Abstract:
Disclosed is a system and method for characterizing optical materials, using steps and equipment for generating a coherent laser light, filtering the light to remove high order spatial components, collecting the filtered light and forming a parallel light beam, splitting the parallel beam into a first direction and a second direction wherein the parallel beam travelling in the second direction travels toward the material sample so that the parallel beam passes through the sample, applying various physical quantities to the sample, reflecting the beam travelling in the first direction to produce a first reflected beam, reflecting the beam that passes through the sample to produce a second reflected beam that travels back through the sample, combining the second reflected beam after it travels back though the sample with the first reflected beam, sensing the light beam produced by combining the first and second reflected beams, and processing the sensed beam to determine sample characteristics and properties.

Description:
ORIGIN OF THE INVENTION 
       [0001]    The invention was made in part by employees of the United States Government and may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefore. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    Smart Optical Materials (“SOM”) are optical materials that can control deep properties such as, for instance, intensity, phase, polarization, and/or coherence of passing lights. SOM include electro-optic materials, non-linear optical crystals, liquid crystals, electro-optic polymers, magneto-optic materials (Faraday Effect and Kerr Effect), electro/thereto-chromic materials, chemicals that induce refractive index or optical density changes, optical materials that depend on temperature and pressure, and phase-change materials. For example, liquid crystal material has different refractive indices under an electric field. In another example, non-linear optical crystal (BaTiO 3 ) material has a dipole moment and electric field that affects domains of similar dipole moments which change the total index of refraction. Characterization of these SOM appears difficult due to the lack of standard methods and commercially available equipment that can measure the intensity, phase of photons and its related polarization. Furthermore, the characterization of the properties of some optical materials ordinarily requires many separate, stand-alone pieces of equipment that make moving samples of optical material from one station to another quite cumbersome. Such a station-to-station characterization process imposes unprotected vulnerability to samples due to the exposure to moisture, dust, and environment-enhanced aging effects. 
       BRIEF SUMMARY OF THE INVENTION 
       [0003]    In view of the foregoing, it is an object of the invention to provide a system and method for characterizing smart optical materials to determine spectral and refractive shifts in terms of deep properties (e.g. intensity, phase, polarization, coherence) of passing lights. 
         [0004]    It is a related object of the invention to provide the ability to characterize smart optical materials in a compact, economical and efficient way. 
         [0005]    These objects are achieved by the present invention, which provides a system and a method for characterizing smart optical materials that can simultaneously measure intensity, phase and polarization of photons passing through the material. The present invention measures intensity, phase, and polarization of passing lights through material while applying various physical and/or chemical quantities (such as voltage, electric field, current, magnetic field, chemical concentration, temperature, pressure, reaction time, etc.) on the material. In a preferred embodiment, the system is miniaturized and comprises a USB interface and exchangeable components for various applications. Such a system can be used as a complete micro spectrometer system. 
         [0006]    In one aspect, the invention provides a method for characterizing optical materials, comprising the steps of providing a sample of optical material, generating a coherent laser light, filtering the coherent laser light in order to remove high order spatial components of laser light, collecting the filtered light and forming a parallel beam of light, splitting the parallel beam of light into a first direction and into second direction toward the sample of optical material so that the parallel beam of light passes through the optical material, applying physical quantities to the sample of optical material, reflecting the beam of light travelling in the first direction to produce a first reflected beam of light, reflecting the beam of light that passes through the optical material to produce a second reflected beam of light that travels back through the optical material, combining the second reflected beam of light after it travels back though the optical material with the first reflected beam of light, sensing the light beam produced by combining the first and second reflected beams of light, and processing the sensed light beam to determine the optical characteristics and properties of the sample of optical material. 
