Patent Publication Number: US-10761021-B2

Title: Apparatus and method for measurement of multilayer structures

Description:
CROSS-REFERENCE TO RELATED PATENT APPLICATIONS 
     This application is a continuation in part of co-pending U.S. patent application Ser. No. 15/585,495, filed on May 3, 2017, the disclosure of which is incorporated herein by reference. 
    
    
     BACKGROUND 
     Technical Field 
     The present invention relates to the non-destructive characterization of multilayer structures including determination of the number of layers, identification of the materials comprising each layer and the thickness of each layer in the multilayer structure. 
     Description of Related Art 
     Non-destructive product verification testing is important in many industries and is extremely important for multilayer structures used for a variety of commercial and military applications. Being able to identify the number of layers as well as the material that each layer is composed of in multilayer structures along with the thickness of each of the layers is becoming more and more important for product verification testing and is also useful in reverse engineering. It is extremely important to verify that the multilayer structures meet specifications in fields including automotive, aerospace and building glazing, transparent armor, compound lenses, semiconductors, displays, and bulletproof glass. 
     There are various methods of identifying single layer optical materials using the wavelength dependence of spectral properties including absorbance, reflectance, emission, scattering, fluorescence, Raman scattering, IR spectroscopy and index of refraction. As an example, the use of Raman spectroscopy is described in the master thesis entitled, “Automated Spectral Identification of Materials Using Spectral Identity Mapping” by Robert Cannon, May 2013. U.S. Pat. No. 6,122,042 entitled “Devices and Methods for Optically Identifying Characteristics of Material Objects” by Irwin Wunderman et al. describes a photometric analysis technique that collects scattered, reflected and emitted light. U.S. Patent Application Publication No. 2001/0043327 entitled “Spectral Identification System” by Bryan Barney et al. discloses the use of spectral reflectance over a broad spectral range from the ultra-violet (UV) to the near infra-red (NIR) to identify materials. U.S. Patent Application Publication No. 2016/0061720 entitled “Method for Characterizing a Product by Means of Topological Spectral Analysis” by Didier Lambert et al. describes a method of creating a database of NIR data and using it to identify materials from their NIR spectra. 
     Optical dispersion in optical materials is the phenomenon in which the phase velocity of a wave depends on the wavelength of light λ traveling through the optical material. This results in a wavelength dependence of phase index of refraction which is different in different materials. An example of using optical dispersion to aid in material identification is provided by U.S. Patent Application Publication No. 2015/0032417 entitled “Systems and Methods for Identifying Optical Materials” by Jurgen Zobel (“Zobel &#39;417” subsequently herein). Zobel &#39;417 describes a method of material identification based on determining the index matching wavelength points for different index of refraction liquid standards. Zobel &#39;417 uses the property of optical dispersion to identify the material in an optical material. In the measurement approach in Zobel &#39;417 the index of refraction at is measured at three wavelengths by placing small grains of the material in different index matching fluids and determining which index matching fluid is the best fit at each of the three selected wavelengths. The temperature of the index of refraction liquid standards is also well characterized and the temperature that best matches the index of refraction of the material under test can also be found. However, the measurement procedure used in Zobel &#39;417 is destructive since it requires the sample to be shattered into small grains and immersing it in the index matching liquids. It also can only measure one material at a time and is tedious. 
     Low-coherence interferometry (LCI) has applications in many fields from medical imaging to glass manufacturing. Low-coherence interferometry is based on using a light source with a relatively short coherence length on the order of 1.0-40 micrometers (μm). The light is split between two arms of an interferometer and then recombined and directed onto a detector. Interference will occur when the path lengths of the two arms of the interferometer are equal to within a few coherence lengths of the light source. 
     There are numerous known configurations of such interferometers, such as the Michelson, Mach-Zehnder, and Fizeau interferometers, and others described in the text, Principles of Optics: Electromagnetic Theory Of Propagation, Interference and Diffraction of Light, M. Born and E. Wolf, Cambridge University Press, Cambridge, N.Y., 1999, 7th ed. Other examples of such interferometer and described in U.S. Pat. No. 6,724,487 of Marcus et al., “Apparatus and method for measuring digital imager, package and wafer bow and deviation from flatness,” and in U.S. Pat. No. 5,596,409 of Marcus et al., “Associated Dual Interferometric Measurement Method for Determining a Physical property of an Object”, the disclosure of which are incorporated herein by reference (“Marcus &#39;409” subsequently herein). The interferometer disclosed therein by Marcus &#39;409 includes a low-coherence interferometer and a coherent light interferometer which are associated with each other by sharing a common variable optical path delay element. A narrow beam of low-coherence light is directed onto the surface of the test object. It is common to focus the beam inside or in proximity to the test object. The reflected light from all of the object interfaces, which the beam traverses, is then collected and analyzed by the interferometer. The interferometer is used to extract the optical distances between all of the optical interfaces in the test object. The physical distances are obtained by dividing the optical distances by the group index of refraction (GRI) of the material which makes up the space between the interfaces. In a typical application, the light beam is directed along the optical axis of a lens. The axial thickness of the lens is then obtained by dividing the measured optical distance by the known group index of refraction of the glass or plastic material of the lens. 
     None of the above methods can both non-destructively determine the number of layers in a multilayer structure and characterize the material used in each of the layers of the multilayer structure in the correct physical order of the materials in the structure. The disclosure of these patents and published patent applications notwithstanding, there remains an unmet need to be able to identify the material that each of the layers in a multilayer structure is composed of non-destructively. There also remains an unmet need to determine the thickness of each of the layers in the multilayer structure while identifying the material composition of each of the layers in the multilayer structure. Such a measurement method and system would be an important advance to the fields of non-destructive product verification testing and reverse engineering. 
     SUMMARY 
     In accordance with the present disclosure, the unmet need for a measurement system and method that enables non-destructive material characterization of each of the layers in a multilayer structure is addressed by providing an interferometer apparatus with a low-coherence tunable light source which can be tuned to a set of k distinct center wavelengths to determine the group index of refraction of each of the layers in the multilayer structure as a function of wavelength. From the wavelength dependence of the group index of refraction data, the material that each of the layers in the multilayer structure is composed of can be identified by comparing the measured data to that of a reference database containing the group index of refraction dispersion curves of known materials. For materials that are not in the reference database, the characterization includes determining the group index of refraction dispersion curve for the material and adding it to the reference database of known material group index of refraction dispersion curves. 
     In a first embodiment of the invention a method of characterizing each layer in a multilayer structure comprising m layers where m is an integer greater than 1 is provided. The method comprises the steps of providing an interferometer apparatus with a low-coherence tunable light source which can be tuned to a set of k distinct center wavelengths where k is an integer greater than 2, aligning a portion of the multilayer structure with respect to a measurement region of the interferometer apparatus, using the interferometer apparatus to observe layers in the multilayer structure and measuring the optical thickness of each of the observed layers in the multilayer structure with the low-coherence tunable light source being tuned to each of the k distinct center wavelengths. The method also includes the step of determining the number of layers m in the multilayer structure by setting m equal to the maximum number of observed layers measured using the low-coherence interferometer with the low-coherence tunable light source tuned to each of the k distinct center wavelengths. The method of characterizing each of the m layers in the multilayer structure may also comprise the steps of comparing the optical thickness measured with the low-coherence tunable light source tuned to each of the k distinct center wavelengths to a reference database of known material group index of refraction dispersion curves measured at the same set of k distinct center wavelengths and determining which layers have a best fit material in the reference database and identifying the material composition of each of the m layers which have a best fit material in the reference database. The multilayer structure may also be comprised of a measurement cell consisting of a top optical flat and a bottom optical flat separated by a spacer containing a receiving surface located above the top optically flat surface of the bottom optical flat and below the bottom optically flat surface of the top flat for disposing a sample containing a layer of a material to be added to the reference database of known materials. 
     A second embodiment of the invention is an apparatus for characterizing each layer in a multilayer structure comprising m layers where m is an integer greater than 1. The apparatus comprises an interferometer having a low-coherence light source tunable to a set of k distinct center wavelengths where k is an integer greater than 2. The apparatus is adapted to observe layers in the multilayer structure, and to measure the optical thickness of each of the observed layers in the multilayer structure while the low-coherence tunable light source is tuned to each of the k distinct center wavelengths. The apparatus also comprises a computer operable to execute an algorithm to determine the number of layers m in the multilayer structure, to determine which of the m layers have a best fit material in a reference database of known material group index of refraction dispersion curves which include data measured at the same set of k distinct center wavelengths, and to identify the material composition and thickness of the layers which have a best fit material in the reference database. 
     These and other aspects, objects, features and advantages of the present invention will be more clearly understood and appreciated from a review of the following detailed description of the preferred embodiments and appended claims, and by reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure will be provided with reference to the following drawings, in which like numerals refer to like elements, and in which: 
         FIG. 1  shows a schematic of a first embodiment of an interferometer apparatus used to measure the optical thickness of each of the layers in a multilayer structure as a function of wavelength. 
         FIG. 1A  shows a schematic of a second embodiment of an interferometer apparatus used to measure the optical thickness of each of the layers in a multilayer structure as a function of wavelength. 
         FIG. 1B  shows a schematic of a third embodiment of an interferometer apparatus used to measure the optical thickness of each of the layers in a multilayer structure as a function of wavelength. 
         FIG. 1C  shows a schematic of a fourth embodiment of an interferometer apparatus used to measure the optical thickness of each of the layers in a multilayer structure as a function of wavelength. 
         FIG. 1D  shows a schematic of a fifth embodiment of an interferometer apparatus used to measure the optical thickness of each of the layers in a multilayer structure as a function of wavelength. 
         FIG. 1E  shows a schematic of a sixth embodiment of an interferometer apparatus used to measure the optical thickness of each of the layers in a multilayer structure as a function of wavelength 
         FIG. 1F  shows a schematic of a seventh embodiment of an interferometer apparatus used to measure the optical thickness of each of the layers in a multilayer structure as a function of wavelength. 
         FIG. 2  shows a laser interferometer signal as a function of optical path length difference between the sample and reference arms in the interferometer. 
         FIG. 3  shows an example low-coherence interferometer scan as a function of optical scan distance of the reference arm of the interferometer. 
         FIG. 4  shows phase index of refraction dispersion curves for some different materials. 
         FIG. 5  shows group index of refraction dispersion curves for some different materials. 
         FIG. 6A  shows normalized group index of refraction dispersion curves for some materials. 
         FIG. 6B  shows an expanded region of the normalized group index of refraction dispersion curves for two of the materials shown in  FIG. 6A . 
         FIG. 7A  shows an embodiment of an index of refraction measurement cell containing a single layer of a material to be added to the reference database of known materials. 
         FIG. 7B  shows the index of refraction measurement cell shown in  FIG. 7A  without the layer of material being present. 
         FIG. 7C  shows a three layer sample which contains a material to be added to the reference database of known materials sandwiched between a first known material and a second known material. 
         FIG. 8  shows a plot of the expected optical thickness of a 25 mm air gap as a function of wavelength. 
         FIG. 9  shows group index of refraction dispersion curves for two materials that intersect at 536.5 nm. 
         FIG. 10  shows a flow chart detailing the steps of a method used to identify the material composition of each layer in a multilayer structure and to determine each layer&#39;s physical thickness. 
         FIG. 11  shows a flow chart detailing the steps of a method to determine the group index of refraction dispersion curve for a known material. 
         FIG. 12  shows a flow chart detailing the steps of a second method to identify the composition of each layer in a multilayer structure and to determine each layer&#39;s physical thickness. 
         FIG. 12A  shows a flowchart containing further details of Step  140  of  FIG. 12 . 
         FIG. 13  shows a flowchart detailing the steps of determining the expected order of trial thickness standard deviation from minimum to maximum of an ideal sample for all the known materials in the reference database. 
     
    
    
