Abstract:
A system, apparatus and method for analysis of a specimen using ellipsometric analysis. Polarization distortions caused by the propagation of polarized light within a substrate upon which a specimen is located are reduced by directing light at selected polarizations at the substrate alone and the specimen on the substrate. Image data is collected for each of the selected polarizations and processed to remove errors due to birefringence. Fourier transform processing is used to obtain polarization phase data for correcting polarization caused by any birefringence in the substrate, and optionally amplitude data.

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     The U.S. Government has certain rights in this invention pursuant to Grant No. 1RC3AI089277-01 awarded by Department of Health and Human Services, National Institutes of Health, National Institute of Allergy and Infectious Diseases. 
    
    
     BACKGROUND 
     1. Field 
     This disclosure relates to specimen analysis through the use of ellipsometry. More particularly, the present disclosure describes improvements in ellipsometric performance during specimen analysis by reducing the impact of birefringence. 
     2. Description of Related Art 
     There are numerous categories of procedures under the general heading of bioassay. Here is a list that is at least exemplary if not exhaustive of the type of bioassays in which the technology known as imaging ellipsometry or sometimes evanescent field imaging is or can be applied: 
     1. Label free DNA hybridization assay. Microarray of single strand DNA can be placed on the surface of the substrate. The binding of the corresponding strand from a sample under study can be detected. The implementation is often used for DNA sequencing and called a DNA chip. 
     2. Label free protein assay. Microarray of proteins can be placed on the surface of the substrate. The binding of the corresponding molecular target can be detected. If the binding molecule is disease related, often peptides, protein produced by the disease, by the host, the protein assay can be used for diagnostic purposes. 
     3. Small molecule discovery assay. A panel of possible biomarker drug candidates can be placed on the substrate. A sample containing the target, often a protein that would trigger a cascade reaction, would be applied and the selective binding can be observed. 
     4. Label free micro-organism capturing assay. Molecules, for example, targeting specific micro-organism can be placed on the surface of the substrate. When the solution containing the specific organism, such as cells, parasites and bacteria, is applied, the organism captured at the surface can be detected. A micro-organism capturing assay can be used for capturing, diagnostic or environmental purposes. The molecule placed on the substrate can be protein, lipid, sugar, bio-inert molecules such as PEG, or a composition of these molecules. 
     5. Cell-based assay. Cells can be placed on the surface of the substrate. Stimulation is introduced to the cells, and the reaction is measured through the reaction footprint of the cells. The dosage and efficacy of the stimulation can be quantified through the reaction of the cells. The typical cell-based assay includes proliferation assay, wound healing assay, toxicity assay. Also the indirect target of the stimulation can be studied through performing the cell-based assay. For example, genetically engineered cells which over or under express a targeted protein can have medicated reaction under the reaction of the stimuli. 
     U.S. Pat. No. 6,859,280 discloses an imaging ellipsometry system which employs a transparent substrate and directs polarized light at the upper surface of the substrate in a manner to produce total internal reflection (TIR) and an evanescent field at the upper surface of the substrate. The system disclosed in U.S. Pat. No. 6,859,280 is designed to sense chemical reactions occurring in an evanescent field at the upper surface of the substrate by sensing intensity changes at locations of the surface which correspond to pixel locations in a two-dimensional sensor such as a charge coupled device (CCD) to which reflected light is directed. The chemical reactions occur by immobilizing an array of receptors on the upper surface of the substrate and sensing changes in polarization of the reflected light due to binding events between analytes (ligands) in a sample introduced to the surface and receptors in the array. Alternatively, a drug is introduced to cells cultured at the upper surface of a transparent substrate for analysis as, for example, by a dose response to carbachol, a cholinergic receptor agonist, resulting in changes to the cells&#39; footprint on the substrate surface sensed as localized intensity changes in the reflected light. Cells are naturally spatially distributed. By producing an image, it allows selective analysis of the changes in the polarization state in the cross-section of the reflected beam which are indicative of the substances in the specimen in the location corresponding to a position in the detector. Therefore, the system may be configured to produce an image which represents the change in polarization state within each of the discrete specimen spots or within the footprint of cultured cells. That change can then be output as an image of physical measurement of physical properties such as density or height. The image refers to a set of values correlated to different spatial positions which can be displayed or compared against each other to contrast differences in physical properties at these positions. 