         [0007]    In another aspect, the invention provides a system for characterizing optical materials including a sample holder for holding a sample of optical material, a laser to generate a coherent laser light, a filter for filtering the coherent laser light in order to remove high order spatial components of laser light, an optical device to collect the filtered light and form a parallel beam of light, an optical beam splitter to split the parallel beam of light into a first direction and into second direction wherein the parallel beam of light travelling in the second direction travels toward the sample holder so that the parallel beam of light passes through the sample of optical material secured within the sample holder, a means for applying physical quantities to the sample of optical material, a first optical reflector to reflect the beam of light travelling in the first direction to produce a first reflected beam of light, a second optical reflector to reflect the beam of light that passes through the optical material to produce a second reflected beam of light that travels back through the optical material, a light combining device to combine the second reflected beam of light after it travels back though the optical material with the first reflected beam of light, an imaging sensor to sense the light beam produced by combining the first and second reflected beams of light; and a processing resource to process the sensed light beam to determine the optical characteristics and properties of the sample of optical material. 
         [0008]    Additional objects, embodiments and details of this invention can be obtained from the following detailed description of the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S) 
         [0009]      FIG. 1  is a perspective view of the smart optical material characterization system of the present invention; 
           [0010]      FIG. 2A  is a perspective view of the smart optical material characterization system of  FIG. 1  utilizing a sample holder configured to hold electro-optical materials; 
           [0011]      FIG. 2B  is a perspective view of a smart optical material characterization system in accordance with another embodiment of the present invention that is configured to test a sample of reflective material; 
           [0012]      FIG. 2C  is a perspective view of a smart optical material characterization system in accordance with a further embodiment that of the present invention that utilizes a sample holder configured to hold magneto-optical materials; 
           [0013]      FIG. 2D  is a perspective view of a smart optical material characterization system in accordance with yet another embodiment of the present invention that utilizes a sample holder configured to hold chemical-optical materials; 
           [0014]      FIG. 3A  is a perspective view of a sample holder configured to hold an electro-optical material in accordance with one embodiment of the present invention; 
           [0015]      FIG. 3B  is a perspective view of a sample holder configured to hold an electro-optical material in accordance with another embodiment of the present invention; 
           [0016]      FIG. 3C  is a perspective view of a sample holder configured to hold an electro-optical material in accordance with a further embodiment of the present invention; 
           [0017]      FIG. 3D  is a perspective view of a sample holder configured as a two-dimensional array in accordance with yet another embodiment of the present invention; 
           [0018]      FIG. 3E  is a perspective view of a sample holder for a reflective material in accordance with yet a further embodiment of the present invention; 
           [0019]      FIG. 3F  is a perspective view of a sample holder configured as an inductive coil for holding a magneto-optical material in accordance with yet another embodiment of the present invention: 
           [0020]      FIG. 3G  is a perspective view of a sample holder configured as a magnet for holding a magneto-optical material in accordance with yet a further embodiment of the present invention; 
           [0021]      FIG. 3H  is a perspective view of a sample holder comprising a heater/refrigerator and a device to hold a chemical in accordance with yet another embodiment of the present invention; 
           [0022]      FIG. 4A  is a diagram illustrating a roundtrip, double-pass-reflection configuration; 
           [0023]      FIG. 4B  is a diagram illustrating a unidirectional, single-pass-ring configuration; 
           [0024]      FIGS. 5A ,  5 B,  5 C and  5 D show data measured by the system of the present invention for a single layer liquid crystal cell; 
           [0025]      FIG. 6A  shows a phase intensity time ripple map and a point intensity measurement graph generated by the system of the present invention for a single layer of liquid crystal cell; 
           [0026]      FIG. 6B  shows a phase intensity time ripple map and a point intensity measurement graph generated by the system of the present invention for a double layer of liquid crystal cell; 
           [0027]      FIG. 7  shows the phase measurement result of the point intensity chart; and 
           [0028]      FIG. 8  shows a multi pixel phase measurement from a phase intensity time ripple map. 
