Abstract:
Faults, dimensions and other characteristics of a material or structure are sensed by a coherent beam&#39;s reflection from the material during ultrasonic or very fast vibration. The reflected beam acquires a phase substantially different from its original phase and from the phase of a reference beam split from the common source beam. The reflected beam and the reference beam are superimposed by diffraction in a photorefractive polymer composite adaptive holographic beamsplitter, and the superimposed beams are detected by a photodetector capable of detecting small interference changes from ultrasonic surface displacements or perturbations. An apparatus and method defining an improved homodyne interferometer for performing the method is described.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    The present invention relates to the art of detecting faults and other characteristics in materials, and more particularly to methods and apparatus for detecting faults and other characteristics in ultrasonically vibrated test material using homodyne interferometers.  
           [0003]    2. Background of the Invention  
           [0004]    Laser ultrasonic receivers based on optical homodyne interferometers have been investigated for some years. Such receivers have been used and proposed for the examination of materials, such as, for example, investigating transient body transformations, inspecting materials such as metals and ceramics at high temperatures for process and quality control, detecting flaws as soon as they are created, measuring production parameters such as thickness and temperature, and determining microstructural properties on-line such as grain size, porosity and the like. In early research, it was realized that a homodyne interferometer could not operate effectively with the speckled beams that result from reflecting from rough surfaces. Furthermore, such early homodyne interferometers could not compensate for aberrations in the signal beam wavefront resulting from slow, dynamic environmental disturbances.  
           [0005]    Time-delay or self-referencing interferometers have been developed, such as the confocal Fabry-Perot which allow the processing of light scattered from rough surfaces with a large field of view. Usually, a phase modulated signal beam is derived from a probe beam scattered or reflected from a vibrating test surface. This beam is demodulated by the slope of the transfer function, which is the transmission versus frequency, of the confocal Fabry-Perot. As a self-referencing or time-delay interferometer, the confocal Fabry-Perot has the ability to process speckled beams from imperfect surfaces. In addition, the particular mirror curvature of the confocal Fabry-Perot provides a much larger field of view than a Fabry-Perot with flat mirrors. The operation of the confocal Fabry-Perot is described in, for example, U.S. Pat. No. 4,659,224. However, the confocal Fabry-Perot requires stabilization of the interferometer length to a fraction of an optical wavelength, thereby adding complexity and cost to the receiver.  
           [0006]    The transmitted signal from a confocal Fabry-Perot is proportional to the amplitude of the Doppler shift of the signal beam frequency upon scattering from a vibrating surface. For constant displacement, the Doppler shift decreases with frequency. As a result, the confocal Fabry-Perot does not work well at low ultrasonic frequencies below approximately one megahertz (1 MHz). Solutions to such problems and limitations have been proposed. See, for example, U.S. Pat. No. 5,131,748 to Monchalin and Ing, where the beam that probes the vibrating surface is caused to interfere inside a photorefractive material with a reference or pump beam, resulting in these two beams diffracting in each other&#39;s direction with a common path and a common wavefront. An electrical signal dependent on phase excursions or perturbations in the reflected or scattered beam produced by the surface vibration is then obtained by a photodetector in one of these paths. For the correct static phase difference between the wavefronts of the two interfering beams, the electrical signal is linearly proportional to the phase excursion and thus to the surface deflection. The photorefractive material acts in effect as a real-time hologram providing an exact overlap of the reference beam with the signal beam for later coherent detection and it compensates for low frequency dynamic environmental distortions in the signal wavefront. However, most materials used previously do not have both a fast response time and a large diffraction efficiency which is desired for uses in many applications. Such systems also do not operate well at low signal beam light levels produced when scattering from a rough surface, as is typical for many workpieces.  
           [0007]    It is still desired further to provide a homodyne interferometer that will have the capability of processing speckled returns from the workpiece with a high field-of-view or étendue. It is desired yet further to obtain an homodyne interferometer having an adaptive holographic beamsplitter which can be fabricated more easily, with greater flexibility and is capable of being fabricated more rapidly and at lower cost. It is a desired object, further, to provide an homodyne interferometer where large coefficients of coupling can be selected and obtained by the application of practical values of electric fields applied across an adaptive beam splitter. It is yet further desired to provide an homodyne interferometer in which the application of a controlled electric field across the adaptive beamsplitter alters and controls the spatial phase of the index grating in the beam splitting element to allow coherent detection in the linear regime. It is still further desired to provide an homodyne interferometer having an adaptive beamsplitter element in which the absorption under typical operating conditions can be set to a low value. It yet still further desired to provide an homodyne interferometer having an adaptive beamsplitter which can be easily processed into a variety of shapes and forms.  
         SUMMARY  
         [0008]    In brief, in accordance with one aspect of the present invention, a coherent, polarized light beam is split, one of the beams being used as a reference beam. The other beam is reflected or scattered from a surface of the material which is vibrated by an ultrasonic frequency source. The reflected beam has its phase shifted in proportion to the surface deflection or perturbation and is impinged on the surface of a photorefractive polymer composite-adaptive holographic beamsplitter. The reference beam is also impinged onto the surface of the polymer composite adaptive holographic beamsplitter to create effectively an interference of the two beams, resulting in a refractive index grating. This grating causes the beams to diffract into each other, so that the original beam and the diffracted beam are co-propagating and have identical wavefronts. The beam with superposed wavefronts is received by a photodetector which senses the high frequency dynamic phase difference between the two beams and produces a signal representative of the perturbations of the vibrating test surface.  
           [0009]    Using the photorefractive polymer composite, the resulting homodyne interferometer has a surface displacement sensitivity which is close to the ideal value. Response times on the order of approximately one millisecond have been measured, thus allowing the receiver to compensate for wavefront disturbances with bandwidths up to approximately one kilohertz (kHz). In addition, this performance can be achieved for values of device absorption as low as ten percent (10%). The polymer composite material adaptive beamsplitter is more versatile in design capabilities, and can be fabricated in less than a day.  
           [0010]    Other novel features which are believed to be characteristic of the invention, both as to organization and methods of operation, together with further objects and advantages thereof, will be better understood from the following description in which preferred embodiments of the invention are described by way of example.  
       