     Multiwell disposables used to contain specimens for analysis are commonly available. For ellipsometric systems where polarized light is employed in the imaging system, the disposable (slide or well) should be birefringence-free to avoid significant reduction of sensitivity in the detection (imaging) of binding events. Birefringence free disposables are usually made from glass and are too expensive to be used in large segments of the market for ellipsometric systems. Plastic disposables, on the other hand, are sufficiently inexpensive to be useful in virtually every segment of the market. But plastics, although promising, presently exhibit birefringence which reduces the sensitivity of system output signals and thus the usefulness of the systems. 
     As indicated above, most existing ellipsometry implementations require a high performance optical material as the substrate which does not alter the relative phase of the two polarizations outside the binding surface. The high performance requirement is an obstacle in reducing the cost of performing ellipsometry and is not always achievable in common optical material. Birefringence in material, which is a phenomenon where the speed of light depends on its direction, can contribute to the polarization phase measured and skew the measured result on binding. That is, birefringence in the material on which a specimen is distributed will skew the polarization phase changes of the light transmitted to the sensor. Hence, the measured polarization may not accurately reflect the polarization change arising from biochemical interactions. 
     Therefore, there exists a need to improve the collection and processing of birefringence-impacted ellipsometry data to allow for lower cost optical material to be used and/or to allow for faster processing of the data. 
     SUMMARY 
     The invention disclosed here describes ways of using existing, 2D detector array based, imaging ellipsometry instruments to measure surface refractive index changes due to increase of surface binding or changes in quality of binding on a birefringent substrate. Fourier transformation is used along with polarization modification apparatus to calculate and reduce the impact of birefringence in a specimen-carrying substrate. The combination of Fourier processing and polarization modification allows for ellipsometry to be performed simultaneously at every point of the detector array, resulting in fast, accurate measurements without requiring a birefringence-free substrate. 
     The invention is based on the recognition that the effects of birefringence in a substrate on ellipsometry measurements on a pattern of specimens on an area of the substrate surface can be obviated by performing Fourier transform calculations on the intensity of cyclically rotating polarized light reflected from the area of the substrate surface and captured by a 2-D detector. Fourier transformation operates to calculate a phase and amplitude for each pixel in the image of the reflected light at each of at least four equally spaced angles in each cycle. Birefringence free ellipsometry measurements of the reflected light at each pixel in the image is obtained by subtracting the measurement taken in the absence of the specimens from the measurement taken with the specimens. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of a system for ellipsometric analysis where polarization orientation is synchronized to image data capture and birefringence is present. 
         FIG. 2  shows a schematic block diagram of a system for ellipsometric analysis, in which the impact of birefringence is reduced. 
         FIG. 3A  illustrates synchronization of a processor to a rotatable linear polarizer. 
         FIG. 3B  illustrates synchronization of a processor to a rotatable or variable retarder. 
         FIG. 4  illustrates data processing steps for generating a phase image that represents phase changes in a measured specimen. 
         FIG. 5A  shows the steps for measuring the phase changes due to a non-birefringent free substrate using the system depicted in  FIG. 2 . 
         FIG. 5B  shows the steps for measuring the phase changes in a substrate and specimen combination using the system depicted in  FIG. 2  and obtaining a phase image that represents phase changes in a measured specimen. 
         FIG. 6  depicts a front-top perspective view of an assembled slide with a multiwell plate attached. 
         FIG. 7  depicts a front-bottom perspective view of the assembled slide and multiwell plate of  FIG. 6 . 
         FIG. 8  depicts an end view of a substrate having a single groove for a single light receiving incident prismatic surface and a single light exiting prismatic surface with an evanescent field resulting from the single internal reflection. 
         FIG. 9  depicts the assembled slide and multiwell plate of  FIGS. 6 and 7  showing the beam of polarized light passing through the slide and reflecting off the surface on which specimens are deposited and including the substrate having a plurality of grooves defining two prismatic light incident surfaces and two prismatic light exiting surface with an evanescent field resulting from the single internal reflection. 
     