           [0029]      FIG. 9  shows a consolidated test platform for loading and subjecting a sample material to various physical quantities. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0030]    Referring to  FIG. 1 , there is shown system  10  of the present invention. System  10  employs a Michelson interferometer which uses a 45° inclined beam splitter, two mirrors, and a screen with a coherent light source such as a laser. An interference pattern is produced from two splitted lights reflected by two mirrors. The Michelson interferometer configuration is well known in the art and therefore, is not discussed in detail herein. System  10  further comprises several other optical components and a processing resource that are discussed in detail in the ensuing description. Laser source  12  generates coherent laser light  14  beam. In a preferred embodiment, system  10  includes a polarizer  16 , wave plates  18 , and neutral density (ND) filter  20 . The wave plate (also known as a retarder) alters the polarization state of a light wave travelling through it. In one embodiment, there is a plurality of wave plates  18 . Neutral density filter  20  achieves the desired light attenuation without changing the other properties of the laser light  14 . Laser light  14  passes through neutral density filter  20  and becomes altered laser light  21 . Laser light  21  passes through spatial filter  22  which removes high-order spatial components from laser light beam  21  and provides a uniform TEM 00  mode light beam  24 . Plano-convex (PCX) lens  26  collects diverging laser light beam  24  from spatial filter  22  and provides parallel TEM 00  beam  28 . Beam splitter  30  divides beam  28  into two different laser light beams  32  and  34  that travel toward mirrors  36  and  38 , respectively. Beam splitter  30  can be configured as a polarizing or non-polarizing beam splitter depending on the measurement necessity. Polarizer  40 , wave plate  42  and neutral density (ND) filter  44  modify or alter laser light beam  32  in order to provide an excellent, high contrast, interference pattern for imaging sensor  46 . Similarly, polarizer  48 , wave plate  50  and neutral density (ND) filter  52  modify or alter laser light beam  34  to provide an excellent, high contrast, interference pattern for imaging sensor  46 . System  10  includes a Smart Optical Material (SOM) sample holder  54  that holds therein a sample of Smart Optical Material. Straight beam  34  travels through sample holder  54  and neutral density filter  52  and then reflected backward from mirror  38 . Therefore, beam  34  travels through sample holder  54  twice, once in the forward direction and once in the backward or reflected direction. Beam  32  is reflected back from mirror  36 . The reflected beams are recombined at beam splitter  30  to form laser light beam  56  which travels toward imaging sensor  46 . In a preferred embodiment, there are no other optical components between beam splitter  30  and imaging sensor  46 . In such an embodiment, laser light beam  56  directly illuminates imaging sensor  46 . Imaging sensor  46  comprises an imaging device to capture the interference patterns of laser light  56 . In one embodiment, imaging sensor  46  is configured as a CCD or NMOS-type imaging sensor. In another embodiment, imaging sensor  46  comprises screen and video camera imaging module that measures the two-dimensional interference pattern. Processing resource  60  is in electrical and optical communication with imaging sensor  46  and processes the interference patterns captured by imaging sensor  46 . Processing resource  60  includes a microprocessor, optical measurement components, optical analysis components, and a display device. In one embodiment, processing resource  60  includes a computer that is configured to implement software that performs analysis on the images and interference patterns detected by imaging sensor  46 . In some embodiments, the system is miniaturized and comprises a USB interface (not shown). 