     DETAILED DESCRIPTION 
     The present description is directed in particular to elements forming part of, or cooperating more directly with, apparatus in accordance to the invention. For a general understanding of the present invention, reference is made to the drawings. It is to be understood that elements not specifically shown or described may take various forms well known to those skilled in the art. In the following description and drawings, identical reference numerals have been used, where possible, to designate identical elements. Figures shown and described herein are provided in order to illustrate key principles of operation of the present invention and are not drawn with intent to show actual size or scale. Some exaggeration, i.e., variation in size or scale may be necessary in order to emphasize relative spatial relationships or principles of operation. One of ordinary skill in the art will be able to readily determine the specific size and interconnections of the elements of the example embodiments of the present invention. The term “providing”, such as for “providing an interferometer apparatus” and the like, when recited in the claims, is not intended to require any particular delivery or receipt of the provided item. Rather, the term “providing” is merely used to recite items that will be referred to in subsequent elements of the claim(s), for purposes of clarity and ease of readability. 
     In the following disclosure, the present invention is described in the context of an apparatus and method of characterizing each layer in a multilayer structure. The characterization includes determining the optical thickness of each of the layers, the number of layers in the multilayer structure, to identify the material comprising each layer of the multilayer structure and to determine the physical thickness of each of its layers. In the context of the present disclosure, a suitable multilayer structure is considered to be an object comprised of m layers where m is a positive integer greater than 1, each of the m layers being at least partially transparent to light over at least part of the optical spectrum and has an optical interface with each of its adjacent layers. The optical spectrum is defined as the portion of the electromagnetic spectrum ranging from the extreme ultraviolet through the far-infrared. When the term “multilayer structure” is used in the context of the present disclosure, it is to be understood that the multilayer structure is partially optically transmissive over at least part of the optical spectrum over which the measurement is performed. The multilayer structure is also required to have “nearly parallel” surfaces at the location of measurement. In the context of the present disclosure the term “nearly parallel” is defined to be parallel within ±3°. Each layer of the multilayer structure should also be 10 μm or greater in physical thickness. Example multilayer structures include automotive, aerospace and building glazing, transparent armor such as that found on tanks and armored vehicles, compound lenses, multilayer semiconductor wafers, displays and bulletproof glass. The multilayer structure may include air layers and liquid layers as well as solid material layers. A measurement cell including a pair of optical flats with or without samples mounted between them is a suitable multilayer structure. 
     Also throughout the present disclosure we use the term mirror which we define as a reflective surface or a partially reflective surface in which a negligible amount of light is transmitted. Furthermore, the terms refractive index and index of refraction can be used interchangeably. In the present disclosure, the terms thickness and physical thickness may be also used interchangeably. 
     Additionally, this description may identify certain components with the adjectives “top,” “upper,” “bottom,” “lower,” “left,” “right,” “horizontal,” “vertical,” “inner,” “outer,” “transmitted,” “reflected,” etc. These adjectives are provided in the context of use of the apparatus as a measurement device, and in the context of the orientation of the drawings, which is arbitrary. The description is not to be construed as limiting the apparatus to use in a particular spatial orientation. The instant apparatus may be used in orientations other than those shown and described herein. As an example in the disclosure we describe light beams incident on beam splitters which split the beam into transmitted and reflected light beams which then interact with different sets of components. It is to be understood that the orientation of the drawing can be altered so that the transmitted beam interacts with the components shown interacting with the reflected light beam and vice versa. When the beam splitter is used in an interferometer we call the two arms of the interferometer sample and reference arms. 
     The following description describes the details of our invention directed at identifying the material composition and physical thickness of each of the layers in a multilayer structure. In the practice of the invention an interferometer apparatus is used to first measure the optical thickness of each of the layers of a multilayer structure in order from top to bottom as a function of wavelength λ of a tunable light source. Throughout the discussion of the invention all materials and multilayer structures are measured at the same set of k distinct center wavelengths of the tunable light source defined as λ j  where j is an integer and j=1 to k inclusively with λ 1  being the shortest center wavelength of the tunable light source and λ k  being the longest wavelength of the tunable light source. Each successive wavelength measured is at a longer wavelength than the previous one so that λ 1 &lt;λ 2 &lt;λ 3  . . . &lt;λ k−1 &lt;λ k . 
     In our context, the term “optical thickness of a layer” is defined as the product of the group index of refraction times the physical thickness [n gi (λ j )t i ] where n gi (λ j ) is the group index of refraction of the ith layer in the multilayer structure measured at wavelength λ j  and t i  is the physical thickness of the ith layer. For a multilayer structure comprised of m layers, the individual layers will be sequentially labeled with integers numbered from 1-m from top to bottom of the multilayer structure. The optical thickness measured for each of the layers will vary with wavelength of the filtered light source due to changes in the group index of refraction as a function of wavelength. The variation in optical thickness as a function of wavelength is different for different materials. In a first approach, we determine the normalized group index of refraction curve for each layer in the multilayer structure and then compare the data to normalized group index of refraction dispersion curves found in a reference database of known materials to identify the statistically best fit material for each of the layers in the multilayer structure. In a second approach we compare the measured optical thickness as a function of measurement center wavelength for each layer in the multilayer structure with a reference database of known material group index of refraction dispersion curves at the same set of center wavelengths and determine if there is a best fit material for that layer in the reference database. It is to be noted, that in order to be able to identify the material composition of a given layer in the multilayer structure, the material comprising that layer must be in the reference database of known materials. In some cases the material comprising a given layer may not yet be in the reference database of known materials. In this case there will usually not be a statistically best fit material for this layer, and the material for that layer will not be identified. We also describe how new materials can be added to the reference database of known material group index of refraction dispersion curves. When new materials are added to the reference data base, previously measured multilayer structures containing unidentified layers can be reanalyzed in order to determine if the material composition of any of the unidentified layers has been recently added to the database. 
     In the following disclosure, we first describe the apparatus and then describe how the optical dispersive properties measured can be used to identify the material that each of the layers in the multilayer structure is composed of and how to determine the physical thickness of each of the layers. We then describe how new materials can be added to the reference database of known materials. 
     Turning now to  FIG. 1 , a schematic of a first embodiment of an interferometer apparatus  100  used to measure the optical thickness of each of the layers in a multilayer structure  28  as a function of wavelength is shown. The interferometer apparatus  100  is a dual interferometer comprising a free-space low-coherence interferometer  110  (shown in the lower dashed rectangle) and a laser interferometer  120  (shown in the upper dashed rectangle). The two interferometers share a common variable optical path delay element  90  as described in Marcus &#39;409. The laser interferometer  120  continuously measures the displacement of the reference path and is used to provide an accurate distance scale for the low-coherence interferometer as described in Marcus &#39;409. 
     As shown in  FIG. 1 , the light source of the free space low-coherence interferometer  110  is a broadband low-coherence light source  10 , and preferably a supercontinuum light source such as an NKT Photonics EXW-12 Supercontinuum light source (SCLS) which emits light over the wavelength range of 400-2400 nanometers (nm). The light coming out of the broadband light source  10  is coupled into a continuously variable wavelength tunable filter  12 . The broadband low-coherence light source  10  and the continuously variable wavelength tunable filter  12  together form a tunable light source  13 . For many materials, the preferred continuously variable wavelength tunable filter is one that can be tuned anywhere between 400 and 850 nm with a bandwidth being variable between 5 and 50 nm such as an NKT Photonics SuperK VARIA tunable wavelength filter. For other materials which do not transmit light in the visible range, including semiconductors such as silicon and germanium, tunable filters in the range of 1100 nm-2400 nm or longer are preferred. The preferred bandwidth range of the tunable filter is between 5-20 nm in order to deliver a near Gaussian wavelength distribution of light into the low-coherence interferometer. Light exiting the tunable filter  12  is coupled into a single mode fiber  14  which is preferably a single mode photonic crystal fiber (PCF) since it will function properly over the entire wavelength range of the tunable filter  12 . The light transmitted through the single mode fiber  14  is coupled into a fiber collimator  16  which forms a collimated beam  18  shown as a pair of parallel solid lines in  FIG. 1 . The collimated light beam  18  is passed through a polarizing beam splitter (PBS)  20  which linearly polarizes the transmitted collimated light beam. The transmitted collimated linearly polarized light beam then passes through a quarter wave plate (QWP)  22  and is input into a beam splitter (BS)  24  which forms a Michelson interferometer. The beam splitter  24 , preferably a 50/50 beam splitter, splits the input collimated beam  18  into a sample arm collimated beam  18 S and a reference arm collimated beam  18 R that travel through the sample and reference arms of the Michelson interferometer respectively. 
     Both the sample arm collimated beam  18 S and the reference arm collimated beam  18 R are comprised of incident light and reflected light portions as described below. The incident light portion of sample arm collimated beam  18 S originates from the beam splitter  24  and passes through sample arm lens  26  and is focused onto the multilayer structure  28  under test as shown by the focusing low-coherence beam  18 F. The focus region of the lens  26  defines the measurement region of the interferometer apparatus. Before measurement, the multilayer structure  28  is mounted in the measurement region of the low-coherence interferometer  110  and aligned so that its top and bottom surfaces are close to normal (within ±3°) to the center axis of the incident low-coherence beam  18 F. The incident light portion of reference arm collimated beam  18 R also originates from the beam splitter  24  and passes through reference arm lens  30  and is focused on the reference mirror  32 . The sample and reference arm lenses  26  and  30  are preferably achromatic doublets or triplets in order to have the same focal length over the entire wavelength range of measurement. 
     The reference arm lens  30  and reference mirror  32  are co-mounted on a variable optical path delay element  90  as is laser reference mirror  32 L. The variable optical path element is preferably a precision linear actuator, voice coil or translation stage which is moved during operation of the interferometer apparatus  100 . Part of the light that is focused on the multilayer structure  28  through sample arm lens  26  reflects off each optical interface of the multilayer structure  28  and is recollimated by the sample arm lens  26  makes up the reflected light portion of sample arm collimated beam  18 S. Similarly, the part of the incident light that is focused on the reference mirror  32  through the reference arm lens  30  and reflects off reference mirror  32  and is recollimated by the reference arm lens  30  makes up the reflected light portion of reference arm collimated beam  18 R. 
     The multilayer structure shown in  FIG. 1  is comprised of 5 layers  28   a - 28   e  and has 6 optical interfaces (air/ 28   a ,  28   a / 28   b ,  28   b / 28   c ,  28   c / 28   d ,  28   d / 28   e  and  28   e /air). Light reflecting back from the reference mirror  32  and each of the optical interfaces in the multilayer structure  28  are re-collimated at their respective reference arm lens  30  and sample arm lens  26  to form the reflected light portions of the reference and sample arm collimated beams  18  R and  18 S respectively. The reflected light portions of the reference and sample arm collimated beams  18 R and  18 S are then recombined at the 50/50 beam splitter  24  to form a collimated low-coherence interference beam. After being recombined the collimated low-coherence interference beam is split again at the same beam splitter  24  into a transmitted or first part of the low-coherence interference beam  18   a  and a reflected or second part of the low-coherence interference beam  18   b . The transmitted low-coherence interference beam  18   a  is incident on the first detector  38   a  of a balanced detector  38  after reflecting off a pair of 45° mirrors  34  and  36 . The reflected low-coherence interference beam  18   b  travels back through the quarter wave plate  22  and is incident on the polarizing beam splitter  20  where it is reflected and is made to be incident on a second detector  38   b  of the balanced detector  38 . The balanced detector  38  signal is filtered, log amplified and the envelope of the low-coherence interferometer signal is measured as a function of distance traveled by the variable optical path delay element  90  during measurement. Use of balanced detection results in an improved signal to noise ratio due to removal of common mode noise and enables the ability to use higher powers without saturating the detector. 
       FIG. 1A  shows a schematic of a second embodiment of an interferometer apparatus  100 A used to measure the optical thickness of each of the layers in a multilayer structure  28  as a function of wavelength. Most of the components of interferometer apparatus  100  and  100 A are the same, and all components of the laser interferometer  120  are the same in both embodiments. The only differences in the components between low-coherence interferometer  110 A and low-coherence interferometer  110  occur in the sample arm of the low-coherence interferometer  110 A. The focusing lens  26  is replaced with a fiber collimator  52  which is used to couple the incident light portion of sample arm collimated beam  18 S into a sample arm optical fiber  54 S which is then input into an optical probe  56  which focuses light onto the multilayer structure  28 . Part of the light that is focused on the multilayer structure  28  through optical probe  56  reflects off each optical interface of the multilayer structure  28  back through optical probe  56  and sent back through optical fiber  54 S and recollimated by fiber collimator  52  to form the reflected light portion of sample arm collimated beam  18 S. As in low-coherence interferometer  110 , the reflected light portions of the reference and sample arm collimated beams  18 R and  18 S of low-coherence interferometer  110 A are recombined at the 50/50 beam splitter  24  to form a collimated low-coherence interference beam. The rest of the interferometer apparatus  100  and  100 A are the same with identical functions. As with the input optical fiber  14 , optical fiber  54 S is preferably a single mode photonic crystal fiber (PCF) since it will function properly over the entire wavelength range of the tunable filter  12 . The optical probe  56  can be readily configured to be portable or hand-held and readily aligned so that it is normal to the top surface of the multilayer structure  28 . Hand-held probes are usually designed with a standoff distance that matches the focal length of the probe, so that when in contact with the top surface of the multilayer structure  28  the structure is automatically placed in the measurement region of the interferometer apparatus. Using an optical probe in the sample arm of the interferometer enables the interferometer apparatus to be portable so that it can be used to measure multilayer structures in their native environments such as building windows, automotive windows and aerospace windows. The optical probe can also be mounted to translation stages so that it can be moved over the surface of the multilayer structure  28 . 
       FIG. 1B  shows a third embodiment of a dual interferometer apparatus  100 B used to measure the optical thickness of each of the layers in a multilayer structure  28  as a function of wavelength. Most of the components of dual interferometer apparatus  100 A and  100 B are the same, and all components of the laser interferometer  120  are the same in both embodiments. The only differences in the components between low-coherence interferometer  110 A and low-coherence interferometer  110 B occur in the reference arm of the low-coherence interferometer  110 B. Instead of the incident light portion of reference arm collimated beam  18 R being directly incident on the reference arm lens  30  as shown in  FIG. 1  and  FIG. 1A , the incident light portion of reference arm collimated beam  18 R shown in  FIG. 1B  part of the collimated beam  18 R region is coupled into a fiber collimator  58 A and transmitted through optical fiber  54 R and coupled into a second fiber collimator  58 B before being incident on reference arm lens  30  which then focuses the incident reference arm light onto reference mirror  32 . Most of the light that is focused on reference mirror  32  passes back through reference arm lens  30 , back through fiber collimator  58 B, and transmitted back through optical fiber  54 R and is recollimated by fiber collimator  58 A to form the reflected light portion of reference arm collimated beam  18 R. As in low-coherence interferometer  110 , the reflected light portions of the reference and sample arm collimated beams  18 R and  18 S of low-coherence interferometer  110 A are recombined at the 50/50 beam splitter  24  to form a collimated low-coherence interference beam. The rest of the dual interferometer apparatus  100 A and  100 B are the same with identical functions. As with the sample arm optical fiber  54 S, optical fiber  54 R is preferably a single mode photonic crystal fiber (PCF) since it will function properly over the entire wavelength range of the tunable filter  12 . The dual interferometer configuration shown in  FIG. 1B  is preferred when the multilayer structure  28  needs to be tested remotely from the rest of the dual interferometer apparatus  100 B. It is usual practice to match the optical path lengths of the sample and reference arm optical fibers  54 S and  54 R to minimize dispersion effects in the low-coherence interferometer. The continuous variable tunable filter  12  can also be replaced with a tunable filter  12   a  containing a discrete set of narrow bandpass filters having distinct center wavelengths as described below during the discussion of  FIG. 1C . 
       FIG. 1C  shows a fourth embodiment of a dual interferometer apparatus  100 C used to measure the optical thickness of each of the layers in a multilayer structure  28  as a function of wavelength. The low-coherence interferometer  110  shown in  FIG. 1  has been replaced with low-coherence interferometer  110 C (contained within the dotted line border) in which the tunable light source  13  has been replaced with a new tunable light source  13 A. All other components of interferometer apparatus  100 C are the same as in interferometer apparatus  100 . The new tunable light source  13 A is comprised of multiple individual low-coherence light sources  11 ,  11   a ,  11   b ,  11   c , and  11   d  which output collimated light each having distinct fixed center wavelengths which are combined into the collimated beam  18 . The tunable light source  13 A may also include a broadband low-coherence light source  10  which also produces a collimated broadband low-coherence light beam. The collimated broadband low-coherence light beam passes through tunable filter  12   a  to limit its center wavelength to a narrow band. Tunable filter  12   a  preferably has a fixed set of one or more distinct center wavelength narrow bandpass filters which are selected one at a time to switch the wavelength of light entering the interferometer  110  between a fixed set of distinct center wavelengths. Tunable filter  12   a  is preferably comprised of a fixed set of narrow bandpass filters mounted on a filter wheel. All of the low-coherence light sources  11 ,  11   a ,  11   b ,  11   c , and  11   d  and the broadband low-coherence light source  10  can be individually turned on or off and include collimators (not shown) at their outputs. During operation of low-coherence interferometer  110 C, light of only one distinct center wavelength is switched on at a time during each set of measurements. 
     Dichroic mirrors  15 ,  15   a ,  15   b ,  15   c  and  15   d  are utilized to combine the light emitting from the respective low-coherence light sources  11 ,  11   a ,  11   b ,  11   c , and  11   d  and the filtered light from broadband low-coherence light source  10  into the single collimated beam  18 . As in interferometer  110  of  FIG. 1 , the collimated light beam  18  passes through polarizing beam splitter (PBS)  20  which linearly polarizes the transmitted collimated light beam. The collimated light beam passing through PBS  20  passes through quarter wave plate  22  which is preferably an achromatic quarter wave plate. The rest of the interferometer  110 C functions as described with respect to the discussion of interferometer  110  of  FIG. 1 . 
     In a first embodiment of tunable light source  13 A, the dichroic mirrors  15 ,  15   a ,  15   b ,  15   c  and  15   d  are comprised of long pass dichroic mirrors with monotonically increasing cutoff wavelength, and low-coherence light sources  11 ,  11   a ,  11   b ,  11   c , and  11   d  also are of monotonically increasing center wavelength. Long pass dichroic mirrors are highly reflective below the cutoff wavelength and highly transmissive above it. When using long pass dichroic mirrors, the following wavelength relationships must be met In order to efficiently combine all of the low-coherence light sources into a single collimated beam  18 : The center wavelength of the first low-coherence light source  11  must be shorter than the cutoff wavelength of the first dichroic mirror  15 . The center wavelength of the second low-coherence light source  11   a  must be longer than the cutoff wavelength of the first dichroic mirror  15  and shorter than the cutoff wavelength of the second dichroic mirror  15   a . The center wavelength of the third low-coherence light source  11   b  must be longer than the cutoff wavelength of the second dichroic mirror  15   a  and shorter than the cutoff wavelength of the third dichroic mirror  15   b . The center wavelength range of the tunable filter  12   a  is limited to center wavelengths which are longer than the cutoff wavelength of the third dichroic mirror  15   b  and shorter than the cutoff wavelength of the fourth dichroic mirror  15   c . The center wavelength of the fourth low-coherence light source  11   c  must be longer than the cutoff wavelength of the fourth dichroic mirror  15   c  and shorter than the cutoff wavelength of the fifth dichroic mirror  15   d . Also the center wavelength of the fifth low-coherence light source  11   d  must be longer than the cutoff wavelength of the fifth dichroic mirror  15   d.    