    
    
     DETAILED DESCRIPTION 
     The exemplary embodiments according to the present invention described in this disclosure provide for analysis of a specimen using ellipsometric analysis while overcoming performance degradation caused by substrate birefringence. 
     The term “specimen” or “specimen spot” or “specimen array” is used to describe a substance or group or array of substances present on the reflection surface of a substrate and within the evanescent field caused by single internal reflection in the substrate so as to be measured by processes and apparatus and systems described herein. In some contexts the term specimen may refer to a substrate with chemicals on it. Sometimes the chemicals are referred to as “probes” or “receptors” and the chemical whose presence or quantity is under study is called an “analyte” or “target” which typically will bind with the receptor, the goal being to measure the difference or absence of difference at the location of the receptor so as to determine that a binding event has or has not occurred. Also, in the case of cell reaction, the reaction can be detected and measured. The present invention also allows readings over time so that temporal changes can be observed. It will be apparent that the invention can be implemented for any circumstance where a change at one or more locations is desired to be imaged over a two dimensional area and the imaging showing changes in the amount or quality of substance at imaged locations. In addition to imaging, data results can also be obtained. The term “image” is used in the conventional sense to a display or other access to a viewable image and also, in context, as defining a two-dimensional detection event relating to an array of pixels such as intensity or phase shift. 
     The content of each of the following US patents is incorporated herein by this reference; U.S. Pat. Nos. 7,981,664; 7,867,783; 7,863,037; 7,799,558; 7,518,724; 7,126,688; 7,023,547; 6,859,280; 6,833,920; and 6,594,011. 
       FIG. 1  shows an imaging ellipsometric measurement system exemplary of the present invention. As shown in  FIG. 1 , a polarized light assembly  210  generates a beam of polarized light with two perpendicular directions of polarization. That light is directed towards a single reflection assembly  220  configured to hold specimens to be analyzed. The reflection assembly  220  reflects the polarized light beam where the polarization of the reflected polarized light beam is impacted by the substrate through which the light passes and the specimens under analysis. The reflected polarized light beam is directed towards a polarization sensitive two dimensional detector  230  that provides an image for analysis by a processor  240 . The processor  240  is synchronized with the polarized light assembly  210  to link the phase of the light produced by the assembly  210  with the image received by the processor  240 . See below for a more detailed explanation of  FIG. 2 . 
     In schematic form,  FIG. 2  illustrates an embodiment of the invention for ellipsometry measurement as in the block diagram of  FIG. 1 . The apparatus can be defined as a single internal reflection apparatus having a polarized light source, a detector assembly and a positioning mechanism for placement of a biochip (variously called bioarray, and microarray and other terms) having biological substances for obtaining information about chemical or biological reactions or events on the biochip. A processor is included to process the data obtained. As shown in  FIG. 2 , the polarized light source  210  may comprise a collimated unpolarized light beam source  211 , a linear polarizer  213 , and a retarder  215 . The linear polarizer  213  produces the linearly polarized light beam from the unpolarized light beam source  211 . The retarder  215  then produces a light beam “A” with a selected polarization, preferably a circularly polarized light beam having two perpendicular directions of polarization. 
     The positioning mechanism comprises supporting and placement structure, schematically shown at  227 , for holding the single reflection assembly  220  (the biochip or other device) under examination in the correct position for single internal reflection. Each of the polarized light source, the detector assembly and the positioning portion may be adjustable in order to accomplish the desired optical effects. The positioning portion  227  may be equipped to change the position of a biochip under examination to place different 2 dimensional areas of its surface within the illumination of the light beam A and to effect its reflection B. 
     The light beam “A” is directed towards the single reflection assembly  220 , which has a specimen  223  placed on a reflection surface  225  of a birefringent substrate  221  which is configured as a prism, or equivalent form (see  FIGS. 8-10 ) to direct the polarized light beam for a single internal reflection at the reflection surface  225  whereby an evanescent field is established, the specimen being within the evanescent field. Upon the single reflection at the reflection surface  225 , the phase of the light with polarization pointing into the specimen changes relative to the light with polarization pointing parallel to the interface. The objective of the ellipsometric measurement system is to measure this phase change, i.e., polarization change caused by the specimen. However, the birefringent substrate  221  may add to this relative phase shift as a function of the path of light within the substrate  221 . 
     The light beam “B” reflected out of the single reflection assembly  220  is directed towards the detector assembly, defining a polarization sensitive two dimensional detection array  230 , which has an analyzer  231  and a two dimensional detector  233 . The two dimensional detector  233  is an array of intensity sensors which produces an intensity output at each sensor that is sent to the processor  240 . Each of the sensors in the array will be referred to as a pixel in this description. The relative phase shift of the reflected light beam, whether the phase shift results from the specimen, birefringence in the substrate, or both, changes the intensity measured by the polarization sensitive two-dimensional array  230 . The processor  240  receives intensity data from the two dimensional detector  233  and is also synchronized with polarization settings of the polarized light source  210 . The processor is programmed to produce an image indicating the physical condition at each pixel in the 2D array of specimens. Operation of the processor as programmed is described below. 