         [0031]    In accordance with the invention, system  10  applies physical quantities on sample holder  54  and measures the dynamic change of the interference pattern in sequence. The variable physical quantities include voltage (electric field), current, magnetic field, chemical concentration (i.e. chemical density and/or reaction time), temperature, pressure, and actuation frequency. Thus, it is to be understood that system  10  includes devices (not shown) such as variable voltage sources and variable current sources that are used to apply a voltage or electrical current to the SOM under test. System  10  also includes devices (not shown) to provide an actuation frequency that is applied to the SOM under test. Similarly, system  10  also may include other devices (not shown) to provide a predetermined pressure that is applied to the SOM under test. As described below, system  10  enables various types of measurements with different sample holders. The sample holders and optical components are exchangeable parts with mountable slots and screws. Referring to  FIGS. 2A-D  and  3 A- 3 H, there are shown various types of sample holder and optical components for each measurement.  FIG. 2A  shows the configuration for electro-optic measurement, i.e. voltage/current versus optical properties such as phase, intensity, polarization, coherence, etc. This is also the configuration shown in  FIG. 1 .  FIGS. 2B and 3E  show system  10 ′ for reflective measurement for MEMS devices, piezoelectric actuator materials, thermal coefficient measurements, and stress/strain measurement. Reflective measurement is accomplished with focusing and collection lens  70  and reflective sample holder  72 . Optical material  73  is secured by the sample holder  72  and has a reflective or diffusive surface. Laser light  75  is reflected from surface  74  and is collected with the focusing and collection lens  70 . Beam splitter  30 ′ directs the collected, reflective light to imaging sensor  46 ′. System  10 ′ is a particularly preferred method to characterize MEMS device movement, piezoelectric actuator materials, thermal expansion, and stress/strain measurement. An optional heater/refrigerator and pressure cell can be used to control temperature or pressure dependent properties.  FIGS. 2C and 3F  show system  10 ″ which is configured for magneto-optical measurement, i.e. magnetic materials with Faraday effect, Kerr effect, Ferro-fluid, etc. System  10 ″ uses a magneto-optical sample holder which comprises induction coil  80  that surrounds the optical material  82 . Induction coil  80  generates a magnetic field along the propagation direction of the laser light.  FIG. 3G  shows an alternate magneto-optical sample holder  85 . Sample holder  85  comprises permanent magnet  86 . Optical material  87  is positioned between sections  86 A and  86 B of permanent magnet  86 . A perpendicular magnetic field is generated by permanent magnet  86 . Both sample holders  80  and  85  can be fabricated with a permanent magnet or electric magnet. Magneto-optical sample holders  80  and  85  are used to characterize ferromagnetic fluid and magnetic materials with Faraday Effect or Kerr Effect. 
         [0032]      FIGS. 2D and 3H  show system  10 ′″ which is configured for chemical-optical property measurements, i.e. optical properties versus chemical concentration, chemical reaction, electro-chemical reaction, etc. System  10 ′″ is configured to characterize numerous materials with advanced optical properties, phase, intensity, polarization, coherence, and etc. System  10 ′ uses chemical sample holder  90 . In one embodiment, sample holder  90  uses heater/refrigerator  92  in order to control temperatures. Sample holder  90  further comprises injection nozzle  94  and extraction nozzle  96 . Chemicals are injected into sample holder  90  with injection and extraction nozzles  94  and  96 , respectively. The chemical concentrations are controlled within sample holder  90 . Chemical reactions are recorded with the dynamic change of the passing laser light&#39;s deep properties, such as phase, intensity, coherence, and polarization in time. In an alternate embodiment, an additional heater, refrigerator, or pressure cell is attached to sample holder  90 . 
         [0033]    Referring to  FIGS. 3A ,  3 B and  3 C, there are shown alternate types of electro-optic sample holders that can be utilized by system  10 . In  FIG. 3A , sample holder  100  comprises a pair of transparent electrodes  102  and  104 . Electrode  102  is the positive electrode and electrode  104  is the negative electrode. Electro-optic material  106  is sandwiched between electrodes  102  and  104 . Electro-optic material  106  may be in the form of thin-film, bulk, liquid, sol-gel, or solid form. During testing of electro-optical material  106 , a voltage is applied to electrodes  102  and  104 . Laser beam  108  passes through transparent electrodes  102  and  104 . In one embodiment, electrodes  102  and  104  are fabricated from indium tin oxide components. Referring to  FIGS. 3B and 3C , there is shown sample holder  150  which has the same general structure as sample holder  100 . Sample holder  150  comprises a pair of transparent electrodes  152  and  154 . Electrode  152  is the positive electrode and electrode  154  is the negative electrode. Electro-optic material  156  is sandwiched between electrodes  102  and  104 . Electro-optic material  156  may be in the form of thin-film, bulk, liquid, sol-gel, or solid form. During testing of electro-optical material  106 , a voltage is applied to electrodes  102  and  104 . Laser beam  158  passes through transparent electrodes  152  and  154  such that the propagation direction of light is perpendicular to the direction of electric-field or current. Referring to  FIG. 3D , there is shown sample holder  200  that is configured as a two dimensional array. Sample holder  200  allows system  10  to analyze multiple SOM cells simultaneously. The sample holders shown in  FIGS. 3A ,  3 B and  3 C can be configured with an array format. 