    
    
     DESCRIPTION OF THE DRAWINGS  
       [0011]    [0011]FIG. 1 is a schematic view showing diagramatically the paths of the signal and reference beams from generation to detection;  
         [0012]    [0012]FIG. 2 is a schematic view of beam paths through the holographic element of FIG. 1 showing the beam paths in component detail;  
         [0013]    [0013]FIG. 3 is a schematic perspective view of a multiple quantum well beamsplitter showing the interference of the two beams;  
         [0014]    [0014]FIG. 4 is a schematic top or plan view of the multiple quantum well beamsplitter of FIG. 3;  
         [0015]    [0015]FIG. 5 is a cross-sectional view showing the layers of a multiple quantum well structure of the completed holographic element of the preferred embodiment of the present invention taken along the view of line  5 - 5  of FIG. 3;  
         [0016]    [0016]FIG. 6 is a cross-sectional view showing the layers of the multiple quantum well structure of the preferred embodiment of the present invention as shown in FIG. 5 after film growth and before further fabrication;  
         [0017]    [0017]FIG. 7 is an exploded cross-sectional view taken along line  7 - 7  of FIG. 3 showing schematically the intensity and diffraction grating patterns within the holographic element;  
         [0018]    [0018]FIG. 8 is a schematic perspective of a composite polymer beamsplitter showing the interference of two beams;  
         [0019]    [0019]FIG. 9 is a schematic top or plan view of the composite polymer beamsplitter of FIG. 15;  
         [0020]    [0020]FIG. 10 is a detailed cross sectional blow-up of the holographic element of FIGS. 8 and 9 showing the development of gratings and the passage of light beams;  
         [0021]    [0021]FIG. 11 is a plot showing the measured coupling coefficients as a function of applied electric field for p-polarized light with an inset showing the measured absorption coefficient α as a function of wavelength λ;  
         [0022]    [0022]FIG. 12 is a plot showing the relative surface displacement sensitivity as a function of the imaginary coupling strength γ I L, for various values of α/γ I , the ratio of the absorption coefficient to the imaginary part of the coupling coefficient; and,  
         [0023]    [0023]FIG. 13 shows the transmitted ultrasonic signal and its echoes in a fused quartz mirror with a wideband transducer bonded to its rear surface.  
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0024]    Referring initially to FIG. 1 of the accompanying drawings where reference numerals correspond to like numerals used in this specification, the reference-beam interferometer two-wave mixing receiver  10  of the preferred embodiment includes a laser generator  12  which generates as its output a coherent light beam  14 . The light beam  14  is directed in the direction of the adjacent arrow by mirror  16  to beamsplitter  18  which divides the beam  14  into a reference beam  20  passing through the splitter  18  and into a probe beam  24  directed toward the workpiece or material  26  to be examined. The reference beam  20  is directed by mirror  22  for superposition with the signal wave, as will be described in greater detail below. The probe beam  24  will be reflected or scattered from the normally rough surface  28  as the return signal beam  32  traveling back along its incident path.  
         [0025]    The surface  28  of the workpiece is vibrated ultrasonically as a result of a pulsed laser  30 . The pulsed laser  30  produces a momentary light beam  31  impinging the workpiece  26  to generate an ultrasonic wave that travels through the workpiece  26  to result in a vibration of the workpiece surface  28 .  
         [0026]    The vibration or displacement of the workpiece surface  28  will impart phase perturbations on the probe beam  24  when it is reflected back as the return signal beam  32 . In addition, the rough surface of the workpiece  26  and turbulence in the optical beam path will cause spatial wavefront distortions on the return signal beam  32 .  
         [0027]    The distorted return signal beam  32  is guided toward the real-time holographic element  36 . The return signal beam  32  is combined or superposed with the reference beam  20  in the holographic element  36 , which results in two output beams  40 ,  44 . The superposition of at least parts of the distorted return signal beam  32  and the reference beam  20  form, as the output, the beam  40 , which is directed to the photodetector  46 .  
         [0028]    The difference in the cumulated path length of beam  20  and the path length of beams  24  and  32  between the beamsplitter  18  and the receiving surface of the holographic element  36  should be less than the coherence length of the laser generator  10 .  
         [0029]    Referring to FIG. 2, the effect of the holographic element  36  on the incident beams  20 ,  32  is shown in greater detail. The reference beam  20  is partially diffracted as beam  20 ′ and superposed on the distorted beam  32  which is partially transmitted as beam  32 ′. The superposed components of the partially diffracted reference beam  20 ′ and the partially transmitted signal beam  32 ′ have identical paths and comprise the resultant beam  40  directed to the photodetector  46 . The incident reference beam has planar wavefronts  21 , while the incident distorted signal beam  32  has distorted wavefronts  33 . The resultant beam  40  will have overlapped wavefronts  41  with the same distortion of wavefronts  33 . The incident reference beam  20  is also partially transmitted through the holographic element  36  as component beam  20 ″, while the incident distorted beam  32  is partially diffracted by the element  36  as component beam  32 ″. The component beams  20 ″,  32 ″ have identical paths and comprise the resultant beam  44 . The resultant beam  44  will have overlapped planar wavefronts  45 .  