     The polarized light source  210  may be configured to produce light with different polarizations or different polarization orientations with respect to the single reflection assembly  220 . Changes to polarization or polarization orientation may be made by rotating the linear polarizer  213 , rotating the analyzer  231 , or changing the retardation value of the retarder  215  to effect polarization phase of the beam “A”. As indicated above, the polarizations obtained by rotating the polarizer and/or retarder and/or changing retardation values are synchronized with the image intensity values received by the processor. 
     In the system shown in  FIGS. 1 and 2 , low or non-birefringent optical components may be chosen to reduce or eliminate the impact of birefringence on the measured polarization. However, plastic slides are relatively low cost, so replacement of plastic slides with non-birefringent glass slides results in significantly increased costs. Disposable plastic multiwell slides or plastic slides with multiple specimen depressions or simply with arrays of spots are typically used in biological specimen analysis.  FIGS. 8-10  depict an exemplary multiwell slide. Such plastic slides allow for the simultaneous analysis of several specimens. It is advantageous to address and reduce or eliminate the birefringence of the plastic slides during ellipsometric analysis. 
     The present invention addresses the problem of birefringence contaminating ellipsometry measurement of specimens by use of a Fourier transform ellipsometry technique. That technique, is generally described for determining polarization with the exemplary system shown in  FIGS. 1 and 2 . In summary, the relative phase of the light used to illuminate a substrate is changed to several values (at least four) and intensity measurements made at each point on the imaging array corresponding to a specimen to be analyzed at each of the relative phase values. Intensity measurements are made at each pixel of the imaging array detector. A Fourier transform is performed on the measurements made for each pixel to solve for the phase of light altered by the specimens under analysis. Performance of Fourier Transforms for each point or pixel can then be used to provide a two-dimensional image depicting the polarization at each point or pixel. Note that this Fourier transform ellipsometry requires at least 4 different relative light phases and additional relative light phases may be needed to achieve desired precision in the determined specimen polarizations. The four different relative light phases are equally spaced within an angular cycle of 360° (e.g. 0°, 90°, 180°, 270°), subject to the requirements of Table 1 below. The advantage of Fourier Transform ellipsometry is that light having only at least four different phases is required for measuring polarization phase in the entire array. This technique then is used to measure the error in polarization phase change introduced by the non-birefringence free substrate and also the total polarization phase shift of the substrate and the specimens, and subtracting the results to eliminate that effect caused by the substrate alone. 
     A non-perfect (i.e., a non-birefringence free) substrate containing no specimen is inserted into a system such as the one depicted in  FIGS. 1 and 2 . The substrate is then sequentially illuminated with light at (at least) four different phases for each pixel in the two dimensional area at which specimens may be placed. Each point is referred to as a pixel as related to the sensor mechanism used. A Fourier transformation is performed on the data for measurements made for each pixel to solve for the phase of light altered by the non-perfect material. Specimens are then added to the substrate and the relative phase changes of the light and intensity measurements are repeated. A Fourier transformation is then performed on the measurements made for each pixel of the substrate-specimen combination to solve for the phase of light at each pixel. The calculated polarization phase change contributed by the substrate can then be subtracted from the calculated polarization phase change of the substrate-specimen combination to obtain the phase change of the specimens alone at each or pixel. The phases acquired by Fourier transform ellipsometry add on top of each linearly, so simple subtraction provides the phase change of the specimen alone. 
     There are several methods to achieve this Fourier transform ellipsometry. These methods include: 1) use of a rotating polarizer; 2) changing the retardation value; 3) use of a rotating retarder; and 4) use of a rotating analyzer. Methods 1 and 2 are mathematically equivalent. Method 3 and 4 provide inferior results when compared to the first two methods. In the system depicted in  FIGS. 1 and 2 , methods 1, 2, or 3 may be implemented within the polarized light assembly  210 . 
       FIG. 3A  shows the synchronization line linked from the processor  240  to linear polarizer  211  such that for every image captured, the relative orientation of the linear polarizer  211  is known. The initial orientation of the linear polarizer does not need to be a particular fixed number. However, as the linear polarizer is rotated, that polarization orientation is made known to the processor  240 . 
     In a slightly different setup, as shown in  FIG. 3B , the synchronization line can be linked to control the orientation of a retarder  215  which delays the phase of one of the two orthogonal light polarizations by a selected value, usually expressed in terms of fractions of a wavelength. Typically, the retarder is a quarter wavelength retarder (called a quarter waveplate), which delays the phase of one polarization by a quarter wavelength (or 90°). If the two orthogonal polarizations have equal amplitude, the quarter waveplate retarder will produce light with a circular polarization. By rotating the retarder  251 , the relative phase delay of the entire light beam is offset by the degree of rotation times two. The retarder  215  may also be a variable retarder (such as a Liquid Crystal Variable Retarder (LCVR)) to provide a selectable phase difference between the two orthogonal polarizations. When a variable retarder is used, no rotation of any assemblies is needed. Typically, an LCVR is controlled by a voltage applied to the LCVR, which adjusts the retardation on the slow axis of the LCVR. The selected phase differences through each cycle of retardation are controlled as phase settings of the retarder. The phase settings can be programmed into the processor to automate the retarder setting changes by commands from the processor to the retarder. 
     The birefringence of the substrate may be modeled as relative phase delay between two orthogonal polarization light beams. The measured intensity emerges from the product of a series of Jones matrix operating on the electric field of the linearly polarized light as shown in Eq. 1 below: 
                   I   =              J   analyzer     ·     J   birefrigence     ·     J   sample     ·     J   birefrigence     ·     J   retarder     ·     E     linear   ⁢           ⁢   polarizer              2             Eq   .           ⁢   1               
where
 
