a significant source of error in determining H(x,y) is ignored. The method and apparatus of the present invention, on the other hand, can advantageously determine both the total phase measured, Φ total  (X,Y), and the test surface phase change on reflection, Φ t  (x,y), and accordingly represents a considerable improvement over prior art procedures and apparatus for profile measuring interference microscopy. 
     The following mathematical expressions have been simplified from those discussed hereinabove to exclude any explicit field (x , y) dependence. Although lacking such explicit field dependence, they are not intended to suggest that none exists. The inventive method herein described, however, is applicable at all points in the field (x, y) of the test surface. 
     The equation for two-beam interference with narrow bandwidth illumination for any singular point in the test surface field is 
     
         I(Δz)=I.sub.t +I.sub.r +2∛(I.sub.t I.sub.r)Re[Υ.sub.tr (Δz)]                   Eq. 3 
    
     where I t  is the test beam intensity, I r  is the reference beam intensity, and Δz=z t  -z r . The symbol Re[] refers to the real part of the expression contained within the brackets and Υ tr  (Δz) is the complex degree of coherence, whose modulus satisfies the relation 0≦|Υ tr  (Δz)|≦1. Where the illumination source is narrow bandwidth and extended, the function representing the complex degree of coherence Υ tr  (Δz) is given by ##EQU1## where I s  (ξη) is the intensity distribution at the entrance pupil of the microscope interferometer objective 22 with spatial coordinates ξ and η. R t  and R r  are the optical path lengths from a point at the entrance pupil along the corresponding test and reference beam paths to the image/interference plane 36. Changing to cylindrical coordinates and making the assumptions of an intensity distribution at the circular entrance pupil of the microscope interferometer objective 22 that is uniform and that there is no significant lateral or radial shear between the test and reference beams, the integral in Eq. 4 can be rewritten as ##EQU2## where the term u is equal to 4πNA 2  Δz/λ 0 . NA is the effective numerical aperture of the microscope interferometer objective 22 and takes into account any vignetting or central obscurations in the beam path. The term Φ t  (ρ) is equal to (1-κNA 2  ρ 2 )Φ t  and represents a parabolic approximation to the exact equation, which is well known in the art and is far more complex, relating the phase change on reflection to the illumination angle of incidence at the test surface 32 for a given material&#39;s complex index of refraction. (See Born &amp; Wolf, Principles of Optics, Sixth (Corrected) Edition, Equations (6) and (13) at page 629; pages 628-629 of that text are expressly incorporated by reference herein.) The constant κ in the approximation (1-κNA 2  κ 2 )Φ t  is obtained using a least squares minimization curve-fitting algorithm to fit Φ40  t  (ρ)=(1-κNA 2  ρ 2 )--the above equation normalized to Φ--to data generated using the exact equation that has itself been normalized to its zero angle of incidence phase change on reflection value. For any given material&#39;s complex index of refraction used in that exact equation, the shape of the resulting curve is substantially independent of material. The value of κ found from curve fitting the normalized approximation to the thereby generated data is unaffected by any potential value of Φ t  in the approximation (1-κNA 2  ρ 2 )Φ t , but is affected slightly by the value chosen for the numerical aperture of the microscope interferometer objective 22. 
     The integral in Eq. 5 can be evaluated to define the real part of the complex degree of coherence function as ##EQU3## Substituting Eq. 6 into Eq. 3 yields the specific equation for two-beam interference with an illumination source that is uniform, extended, and narrow bandwidth and for a test surface that has a wavelength and illumination angle-dependent phase change on reflection: ##EQU4## 
     FIG. 3 is a plot, prepared using Eq. 7, of the two-beam axial interference intensity 66 as a function of Δz when the test surface 32 and reference surface 24 are formed of a dielectric material--i.e. when Φ t  is equal to 0 or 7π. Both the interference intensity pattern 66 and the coherence modulus function 68 are centered at the axial position of zero geometrical path difference (i.e. z=0) between the test surface 32 and the reference surface 24. 
     FIG. 4 shows the same plot where the test surface 32 is formed of a non-dielectric material and, therefore, exhibits a phase change on reflection of Φ t . It will be seen that the coherence modulus function 72 is shifted relative to the axial position of zero geometrical path difference by -κΦ t  λ O  2πand the interference intensity pattern 70 is also shifted in phase relative to the axial position of zero geometrical path difference by {1-(κNA 2  /2)}Φ t . This results from the use of an extended, narrow bandwidth illumination source and enables, in accordance with the present invention, ready measurement of the phase change that is due solely to reflection from the test surface itself. 
     As can be seen from Eq. 7, the axial extent of the coherence modulus 72 depicted in FIG. 4 is a function of the effective numerical aperture NA of the microscope interferometer objective 22. Thus, the larger the numerical aperture NA of the interferometer objective 22, the smaller the axial extent of the sinc coherence modulus 72. At Δz=-Φ t  λ O  /2π--i.e. the axial position of the center of the coherence modulus--Eq. 7 reduces to 
     