         [0030]    Referring to FIG. 3, a perspective view of the structure of the photorefractive, holographic adaptive beamsplitter element  36  as a multiple quantum well structure can be seen in greater detail. The element  36  consists of the semiconductor structure  58  with metal electrodes  52 ,  54  mounted on a supporting substrate  82  a few millimeters (mm) thick. The substrate  82  may be sapphire, glass or a pyrex material, as is commonly used. The semiconductor structure  58  has a first electrode  52  and a second electrode  54  at opposite ends of the incident surface  60 , best seen in FIG. 4, which is a top or plan view of the holographic element  36  of FIG. 3. A potential field  37  is maintained across the structure  58  between the electrodes  52 ,  54  by a direct current power supply  61 . Between the electrodes  52 ,  54  a portion of the semiconductor structure  58  is exposed to form the incident surface  60 . The surface  60  of the semiconductor structure  58  receives the incident beams  20 ,  32 . A centerline  62  indicating the line normal to the surface  60  is also shown.  
         [0031]    The incidence of the two beams  20 ,  32  onto the surface  60  of the element  36 , referring again to FIGS. 3, 4, results in the intensity grating planes  64 , caused by the interfering beams. The intensity grating creates the diffracton grating, shown schematically by the evenly dashed lines,  65 , in FIG. 3.  
         [0032]    [0032]FIG. 5 shows a cross-sectional view of the holographic element  36  comprising the semiconductor structure  58 , electrodes  52 ,  54  and supporting substrate  82 . As seen in FIG. 5 the semiconductor structure  58  is supported on the substrate  82  using a transparent nonconductive epoxy  83 . Specifically shown in FIG. 5 is the supporting substrate  82  and epoxy  83  supporting a first layer  80  consisting of 1500 Angstroms of 10% aluminum gallium arsenide (Al 0.1 Ga 0.9 As). The next layer  78  is the active photoconductive electro-optic layer and consists of an eighty-five period multiple quantum well structure consisting of alternating layers of 75 Angstrom thick gallium arsenide (GaAs) quantum wells and 100 Angstrom thick 10% Al 0.1 Ga 0.9 As barriers. The next layer  76  consists of 10% aluminum gallium arsenide (Al 0.1 Ga 0.9 As) of approximately 2500 Angstroms thickness. The next layer  74  consists of GaAs at approximately 100 Angstrom thickness. The GaAs layer  74  now forms the top layer of the semiconductor structure  58  and comprises the surface  60  facing the incoming wavefronts  20 ,  32  (best seen in FIGS. 3, 4).  
         [0033]    The method of fabricating the semiconductor structure  58  comprises an epitaxial growth of multiple layers by molecular beam epitaxy, best illustrated in FIG. 6. Beginning with an epitaxial-ready gallium arsenide substrate  50  which is approximately 0.5 millimeter (mm) thick, a first layer  68  of gallium arsenide (GaAs) approximately 5000 Angstroms thick is grown. This layer  68  is useful to planarize the surface to ensure good epitaxial crystal growth. Next, a second layer  70  of 50% aluminum gallium arsenide (Al 0.5 Ga 0.5 As) is grown approximately for 5000 Angstroms. This layer is used as an etch stop layer during wet chemical etching (19 parts hydrogen peroxide and 1 part ammonium hydroxide) in device fabrication. A third layer  72  of aluminum arsenide (AlAs) is then grown for approximately 200 Angstroms. This layer  72  serves as a lift-off layer during device fabrication which is etched off during a 50% hydrofluoric acid etch in order to form an optically flat surface.  
         [0034]    Next a fourth layer  74  of GaAs is grown for approximately 100 Angstroms. This layer  74  plays a role in the fabrication procedure of the final device, which is the stop etch layer for the 50% hydrofluoric acid etch and also acts as a passivation layer of the final device, the photorefractive multiple quantum well, real time holographic element  36 . A fifth layer  76  of 10% aluminum gallium arsenide (Al 0.1 Ga 0.9 As) of approximately 2500 Angstroms thickness is grown next. This spacer layer  76  is used to control the thickness of the device to set the preferred Fabry-Perot condition, to enhance the diffractive performance of the holographic element  36  without changing the optical properties of the active layer  78 . A sixth layer  78  comprises an eighty-five period multiple quantum well structure consisting of 75 Angstrom thick GaAs quantum wells and 100 Angstrom thick 10% aluminum gallium arsenide (Al 0.1 Ga 0.9 As) barriers. This multiple quantum well layer  78  forms the active photoconductive electro-optic layer of the holographic element  36 . A seventh layer  80  is grown to approximately 1500 Angstroms consisting of 10% aluminum gallium arsenide (Al 0.1 Ga 0.9 As).  
         [0035]    Characteristics of the multiple quantum well (MQW) can be modified by varying the thickness and/or material composition of the various layers as desired.  
         [0036]    The as-grown structure  86  is proton implanted from the top surface  84  of layer  80  at different energies and doses to control the number and profile of defects created in the active electro-optic layer  78 . The structure  86  is then cleaved into approximately 2 mm×2 mm squares, and mounted at its top surface  84  as seen in FIG. 5, that is the end having the layer consisting of Al 0.1 Ga 0.9 As to a supporting substrate  82  (FIG. 4) using a transparent nonconductive epoxy  83 .  
         [0037]    The GaAs substrate  50  is lapped using fine alumina grit to a thickness of 100 microns. The structure  86  is then subjected to a wet chemical etch consisting of 19 parts hydrogen peroxide and 1 part ammonium hydroxide. This etch removes the remaining GaAs substrate  50  and the 5000 Angstrom GaAs epilayer  68 . The etch stops somewhere in the etch stop layer  70  of Al 0.5 Ga 0.5 As. The structure  86  is then subjected to a 50% hydrofluoric acid solution which removes the remaining Al 0.5 Ga 0.5 As layer  70  and the AlAs layer  72 , resulting in an almost optically flat surface of layer  74 , which becomes the surface  60 . The electrodes  52 ,  54  are then evaporated on the surface  60  (best seen in FIGS. 3, 4,  5 ) with an interelectrode spacing of approximately 1 mm.  