               E     linear   ⁢           ⁢   polarizer       =     [           cos   ⁡     [   p   ]                 sin   ⁡     [   p   ]             ]           
and p is the orientation of the linear polarizer.
 
     The Jones matrices for the other components of Eq. 1 are shown in Eqs. 2-5 below. Eq. 2 shows the Jones matrix for the retarder: 
                     J   retarder     =       Exp   (           ⁢       -   ⅈ     ·           ⁢     d   2       )     ⁢           [           ⁢             cos   ⁡     (     d   2     )       +       ⅈ   ·     sin   ⁡     (     d   2     )         ⁢     cos   ⁡     (     2   ⁢           ⁢   r     )                   ⅈ   ·     sin   ⁡     (     d   2     )         ⁢     sin   ⁡     (     2   ⁢           ⁢   r     )                     ⅈ   ·     sin   ⁡     (     d   2     )         ⁢     sin   ⁡     (     2   ⁢           ⁢   r     )                 cos   ⁡     (     d   2     )       +       ⅈ   ·     sin   ⁡     (     d   2     )         ⁢     cos   ⁡     (     2   ⁢           ⁢   r     )                 ⁢           ]                 Eq   .           ⁢   2               
where d is the retardation and r is the orientation of the retarder (either a quarter wave plate or LCVR).
 