     The low-coherence light sources  11 ,  11   a ,  11   b ,  11   c  and  11   d  in the tunable light source  13 A are preferably comprised of superluminescent diode (SLED) light sources which are pigtailed to single mode optical fibers with fiber collimators attached to the output end of the optical fiber. In an example of the first embodiment of tunable light source  13 A, the first, second, third, fourth and fifth low-coherence light sources  11 ,  11   a ,  11   b ,  11   c  and  11   d  may be comprised of superluminescent diodes (SLED) having center wavelengths of 405 nm, 450 nm, 495 nm, 790 and 850 nm respectively. Also, the first, second, third, fourth and fifth dichroic mirrors  15 ,  15   a ,  15   b ,  15   c ,  15   d  and  15   e  may be long pass dichroic mirrors with cutoff wavelengths of 425 nm, 475 nm, 510 nm, 770 nm and 820 nm respectively. The broad band low-coherence light source  10  may be a supercontinuum light source such as a YSL Photonics SC5 supercontinuum light source; and tunable filter  12   a  may be comprised of a filter wheel containing 5 narrow bandpass filters having center wavelengths of 550, nm 600, nm 650 nm, 700 nm and 750 nm. 
     Although five low-coherence light sources and five dichroic mirrors are shown in the tunable light source  13 A in  FIG. 1C , it is to be understood that the number of low-coherence light sources and the number of dichroic mirrors shown in the tunable light source  13 A can changed together to form alternate embodiments of tunable light source  13 A. Other alternate embodiments of the tunable lightsource  13 A can also be constructed without having broadband low-coherence light source  10  being present. 
     In a second embodiment of tunable light source  13 A, dichroic mirrors  15 ,  15   a ,  15   b ,  15   c  and  15   d  are comprised of short pass dichroic mirrors which are highly reflective above the cutoff wavelength and highly transmissive below it. The short pass dichroic mirrors  15 ,  15   a ,  15   b ,  15   c  and  15   d  have monotonically decreasing cutoff wavelength and the low-coherence light sources  11 ,  11   a ,  11   b ,  11   c , and  11   d  also are of monotonically decreasing center wavelength. When using short pass dichroic mirrors the following wavelength relationships must be met In order to efficiently combine all of the low-coherence light sources into a single collimated beam  18 : The center wavelength of the first low-coherence light source  11  must be longer than the cutoff wavelength of the first dichroic mirror  15 . The center wavelength of the second low-coherence light source  11   a  must be shorter than the cutoff wavelength of the first dichroic mirror  15  and longer than the cutoff wavelength of the second dichroic mirror  15   a . The center wavelength of the third low-coherence light source  11   b  must be shorter than the cutoff wavelength of the second dichroic mirror  15   a  and longer than the cutoff wavelength of the third dichroic mirror  15   b . The center wavelength range of the tunable filter  12   a  is limited to center wavelengths which are shorter than the cutoff wavelength of the third dichroic mirror  15   b  and longer than the cutoff wavelength of the fourth dichroic mirror  15   c . The center wavelength of the fourth low-coherence light source  11   c  must be shorter than the cutoff wavelength of the fourth dichroic mirror  15   c  and longer than the cutoff wavelength of the fifth dichroic mirror  15   d . Also, the center wavelength of the fifth low-coherence light source  11   d  must be shorter than the cutoff wavelength of the fifth dichroic mirror  15   d.    
       FIG. 1D  shows a fifth embodiment of the interferometer apparatus  100 D used to measure the optical thickness of each of the layers in a multilayer structure  28  as a function of wavelength. Most of the components are the same as that of interferometer apparatus  100 B shown in  FIG. 1B  with the exception that the low-coherence interferometer  110 D incorporates tunable light source  13 A as described with reference to  FIG. 1C , and the optical probe  56  of low-coherence interferometer  110 B is now shown to include a fiber collimator  53  coupled to a portable optical probe  57 . The portable optical probe also has a probe mounting surface  57 S which usually includes a three-point mount for automatically aligning the probe  57  to the top surface of the multilayer structure  28  being measured. The length of the sample arm optical fiber  54 S is set in order to place the front end of the mounting surface  57 S of the portable optical probe at the location of the start of the measurement region of the interferometer. The portable optical probe could be handheld at the surface or set in place. Fiber collimators  52 ,  53 ,  58 A and  58 B are preferably off axis parabolic mirror achromatic collimators such as ThorLabs connectorized protected silver reflective collimators. As with the configuration shown in  FIG. 1B , the sample arm optical fiber  54 S and reference arm optical fiber  54 R are preferably photonic crystal fibers (PCF) which remain single mode over the entire wavelength range of tunable light source  13 A, and of matched path length in order to minimize dispersion effects in the low-coherence interferometer. 
       FIG. 1E  shows a sixth embodiment of the interferometer apparatus  100 E used to measure the optical thickness of each of the layers in a multilayer structure  28  as a function of wavelength. In addition to the first balanced detector  38  which detects interfering light in a first wavelength region of the optical spectrum, the low-coherence interferometer  110 E of interferometer apparatus  100 E includes a second balanced detector  39  which detects interfering light in a second wavelength region of the optical spectrum. The low-coherence tunable light source in this embodiment includes a new second section  13 B in addition to the tunable light source  13 A (first section). All of the individual light sources in the low-coherence tunable light source first section  13 A emit light with center wavelengths within a first wavelength region of the optical spectrum, and all of light sources in the low-coherence tunable light source second section  13 B emit light with center wavelengths within a second wavelength region of the optical spectrum. As with the tunable light source first section  13 A, the low-coherence tunable light source second section  13 B can be comprised of multiple low-coherence light sources having different center wavelengths and may also include a broadband low-coherence light source with its own tunable filter. All of the individual light sources making up the low coherence tunable light source second section  13 B can be turned on or off individually and only one center wavelength is turned on at a time during each set of measurements. 
     In the embodiment shown in  FIG. 1E , optical interference at wavelengths emitted by tunable light source  13 A is detected by the first balanced detector  38 , and optical interference at wavelengths emitted by the second tunable light source  13 B is detected by the second balanced detector  39 , thus allowing simultaneous measurement of optical interference from light of one center wavelength emitted by tunable light source  13 A while measuring optical interference from light of one center wavelength emitted by tunable light source  13 B. First and second balanced detectors  38  and  39  preferably are comprised of silicon (Si) and indium gallium arsenide (InGaAs) detectors respectively. Si detectors can be used to measure light having wavelengths from 320-1060 nm while InGaAs detectors can be used to measure light having wavelengths from 800-1700 nm. 
     In  FIG. 1E , the example second tunable light source  13 B is shown to be comprised of sixth and seventh low-coherence light sources  11   e  and  11   f , a wavelength division multiplexer (WDM)  21  and a fiber collimator  23 . Sixth and seventh low-coherence light sources  11   e  and  11   f  have distinct fixed center wavelengths which are in the second spectral region of the optical spectrum. The light emitted from low-coherence light sources  11   e  and  11   f  is combined into a single beam using the fiber optic wavelength division multiplexer (WDM)  21 . The sixth and seventh low-coherence light sources  11   e  and  11   f  are preferably 1310 nm and 1550 nm SLEDs. The combined beam traveling down the output fiber of WDM  21  is collimated at the fiber collimator  23  to form second collimated beam  19 . The second collimated beam  19  passes through a second polarizing beam splitter (PBS)  20   a  to linearly polarize the transmitted collimated light beam  19 . The transmitted collimated linearly polarized light beam  19  then passes through a second quarter wave plate (QWP)  22   a  and is reflected at a sixth dichroic mirror  15   e  where it is combined with collimated beam  18  to form the combined collimated beam  25 . The sixth dichroic mirror  15   e  is preferably a short pass dichroic mirror which has a cutoff wavelength longer than the longest center wavelength which the tunable light source  13 A is tuned to and shorter than the shortest center wavelength that the second tunable light source  13 B is tuned to. As an example, the short pass dichroic mirror  15   e  may have a cutoff wavelength in the range 870-1280 nm when the light sources comprising tunable light source  13 A are those given in the example of the first embodiment of tunable light source  13 A and the sixth and seventh low-coherence light sources  11   e  and  11   f  are 1310 nm and 1550 nm SLEDs. The combined collimated beam  25  is input into the beam splitter (BS)  24  which forms the Michelson interferometer. The beam splitter  24  splits the input combined collimated beam  25  into a sample arm combined collimated beam  25 S and a reference arm combined collimated beam  25 R that travel through the sample and reference arms of the Michelson interferometer respectively. 
     The sample arm combined collimated beam  25 S and the reference arm combined collimated beam  25 R shown in low-coherence interferometer  110 E shown in  FIG. 1E  interact with the sample and reference arms of the low-coherence interferometer in the same way as described with reference to the discussion of  FIG. 1 . The light portion of the reference arm combined collimated beam  25 R being reflected from the reference mirror  32  and the light portion of the sample arm combined collimated beam  25 S being reflected off of each optical interface of the multilayer structure  28  are recombined at the beam splitter  24  and split again into a first combined low-coherence interference beam  25   a  and a second combined low-coherence interference beam  25   b . The first combined low-coherence interference beam  25   a  is incident on a seventh dichroic mirror  15   f  which preferably is a low pass dichroic mirror having the same cutoff wavelength as the sixth dichroic mirror  15   e . Light at wavelengths longer than the cutoff wavelength of the seventh dichroic mirror  15   f  is reflected at dichroic mirror  15   f  forming the first part of the second low-coherence interference beam  19   a  and is incident on the first detector  39   a  of the second balanced detector  39 . The shorter wavelength portion called the first part of the low-coherence interference beam  18   a  is transmitted through dichroic mirror  15   f  and is made to be incident on the first detector  38   a  of balanced detector  38  after reflecting off the pair of 45° mirrors  34  and  36 . 
     The second combined low-coherence interference beam  25   b  travels back through the sixth dichroic mirror  15   e  which again separates the longer wavelength portion of the second low-coherence interference beam  25   b  from the shorter wavelength portion of the interfering light. The longer wavelength portion called the second part of the second low-coherence interference beam  19   b  is reflected at dichroic mirror  15   e  and passes back through the second quarter wave plate  22   a  and into the second polarizing beam splitter  20   a  where it is reflected and is made to be incident on the second detector  39   b  of balanced detector  39  after being reflected by a pair of 45° mirrors  35  and  37 . The shorter wavelength portion called the second part of the low-coherence interference beam  18   b  is transmitted through dichroic mirror  15   e  and back through quarter wave plate  22  and is incident on the polarizing beam splitter  20  where it is reflected and is made to be incident on a second detector  38   b  of the balanced detector  38 . 
       FIG. 1F  shows a seventh embodiment of the interferometer apparatus  100 F used to measure the optical thickness of each of the layers in a multilayer structure  28  as a function of wavelength which includes a portable or handheld optical probe interface to the structure under test. Most of the components are the same as that of interferometer apparatus  100 E shown in  FIG. 1E  with the exception that the low-coherence interferometer  110 F incorporates all of the components shown in the sample and reference arms of the Michelson interferometer shown in  FIG. 1D . The sample arm now includes the handheld or portable optical probe  57  coupled to the instrument via a sample arm optical fiber  54 S, and the reference arm now includes a reference arm optical fiber  54 R which preferably has the same length as sample arm optical fiber  54 S. As with the configuration shown in  FIG. 1D , the sample arm optical fiber  54 S and reference arm optical fiber  54 R are preferably photonic crystal fibers (PCF) which remain single mode over the entire wavelength range of tunable light source first section  13 A and tunable light source second section  13 B. It is also usual practice to match the optical path lengths of the sample and reference arm optical fibers  54 S and  54 R in order to minimize dispersion effects in the low-coherence interferometer. 
     As with the low-coherence light sources  11 ,  11   a ,  11   b ,  11   c , and  11   d , and the broadband low-coherence light source  10  in tunable light source  13 A, light sources  11   e  and  11   f  can be individually turned on or off, and only one of them is turned on at any given time during measurements. Since the interferometers  100 E and  100 F contain two balanced detectors, two wavelengths from the set of k distinct center wavelengths can be measured simultaneously. One center wavelength from tunable light source  13 A can be measured simultaneously with a measurement made using light source  11   e  or  11   f . Interfering light from any one of the fixed wavelength light sources of tunable light source  13 A can be measured using balanced detector  38  simultaneously with the measurement of interfering light from light sources  11   e  or  11   f  using the second balanced detector  39 . 
     Although two low-coherence light sources  11   e  and  11   f  are shown to be detected by the second balanced detector  39 , more low coherence light sources can be added which emit light in the second wavelength region of the optical spectrum, and then combined together using collimators and dichroic filters as described with reference to the discussion of tunable light source  13 A. Other embodiments could also include a broadband low coherence light source that operates in the second wavelength region of the optical spectrum with a tunable filter containing a discrete set of narrow bandpass filters having distinct center wavelengths in the second wavelength region of the optical spectrum, which are combined with the low coherence light sources such as  11   e  and  11   f.    
     The laser interferometer  120  shown at the upper portion of  FIG. 1 ,  FIG. 1A ,  FIG. 1B ,  FIG. 1C ,  FIG. 1D ,  FIG. 1E , and  FIG. 1F  is the same in all of the interferometer configurations  100 ,  100 A,  100 B,  100 C,  100 D,  100 E and  100 F. A collimated light beam  42  is emitted from a laser  40 , preferably a 632 nm HeNe laser. The collimated light beam  42  is incident on a 45° mounted mirror  44  and is incident on a beamsplitter  46 , preferably a 50/50 beamsplitter cube. The beam splitter  46  splits the collimated laser beam  42  into sample and reference collimated laser beams  42 S and  42 R that are incident on stationary mirror  48  and laser reference mirror  32 L respectively. Collimated laser light reflecting back from the laser reference mirror  32 L and the stationary mirror  48  are recombined at the beam splitter  46  and the resulting laser interference beam  42 C is incident on a detector  50 . As described above, the laser reference mirror  32 L is co-mounted with the reference arm lens  30  and reference mirror  32  of low-coherence interferometer  110  on the variable optical path delay element  90 . This causes the low-coherence interferometer and the coherent light interferometer to be coupled so that the optical path difference between the two arms in each of the respective interferometers changes by the same amount as a function of travel of the variable optical path delay element  90 . In a preferred embodiment, reference mirror  30  and laser reference mirror  32 L are comprised of the front and back surfaces of a single optically flat dual sided mirror. The laser interferometer  120  acts as a reference interferometer which is used to accurately track the optical path difference between the two arms in the low-coherence interferometer  110 . 
     During operation of dual interferometer apparatus  100 ,  100 A,  100 B,  100 C,  100 D,  100 E or  100 F, the variable optical path delay element  90  is repetitively scanned at nearly constant velocity from a start position to an end position followed by scanning from the end position to the start position. The variable optical path delay element is typically actuated with a trapezoidal profile in which there is an acceleration phase, a constant velocity phase to within ±10% and a deceleration phase. Since the laser  40  has a very long coherence length, constructive interference occurs in the laser interferometer  120  whenever the difference in the path length between the stationary reference arm and the moving arm differ by mλ/2 where m is an integer and λ is the wavelength of the laser light source, as shown in  FIG. 2 .  FIG. 2  shows an example laser interferometer signal  60  as a function of optical path difference between the two arms of the interferometer normalized to the wavelength λ of the laser. The optical path difference from the start of each scan and velocity of the laser and low-coherence interferometers are the same at all times. Locations of the zero crossings  62  of the laser interferometer signal  60  measured with detector  50  as shown in  FIG. 2  can be used as a distance scale to trigger data acquisition of the low-coherence interferometer balanced detector (BD) signal at known distance intervals. Locations of the maxima and minima of the laser interference signal  60  can also be used as the distance scale. Thus, the reference interferometer is used to accurately track the location of the variable optical path delay element as it is repetitively scanned. 
     Constructive interference occurs in the low-coherence interferometer  110  when the optical path length from the beam splitter  24  to the reference mirror  32  is equal in length to the optical path length from the beam splitter  24  to an optical interface of the multilayer structure  28  within a few coherence lengths of the low-coherence light source  10 , which is typically on the order of 5-25 μm. In order to be able to observe all of the optical interfaces in the multilayer structure  28 , the variable optical path delay element  90  must travel a distance greater than the total optical path in the multilayer structure  28 . Also, the optical path length from the beam splitter  24  to the reference mirror  32  at the start position of the reference mirror  32  is required to be less than the optical path length from the beam splitter  24  to the first optical interface (air/ 28   a ) in the multilayer structure  28  and the optical path length from the beam splitter  24  to the reference mirror  32  at the end position of the reference mirror  32  is required to be greater than the optical path length from the beam splitter  24  to the last optical interface ( 28   e /air) in the multilayer structure  28 . As the variable optical path delay element  90  is moved from its start position to its end position all of the optical interfaces in the multilayer structure will be observed, an example of which is shown in  FIG. 3 . In addition, when the variable optical path delay element  90  is scanned from its end position to its start position all of the optical interfaces in the sample will be observed in reverse order. The distance between the start position and the end position is larger than the total optical thickness of the m layer multilayer structure. 
     During operation of dual interferometer apparatus  100 ,  100 A,  1006 ,  100 C,  100 D,  100 E or  100 F the measured signals of balanced detector  38  and balanced detector  39  (in apparatus  100 E and  100 F) are filtered and log amplified, and the envelope of the log amplified low-coherence interferometer signals are digitized using a high-speed data acquisition card, displayed on a monitor and stored in a computer as a function of distance traveled by the variable optical path delay element  90  during measurement. The locations of the peaks in the amplified low-coherence envelope signal as a function of distance define the locations of the optical interfaces in the multilayer structure being measured. The amplified low-coherence envelope signal is analyzed with a computer in order to determine the true peak locations of the optical interfaces with respect to the start of scan location. Multiple scans are performed at each of the k measurement wavelengths and files containing the locations of all the observed optical interfaces at each of the k measured wavelengths are recorded. 
     The computer also has a data base of known material group index of refraction dispersion curves stored in memory, and all calculations are done with the computer. The computer is operable to execute an algorithm, which is used to determine the number of layers m in the multilayer structure, to determine which of the m layers have a best fit material in a reference database of known material group index of refraction dispersion curves which include data measured at the same set of k distinct center wavelengths, and to identify the material composition and thickness of the layers which have a best fit material in the reference database. 
       FIG. 3  shows an example low-coherence interferometer scan  70  (also called an interferogram) as a function of optical scan distance of the variable optical path delay element  90  showing the locations of all of the optical interfaces in an exemplary 5-layer multilayer structure  28  using the filtered low-coherence light source centered at 650 nm. The log amplified signal coming from the balanced detector  38  is shown as a function of optical distance referenced from the location of the start of the scan. The optical scan distance is calculated from the measured laser interferometer signal. Peaks  71 ,  72 ,  73 ,  74 ,  75  and  76  are observed at the locations of each optical interface in the multilayer structure  28  and correspond to the air/ 28   a ,  28   a / 28   b ,  28   b / 28   c ,  28   c / 28   d ,  28   d / 28   e  and  28   e /air interfaces respectively. In the 5-layer structure, there are 6 optical interfaces and in general for a m layer multilayer structure there are m+1 optical interfaces including the top and bottom air interfaces of the multilayer structure. The distances between successive optical interfaces shown by letters a, b, c, d and e correspond to the optical thickness of each of the layers  28   a ,  28   b ,  28   c ,  28   d  and  28   e  respectively. Since the low-coherence interferometer data is sampled at known distance intervals, peak location algorithms can be applied to find the true locations of all of the peaks in the low-coherence interferometer data. For example, when using a low-coherence source that has a Gaussian wavelength profile, the amplified signal also has a Gaussian envelope and with log amplification the signal at each peak looks like a quadratic function. Multiple measured points around the peak could then be fit to a quadratic function to find the true location of the peak. Multiple scans are averaged and statistics for measurement reproducibility are obtained. TABLE 1 shows the measured optical thickness for each of the 5 layers of the multilayer structure measured in  FIG. 3  along with its standard deviation for 100 repeat measurements. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 650 nm optical thickness and standard deviation for a 5-layer structure. 
               