         [0038]    [0038]FIG. 7 shows in an exploded view the patterns of the intensity grating  64  and the complex diffraction grating  65  in the structure  58 . The intensity grating is shown schematically by the solid lines  64 . The diffraction grating is shown by the dashed lines  65 .  
         [0039]    In operation, the photorefractive multiple quantum well, real-time holographic element  36  acts as an adaptive beamsplitter matching the wavefronts of the return signal  32  and the reference beam  20 . The return signal  32  acquires a phase perturbation relative to the phase of the reference beam  20  caused by the ultrasonic vibration of the surface  28 .  
         [0040]    When the reference beam  20  and the return signal beam  32  interfere in the photorefractive multiple quantum well holographic element  36 , they produce a complex refractive index and absorption grating  65  that records the spatial phase profile of the return signal beam  32 . This holographic recording and subsequent readout process yields an output beam  40  that is a composite or superposition of the partially transmitted signal beam  32 ′ and the partially diffracted reference beam  20 ′. The holographic combination of these beams insures that they have precisely overlapped wavefronts.  
         [0041]    The separate beams  20 ′,  32 ′ that contribute to the composite beam  40  have a static relative longitudinal phase difference apart from the phase perturbation acquired by the return signal  32  from the ultrasonic vibration of the workpiece surface  28 . The static relative longitudinal phase depends on the design of the holographic element  36 , on the applied electric field (E)  37  and on the chosen wavelength on the beam  14  from light source  12 . These factors determine a spatial shift of the complex grating  65  in the element  36  relative to the optical interference pattern  64  created by the return beam  32  and the reference beam  20 . This spatial shift contributes to the static relative longitudinal phase of the separate beams  20 ′,  32 ′ that contribute to the composite beam  40 . Specifically, this static relative longitudinal phase is equal to the photorefractive phase shift plus or minus the wavelength-dependent phase of the signal  20 ′ diffracted by the complex grating, plus or minus 90 degrees.  
         [0042]    Optimally, the static relative longitudinal phase is adjusted in operation such that it is as close as possible to the 90 degree quadrature condition. However, good detection using the principles of this invention is achieved with shifts in the ranges of from 30 degrees to 150 degrees, and from 210 degrees to 330 degrees. In any case, no path-length stabilization is required to maintain this condition as with a conventional interferometer system.  
         [0043]    One unique feature of the preferred embodiment of the present invention is the ability to produce the required value of the relative phase by adjusting the applied electric field  37  or by adjusting the wavelength of the laser beam  14 .  
         [0044]    The relative longitudinal phase for the superposed output beam  40  is independent of any wavefront changes on the input beams  20 ,  32  due to turbulence, vibrations and the like as long as the wavefront changes occur on a time scale that is slow relative to the grating buildup time. The grating buildup time, as used in this specification, is the time required for the amplitude of the refractive index and absorption gratings to reach a given fraction of its final steady-state value. The changes that occur very rapidly, such as the perturbations modulated on the return distorted signal beam  32  as a result of the ultrasonic vibrations of the workpiece surface  28 , will be transferred to the output beam  40  and be detected by the detector  46 . It has been found that a suitable detector  46  may be a Model 1801 provided by New Focus, Inc. of Santa Clara, Calif.  
         [0045]    As described above, the homodyne interferometer constructed of the photorefractive quantum wells operates by combining two coherent laser beams consisting of the signal beam  32  and the reference beam  20 . Their interference pattern  64  is converted into a complex diffraction grating  65  in the photorefractive quantum well layer  78 . The diffraction grating  65  is composed of changes in both the refractive index and the absorption. The periodicity of the diffraction grating  65  matches the periodicity of the interference intensity pattern  64  generated by beams  32  and  20 . However, the complex diffraction grating  65  is generally shifted relative to the intensity pattern  64 . This spatial shift of the gratings is described in terms of the photorefractive phase shift φ 0 .  
         [0046]    A key parameter that allows different homodyne interferometers to be compared is the signal-to-noise ratio of the laser-based ultrasound device. The signal-to-noise ratio defines the smallest surface displacement that can be detected above the noise level for a defined detection bandwidth and for a defined power level on the detector.  
         [0047]    For the embodiment of the homodyne interferometer described here, the signal is determined by a complex phase shift of the electromagnetic wave after traversing the thin semiconductor film. The complex phase shift is  
               δ   K     =           2      π                     n   K          (   λ   )          L                    λcos                   θ   ′         +     i              α   K          (   λ   )          L       2      cos                   θ   ′                     (   1   )                               
 