     Eq. 3 shows the Jones matrix for the specimen: 
                     J   sample     =     [         1       0           0         Exp   ⁡     (     ⅈ   ·     δ   sample       )             ]             Eq   .           ⁢   3               
where δ specimen  is the amount of phase shift introduced by the specimen at the specimen to substrate interface.
 
     Eq. 4 shows the Jones matrix for light transmission through the birefringent substrate: 
                     J   birefrigence     =         [           cos   ⁡     (   b   )             sin   ⁡     (   b   )                 -     sin   ⁡     (   b   )               cos   ⁡     (   b   )             ]     ⁡     [         1       0           0         Exp   ⁡     (     ⅈ   ·     δ   birefrigence       )             ]       ⁢           [           cos   ⁡     (   b   )             -     sin   ⁡     (   b   )                   sin   ⁡     (   b   )             cos   ⁡     (   b   )             ]                 Eq   .           ⁢   4               
where δ birefringence  is the amount of phase shift introduced by the birefringence in the substrate, and b is the orientation of the birefringence. For simplification, b is assumed to be 0 for the following derivations. This implies that the direction of the molecules in the birefringent material are either parallel or perpendicular to the specimen plane, which is realistic for most substrates. This term operates on the electric field twice, once when the light enters the substrate and once when it exits the substrate. Eq. 5 shows the Jones matrix for the analyzer:
 
                     J   analyzer     =     [             cos   ⁡     (   a   )       2             cos   ⁡     (   a   )       ⁢     sin   ⁡     (   a   )                     cos   ⁡     (   a   )       ⁢     sin   ⁡     (   a   )                 sin   ⁡     (   a   )       2           ]             Eq   .           ⁢   5               
where a denotes the orientation of the analyzer.
 
     As shown by Eqs. 2 through 5, the full expansion of the final intensity value depends on the orientations of the different components in the optical path. However, the final intensity I can be simplified if some of the orientational parameters are assumed to have certain constant values. For example, if the orientations of the analyzer, a, and the linear polarizer, p, are chosen as 0.25π and the orientation of the retarder, r, is chosen as 0π, the intensity may be described as shown below in Eq. 6: 
     
       
         
           
             
               
                 
                   I 
                   = 
                   
                     
                       cos 
                       ( 
                       
                         
                           
                             d 
                             + 
                             
                               δ 
                               sample 
                             
                           
                           2 
                         
                         + 
                         
                           δ 
                           birefrigence 
                         
                       
                       ) 
                     
                     2 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   6 
                 
               
             
           
         
       
     
     Birefringence can decrease or increase the intensity changes that would result just from a phase shift (i.e., polarization change) due to the specimen. It depends on which part of the cosine curve the phase shift of the specimen is at. For example, if the specimen phase shift is a small change around a multiple of 2π (where 2π is a polarization null), birefringence would offset the function from the insensitive plateaus and, in fact, increase the sensitivity of intensity to the phase shift due to the specimen. 
     In Eq. 6, the intensity is shown to be a function of variable retardation, since d is the variable retardation value. In other embodiments, the linear polarizer or retarder orientation may be variable, while the other components are fixed. In all three scenarios discussed above, the orientations of the linear polarizer  213 , retarder  215 , and the analyzer  231  are important. Table 1 describes required orientations of these components, relative to 0°, where 0° is pointing up perpendicularly into the specimen  223 . The orientations are absolute angular differences from 0°. The direction of the difference, which would result in a constant offset of the measured value, does not matter. 
     
       
         
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Polarizer  
                 Retarder  
                 Analyzer  
                   
               
               
                 Method 
                 Angle 
                 Angle 
                 Angle 
                 Retardation 
               
               
                   
               
             
             
               
                 Rotating Polarizer  
                 variable 
                  0° or 90° 
                 ±45° 
                  ±90° 
               
               
                 Rotating Retarder 
                 ±45° 
                 variable 
                 ±45° 
                  ±90° 
               
               
                 Variable 
                 ±45° 
                 ±0° or 90° 
                 ±45° 
                 Variable 
               
               
                 Retardation 
                   
                   
                   
                   
               
               
                 Rotating Analyzer 
                 ±45° 
                  0° or 90° 
                 variable 
                 ±180° 
               
               
                   
               
             
          
         
       
     
     The intensities as a function of the controlled variable are described in the equations set forth below. The intensity at each pixel of the two dimensional detector  233  may be different during a single measurement, because the phase changes due to the birefringent substrate may be spatially changed. Eq. 7 below shows the intensity obtained with the variable retardation method described above. Note that the intensity is a function of the condition of the specimen, the birefringence of the substrate, and the controlled variable retardation. 
     