         [0034]    In at least one advantageous embodiment of the invention, the sample holders are combined into a consolidated test platform for applying multiple external influences such as electric, magnetic, thermal, and/or mechanical loads. An exemplary consolidated test platform  300  is shown in  FIG. 9 , where a sample  350  can be loaded and subjected to a selected field effect, electric, magnetic, thermal, or mechanical compression and tension for assaying the changes in optical characteristics. Such a test platform  300  includes housing components  302 ,  304  for rotational specimen holder  310  held by specimen support  306 . Mechanical force  322  can be applied by compression means  324  or tension means  326 . Test platform  300  allows either the application of a single field or even multiple fields simultaneously. In  FIG. 9 , electromagnetic pairs ( 312 ,  314 ) that face each other have a hole through the axial centerline for a probe beam  308  to pass through. The magnetic strength to the specimen on a test platform is controlled by the external power supply (not shown) for the electromagnet ( 312 ,  314 ). The electric field is provided by two electrodes ( 316 ,  318 ) that are beneficially aligned very close to the front and back surfaces of the sample  350  specimen. The electric field strength is controlled by the power supply (not shown) to the electrodes ( 316 ,  318 ). The incident angle of either magnetic or electric field is an important factor for determining the response along with the dipole orientation of the smart optical material in a specific direction and can be changed by the rotational specimen holder  310  which can be pivoted on the bottom floor  306  and top cap  322  of the instrument housing ( 302 ,  304 ) for rotational purposes. The sample  350  sitting on a specimen holder  310  can be grabbed by two mechanical grips (not shown) at the top and bottom in order to determine the mechanical compression ( 324 ), tension ( 326 ), and shear effects on the smart optical material. To create a shear effect on a specimen, the specimen grabber (not shown) that is attached to the top cap  322  rotates while the specimen support anchored on the housing floor  306  is fixed. Moreover, to see a thermal effect, the test platform encompasses a thermal gun  320  that can inject an infrared beam to the sample  350  specimen for determining thermal loading effect. The inventors believe that such a consolidated test platform can be installed within the compartment of the instant invention&#39;s interferometry system, with power supplies being advantageously placed outside the housing of such interferometry system. 
         [0035]    As described above, a system of the present invention can he configured to implement roundtrip, double-pass beam measurement. As shown in  FIG. 1 , system  10  is configured to implement roundtrip, double-pass beam measurement. Another example is system  10 ″ which is shown in  FIG. 4A . Beam  34 ″ passes through the sample optical material in sample holder  80  twice, once in the forward direction and once in the backward or reverse direction as indicated by arrow  175  in  FIG. 4A . The fact that beam  34 ″ passes through the sample of optical material twice improves the accuracy of the measurement by a factor of two. Beam  32 ″ is also reflected by mirror  36 ″ and travels back through beam splitter  30 ″ as indicated by arrow  176 . 
         [0036]    The system of the present invention can also be configured in a unidirectional, single pass, beam path configuration. Such a configuration is necessary because characterization of some optical materials require a unidirectional, single pass, beam path. For example, Faraday rotator material under a magnetic field rotates the polarization of light by +45 degrees in a forward beam and −45 degrees in a backward beam along a magnetic field direction producing a total of 90 degrees rotation. If a user wants to measure a sample with a single beam pass configuration, the system of the present invention can be configured as shown by system  200  in  FIG. 4B . System  200  comprises laser  202 , polarizer  204 , wave plates  206 , neutral density filter  208 , spatial filter  210  and plano-convex (PCX) lens  212  which provide the same function as like components discussed in the foregoing description with respect to system  1 . 0 . System  200  further comprises beam splitter  214  and mirrors  216 ,  218  and  220 . Mirrors  216 ,  218  and  220  are arranged as  45  degree angle mirrors. The laser light beam travels through beam splitter  214 , through polarizer  222  and optical material in sample holder  80  as indicated by arrow  224 . The laser light beam is then reflected at a 45 degree angle by mirror  216  as indicated by arrow  226 . The laser light beam is then reflected at a 45 degree angle by mirror  218  as indicated by arrow  228 . The laser light beam is then reflected by mirror  220  as indicated by arrow  230 . The laser light beam then passes through optical components  232 ,  234  and  236 , such as a polarizer, wave plate and/or neutral density filter. The laser light beam is then directed to imaging sensor  238  by beam splitter  214  as indicated by arrows  240 . Imaging sensor  238  functions in the same manner as imaging sensor  46  (see  FIG. 1 ). A processing resource (not shown) similar to processing resource  60  is in optical signal communication with imaging sensor  238 . 