         [0048]    where λ is the wavelength, L is the thickness of the active layer  78 , θ′ is the angle between the direction of propagation and the surface normal, η K  is the wavelength-dependent K-th Fourier coefficient of the refractive index grating and α K  is the K-th Fourier coefficient of the absorption grating in the device, where K=±1,0 are the grating vectors of interest in two-wave mixing.  
         [0049]    This complex phase shift modulates the amplitude and phase of the reference wave  20  causing it to partially diffract in the direction of the signal beam  32 . The copropagating partially diffracted wave  20 ′ and the partially transmitted signal beam  32 ′ together comprise the beam  40  that reaches the photodetector  46 .  
         [0050]    Homodyne detection occurs because there is a phase relationship between the partially diffracted reference beam  20 ′ and the partially transmitted signal beam  32 ′. The superposed beam  40  is given by  
                 E   40     =         E   32        exp                   (     i                   δ   o       )       +       1   2          δ   1          E   20        exp                   i        (       δ   o     +     φ   o     +         4      π     λ          d        (   t   )         +     π   2       )             ,           (   2   )                               
 
         [0051]    where E 40  is the amplitude of the combined beam after leaving the holographic element  36 , E 32  is the amplitude of the signal beam incident on the holographic element  36 , E 20  is the amplitude of the reference beam incident on the holographic element  36 , φ 0  is the photorefractive phase shift defined by the spatial shift of the optical gratings relative to the intensity pattern, and d(t) is the time-dependent surface displacement of the workpiece surface  28 .  
         [0052]    The combined beam  40  can be expressed as  
               E   40     =     exp                     (     i                   δ   o       )     [       E   32     +          γ             E   20        exp                   i   (       φ   o     +     β        (   λ   )       +         4      π     λ          d        (   t   )         +     π   2       ]                     (   3   )                               
 
         [0053]    where  
               β        (   λ   )       =       tan     -   1            [       λ     4      π                α   1          (   λ   )           n   1          (   λ   )           ]               (   4   )                               
 
         [0054]    is a phase associated with the relative contributions of the index and absorption gratings to the beam  40 , and  
                    γ        (   λ   )            =           (       π                     n   1          (   λ   )          L       λcos                   θ   ′         )     2     +       (           α   1          (   λ   )          L       4      cos                   θ   ′         )     2                 (   5   )                               
 
         [0055]    is the magnitude of the coupling efficiency between the two beams  20  and  32 .  
         [0056]    The optimal homodyne detection occurs when the total relative longitudinal phase of partially transmitted signal beam  32 ′ relative to the partially diffracted reference beam  20 ′ is equal to π/2. From Equation(3) this condition is satisfied when  
         φ 0 =−β(λ)  (6) 
         [0057]    This condition satisfies the requirements for linear detection of the surface displacement d(t).  
         [0058]    The photorefractive phase shift φ 0  of the photorefractive quantum wells is a function of the applied electric field, the fringe spacing, the wavelength or the defect density. The unique feature of the photorefractive quantum wells is that condition of Equation (6) can always be satisfied for any photorefractive phase shift φ 0  by tuning the wavelength λ around the excitonic resonances.  
         [0059]    Using the above relations we can write an expression for the total power in the combined beam  40  incident on the detector:  
                 P   40     =       [              E   32          2     +            γ        2                 E   20          2       +     2           γ             E   20          E   32        sin          4      π     λ          d        (   t   )           ]          exp        (       -     α   o          L     )           ,           (   7   )                               
 
         [0060]    where α 0  is the static value of the absorption coefficient. If we assume that |γ|&lt;&lt;1 and write d(t)=d 0 cos(ωt), then  
               P   40     =       [              E   32          2     +     2           γ             E   20          E   32            4      π     λ          d   o        cos                   (     ω                 t     )         ]        exp                     (       -     a   o          L     )     .               (   8   )                               
 
         [0061]    As expected from the principles of coherent detection, the introduction of a sinusoidal phase modulation produces an amplitude-modulated signal at the photodetector.  
         [0062]    Using similar concepts, the signal-to-noise ratio (S/N) is given by  
                 S   N     =         η        (     Δ                   P   40       )       /   hv             η                   P   32                 -     α   o          L         hv          (     Δ                 f     )             ,           (   9   )                               
 
         [0063]    where η is the quantum efficiency, ΔP 40  is the magnitude of the time-varying portion of the transmitted power [given by the second term in Equations (7) and (8)], hv is the photon energy, and Δf is the detection bandwidth. Substituting for ΔP 40 , we find  
               S   N     =             η                   P   20                      hv        (     Δ                 f     )                     -         α   o        L     2                   γ        (   λ   )                   4      π     λ          d        (   t   )                 (   10   )                               
 
         [0064]    Another commonly used parameter used to characterize a laser ultrasonic receiver is the minimum detectable surface displacement amplitude d min , expressed in Angstroms times the square root of W/Hz. This parameter corresponds to the minimum detectable displacement (for which S/N=1) for 1 watt (W) incident power and 1 Hertz (Hz) detection bandwidth. With this definition, the minimum detectable surface displacement amplitude can be written as  
                 d   min          (   λ   )       =       λ     4      π              hv   η            1          γ        (   λ   )                 exp                   (         a   o        L     2     )               (   11   )                               
 