            
           
           
               
               
               
            
               
                   
                   
                 Standard Deviation 
               
               
                 Layer # 
                 Optical Thickness (μm) 
                 (μm) 
               
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 3857.52 
                 0.16 
               
               
                 2 
                 500.94 
                 0.17 
               
               
                 3 
                 62.60 
                 0.06 
               
               
                 4 
                 1112.14 
                 0.20 
               
               
                 5 
                 3162.65 
                 0.19 
               
               
                   
               
            
           
         
       
     
     When measuring a multilayer structure, the multilayer structure  28  is mounted in front of and normal to the lens  26  shown in  FIG. 1 ,  FIG. 1C  and  FIG. 1E , or optical probe  56  shown in  FIG. 1A , or  FIG. 1B , or optical probe  57  shown in  FIG. 1D  and  FIG. 1F . This allows the low-coherence incident light to be focused inside the multilayer structure and to maximize the magnitude of the light reflected back from each optical interface of the multilayer structure  28 . A sequence of measurements is performed at the same location in the multilayer structure  28  having m layers to measure the optical thickness of each of the m layers in the multilayer structure as a function of wavelength. Multiple scans are measured at each wavelength and averaged. When using interferometer configurations  100 ,  100 A and  100 B, the sequence of measurements is performed by setting the tunable filter  12  to transmit light of a first center wavelength λ 1  followed by changing the center wavelength range of the tunable filter  12  by known increments, preferably in the range of 5-10 nm wavelength intervals over the entire wavelength range of the measurements which is preferably over the range of 400-840 nm for many materials. As an example, if we select 5 nm wavelength intervals throughout the wavelength range of 400-840 nm there will be 89 distinct wavelengths chosen for measurement. Alternatively a fixed set of k distinct center wavelengths can be chosen for measurement. We use the convention that the shortest center wavelength for the filtered light source is λ 1  and the longest wavelength used for the filtered light source is λ k  where k is the number of different wavelengths used to measure the optical thicknesses of each of the layers in the multilayer structure. For each center wavelength λ j  of the tunable filter  12 , where j=1 to k, the resultant measured optical thicknesses are [n gi (λ j )t 1 ], [n g2 (λ j )t 2 ], . . . [n gm (λ j )t m ] for each of the m layers in the multilayer structure  28 . The center wavelength for each successive λ j  is longer than λ j−1 . When using the interferometer configurations  100 C,  100 D,  100 E and  100 F, the fixed set of k distinct center wavelengths are determined by the makeup of tunable light source  13 A and  13 B. 
     The measured optical thicknesses of each layer include the physical thicknesses t 1 , t 2  . . . t m  of each of the m layers in the multilayer structure  28 , which are independent of each other, and the measurements at each measurement wavelength λ j  are performed without moving the sample. The physical thicknesses t 1 , t 2  . . . t m  do not change with the measurement center wavelength of the light source λ j . This allows us to select one center measurement wavelength as a reference wavelength which we call λ O , and we can calculate the ratio of measured optical thickness at each measurement wavelength to that measured at the selected reference wavelength λ O . Since the same layer physical thickness appears in the numerator and the denominator, the ratio of optical thickness ratio at wavelength λ j  for the ith layer is equal to the normalized group index of refraction  n gi   (λ j ) of the ith layer where i=1 to m is given by the relationship 
     
       
         
           
             
               
                 
                   
                     
                       
                         n 
                         gi 
                       
                       _ 
                     
                     ⁡ 
                     
                       ( 
                       
                         λ 
                         j 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               n 
                               gi 
                             
                             ⁡ 
                             
                               ( 
                               
                                 λ 
                                 j 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             t 
                             i 
                           
                         
                         ] 
                       
                       
                         [ 
                         
                           
                             
                               n 
                               gi 
                             
                             ⁡ 
                             
                               ( 
                               
                                 λ 
                                 o 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             t 
                             i 
                           
                         
                         ] 
                       
                     
                     = 
                     
                       
                         
                           [ 
                           
                             
                               n 
                               gi 
                             
                             ⁡ 
                             
                               ( 
                               
                                 λ 
                                 j 
                               
                               ) 
                             
                           
                           ] 
                         
                         
                           [ 
                           
                             
                               n 
                               gi 
                             
                             ⁡ 
                             
                               ( 
                               
                                 λ 
                                 o 
                               
                               ) 
                             
                           
                           ] 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     The wavelength dependence of the normalized group index of refraction  n gi   (λ j ) for each of the m layers of the multilayer structure as a function of wavelength λ j , where j=1 to k defines the normalized group index of refraction dispersion curve of the material in the ith layer over the wavelength range of the measurement. 
     We have found that both the group index of refraction dispersion curve and the normalized group index of refraction dispersion curves are unique for most materials as described in detail below. Thus, the shape of the measured group index of refraction dispersion curves and normalized group index of refraction dispersion curves for each of the m layers can be used to identify the material composition of each of the layers. Material identification can be done by comparing the measured group index of refraction dispersion curves or the normalized group index of refraction dispersion curves at the measured center wavelengths λ j  where j=1 to k to those found in a material database of reference materials with known group index of refraction dispersion curves or normalized group index of refraction dispersion curves with data points at the same set of center wavelengths and performing a statistical best fit analysis. The normalized group index of refraction dispersion curves for the materials in the database of known materials is derived from the group index of refraction dispersion curve database as shown in Equation 1. 
     The reference database of known materials is required to include the group index of refraction dispersion curves for all materials in the database to enable determination of physical thickness from measured optical thickness measurements. Once the material is identified from its known group index of refraction dispersion curve or its known normalized group index of refraction dispersion curve, we can then look up its group index of refraction dispersion curve at each of the measured center wavelengths λ j  and calculate the layer physical thickness by dividing the measured optical thickness data by the group index of refraction for the material at each measured wavelength λ j . 
     There are two methods of getting data from different materials into the group index of refraction database of known materials or the normalized group index of refraction database of known materials using a reference wavelength λ o . The first method uses published databases of phase refractive index data versus wavelength and then calculates the group index of refraction and normalized group index of refraction dispersion curves from the published data and equations. The second method uses a group index of refraction cell attached to the measurement apparatus used in the practice of this invention, an embodiment of which is shown in  FIGS. 7A and 7B . These two methods are described below. 
     The phase index of refraction is related to the property of optical dispersion. The phase index of refraction dispersion curve has been found to be unique for most optical materials. Instruments for measuring the wavelength dependence of the phase index of refraction which is called a dispersion curve include spectral ellipsometers, spectral goniometers and refractometers. A published database of the phase index of refraction dispersion curves for various materials can be found at M. N. Polyanskiy, “Refractive Index Database”, https://refractiveindex.info (subsequently herein “Polyanskiy”). Optical dispersion in optical materials is the phenomenon in which the phase velocity v p (λ) of a wave depends on the wavelength of light λ traveling through the optical material. The phase index of refraction n p (λ) of a material is defined as 
     