       
         
           
             
               
                 
                   
                     I 
                     ⁡ 
                     
                       ( 
                       
                         phase 
                         retardation 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       cos 
                       ( 
                       
                         
                           
                             
                               phase 
                               sample 
                             
                             + 
                             
                               phase 
                               retardation 
                             
                           
                           2 
                         
                         + 
                         
                           phase 
                           birefrigence 
                         
                       
                       ) 
                     
                     2 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   7 
                 
               
             
           
         
       
     
     Eq. 8 below shows the intensity obtained with the rotating polarizer method. 
     
       
         
           
             
               
                 
                   
                     I 
                     ( 
                     
                       polarizer 
                       ⁢ 
                       
                         
                             
                         
                         ⁢ 
                         
                             
                         
                       
                       ⁢ 
                       orientation 
                     
                     ) 
                   
                   = 
                   
                     
                       cos 
                       ( 
                       
                         
                           phase 
                           rotation 
                         
                         - 
                         
                           
                             phase 
                             sample 
                           
                           2 
                         
                         - 
                         
                           phase 
                           birefringence 
                         
                       
                       ) 
                     
                     2 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   8 
                 
               
             
           
         
       
     
     Eq. 9 below shows the intensity obtained with the rotating retarder method where the retarder is a half-wave plate. 
     
       
         
           
             
               
                 
                   
                     I 
                     ⁡ 
                     
                       ( 
                       
                         retarder 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         orientation 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         - 
                         
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   phase 
                                   sample 
                                 
                                 + 
                                 
                                   2 
                                   × 
                                   
                                     phase 
                                     birefringence 
                                   
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     cos 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         2 
                                         × 
                                         
                                           phase 
                                           orientation 
                                         
                                       
                                       ) 
                                     
                                   
                                   2 
                                 
                               
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   9 
                 
               
             
           
         
       
     
     Eq. 10 below shows the intensity obtained if the analyzer is rotated. 
     
       
         
           
             
               
                 
                   
                     I 
                     ⁡ 
                     
                       ( 
                       
                         analyzer 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         orientation 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         - 
                         
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   phase 
                                   sample 
                                 
                                 + 
                                 
                                   2 
                                   × 
                                   
                                     phase 
                                     birefrigence 
                                   
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     cos 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         phase 
                                         orientation 
                                       
                                       ) 
                                     
                                   
                                   2 
                                 
                               
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   10 
                 
               
             
           
         
       
     
     Polarization phase can be extracted from all pixels of the two dimensional imaging array by performing a Fourier transformation on as few as four images at each pixel. The images should be spaced evenly through a complete cycle of these periodic functions (the period is 180° for square of cosine functions). For example, if four images are taken using the variable retardation method, each image should be retarded by 90° from each other as indicated by Eq. 7 above. If the rotated polarizer or analyzer method is used, the polarizer should be rotated 45° in each image as indicated by Eqs. 8 or 10 above. If the rotated retarder method is used, the retarder should be rotated by 22.5° from image to image as indicated by Eq. 9 above. 
     The phase change, as one value, is extracted from the images by performing a Fourier transform, in a manner similar to the Fourier transform ellipsometry described above. If four images are taken, then at a given imaging location, the four intensity values are fed into the Fourier transform which generates two numbers, amplitude and phase. When the Fourier transform is applied on every single pixel, an image of amplitude values and an image of phase values would be generated. The phase value of the specimen can be extracted by performing the Fourier transform ellipsometry before the specimen is added, so that the result obtained contain only the birefringence phase impact. This is termed a baseline measurement. The specimen is then added and the Fourier transform ellipsometry is performed again using multiple images. Simple subtraction is then used to remove the impact of birefringence from the measured signal. 
     Eq. 11 and 12 below show how Fourier transformation is performed with data obtained from the use of a variable retarder. Eq. 7 to 10 can be expanded and expressed as terms that contain the controlled variable, which can be the orientation of a component or the retardation value, and terms that are not directly controllable. The Fourier method extracts the exact phase shift from the terms containing the controllable variables, denoted as δ in Eq. 11. The Fourier transformation of the not-directly controllable terms yields zero. The change in specimen phase shift, δ 0 , over time can be viewed as a change from the baseline which includes the birefringence. In a continuous mathematical model, intensity images as functions of δ undergo the Fourier Transformation as shown below: 
     