         [0065]    where the minimum detectable displacement (d min ) is a function of wavelength and is a minimum near the center wavelength of the exciton transitions. For the structure described in the Example given below, the projected value at the peak of the curve is approximately d min =2.9×10 −6  Å (W/Hz) ½ . We have extended this same calculation to a structure with 30% aluminum barriers, for which we find d min =5.5×10 −7  Å (W/Hz) ½ . This value is substantially better than the value for a confocal Fabry-Perot interferometer in transmission, but with a broader bandwidth and without the requirement for length stabilization.  
         [0066]    We have found several advantages when using a polymer composite as a bulk photorefractive, holographic beamsplitter element in such an interferometer. First, a polymer composite allows for large coupling coefficients at practical values of the applied electrical field E o . Further, an applied field alters the spatial phase of the index grating in the polymer composite which allows coherent detection in the linear regime. As another advantage, the device absorption under typical operating conditions can be low.  
         [0067]    As has been discussed by P. Delaye, et al., in the  Proc. SPIE  (1996) v. 2782, at p. 464, et seq., the importance of the sensitivity as a figure of merit can be seen by first considering the detection process for an ideal, plane-wave homodyne interferometer in the shot noise limit. In such a case, the signal-to-noise ratio is given by the following equation:  
                 S   N     =       (         2                 η                 P       hv        (   BW   )           )        Δ       ,           (   12   )                               
 
         [0068]    where η is the detector quantum efficiency, P is the signal beam power at the entrance to the detector, h is Planck&#39;s constant, v is the optical frequency, BW is the electronic bandwidth and Δ is the rms phase excursion in radians. If the phase excursion results from the interrogation of a vibrating surface at normal incidence, then Δ=(4π/λ)d, where λ is the optical wavelength and d is the rms surface displacement amplitude. In this case, Equation 12 becomes:  
               S   N     =       (         2                 η                 P       hv        (   BW   )           )          (       4      π     λ     )          d   .               (   13   )                               
 
         [0069]    For an ideal homodyne interferometer, an expression for the minimum detectable surface displacement is derived from Equation 13 to be:  
               d   lim   ideal     =       (     λ     4      π       )            hv     2      η                   (   14   )                               
 
         [0070]    We find at this limit, that d lim   ideal =2.7×10 −7  Å (W/HZ) ½  at a wavelength of 670 nm, with η=0.63. By comparison, the sensitivity for a confocal Fabry-Perot (“CFP”) in transmission is approximately 3×10 −6  Å (W/Hz) ½ , that is, the CFP is approximately ten times less sensitive than the ideal homodyne limit.  
         [0071]    We define above an amplitude coupling coefficient γ. This parameter is used in the wave equations which determine the distribution of amplitude and phase between the two beams  20 ,  32 , and is introduced as an exponential propagation factor (γz). The coupling coefficient is complex and is thus written as γ=γ R +iγ I . For a pure index grating, the real part of γ gives rise to energy transfer, while the imaginary part of γ gives rise to phase coupling. The magnitude of γ is determined by the space charge field and the electro-optic response. The spatial phase of γ is determined by the charge transport mechanism. When γ is purely imaginary (γ=γ I ), the grating spatial phase is 0° and we have the ideal condition for linear detection. Even where there is a contribution from the real part of γ and the phase is not 0°, the linear signal still dominates as long as γ I  does not equal zero.  
         [0072]    With these definitions, the signal-to-noise ratio in the shot-noise limit for a homodyne receiver based on two-wave mixing is given by:  
                 S   N     =           2      η                 P       hv        (   BW   )                (       4      π     λ     )        exp                   (     -       α                 L     2       )        sin                   (       γ   I        L     )        d       ,           (   15   )                               
 
         [0073]    where α is the power absorption coefficient and L is the sample thickness. In such a case, the noise-equivalent surface displacement amplitude is:  
               d   lim     =       λ     4      π                  hv     2      η              [         exp        (       α                 L     2     )       /   sin                     (       γ   I        L     )       ]       .               (   16   )                               
 