         [0037]    In all of the embodiments described in the foregoing description, the beam splitters, mirrors and filters are interchangeable parts. The splitting ratio of the beam splitter depends upon measurement necessities and may be, for example and without limitation, ratios such as 50:50. 10:90, 30:70, 60:40, or 80:20. 
         [0038]    The system of the present invention can use any one of several interference pattern recording configurations. One interference pattern recording configuration is direct recording on the imaging detector. In this configuration, a detector is used to record the interference pattern directly with or without an attenuator or screen. Another interference pattern recording configuration is an equally angled (θ 1 =θ 2 ) screen and camera module. In this configuration, the angle (θ 1 ) between the normal vector of the screen and incoming interference pattern beam is the same as the angle (θ 2 ) between the camera module and normal vector of screen such that distortion of interference pattern by angle θ 1  is automatically corrected by the angle θ 2  of the camera. A further interference pattern recording configuration is recording at an oblique angle. In this recording configuration, the camera module is at oblique angle θ 3  and it has to be numerically corrected in the software of processing resource  60 . The various embodiments of the characterizing systems described in the foregoing description may use any of these three recording configurations. 
         [0039]    The present invention provides multi-functional and multi-conditional capabilities for any given optical system and thus, consolidates and covers all characterization processes into a single event job by a single system. Since the present invention improves precise control of phase and polarization of passing lights through Smart Optical Materials, the present invention has many applications including, but not limited to, phase-shift lithography, 3D stereo displays, holography and digital holographic displays, phase contrast microscopy, interferometers, waveguide modulators for fiber optical communication, vibrato-meters, adaptive telescopes, LIDAR, optical data storage, medical and pharmaceutical instruments, and the chemical industry. Other applications to which the present invention may be applied include refractive indices (static and real-time measurements under the varying electric field), spectral shift (static and real-time measurements under the varying electric field), and optical coatings (spectral uniformity based on optical surface and coating thickness), and measurement of the Stark effect, Zeeman effect, Faraday effect and Kerr effect. Other applications of the present invention include the characterization of non-linear optical materials, liquid crystals, electro-optic polymers, magneto-optic materials, and chromic materials. Further applications of the present invention include the measurement of absorption, reflection, transmission, polarization, intensity, phase, wavelength, and coherence. 
         [0040]    The following example further illustrates the invention but, of course, should not be construed as in any way limiting its scope. 
       EXAMPLE 
       [0041]    This example demonstrates a test measurement in accord with at least one embodiment of the invention, 
         [0042]    The test measurement was made with a transparent liquid crystal phase retarder. The liquid crystal layer was inserted between two transparent electrode layers and voltages from −10V to +10V were applied.  FIGS. 5A ,  5 B,  5 C and  5 D show the data, measured by system  10 , with a single layer of liquid crystal cell. System  10  provided a real-time display of the interference pattern, which is shown in  FIG. 5A . Referring to  FIG. 5A , a reference analysis zone was chosen by a user and displayed as a rectangle at the center of interference ripple with a horizontal line and vertical line.  FIG. 5B  is a graph showing real-time pixel intensity data from the horizontal line and vertical line shown in  FIG. 5A . The user set the starting and ending voltages of a linear voltage scan-window and input the number of measurements, initial and step delay time. While applying voltages or currents to the sample of optical material, the processing resource  60  collected real-time data from the interference pattern provided by imaging sensor  46 .  FIG. 5C  is a point intensity chart and shows collected data from the center of the interference ripple shown in  FIG. 5A . As shown in  FIG. 5C , sequential line intensity profiles on the vertical and horizontal lines of  FIG. 5A  were collected as system  10  applied various physical quantities on the optical material in time. The dynamic changes of this one-dimensional intensity profile (X-axis) were plotted with Y-axis as time or applied physical quantity, making a two-dimensional contour map shown in  FIG. 5D . This contour map is referred to as a Phase Intensity Time Ripple Map (or Dynamic Photon Intensity Phase Map) since it recorded dynamic change of photon phase and intensity information with variation of applied physical/chemical quantities in time. In the real-time interference pattern display window, it appeared as though concentric ripples were disappearing into the center or generating out of the center depending on whether the refractive index was increasing or decreasing under applied physical/chemical quantities in time. 