       
         
           
             
               
                 
                   
                     
                       n 
                       p 
                     
                     ⁡ 
                     
                       ( 
                       λ 
                       ) 
                     
                   
                   = 
                   
                     c 
                     
                       
                         v 
                         p 
                       
                       ⁡ 
                       
                         ( 
                         λ 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     where c is the speed of light in vacuum and v p (λ) is the phase velocity. A plot of index of refraction as a function of wavelength is called a dispersion curve.  FIG. 4  shows example phase index of refraction versus wavelength data for some example materials including soda lime glass, Schott N-BK7 borosilicate glass, poly(methyl methacrylate) PMMA and polycarbonate (PC) based on the Sellmeier equation from Polyanskiy for each of these materials. 
     The group index of refraction of a material is related to the phase index of refraction by the relationship 
     
       
         
           
             
               
                 
                   
                     
                       n 
                       g 
                     
                     ⁡ 
                     
                       ( 
                       λ 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         n 
                         p 
                       
                       ⁡ 
                       
                         ( 
                         λ 
                         ) 
                       
                     
                     - 
                     
                       λ 
                       ⁢ 
                       
                         
                           
                             dn 
                             p 
                           
                           ⁡ 
                           
                             ( 
                             λ 
                             ) 
                           
                         
                         dλ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where n g (λ) is the group index of refraction and dn p (λ)/dλ is the derivative of the phase index of refraction as a function of wavelength λ.  FIG. 5  shows the calculated group index of refraction dispersion curve for the same set of materials shown in  FIG. 4 .  FIG. 6A  shows the normalized group index of refraction dispersion curve  n g   (λ) calculated from the relationship 
                         n   g     _     ⁡     (   λ   )       =         n   g     ⁡     (   λ   )           n   g     ⁡     (     λ   o     )                 (   4   )               
using 400 nm as the reference wavelength λ o  for the same set of materials shown in  FIG. 4  and  FIG. 5 .  FIG. 6B  shows an expanded view of the normalized group index of refraction dispersion curves for N-BK7 and soda lime glass over the range of 400 nm to 850 nm.
 
     We can add a prospective material (e.g., a presently unknown material or a material that has a known identity but unknown properties to be characterized by the methods of the present disclosure, resulting in it becoming a known material) to the group index of refraction reference database of known materials by first calculating the group index of refraction as a function of wavelength from its known phase index of refraction data (see Polyanskiy) using Equation 3 and then extracting the calculated values of group index of refraction at the same set of k distinct center wavelengths of the tunable light source defined as λ j  where j is an integer and j=1 to k inclusively with λ 1  being the shortest center wavelength of the tunable light source and λ k  being the longest wavelength of the tunable light source that are used in all measurements. 
     The second method of getting data from different prospective materials into the group index of refraction database of known materials or the normalized group index of refraction database of known materials using a reference wavelength λ o  uses a group index of refraction measurement cell attached to the measurement apparatus, an embodiment of which is shown in  FIGS. 7A and 7B . The measurement cell is a special type of multilayer structure which consists of a top optical flat and a bottom optical flat separated by a spacer which contains a receiving surface located above the top optically flat surface of the bottom optical flat and below the bottom optically flat surface of the top flat for disposing a sample containing a layer of a prospective material to be added to the database of known materials. 
     The sample containing a layer of the prospective material to be added to the database of known materials can either be a single layer of the prospective material or a three layer laminate containing the prospective material to be added to the database sandwiched between a first known material and a second known material. The first and second known materials are required to be already in the database of known materials and they could be comprised of the same material. The three layer laminate is required to be used when a single layer sample of the prospective material cannot be measured, which is the case for many polymeric adhesive layers including polyvinyl butyral (PVB), thermoplastic polyurethane (TPU), and ethylene-vinyl acetate (EVA). The sample containing a layer of the prospective material to be added to the database of known materials is required to have top and bottom surfaces which are approximately parallel (within ±3°). 
       FIG. 7A  shows an example group index of refraction measurement cell with a sample  82  containing a layer of a prospective material to be added to the database of known materials being disposed between a pair of optical flats, and  FIG. 7B  shows the group index of refraction cell without the sample  82  contained therein. The optical probe  56  shown in  FIG. 7A  and  FIG. 7B  is the same optical probe  56  that is attached to the sample arm optical fiber  54 S of the dual interferometer embodiments shown in  FIG. 1A  and  FIG. 1B . The optical probe  56  is mounted at a fixed distance above a measurement cell  80  which is used to determine group index of refraction dispersion curves and normalized group index of refraction dispersion curves of the layer of the prospective material to be added to the database of known materials. The optical probe used in  FIG. 7A  and  FIG. 7B  could also be the portable optical probe  57  shown in  FIG. 1D  and  FIG. 1F . Two sets of measurements are required, a first set with the sample  82  containing a layer of a prospective material to be added to the database of known materials present in the measurement cell  80 , and a second set of measurements without the sample  82  being present as described below. 
     The group index of refraction measurement cell  80  shown in  FIG. 7A  and  FIG. 7B  is comprised of a top optical flat  84  having a bottom optically flat surface F 1  and a bottom optical flat  86  having a top optically flat surface F 2  separated by a spacer  88  containing a cavity  78  between the bottom optically flat and the top optically flat surfaces F 1  and F 2 . The spacer  88  causes the separation of surfaces F 1  and F 2  to be at a constant physical distance d o , (also called the total gap) as shown in  FIG. 7B . The spacer  88  also contains a receiving surface RS at a distance d 2  above the top optically flat surface F 2  of the bottom optical flat  86  for disposing the sample  82  containing a layer of a prospective material to be added to the database of known materials at a fixed position in cavity  78 . The optically flat surfaces F 1  and F 2 , the upper and lower surfaces of the spacer  88 , and the receiving surface RS are constructed to be parallel to each other. The receiving surface RS divides the cavity into a larger diameter upper cavity between surfaces F 1  and RS and a smaller diameter lower cavity between surfaces RS and F 2 . 
     Although the receiving surface RS is shown as a ledge for holding the sample  82  in place, other configurations for the receiving surface are possible. As an example, the receiving surface could be a clamp mounted externally to the measurement cell which holds the sample  82  near its perimeter and is adjusted to cause the bottom surface of the sample to be a fixed distance above the top surface F 2  of the bottom optical flat  86 . Typical dimensions for the diameters of the upper and lower parts of the cavity are 30-150 mm and 5-25 mm respectively. 
     The sample  82  containing a layer of a prospective material to be added to the database of known materials is required to be flat so that is has top and bottom surfaces which are nominally parallel to each other within a few degrees. The measurement cell  80  preferably includes a thermal control system (not shown) including a thermostat (not shown) to cause the measurement cell  80  to remain at a constant known temperature (±0.1° C.) throughout each set of measurements. Typical dimensions of the distance between surface F 1  and F 2  of cavity are 5-50 mm. The optical probe  56  is also normally aligned with respect to the optically flat surfaces of the measurement cell  80 . The sample  82  containing a layer of a prospective material to be added to the database of known materials should have a physical thickness of at least 10 μm and can be as thick as 40 mm or more and is preferably in the range of 0.1 to 20 mm in physical thickness. 
     The following measurement procedure is used to add a new material to the group index of refraction dispersion curve and normalized group index of refraction dispersion reference database of known materials. A sample  82  containing the layer of the prospective material to be added to the database of known materials is first disposed into the measurement cell  80  at the receiving surface RS. The sample must be large enough so that it does not fall into the lower part of the cavity between the receiving surface RS and the top surface F 2  of the bottom optical flat  86 . The sample  82  shown in  FIG. 7A  is a single layer sample of the prospective material to be added to the database of known materials. During the first part of the measurement shown in  FIG. 7A , the sample  82  containing the layer of the prospective material to be added to the database of known materials is mounted onto the receiving surface RS of the measurement cell  80  with the dual interferometer measuring at the same set of k distinct center wavelengths of the tunable light source λ j , where j is an integer and j=1 to k inclusively with λ 1  being the shortest center wavelength of the tunable light source and λ k  being the longest wavelength of the tunable light source as used when measuring unknown multilayer structures  28 . 
     From the geometry in  FIG. 7A , the optical interfaces that are observed in sequence during a low-coherence interferometer scan are the top surface of top optical flat  84 , the bottom surface F 1  of the top optical flat  84 , the top surface of the layer of prospective material  82  to be added to the database of known materials, the bottom surface of the layer of prospective material  82 , the top surface F 2  of bottom optical flat  86  and the bottom surface of bottom optical flat  86 . The physical distance between the bottom surface F 1  of the top optical flat  80  and the top surface of prospective material sample  82  is defined as d 1  (the top gap thickness): the physical distance between the top surface of the layer of prospective material  82  and the bottom surface of the layer of prospective material  82  is the thickness of the layer of prospective material  82 , t m ; and the physical distance between the bottom surface of the layer of prospective material  82  and the top surface F 2  of bottom optical flat  86  is d 2  (the bottom gap thickness). The layer of prospective material  82  has a group index of refraction n gm (λ j ) at each measured wavelength of the low-coherence tunable source where j=1 to k and the air inside the cavity air has an index of refraction n a (λ j ). We define T 1 (λ j ) as the measured optical thickness of the top air gap, T 2 (λ j ) as the optical thickness of the layer of prospective material to be added to the database of known materials and T 3 (λ j ) as the measured optical thickness of the bottom air gap. For each measured wavelength λ j , the measured optical thicknesses T 1  (λ j ), T 2 (λ j ) and T 3 (λ j ) are given by
 
 T   1 (λ j )=[ n   a (λ j ) d   1 ], T   2 (λ j )=[ n   gm (λ j ) t   m ], T   3 (λ j )=[ n   a (λ j ) d   2 ]  (5)
 
where d 1  and d 2  are the top and bottom physical air gap thicknesses, respectively and n a (λ j ) is the known group index of refraction of air at each of the measurement wavelengths. After these three parameters are measured as a function of wavelength, the sample is removed from the cell as shown in  FIG. 7B  and the optical distance [n a (λ)d o ] is measured as a function of wavelength λ. The cavity  78  gap physical distance d 0  (gap) is then calculated at all of the measured wavelengths λ j  by the relationship
 
                       d   o     ⁡     (     λ   j     )       =       [         n   a     ⁡     (     λ   j     )       ⁢     d   o       ]         n   a     ⁡     (     λ   j     )                 (   6   )               
where d o (λ j ) is the measured value of physical distance d o  using center wavelength λ j . The mean value of d o (λ j ) is calculated and is set equal to d 0 .
 
     Similarly the top and bottom air gap distances d 1  and d 2  shown in  FIG. 7A  can be found from the relationships 
                         d   1     ⁡     (     λ   j     )       =       [         n   a     ⁡     (     λ   j     )       ⁢     d   1       ]         n   a     ⁡     (     λ   j     )           ;       and   ⁢           ⁢       d   2     ⁡     (     λ   j     )         =       [         n   a     ⁡     (     λ   j     )       ⁢     d   2       ]         n   a     ⁡     (     λ   j     )                   (   7   )               
where d 1 (λ j ) and d 2 (λ j ) are the measured values of physical distances d 1  and d 2  using center wavelength λ j . The mean values of d 1 (λ j ) and d 2 (λ j ) are calculated and are set equal to d 1  and d 2  respectively. The phase and group index of refraction of air have been well characterized as a function of wavelength and temperature as described by Jack A. Stone and Jay H. Zimmerman, in the NIST, Engineering Metrology Toolbox, “Index of refraction of air” which can be found at http://emtoolbox.nist.gov/Wavelength/Documentation.asp.  FIG. 8  shows a plot of the expected optical thickness for a 25 mm physical air gap distance d o  as a function of wavelength at 20° C. The group index of refraction of air as a function of wavelength is included in the reference database of known materials.
 