         [0074]    The term in brackets in Equation 16 contains all material-related parameters. By comparison with Equation 14, it can be seen that we can approach the classical homodyne limit for low absorption and for γ I L approaching or approximating π/2. It has been calculated by P. Delaye, et al.,  Proc. SPIE  (1996),v. 2782, p.464 et seq., that sensitivity values within a factor of two of the classical limit can be obtained where α/γ I  is less than or equal to 0.5. For this limit, a favorable and tolerant condition exists for photorefractive polymer composites characterized by values of α/γ I  on the order of 0.01 at 676 nm for an applied field of 60 V/μm. At shorter wavelengths, the absorption coefficient rises rapidly, yielding faster response times. Even at shorter wavelengths, a considerable increase in the absorption coefficient (a) can be tolerated without violating the condition α/γ I &lt;0.5.  
         [0075]    By selecting different constituent materials of the polymer composite, it is possible to optimize several physical properties for photo-refractivity, such as, for example, photosensitivity, photo-conductivity and electro-optic response. By selection of the constituent materials, suitable polymer composites can be made with lower costs and quick synthesis, and can be easily processed into a variety of different shapes and forms.  
         [0076]    Referring again to FIG. 1 of the drawings, a homodyne, reference beam interferometer  10  includes, as in the preferred embodiment, a laser generator  12  which generates as its output a polarized, coherent light beam  14  directed by mirror  16  to a beamsplitter  18 . The beamsplitter  18  divides the beam  14  to create a reference beam  20  and a probe beam  24 . The reference beam  20  passes through the beamsplitter  18  to be directed by mirror  22  toward the holographic element  36 . The probe beam  24  is directed by the beamsplitter  18  as beam  24  to the workpiece  26 , at its surface  28 . Surface  28  is normally rough so that the reflected beam  32  from or off of it is speckled and will have spatial wavefront distortions. Again, the workpiece  28  is vibrated at ultrasonic frequencies by pulsed laser  30  impinging the workpiece through its output beam  31 , as explained above. The vibration of the workpiece surface  28  will impart a phase perturbation on the speckled reflection signal beam  32 . The beams  30 ,  32  are directed or guided, as explained above, as is normally done by mirrors or lenses to the holographic element  36 , resulting in two output beams  40 ,  44 , one of which will be guided toward and detected by detector  46 , all as will be explained in greater detail below.  
         [0077]    The signal beam  32  and the reference beam  20  will be diffracted in the holographic element  36  with a result similar to that shown in FIG. 2. The signal beam  32 , having the distortions  33  will pass through the holographic element  36  with part of the beam  32 ′ being passed directly as a component part  32 ′ of beam  40 , having the distortion in its wavefront  41 . Part of the signal beam  32  will be diffracted as component part  32 ″ of beam  44  having planar wavefronts  45 . Similarly, the reference beam  20  will have part of its beam passed directly through the holographic element  36  resulting as a component part  20 ″ of beam  44  having its composite wavefront  45  planar. Part of the reference beam  20  will be diffracted and become a component part  20 ′ of the beam  40  having the distortions in its wavefront  41 .  
         [0078]    As better seen in the perspective view of FIG. 8 and the plan view of FIG. 9, the holographic element  36  comprises a “sandwich” having a receiving surface  92  comprised of a glass or another transparent window material having a small thickness and coated on the inside with indium-tin-oxide (ITO)  94  or another substantially transparent electrically conductive layer. The inside surface coated with the ITO is electrically connected to a direct current voltage source power supply to establish a potential difference across the sandwich. Spaced a small distance from the receiving surface  92  is exit plane or exit surface  100 , comprising also a glass window having a small thickness and having its inside surface comprising an ITO coating  102 . The ITO coating surface  102  of the exit glass  100  is electrically connected to ground  104 , so that the power supply  96  can establish a potential between these glasses  92 ,  100  and their interior facing surfaces  94 ,  102 . Between these glass surfaces  92 ,  100  is a polymer composite  106  according to the principles of this invention. A polymer composite suitable for the practice of this invention is PVK:7-PDCST:BBP:C 60 .  
         [0079]    [0079]FIG. 10, a cut-away view of the holographic element, schematically shows the passage of the reference and signal beams through the element  36 , where like reference numerals indicate the same beams and beam confgurations as shown in FIGS. 1 and 2. The beams  20 ,  32  interfere in the polymer composite  106  thereby producing an intensity grating  110 . This intensity grating  110  writes or establishes a diffraction grating  112 . When an electrical voltage is applied from the power supply or voltage source  96 , an electrical field E o  is established across the polymer composite  106 , enhancing the diffraction gratings  112 . The electrical field E o  enhances the amplitude of the coupling coefficient and also controls its phase.  
         [0080]    To demonstrate the utility of a photorefractive polymer composite for adaptive interferometry, two experiments were performed. We set forth below the conditions, parameters and results of these experiments by way of example in order to further describe our invention:  
       EXAMPLE I  
       [0081]    Polymer components consisting of (i) the charge-transporting network poly(n-vinyl carbazole) (PVK), (ii) a derivative of the nonlinear optical chromophore 4-piperidinobenzylidenemalononitrile (PDCST), (iii) the fullerene C 60 , and (iv) the liquid plasticizer butyl benzyl phthalate (“BBP”), were dissolved in the ratio 49.5:35:15:0.5 percent by weight in a four to one by volume solvent mixture of toluene and cyclohexanone. The mixture was subsequently dripped onto indium tin oxide (ITO) coated glass plates at a temperature of 45° Centigrade and left to dry overnight in an oven maintained at 130° Centigrade. The plates were assembled at 150° Centigrade with mylar spacers, yielding a sample of thickness (L) equaling 135 micrometers (μm). The wavelength dependence of the power absorption coefficient (α) is shown in the inset of the plot depicted in FIG. 11, where α=9 per centimeter (cm −1 ) at the operating wavelength of 676 nanometers (nm). The refractive index (n) was measured to be n=1.63. The glass transition temperature was measured, using a modulated differential scanning calorimeter, and found to be 28° Centigrade. The material is, therefore, classed as a low glass-transition temperature material. Accordingly, coarse temperature stabilization was used to avoid heating to the glass-transition temperature. In this first experiment, the amplitude gain coefficient as a function of the applied electric field was measured in a series of two-wave mixing runs using the structure shown in FIGS. 1, 2,  8  and  9 . Each measurement comprised two stages. In the first stage, two p-polarized beams of equal intensity were overlapped inside the composite polymer