         [0043]    System  10  also provided the same type of data for a double layer of a liquid crystal cell.  FIGS. 6A and 6B  provide a comparison of data for single and double layers of liquid crystal cell.  FIG. 6A  pertains to a single layer of liquid crystal cell.  FIG. 6B  pertains to a double layer of liquid crystal cell. In  FIG. 6A  and  FIG. 6B , the upper contour map was known as a Phase Intensity Time Ripple Map (also known as a Dynamic Photon Intensity Phase Map), and the lower graph was a point intensity measurement graph. Double layers of liquid crystal cells generated twice as many phase intensity changes than that of a single layer liquid crystal cell. The present invention not only measured dynamic change of just one point but also of the whole line. The vertical cross-section of the Phase Intensity Time Ripple Map showed dynamic change of photon intensity at one pixel. In  FIG. 6A , line  300  in the point intensity chart shows dynamic photon intensity change at center point (cross-point of horizontal and vertical lines) and line  302  shows that of a side-reference point. Similarly, in  FIG. 6B , line  304  in the point intensity chart shows dynamic photon intensity change at center point (cross-point of horizontal and vertical lines) and line  306  shows that of a side-reference point. 
         [0044]    Referring to  FIG. 7 , there is shown the phase measurement result of the point intensity chart corresponding to the liquid crystal single layer (see  FIG. 6A ). The intensity is maximized at the phase angles of 0°, 360°, 720° and so on from the center while it is minimized at the phase angles of 180°, 540°, 900° and so on. The absolute phase angle changes were determined by measuring the maximum and minimum points of photon intensities with respect to the reference point&#39;s intensity changes. Intermediate phase angle values were measured as interpolation of photon intensities with respect to a reference point&#39;s photon intensity change. For instance, the middle point with zero bias voltage (0V) has 160 mV of photon intensity and maximum photon intensity of 200 mV between 0° phase angle points. Thus, this made absolute the phase angle change of cos-1 (160 mV/200 mV)=36.8°. 
         [0045]    Referring to  FIG. 8 , there is shown a multi-pixel phase measurement derived from a phase intensity time ripple map. Processing resource  60  located the local maxima and minima region in the phase intensity time ripple map. In one embodiment, numerical calculation with simulated annealing was used to find local maxima regions for phase angle differences of 0°, 360°, 720° and so on. Similarly, another numerical calculation with simulated annealing was used to locate local minima regions for phase angle differences of 180°, 540°, 900° and so on. Based on these mathematical calculations, contour lines for maximum region and minimum region were located. Processing resource  60  calculated intermediate phase angles as interpolated equal-intensity contours between maxima and minima regions. Processing resource  60  calculated phase angles of whole lines instead of just a few points. 
         [0046]    All references, including publications, patent applications, and patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein. 
         [0047]    The use of the terms “a” and “an” and “the” and similar referents in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The terms “comprising,” “having,” “including,” and “containing” are to be construed as open-ended terms (i.e., meaning “including, but not limited to,”) unless otherwise noted. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention. 
         [0048]    Preferred embodiments of this invention are described herein, including the best mode known to the inventors for carrying out the invention. Variations of those preferred embodiments may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate, and the inventors intend for the invention to be practiced otherwise than as specifically described herein. Accordingly, this invention includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly contradicted by context.