     Temperature control of the measurement cell  80  is important for accurate measurements. The group and phase index of refraction of most materials are slightly temperature dependent. The refractive index of air is 1.0002684 at 20° C. and 1.0002637 at 25° C., and the change with temperature is −9.43×10 −7 /° C. at 20° C. and −9.22×10 −7 /° C. at 25° C. For the 25 mm physical path length cuvette measured in air, a 1° C. temperature change will result in a 23.6 nm error in the calculation of the physical path length d o  of the cavity  78  in the measurement cell  80  when measured at 20° C., and a 23.1 nm error when measured at 25° C. Most other optical materials including glasses and plastics have larger changes in refractive index with temperature than air. As examples the change in refractive index with temperature near room temperature for acrylic materials is approximately −8.5×10 −5 /° C. and for N-BK7 glass refraction, the value is 1.6×10 −5 /° C. 
     From the measured parameters d o , d 1  and d 2 , we can then calculate the physical thickness t m  of the layer of prospective material  82  to be added to the database of known materials from the relationship
 
 t   m   =d   o   −d   1   −d   2   (8)
 
The physical distances d o , d 1  and d 2  are independent of wavelength, and the statistical variation in the measured values as a function of wavelength is an indication of the instrument&#39;s measurement repeatability. The physical thickness t m  of the prospective material  82  is also independent of wavelength. Once the physical thickness t m  of the layer of prospective material  82  is known, we can then calculate the group index of refraction at each of the measured wavelengths λ j  of the prospective material sample  82  as a function of wavelength from the relationship
 
     
       
         
           
             
               
                 
                   
                     
                       n 
                       gm 
                     
                     ⁡ 
                     
                       ( 
                       
                         λ 
                         j 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               n 
                               gm 
                             
                             ⁡ 
                             
                               ( 
                               
                                 λ 
                                 j 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             t 
                             m 
                           
                         
                         ] 
                       
                       
                         t 
                         m 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Once we know the group index of refraction of the layer of the prospective material  82  to be added to the database of known materials as a function of wavelength, we can then add its group index of refraction dispersion curve to the known material database. The normalized group index of refraction dispersion curve is then also calculated using the standard reference wavelength λ o . The measured group index of refraction as a function of wavelength for the newly measured and known material is first added to the reference material database of known material group index of refraction dispersion curves. The normalized group index of refraction dispersion curve for this newly known material is now calculated by dividing the group index of refraction dispersion curve by the reference wavelength λ o  as described above using Equation 4. 
     With some materials such as adhesive layers, it is not possible to produce a single layer of the material that can be measured in an index of refraction cell. In these cases the layer of prospective material to be added to the group index of refraction database of known materials can be disposed between a layer of a first known material and a layer of a second known material as shown in  FIG. 7C .  FIG. 7C  shows the three layer structure as having a first layer of known material having group index of refraction n gi (λ) and thickness t 1 , with a middle layer of the prospective material to be added to the reference database having group index of refraction n gm (λ) and thickness t m , and a second layer of known materials having group index of refraction n g2 (λ) and thickness t 2 . When the three layer laminate containing the layer of the prospective material to be added to the database of known materials shown in  FIG. 7C  is disposed in the measurement cell, the optical thicknesses of the first layer of known material [n g1 (λ)t 1 ] and second layer of known material [n g2 (λ)t 2 ] are measured at each of the k distinct center wavelengths using the interferometer apparatus, in addition to the optical thickness of the layer of the prospective material to be added to the database of known materials [n gm (λ)t m ] and the top and bottom air gap optical thicknesses [n a (λ)d 1 ] and [n a (λ)d 2 ]. 
     The thicknesses of the top and bottom air gaps d 1  and d 2  are determined by dividing the top and bottom air gap optical thicknesses measured at each of the k distinct center wavelengths by the group index of refraction of air at each of the k respective wavelengths using Equation 7 and calculating the mean values of the top and bottom air gap. The thicknesses of the first known material t 1  and the second known material t 2  are determined by dividing the measured optical thicknesses at each of the k distinct center wavelengths of the first and second known materials by their respective known group indexes of refraction at each of the k respective wavelengths and calculating the mean values of the thickness of the first known material and the second known material. The known group indexes of refraction are found in the group index of refraction database of known materials. 
     As described above with reference to Equation 6, the thickness of the total airgap is determined by dividing the total air gap optical thicknesses measured at each of the k distinct center wavelengths by the group index of refraction of air at each of the k respective wavelengths and calculating the mean value of the thickness of the total air gap without the three layer sample being disposed in the measurement cell. The thickness t m  of the layer of the prospective material to be added to the database of known materials is then determined by subtracting the sum of the top air gap thickness d 1 , the first known material thickness t 1 , the second known material thickness t 2  and the bottom air gap thicknesses d 2  from the total air gap thickness d o , by the relationship
 
 t   m   =d   o   −d   1   −d   2   −t   1   −t   2 .  (10)
 
     The group index of refraction dispersion curve of the prospective material to be added to the database of known materials is then calculated by dividing the optical thickness of the prospective material to be added to the group index of refraction database of known materials measured at each of the k distinct center wavelengths by the thickness of the layer of the prospective material to be added to the database of known materials. The group index of refraction data for the newly characterized known material measured using the index of refraction measurement cell is then added to the database of known material group index of refraction dispersion curves, and its Sellmeier equation is calculated based on the measured center wavelength group index of refraction data and is also added to the database. 
     The reference database of known materials also includes the derived group index of refraction Sellmeier equation for each of the known and measured prospective materials, which is given by the relationship 
     
       
         
           
             
               
                 
                   
                     
                       
                         n 
                         g 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         λ 
                         ) 
                       
                     
                     - 
                     1 
                   
                   = 
                   
                     
                       ∑ 
                       i 
                       m 
                     
                     ⁢ 
                     
                       
                         
                           B 
                           i 
                         
                         ⁢ 
                         
                           λ 
                           2 
                         
                       
                       
                         
                           λ 
                           2 
                         
                         - 
                         
                           C 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     where i and m are integers and i varies from 1 to m and B i  and C i  are constants. For most optical glasses, three sets of coefficients are used (m=3) and for many plastics only one set of coefficients is needed (m=1). The group index of refraction of prospective material samples  82  measured as a function of wavelength are converted to the Sellmeier form of Equation 10 by calculating the best fit coefficients B i  and C i  to the measured data. 
     The measurement cell  80  shown in  FIG. 7  can also be used to measure the total physical thickness of a multilayer structure  28 . The optical thickness of the total gap in the cell d o  is first measured without the multilayer structure being present. Then the multilayer structure is placed in the measurement cell in the same location of the prospective material sample  82  and the optical thicknesses of the top air gap d 1  and the bottom air gap d 2  are measured as before and applying Equation 8 to get the total physical thickness. The total physical thickness measurement can become important to distinguish between two materials which have very close normalized group index of refraction profiles since they will generally have different group index of refraction values. Comparing the total physical thickness of the multilayer structure measured in the measurement cell with that obtained by identifying the best fit materials for each layer of the multilayer structure from their calculated normalized group index of refraction dispersion curves to a reference database of known materials group index of refraction dispersion curves can also be used as a confirmation for the materials identification. 
     The measurement cell for measuring the total physical thickness of the multilayer structure  28  or a sample containing the layer of a prospective material to be added to the database of known materials group index of refraction dispersion curves (both referred to as a test object) can also have a different structure to that shown in  FIG. 7A  and  FIG. 7B . When the test object is installed in a suitable measurement cell, the measurement cell must have a top optically flat surface located above the top surface of the test object to form an upper airgap and a bottom optically flat surface located below the bottom surface of the test object to form a lower airgap. The requirements are that the two optically flat surfaces are parallel to each other and remain a fixed distance apart. The multilayer structure  28  is mounted between the top and bottom optically flat surfaces so that its outer surfaces at the location of measurement are nearly parallel to the top and bottom optically flat surfaces of the measurement cell. During measurements using the interferometer apparatus, the optical thickness of the upper airgap and the lower air gap are also measured along with the optical thickness of each of the observed layers in the test object as a function of wavelength of the low-coherence tunable light source. The receiving surface RS may be defined as any structure that causes the sample  82  or  82 A to remain at a fixed distance above the top surface F 2  of the bottom optical flat  86  when disposed between the pair of optical flats. 
     For an m layer sample the maximum number of observed optical interfaces will be m+1. Thus, the number of layers in the multilayer structure is equal to 1 less than the maximum number of optical interfaces measured in the sample as a function of incident wavelength λ j  of the filtered low-coherence light source  13 . When measuring a multilayer optical structure having m layers there are usually m+1 optical interfaces observed in an interferometer distance scan. In some cases all of the optical interfaces in the multilayer structure may not be observed at all of the measured wavelengths λ j . This occurs when the group index of refraction is the same or nearly the same for two adjacent layers in the multilayer structure  28 . 
       FIG. 9  shows an example of two group index of refraction dispersion curves for dense flint glass and for polycarbonate plastic in which the dispersion curves cross at a wavelength of 536.5 nm where both materials have a group index of refraction of 1.6682. For the dual low-coherence interferometer apparatus  100 ,  100 A,  100 B,  100 C,  100 D,  100 E, and  100 F shown in  FIG. 1 ,  FIG. 1A ,  FIG. 1B ,  FIG. 1C ,  FIG. 1D ,  FIG. 1E , and  FIG. 1F  respectively, the individual optical interfaces for each layer will not be observable when the group index of refraction of two adjacent layers differ by less than about 0.001. For the example shown in  FIG. 9 , the instrument will not see the optical interface when for center wavelengths between 532.5-539.5 nm when dense flint glass is adjacent to polycarbonate plastic. When the ith and ith+1 layers of an m layer multilayer structure have the same group index of refraction to within 0.001 at a wavelength λ c , no discernable optical interface will occur between the layers i th  and the i+1  th  layers and the measured optical thickness of these layers will be [n gi (λ c )t i +n gi (λ c )t i+1 ] and only m−1 layers will be observed in the measured interferogram similar to that shown in  FIG. 3 . The wavelength regions where less than the usual number of measured layers occur can be readily found in the analysis since there will be less than m+1 optical interfaces in the measured interferograms in these relatively narrow regions of the optical spectrum. It is also relatively easy to tell which optical interface is missing in the data by looking at its relative location in the interferogram scan. The optical thickness data for the two layers containing the missing optical interface can then be omitted from the normalized group index of refraction calculations described in Equation 1. 
     In order to determine how many layers are in the multilayer structure, we first determine the maximum number of optical interfaces observed in the interferometer scans as a function of center wavelength λ j  of the filtered low-coherence light source  13  as the center wavelength is varied from λ 1  to λ k . Most of the scans at different center wavelengths will have the same number of optical interfaces observed in the multilayer structure which is equal to the maximum number of optical interfaces and equal to m+1 where m is the number of layers in the multilayer structure  28  being tested. In some multilayer structures one to a few wavelength regions will have fewer peaks. When this occurs, 1-3 adjacent center wavelengths could be missing an optical interface at regions when the group index of refraction of the adjacent layers cross each other as shown in the example of  FIG. 9 . The air-top layer interface and the bottom layer-air interface will always be observed since the index of refraction of all solid materials is always greater than one. 
       FIG. 10  is a flow chart  150  showing the steps performed in carrying out a method of identifying the material composition of each layer in a multilayer structure and to determine each layers physical thickness. The first Step  152  is to provide an interferometer apparatus with a tunable low-coherence light source. Suitable interferometer apparatuses  100 ,  100 A,  100 B,  100 C,  100 D,  100 E, and  100 F have been described with reference to the descriptions of  FIG. 1 ,  FIG. 1A ,  FIG. 1B ,  FIG. 1C ,  FIG. 1D ,  FIG. 1E , and  FIG. 1F  respectively. Step  152  is followed by Step  154  in which the portion of the multilayer structure to be tested is aligned with respect to the interferometer apparatus. In some cases the multilayer structure will be set up in the measurement region of the instrument such as that shown in  FIG. 1 . In many cases the multilayer structure could be something mounted in its location of use such as a window in a vehicle, aircraft or a building and a portable interferometer apparatus having a portable optical probe is used, which will automatically align with the multilayer structure in situ. After the multilayer structure is mounted and aligned, Step  154  is followed by Step  156  in which the interferometer apparatus is used to measure the optical thickness of each of the observed layers in the multilayer structure as a function of center wavelength of the low-coherence tunable light source. A standard set of k center wavelengths λ j  is selected where j=1 to k with λ 1  being the shortest wavelength, λ k  being the longest wavelength and each successive λ j  is longer than λ j−1 . The locations of the peaks in interferometer scans obtained at each of the k distinct center wavelengths are determined and the scan distances between each successive optical interface define the optical thicknesses being measured. The total number of layers measured at each measurement wavelength λ j  is noted in this Step. 
     Step  156  is followed by Step  158  in which the number of layers m in the multilayer structure is determined. The number of layers m in the multilayer structure is set equal to the maximum number of layers observed in Step  156 . Typically the number of observed layers m will be the same and equal to the maximum number of observed layers for all or almost all of the measured wavelengths λ j  of the tunable low-coherence light source. Adjacent layers will not be observed at small wavelength ranges where their group index of refraction dispersion curves cross each other as discussed above during the discussion of  FIG. 9 . 
     It is relatively easy to determine which layers are missing from the peak location data as a function of the k distinct center wavelengths and the optical thickness data. When there is a single missed optical interface, the observed optical thickness will be the sum of two adjacent layers optical thickness. The optical thickness data measured with low-coherence light source center wavelengths containing missed optical interfaces are eliminated from the measured optical thickness data before proceeding to the next step  158 . 
     Step  158  is followed by Step  160  in which the normalized group index of refraction dispersion curves are calculated for each of the m layers in the multilayer structure by selecting one center wavelength of the tunable light source as a reference wavelength and calculating the ratio of the measured optical thickness at each measurement wavelength to that measured at the selected reference wavelength for each of the m layers in the multilayer structure. Step  160  is followed by step  162  in which the material that each layer in the m layer multilayer structure is comprised of is identified by comparing its calculated normalized group index of refraction dispersion curve to a reference database of known materials group index of refraction dispersion curves and finding the best fit material for each of the m layers in the multilayer structure. Step  162  is followed by Step  164  in which the physical thickness of each of the m layers of the multilayer structure is determined by dividing the measured optical thickness at each measured center wavelength of the tunable light source by the group index of refraction of the identified material at the respective measured center wavelength and calculating its average value for each of the m layers in the multilayer structure. 
       FIG. 11  is a flow chart  170  showing the steps of a method to determine the group index of refraction dispersion curve for a prospective material, which is to be added to the group index of refraction database of known materials. The first Step  172  is to provide a flat sample containing a layer of the prospective material to be added to the group index of refraction database of known materials. The sample containing a layer of the prospective material to be added to the group index of refraction database of known materials can either be a flat single layer sample of the prospective material or a three layer laminate with the prospective material to be added to the group index of refraction database sandwiched between a first known material in the database and a second known material in the database. 
     Step  172  is followed by Step  174  in which a measurement cell with optically flat surfaces is provided. The measurement cell will be comprised of a top flat having a bottom optically flat surface and a bottom optical flat having a top optically flat surface which are separated by a total gap larger than the physical thickness of the flat single layer sample, and the bottom and top optically flat surfaces are parallel to each other. Step  174  is followed by Step  176  in which an interferometer apparatus having a low-coherence tunable light source and an optical probe is provided and normally aligned to the optically flat surfaces of the measurement cell provided in Step  174 . 
     Step  176  is followed by Step  178  in which the gap between the bottom optically flat surface of the top flat and the top optically flat surface of the bottom flat of the measurement cell is determined. This measurement is performed by measuring the optical distance of the gap as a function of wavelength of the low-coherence tunable light source and dividing by the group index of refraction of air at each of the respective wavelengths and calculating the average value of the gap measured as a function of wavelength of the tunable light source. All Steps with measurements that are measured as a function of wavelength of the tunable light source are measured at the same set of k distinct center wavelengths of the tunable light source defined as λ j  where j is an integer and j=1 to k inclusively with λ 1  being the shortest center wavelength of the tunable light source and λ k  being the longest wavelength of the tunable light source. Each successive wavelength measured is at a longer wavelength than the previous one so that λ 1 &lt;λ 2 &lt;λ 3 . . . &lt;λ k−1 &lt;λ k . 
     Step  178  is followed by Step  180  in which the sample containing the layer of the prospective material to be added to the group index of refraction database of known materials is mounted in the measurement cell in the gap between the bottom optically flat surface of the top flat and the top optically flat surface of the bottom flat. The sample containing the layer of the prospective material is mounted so that it is parallel to the optically flat surfaces of the measurement cell. Step  180  is followed by Step  182  in which the interferometer apparatus is used to determine the top gap between the bottom optically flat surface of the top flat and the top surface of the sample containing the layer of prospective material to be added to the database, the optical thickness of each of the layers of the sample containing the layer of prospective material to be added to the database and the bottom gap between the bottom surface of the sample containing the layer of prospective material to be added to the database and the top optically flat surface of the bottom flat as a function of wavelength of the low-coherence tunable light source. The top gap and the bottom gap are determined by measuring the optical distance of the top and bottom gaps as a function of wavelength of the low-coherence tunable light source and dividing the top and bottom gap optical distances by the group index of refraction of air at each of the respective measured wavelengths and calculating the average values of the top and bottom gaps. 
     Step  182  is followed by Step  184  in which the thickness of the layer of prospective material to be added to the database is determined. When the sample containing the layer of prospective material is a single layer sample its thickness is determined by subtracting the sum of the top gap d 1  and the bottom gap d 2  from the total gap d o  of the measurement cell. When the sample containing the layer of prospective material is a three layer laminate with the prospective material to be added to the group index of refraction database sandwiched between a first known material in the database and a second known material in the database, the thicknesses of the first known material and the second known materials are first determined. This is performed by dividing the measured optical thicknesses at each of the k distinct center wavelengths of the first and second known materials by their respective known group indexes of refraction at each of the k respective wavelengths and calculating the mean values of the thicknesses t 1  and t 2  of the first known material and the second known material, respectively. 
     The thickness of the layer of the prospective material to be added to the database is then determined by subtracting the sum of the top gap d 1 , the first known material thickness t 1 , the second known material thickness t 2  and the bottom gap d 2  from the total gap d o  of the measurement cell. Step  184  is followed by Step  186  in which the group index of refraction dispersion curve for the layer of prospective material is determined. This is done by dividing the optical thickness of the prospective material layer measured as a function of wavelength of the low-coherence tunable light source by the calculated physical thickness of the prospective material layer. At this point, the characterization of the prospective material is complete, thereby establishing it as another known material. The group index of refraction GRI dispersion curve data measured as a function of wavelength for the newly established known material can then added to the database of known materials. The measured data as a function of wavelength for the new known material can also be put in the form of a Sellmeier equation by calculating the best fit Sellmeier coefficients B i  and C i  to the measured data. 
       FIG. 12  shows a flow chart  130  showing the steps performed in carrying out of an alternate method of characterizing each layer in a multilayer structure comprising m layers where m is an integer greater than 2. The characterization includes determine the number of layers m in the multilayer structure and identifying the material composition of the layers in the structure. This method uses the group index of refraction database of materials without calculating the normalized group which was described with reference to  FIG. 10 . The first Step  132  is to provide an interferometer apparatus with a tunable low-coherence light source which can be tuned to at least a set of k distinct center wavelengths where k is an integer greater than 2. Any of the suitable interferometer apparatus described in Step  152  of  FIG. 10  can be utilized in Step  132 . 
     Step  132  is followed by Step  134  in which the multilayer structure is aligned with respect to the measurement region of the interferometer apparatus. Use of the portable optical probe  57  shown in  FIG. 1D  and  FIG. 1F , which automatically aligns itself to the front surface of the multilayer structure when placed in contact with the surface, is the preferred method of ensuring alignment. Step  134  is followed by Step  136  in which the interferometer apparatus is used to measure the optical thickness of each of the observed layers in the multilayer structure with the low-coherence tunable light source being tuned to each of the set of k distinct center wavelengths. During step  136 , the low-coherence tunable light source is tuned to each of the set of k distinct center wavelengths. At each measurement wavelength, the variable optical path delay element  90  of the interferometer apparatus is repetitively scanned to determine the locations of the observed optical interfaces in the multilayer structure being tested. The distances between the observed locations of adjacent optical interfaces are calculated for each scan, and data for corresponding layers are averaged. TABLE 2 shows the measured average optical thickness for an example three layer structure. The set of k distinct center wavelengths used to measure the example three layer structure is shown in column 1 of TABLE 2. Columns 2-4 of TABLE 2 show the average layer thickness in micrometers (μm) for each of the observed layers in the example three layer structure measured as a function of wavelength. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Measured optical thickness of each layer in a multilayer structure at a 
               