configured in the configuration of FIG. 8. The steady-state amplification (g 1 ) of the signal beam  32  was measured as g 1 =I 1 (with pump)/I 1 (without pump) in order to account for optical absorption in the polymer composite  106 . The measured amplification and the known thickness were used to determine the real part of the coupling coefficient (γ R ). During the second stage, the interference pattern was translated at a constant rate much faster than the response speed of the polymer composite material  106 . The resulting homodyne mixing leads to sinusoidal oscillations in the output intensities of the two beams  20 ,  32 . The steady-state phase shift of the grating was calculated from the steady-state amplification of the signal beam  32  (g 1 ) and the amplitude of the oscillation of the beam  32 . The imaginary component of γ can be calculated from the real component of γ and the steady state phase shift. In our experiment, the phase shift measurement only carried out for the s-polarized light which experiences a much smaller gain coefficient than p-polarized light, in order to reduce the complications associated with phase shift analysis in the presence of large energy- and phase-coupling. The experimental results are plotted in FIG. 11. The solid lines are fits using the theoretical expression for the coupling coefficient. In the usual case where E o  is much less than E q , where E q  is the trap-limited field, the imaginary part of coupling coefficient (γ I ) is proportional to the square of the applied voltage E o , and the ratio of the real part of the coupling coefficient γ R  to the imaginary part of the coupling coefficient γ I  is approximately equal to the ratio of E o  to E q . In this example, the trap densities of the photorefractive polymer composite are large, on the order of 10 17  cm −3 . It is believed that these trap densities, combined with the small dielectric constant, result in the large values for E q  that we have observed, up to 90 V/μm. It is believed that these large values for E q  combine with the large electro-optic response from the orientational enhancement effect to produce the large gain coefficients observed.  
         [0082]    In FIG. 12, we show the plot of our calculated values of the surface displacement sensitivity d lim  normalized to the ideal homodyne detection limit d lim   ideal  of Equation 14 above. This relative detecting limit is equal to the factor in brackets in Equation 16 above. This bracketed expression contains all material dependent quantities. Its ideal value is unity. The solid circles or dots of FIG. 12 were determined from the data plotted in FIG. 11 for E o = 60 V/μm and λ=676 nm. The independent variable was the thickness L. At these selected values of E o  and λ, the potential performance of the photorefractive polymer composite beam holographic element  36  at the optimum thickness of L=0.22 mm is only twenty percent higher than the classical detection limit.  
         [0083]    To measure the surface displacement sensitivity of the polymer composite described above in Example I, an experiment was performed, the results of which we set forth by way of example in order to further describe our invention:  
       EXAMPLE II  
       [0084]    A two-wave mixing receiver as schematically described in FIG. 1 was used, with the exception that a flat mirror was used to simulate a workpiece, and an electro-optic phase modulator was inserted in the reference beam. The photorefractive polymer composite was the same as used in Example I above. The power of the reference light beam  20  was selected at thirty-eight (38) times the power in the signal beam  32 . The detector was a New Focus model 1801 silicon photodiode with integrated amplifier having a bandwidth of 125 MHz. The actual signal bandwidth was set or preselected by the digital oscilloscope to be 30 MHz. A separate calibration of the modulator showed the peak-to-peak phase excursion at 10 volts peak-to-peak drive, to be 0.22 radians. From observations with a spectrum analyzer, the signal-to-noise ratio was found to be one, S/N=1, for a peak-to-peak modulator drive of 0.2 volts peak-to-peak. For this drive voltage, the phase excursion was calculated to be 4.4×10 −3  radians peak-to-peak, or 1.6×10 −3  radians root mean square (“rms”). For a wavelength (λ) of 676 nm, the equivalent surface displacement (d) was 0.083 nm rms. The signal power on the photodetector  46  was measured to be 23 microwatts (μW). Using this value for power, and having an oscilloscope bandwidth of 30 MHz, a surface displacement sensitivity (d lim ) of 7.2×10 −8  nm (W/Hz) ½—  was determined. This value demonstrates an homodyne detection system having a sensitivity that is within a factor of three of the classical limit for an ideal homodyne system.  
         [0085]    We have also used this homodyne receiver to detect ultrasonic wave produced by a five Megahertz wideband piezoelectric transducer bonded to a quartz mirror. We set forth by way of example this experiment in order to further describe our invention:  
       EXAMPLE III  
       [0086]    This experiment was performed using the homodyne receiver system as used in Examples I and II, above, having the arrangement shown in FIGS. 1, 2,  8  and  9 . The workpiece in this case was a fused quartz mirror which was energized by a 5 MHz wideband piezoelectric transducer bonded to its rear surface. The transducer had high damping, and produced a single ultrasonic pulse. The ultrasonic wave was recorded using a probe beam from a 15 mW laser diode at 690 nm. The resulting signal beam was mixed in the polymer composite sample described in Examples I and II above. The output signal detected at the photo-detector  46  is shown in FIG. 13. In FIG. 13, the transmitted signal can be readily identified, and its various echoes distinguished.  
         [0087]    It may be appreciated that the data of these experiments demonstrate the feasibility of the photorefractive polymer composite ultrasound receiver to remotely detect surface displacements with good signal-to-noise ratios.  
         [0088]    It may be seen by the foregoing experiments and examples that the trap density and the grating phase can be controlled. Further, it may be appreciated that the relatively higher resistance characteristic of the polymer composite results in less current, less power dissipation and therefore less heating. By controlling the trap density, the coupling coefficient can be controlled so that we can approach the optimum or classical homodyne limit of approximately γ I L≈π/2.  
         [0089]    The foregoing detailed description of our invention and of preferred embodiments as to products, compositions and processes, is illustrative of specific embodiments only. It is to be understood, however, that additional embodiments may be perceived by those skilled in the art. For example, while the present invention has been described with reference to the composite polymer as illustrated in FIGS. 8 and 9, the composition of the polymer composite may be varied to suit design choices and considerations. For example, all or some of the molecular functionalities providing photorefractive behavior to the material could be attached covalently to the polymer. The ability to control the phase and to achieve the desired design features can to some extent be accomplished with such more simple design structures. Accordingly, it is to be understood that the scope of my invention is to be limited solely by the following appended claims.