         I=I.sub.t +I.sub.r +2∛I.sub.t I.sub.r cos [(1-2κ)Φ.sub.t ]                                                         Eq. 8 
    
     yielding an equation from which the test surface phase change on reflection, Φ t , can be obtained uniquely at any point in the test surface field (x, y) since κ can be analytically derived and known a priori. 
     The two-beam interference intensity pattern detected by the detector array 30 and digitized and stored in the computer 38 can be analyzed by any number of methods to provide Φ t , the test surface phase change on reflection, at any given point in the test surface field (x, y) . In a preferred embodiment of the invention a least squares minimization curve-fitting algorithm is employed to fit the following equation to the stored two-beam interference intensity data 
     
         I&#39;.sub.i =k.sub.0 +k.sub.1 cos [k.sub.2 i+k.sub.3 ] sinc [k.sub.4 i+k.sub.5 ]                                                         Eq. 9 
    
     and to thereby evaluate the parameters k 2 , k 3 , k 4 , and k 5 . Eq. 9, in which i denotes the sequential position of a given data point within the two-beam interference intensity data, is identical to Eq. 7 except that the constants in Eq. 7 have been combined where possible into one constant. The phase at the center of the coherence modulus is then -k 2  (k 5  /k 4 )+k 3 . Since the reference surface 25 is nearly always coated with a non-dielectric, two interference intensity measurements are needed to find the composition-dependent phase change on reflection from the test surface 32. One measurement is made on a dielectric test surface and the other on the test surface of interest. The phase at the center of each of the two coherence moduli is first found for both measurements by curve-fitting Eq. 9 to the two respective interference intensity data sets. The two phases are then subtracted one from the other, and the result is divided by (1-2κ) to obtain the composition-dependent phase change on reflection Φ t   of the test surface 32. The value Φ t  thereby obtained is then subtracted from the total measured phase Φ total , yielding a test surface profile measurement of significantly enhanced accuracy than heretofore attainable. 
     In an alternate embodiment of the inventive method, a coherence modulus is calculated using the stored two-beam interference intensity data and the following equation: ##EQU5## where i is, as before, the sequential position of a given data point within the two-beam interference intensity data set and n is one-fourth the number of data points taken per interference fringe. The data outside the minima of the central lobe of the coherence modulus thereby calculated are discarded, and a least squares minimization curve-fitting algorithm is used to fit the following parabolic equation to the the stored two-beam interference intensity data: 
     
         M&#39;.sub.i =C.sub.o +C.sub.1 i+C.sub.2 i.sup.2               Eq. 11 
    
     to find the parameters c 1  and c 2 . The peak value of the calculated coherence modulus M i  is found where M&#39; i  is equal to -c 1  (2c 2 ). This axial position is taken for the center of the calculated coherence modulus. The axial position of the center of the peak fringe of the two-beam interference intensity data nearest the center of the calculated coherence modulus is next determined by first locating the peak intensity value nearest the calculated coherence modulus. A second parabolic equation is then curve-fitted to a selected number of intensity data points on either side of and including the peak intensity value to find a second set of parameters c&#39; 1  and c&#39; 2 . The value of -c&#39; 1  /(2c&#39; 2 ) is the axial position at which the peak fringe nearest the center of the calculated coherence modulus is a maximum. The difference between the axial position where the calculated coherence modulus is a maximum and the axial position where the peak fringe nearest the center of the coherence modulus is a maximum is then calculated. This procedure is repeated twice, once for a dielectric test surface and once for the test surface of interest. The two results are subtracted, one from the other, and this difference is divided by (1-2κ) to obtain the composition-dependent phase change on reflection Φ t  of the test surface 32. The value Φ t  thereby obtained is then subtracted from the total measured phase Φ total , yielding a test surface profile measurement of significantly enhanced accuracy than heretofore attainable. 
     The present invention may be broadly described as a non-contact method of determining a phase change on reflection from a test surface of unknown topography and composition, wherein the method includes the steps of producing a first illumination beam and a second illumination beam from an extended, narrow bandwidth source; establishing on a detector an interference beam having an intensity which results from the interference between a first wavefront and a second wavefront, the first wavefront being formed by reflection of the first illumination beam from at least one point on a reference surface of known topography and composition and the second wavefront being formed by reflection of the second illumination beam from a corresponding point on a test surface of unknown topography and composition; moving one of the reference surface and the test surface relative to the other said surface over a predetermined linear range of motion so as to translate one of the first and second wavefronts relative to the other said wavefront and thereby vary the interference beam intensity and create an interference intensity pattern on the detector; identifying a point of maximum interference contrast of the interference intensity pattern on the detector at a position along the predetermined linear range of motion; and determining a phase shift introduced by said reflection of the second illumination beam from the test surface by analyzing the interference intensity pattern at the point of maximum interference contrast to thereby determine the composition-dependent phase change on reflection from the test surface. 
     While there have been shown and described and pointed out fundamental novel features of the invention as applied to preferred embodiments thereof, it will be understood that various omissions and substitutions and changes in the form and details of the disclosed methods and apparatus may be made by those skilled in the art without departing from the spirit of the invention. It is the intention, therefore, to be limited only as indicated by the scope of the claims appended hereto.