               
                 set of k distinct center wavelengths in nanometers (nm). 
               
            
           
           
               
               
               
               
               
            
               
                   
                 nm 
                 Layer 1 
                 Layer 2 
                 Layer 3 
               
               
                   
                   
               
               
                   
                 450 
                 14556.559 
                 2313.334 
                 16928.428 
               
               
                   
                 500 
                 14439.139 
                 2295.726 
                 16819.394 
               
               
                   
                 520 
                 14395.134 
                 2287.972 
                 16779.671 
               
               
                   
                 550 
                 14345.488 
                 2279.946 
                 16733.898 
               
               
                   
                 568 
                 14324.352 
                 2275.993 
                 16713.207 
               
               
                   
                 600 
                 14286.820 
                 2270.064 
                 16676.923 
               
               
                   
                 650 
                 14235.187 
                 2261.316 
                 16628.431 
               
               
                   
                 700 
                 14198.418 
                 2254.911 
                 16593.237 
               
               
                   
                 750 
                 14166.297 
                 2250.388 
                 16567.469 
               
               
                   
                   
               
            
           
         
       
     
     Step  136  is followed by Step  138  in which the number of layers m in the multilayer structure is determined. The number of layers m in the multilayer structure is set equal to the maximum number of layers observed in Step  136 . For the example shown in TABLE 2, the maximum number of observed layers is three. Step  138  is followed by step  140  in which the measured optical thickness of each of the m layers is compared with the reference database of known material group index of refraction dispersion curves to determine if there is a best fit material for each of the m layers. 
     TABLE 3 shows group index of refraction data for six materials in the reference database of known material group index of refraction dispersion curves measured at the same set of k distinct center wavelengths, as were used to measure the example three layer structure. In general, the reference database of known material group index of refraction dispersion curves will include many more materials, but we show only these six materials to illustrate the procedure. Column 1 of TABLE 3 shows the same measurement wavelengths (λ) corresponding to those in Column 1 of TABLE 2. Columns 2-7 of TABLE 3 show the group indices of refraction for Starphire® (a low iron soda lime glass manufactured and sold by PPG Industries, Inc. of Pittsburgh Pa.), polycarbonate (PC), Borofloat® 33 glass (a borosilicate glass manufactured and sold by SCHOTT North America, Inc. of Louisville Ky.), Plexiglas® (a polymethyl methacrylate polymer manufactured and sold by Evonik Röhm GmbH of Darmstadt, Germany), thermoplastic polyurethane (TPU), and polyvinyl butyral (PVB), respectively, measured at the same set of nine wavelengths A in nanometers (nm) shown in Column 1 which were used to measure the example three layer multilayer structure (TABLE 2). 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Reference Database of Known Materials Group index of refraction example 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 λ (nm) 
                 Starphire ® 
                 PC 
                 Borofloat ®33 
                 Plexiglas ® 
                 TPU 
                 PVB 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 450 
                 1.576317 
                 1.711855 
                 1.515214 
                 1.545711 
                 1.554085 
                 1.540102 
               
               
                 500 
                 1.563301 
                 1.676538 
                 1.505010 
                 1.532056 
                 1.540571 
                 1.528118 
               
               
                 520 
                 1.558843 
                 1.664046 
                 1.501810 
                 1.527613 
                 1.534187 
                 1.523057 
               
               
                 550 
                 1.553571 
                 1.649943 
                 1.497665 
                 1.522171 
                 1.527450 
                 1.517760 
               
               
                 568 
                 1.551225 
                 1.643901 
                 1.495855 
                 1.519691 
                 1.525889 
                 1.515164 
               
               
                 600 
                 1.547017 
                 1.633606 
                 1.492583 
                 1.515411 
                 1.521523 
                 1.511143 
               
               
                 650 
                 1.541637 
                 1.620040 
                 1.488482 
                 1.509814 
                 1.514354 
                 1.505197 
               
               
                 700 
                 1.537446 
                 1.610018 
                 1.485313 
                 1.505450 
                 1.509939 
                 1.501099 
               
               
                 750 
                 1.534125 
                 1.601808 
                 1.482818 
                 1.501956 
                 1.506624 
                 1.498063 
               
               
                   
               
            
           
         
       
     
     In Step  140 , the layers which have a known best fit material are determined. During Step  140 , the optical thickness measured with the low-coherence tunable light source tuned to each of the k distinct center wavelengths, for each of the m layers, is compared to a reference database of known material group index of refraction dispersion curves measured at the same set of k distinct center wavelengths, in order to determine which layers have a best fit material in the reference database of known materials The comparison includes applying a best fit material identification algorithm to the measured optical thickness data, which utilizes the known material group index of refraction reference database to determine the best fit material, if it exists, for each of the m layers in the multilayer structure. Each of the layers of the multilayer structure having best fit materials can be identified as being composed of the best fit material for that layer. Step  140  is followed by step  142  in which the thickness of each of the identified layers is determined. 
     Further details of Step  140  are shown in  FIG. 12A  utilizing a preferred material identification algorithm. All of the Substeps  140 A- 140 D shown in  FIG. 12A  are applied to each of the m layers in the multilayer structure individually. In Substep  140 A a set of k trial thickness values is calculated for each material in the reference database of known materials group index of refraction utilizing the optical thickness data measured at each of the k distinct center wavelengths for each of the m layers in the multilayer structure. The sets of k trial thickness values for each of the m layers in the multilayer structure are calculated by dividing the measured optical thickness of the layer in the multilayer structure measured at each of the k distinct center wavelengths by the known group index of refraction at each of the k corresponding wavelengths for each known material in the reference database. At the completion of Substep  140 A, there will be a set of k trial thickness values for each known material in the group index of refraction database of known materials for each of the m layers in the multilayer structure. Substep  140 A is followed by Substep  140 B in which the mean and standard deviation (STD) of each of the sets of k trial thickness values are calculated for each of the known materials in the reference database. Substep  140 B is followed by Substep  140 C in which the material composition having the minimum standard deviation in its trial thickness is identified and selected. Substep  140 C is followed by Substep  140 D in which a set of criteria are used to determine if the material having the minimum trial thickness standard deviation can be considered to be the best fit material. If the criteria are met, the material having the minimum trial thickness standard deviation is the best fit material for that layer, but if the criteria are not met there is no best fit material in the reference database of known materials for that layer. 
     The following preferred criteria can be used to determine if the material having the minimum trial thickness standard deviation can be concluded to be the best fit material. The first criterion, shown as criterion  140 D 1  in  FIG. 12A , is that the material having the minimum trial thickness standard deviation must also have the maximum ratio of the mean trial thickness to the trial thickness standard deviation (mean/STD) for each of the known materials in the reference database. The second criterion that needs to be satisfied, shown as criterion  140 D 2  in  FIG. 12A , is to determine if the measured order of trial thickness standard deviation from minimum to maximum for all the known materials in the reference database measured for the layer matches the expected order of trial thickness standard deviation from minimum to maximum for all the known materials in the reference database for an ideal sample of known thickness of the material having minimum trial thickness standard deviation. 
     An ideal sample is defined as one which has the same measured thickness at all of the measured wavelengths. The expected order for an ideal sample for each known material in the reference database can be determined by the procedure described in  FIG. 13 .  FIG. 13  shows a flowchart  190  detailing the steps of determining the expected order of trial thickness standard deviation from minimum to maximum for all the known materials in the reference database for an ideal sample of known thickness of the material having minimum trial thickness standard deviation. First, select the material having the minimum trial thickness standard deviation and construct an ideal sample of the selected material having an ideal thickness equal to the mean trial thickness measured for that material (Step  191 ). Next, calculate the ideal optical thickness for the selected material at each of the set of k distinct center wavelengths by multiplying the ideal thickness of the selected material by the group index of refraction of the selected material at the corresponding set of k distinct center wavelengths (Step  193 ). Next, using the ideal optical thickness data, calculate ideal trial thickness values as a function of measurement wavelength for all of the materials in the reference database of known materials (Step  195 ). The sets of k ideal trial thickness values for each of the m layers in the multilayer structure are calculated by dividing the ideal optical thickness of the layer in the multilayer structure at each of the k distinct center wavelengths by the known group index of refraction at each of the k corresponding wavelengths for each known material in the reference database. Step  195  is followed by Step  197  in which the mean ideal trial thickness and ideal trial thickness standard deviations are calculated for all of the materials in the reference database of known materials. Step  197  is followed by Step  199  in which the order from minimum to maximum ideal trial thickness standard deviation for all of the known materials in the reference database is determined. The order determined in Step  199  is defined as the expected order for the ideal sample. It is also noted that the trial thickness standard deviation of the ideal sample material will always be zero (0). 
     It has been found that when a layer in a multilayer structure containing a known material is measured by the method outlined in  FIG. 12  and  FIG. 12A , it will have the minimum trial thickness STD, and the order from lowest to highest calculated trial thickness standard deviation of all of the known materials in the reference database will always be the same for that material. Only when the measured order of trial thickness standard deviation agrees with the expected order for an ideal sample of the material having minimum trial thickness standard deviation can the material comprising that layer can be properly identified (outlined in  FIG. 13 ). 
     An example follows, showing how to determine the best fit material for the first layer of the example three layer structure having the data shown in TABLE 2, using the procedure described in  FIG. 12A  and  FIG. 13 . The trial thicknesses for the first layer of the example three layer structure (column 2 in TABLE 2) are calculated by dividing the measured optical thickness at each of the k measurement wavelengths by each of the known group index of refraction of each of the materials in the reference database at each of the k corresponding wavelengths. The top portion of TABLE 4 (first 11 rows) shows the calculated trial thickness for the first layer of the example three layer structure for the six materials shown in TABLE 3. In particular, the third row of TABLE 4 is obtained by dividing the measured optical thickness of the example three layer structure measured at 450 nm by the known group index of refraction at 450 nm of each of the known materials in TABLE 3. 
     Columns 2-7 of TABLE 4 show the trial thicknesses calculated for the six known materials in the reference data base. Each successive row is calculated using the same set of measurement wavelengths from the known group index of refraction data base as used to measure the example 3 layer structure (Substep  140 A). The last four rows of TABLE 4 show mean trial thickness, trial thickness standard deviation (STD), the ratio of the mean/STD of the trial thickness for the first layer of the example three layer structure shown in rows 3-11 of TABLE 4 (Substep  140 B) and the order from minimum to maximum trial thickness standard deviation. The material in the reference database of known materials that has the minimum trial thickness standard deviation is selected as a candidate best fit material for that layer. From the data shown in TABLE 4, the candidate best fit material for the first layer of the example three layer structure can be identified as Starphire® glass (Substep  140 C). It is noted that its trial thickness standard deviation is less than 1 μm and the second lowest trial thickness standard deviation (PVB in TABLE 4) is 4 times as great. 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Layer 1 calculated trial thickness values for known materials 
               
               
                 in the reference database and their statistics. 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 λ (nm) 
                 Starphire ® 
                 PC 
                 Borofloat ®33 
                 Plexiglas ® 
                 TPU 
                 PVB 
               
               
                   
               
            
           
           
               
            
               
                 layer 1 trial thicknesses 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 450 
                 9234.537 
                 8503.385 
                 9606.930 
                 9417.389 
                 9366.641 
                 9451.687 
               
               
                 500 
                 9236.314 
                 8612.474 
                 9594.051 
                 9424.682 
                 9372.588 
                 9448.966 
               
               
                 520 
                 9234.497 
                 8650.685 
                 9585.189 
                 9423.284 
                 9382.909 
                 9451.474 
               
               
                 550 
                 9233.879 
                 8694.535 
                 9578.571 
                 9424.361 
                 9391.788 
                 9451.75 
               
               
                 568 
                 9234.219 
                 8713.632 
                 9576.033 
                 9425.835 
                 9387.545 
                 9453.995 
               
               
                 600 
                 9235.074 
                 8745.571 
                 9571.877 
                 9427.688 
                 9389.816 
                 9454.313 
               
               
                 650 
                 9233.810 
                 8786.938 
                 9563.561 
                 9428.437 
                 9400.172 
                 9457.357 
               
               
                 700 
                 9235.066 
                 8818.794 
                 9559.210 
                 9431.343 
                 9403.305 
                 9458.683 
               
               
                 750 
                 9234.121 
                 8843.943 
                 9553.635 
                 9431.901 
                 9402.673 
                 9456.409 
               
            
           
           
               
            
               
                 layer 1 trial thickness statistics 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 mean 
                 9234.613 
                 8707.773 
                 9576.562 
                 9426.102 
                 9388.604 
                 9453.848 
               
               
                 STD 
                 0.7836 
                 107.7549 
                 17.0460 
                 4.4448 
                 12.9032 
                 3.1827 
               
               
                 Mean/STD 
                 10468.340 
                 80.846 
                 559.897 
                 2132.933 
                 731.513 
                 2990.546 
               
               
                 STD order 
                 1 
                 6 
                 5 
                 3 
                 4 
                 2 
               
               
                   
               
            
           
         
       
     
     We next check that the two criteria are met. Since, it is found that the Mean/STD for Starphire® is 3.5 times larger than the second largest value. (PVB) the first criterion is met. We next calculate the expected order of trial thickness standard deviation for an ideal sample of known thickness of Starphire® as described in  FIG. 13 . It is convenient to set the ideal thickness equal to the mean thickness of the material having minimum measured trial thickness standard deviation, 9234.613 μm for Starphire® in this example. Next, calculate the optical thickness that would be measured using the mean thickness for Starphire® at each of the same set of k measurement center wavelengths. Using the ideal optical thicknesses for the Starphire® sample, we calculate a set of ideal trial thickness for all the known materials in the reference database by dividing the ideal optical thickness of the Starphire® sample at each of the set of k measurement wavelengths by the group index of refraction of each material in the reference database at each of the k corresponding wavelengths. We then determine the average ideal trial thickness and ideal trial thickness standard deviations for each of the known materials in the reference database. The expected order of ideal trial thickness standard deviation from minimum to maximum is then determined for the ideal Starphire® sample. 
     TABLE 5 shows the results of these calculations using the reference database for the same six known materials shown in Tables 3 and 4. The results shown are for an ideal sample of 9234.613 μm thick Starphire®, which is shown to have an ideal trial thickness standard deviation of 0. The bottom line in TABLE 5 shows the expected order of ideal trial thickness standard deviation from minimum to maximum for an ideal sample of Starphire®. For Starphire®, using the six known materials in the known group index of refraction database of known materials, the expected order for ideal trial thickness standard deviation minimum to maximum for all the known materials in the reference database is Starphire®, PVB, Plexiglas®, TPU, Borofloat® 33 and PC. Since the measured trial thickness standard deviation order for Starphire® shown in TABLE 4 matches the expected ideal trial thickness standard deviation order shown in TABLE 5, the second criterion is met, and we can say that the best fit material for the first layer of the example three layer structure (data shown in TABLE 2) is Starphire®. We then find that the first layer of the example three layer structure is composed of 9234.613 μm thick Starphire®, the mean trial thicknesses for the selected material. 
     
       
         
           
               
             
               
                 TABLE 5 
               
               
                   
               
               
                 Calculated ideal trial thickness values and statistics for known materials 
               
               
                 in the reference database assuming layer 1 is Starphire ®. 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 λ (nm) 
                 Starphire ® 
                 PC 
                 Borofloat ®33 
                 Plexiglas ® 
                 TPU 
                 PVB 
               
               
                   
               
               
                 450 
                 9234.613 
                 8503.454 
                 9607.009 
                 9417.466 
                 9366.717 
                 9451.765 
               
               
                 500 
                 9234.613 
                 8610.887 
                 9592.284 
                 9422.945 
                 9370.862 
                 9447.225 
               
               
                 520 
                 9234.613 
                 8650.794 
                 9585.309 
                 9423.403 
                 9383.027 
                 9451.593 
               
               
                 550 
                 9234.613 
                 8695.227 
                 9579.333 
                 9425.110 
                 9392.535 
                 9452.502 
               
               
                 568 
                 9234.613 
                 8714.004 
                 9576.441 
                 9426.237 
                 9387.946 
                 9454.399 
               
               
                 600 
                 9234.613 
                 8745.134 
                 9571.399 
                 9427.217 
                 9389.347 
                 9453.841 
               
               
                 650 
                 9234.613 
                 8787.701 
                 9564.392 
                 9429.257 
                 9400.989 
                 9458.179 
               
               
                 700 
                 9234.613 
                 8818.362 
                 9558.741 
                 9430.880 
                 9402.844 
                 9458.219 
               
               
                 750 
                 9234.613 
                 8844.415 
                 9554.144 
                 9432.404 
                 9403.174 
                 9456.913 
               
               
                   
               
               
                   
                   
                 statistics 
               
               
                   
               
               
                 mean 
                 9234.613 
                 8707.775 
                 9576.561 
                 9426.102 
                 9388.604 
                 9453.848 
               
               
                 STD 
                 0.0000 
                 107.9704 
                 16.7829 
                 4.5631 
                 13.2750 
                 3.5824 
               
               
                 STD Order 
                 1 
                 6 
                 5 
                 3 
                 4 
                 2 
               
               
                   
               
            
           
         
       
     
     Following the same procedure shown in  FIG. 12A  and  FIG. 13 , the second layer of the example three layer structure is found to be composed of 1502.2 μm thick PVB. When a layer is identified as PVB, the expected order for minimum to maximum trial thickness standard deviation is found to be PVB, Plexiglas®, Starphire®, TPU, Borofloat® 33 and PC. Similarly, the third layer of the example three layer structure is found to be composed of 11172.9 μm thick Borofloat® 33. When a layer is identified as Borofloat® 33 glass, the expected order for minimum to maximum trial thickness standard deviation is found to be Borofloat® 33, Starphire®, PVB, Plexiglas®, TPU and PC. 
     Although the interferometer apparatus and examples have been described herein as including a dual interferometer in the standard Michelson configuration it is noted that other interferometer configurations can be utilized including Mach Zehnder configurations and autocorrelator mode configurations as described in Marcus &#39;409. Also the reference interferometer can be replaced with a highly accurate optical encoder on the variable optical path delay element  90 . 
     The invention has been described in detail with particular reference to certain example embodiments thereof, but it will be rather apparent to those skilled in the art that the foregoing detailed disclosure is intended to be presented by way of example only, and is not limiting. Various alterations, improvements, and modifications will occur to those skilled in the art, though not expressly stated herein. These alterations, improvements, and modifications are intended to be suggested hereby, and are within the spirit and scope of the invention. Additionally, the recited order of processing elements or sequences, or the use of numbers, letters, or other designations therefore, is not intended to limit the claimed processes to any order except as may be specified in the claims. 
     PARTS LIST 
     
         
           10  Broadband Low-Coherence Light Source 
           11  First Low-Coherence Light Source 
           11   a  Second Low-Coherence Light Source 
           11   b  Third Low-Coherence Light Source 
           11   c  Fourth Low-Coherence Light Source 
           11   d  Fifth Low-Coherence Light Source 
           11   e  Sixth Low-Coherence Light Source 
           11   f  Seventh Low-Coherence Light Source 
           12  Variable Wavelength Tunable Filter 
           12   a  Tunable Filter 
           13  Tunable Light Source 
           13 A Tunable Light Source 
           13 B Tunable Light Source Second Section 
           14  Optical Fiber 
           15  First Dichroic Mirror 
           15   a  Second Dichroic Mirror 
           15   b  Third Dichroic Mirror 
           15   c  Fourth Dichroic Mirror 
           15   d  Fifth Dichroic Mirror 
           15   e  Sixth Dichroic Mirror 
           15   f  Seventh Dichroic Mirror 
           16  Fiber Collimator 
           18  Collimated Beam 
           18   a  Transmitted or First Part of the Low-Coherence Interference Beam 
           18   b  Reflected or Second Part of the Low-Coherence Interference Beam 
           18 F Focusing Low-Coherence Beam 
           18 R Reference Arm Collimated Beam 
           18 S Sample Arm Collimated Beam 
           19  Second Collimated beam 
           19   a  First Part of the Second Low-Coherence Interference Beam 
           19   b  Second Part of the Second Low-Coherence Interference Beam 
           20  Polarizing Beam Splitter 
           20   a  Second Polarizing Beam Splitter 
           21  Wavelength Division Multiplexer 
           22  Quarter Wave Plate 
           22   a  Second Quarter Wave Plate 
           23  Fiber Collimator 
           24  Beam Splitter 
           25  Combined Collimated Beam 
           25   a  First Combined Low-Coherence Interference Beam 
           25   b  Second Combined Low-Coherence Interference Beam 
           25 R Reference Arm Combined Collimated Beam 
           25 S Sample Arm Combined Collimated Beam 
           26  Sample Arm Lens 
           28  Multilayer Structure 
           28   a  First Layer 
           28   b  Second Layer 
           28   c  Third Layer 
           28   d  Fourth Layer 
           28   e  Fifth Layer 
           30  Reference Arm Lens 
           32  Reference Mirror 
           32 L Laser Reference Mirror 
           34  Mirror 
           35  Mirror 
           36  Mirror 
           37  Mirror 
           38  Balanced Detector 
           38   a  First Detector 
           38   b  Second Detector 
           39  Second Balanced Detector 
           39   a  First Detector 
           39   b  Second Detector 
           40  Laser 
           42  Collimated Laser Beam 
           42 C Laser Interference Beam 
           42 R Reference Arm Collimated Laser Beam 
           42 S Sample Arm Collimated Laser Beam 
           44  Mirror 
           46  Beam Splitter 
           48  Mirror 
           50  Detector 
           52  Fiber Collimator 
           53  Fiber Collimator 
           54 S Sample Arm Optical Fiber 
           54 R Reference Arm Optical Fiber 
           57  Optical Probe 
           60  Portable Optical Probe 
           57   s  Optical Probe Mounting Surface 
           58 A Fiber Collimator 
           58 B Fiber Collimator 
           62  Laser Interference Signal 
           70  Zero-Crossings 
           71  Low-Coherence Interferometer Scan 
           71  First Optical Interface Location 
           72  Second Optical Interface Location 
           73  Third Optical Interface Location 
           74  Fourth Optical Interface Location 
           75  Fifth Optical Interface Location 
           76  Sixth Optical Interface Location 
           78  Cavity 
           80  Measurement Cell 
           82  Sample 
           82 A Three layer Sample 
           84  Top Flat 
           86  Bottom Flat 
           88  Spacer 
           90  Variable Optical Path Delay Element 
           100  Interferometer Apparatus 
           100 A Interferometer Apparatus 
           100 B Interferometer Apparatus 
           100 C Interferometer Apparatus 
           100 D Interferometer Apparatus 
           100 E Interferometer Apparatus 
           100 F Interferometer Apparatus 
           110  Low-Coherence Interferometer 
           110 A Low-Coherence Interferometer 
           110 B Low-Coherence Interferometer 
           110 C Low-Coherence Interferometer 
           110 D Low-Coherence Interferometer 
           110 E Low-Coherence Interferometer 
           110 F Low-Coherence Interferometer 
           120  Laser Interferometer 
           130  Flow Chart 
           132  Step 
           134  Step 
           136  Step 
           138  Step 
           140  Step 
           140 A Substep 
           140 B Substep 
           140 C Substep 
           140 D Substep 
           140 D 1  Criterion 
           140 D 2  Criterion 
           142  Step 
           150  Flow Chart 
           152  Step 
           154  Step 
           156  Step 
           158  Step 
           160  Step 
           162  Step 
           164  Step 
           170  Flow Chart 
           172  Step 
           174  Step 
           176  Step 
           178  Step 
           180  Step 
           182  Step 
           184  Step 
           186  Step 
           190  Flow Chart 
           191  Step 
           193  Step 
           195  Step 
           197  Step 
           199  Step