       
         
           
             
               
                 
                   X 
                   = 
                   
                     
                       
                         ∫ 
                         0 
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           π 
                         
                       
                       ⁢ 
                       
                         
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   δ 
                                   + 
                                   
                                     δ 
                                     0 
                                   
                                 
                                 2 
                               
                               ) 
                             
                           
                           2 
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             δ 
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ⅆ 
                           δ 
                         
                       
                     
                     = 
                     
                       
                         π 
                         2 
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           
                             δ 
                             0 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   11 
                 
               
             
             
               
                 
                   Y 
                   = 
                   
                     
                       
                         ∫ 
                         0 
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           π 
                         
                       
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               
                                 δ 
                                 + 
                                 
                                   δ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             δ 
                             ) 
                           
                         
                         ⁢ 
                         
                           ⅆ 
                           δ 
                         
                       
                     
                     = 
                     
                       
                         π 
                         2 
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           
                             δ 
                             0 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     The exact phase shift can then be computed as shown in Eq. 12 below: 
     
       
         
           
             
               
                 
                   
                     δ 
                     0 
                   
                   = 
                   
                     arctan 
                     ⁡ 
                     
                       ( 
                       
                         Y 
                         X 
                       
                       ) 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   12 
                 
               
             
           
         
       
     
     In practice, the variable retardation values can be set to discrete values, such as 0, 0.5π, π and 1.5π to obtain a reasonable calculation for the exact phase shift. Eqs. 11 can be discretized as 
                     X   =       ∑     i   =   0     n     ⁢       cos   ⁡     (     i   *       360   ⁢   °     n       )       ⁢     I   i           ⁢     
     ⁢     Y   =       ∑     i   =   0     n     ⁢       sin   ⁡     (     i   *       360   ⁢   °     n       )       ⁢     I   i                   Eq   .           ⁢   13               
where n is the total number of measurements, i is the index of each measurement, and I is the intensity value measured. Note also that Eq. 11 is expressed in terms of varying the retardation. Similar equations can be derived when the orientations of the linear polarizer or retarder are varied.
 
     In Eqs. 9 to 10, the square of cosines are modulated by the functions of the specimen variables: the phase of the specimen and the phase of the birefringence. The functional forms are cosine functions, similar to the phase part. When the specimen variables are in the format of Eqs. 9 to 10, that is, appearing as the modulation of the controlled variable, they can be extracted from the amplitude of the Fourier transform, as shown in Eqn. 14.
 
Amplitude=√{square root over ( X   2   +Y   2 )}  Eq. 14
 
It is also possible to mix the above modes and control more than two variables on the instrument at the same time. For example, when the phases of specimen and birefringence add up to exactly integer multiple of 360°, the amplitude of Eq. 8 becomes zero regardless of the orientation of the analyzer. The phase cannot be measured when there is no amplitude. In this case, rotating the retarder or changing the polarizer orientation by a fixed amount can move the amplitude away from the zero point.
 
       FIG. 4  illustrates the data processing steps according to an embodiment of the present invention. The following explains how data is acquired and sent to a specially programmed computer which is programmed to perform the calculations in order to correct for birefringence caused by the substrate or slide on the surface of which the specimens have been deposited over a 2D area and thereby provide an image based only on the phase changes caused by the specimens in the evanescent field in which the 2D area is contained. In step  401 , a substrate is positioned within a single reflection assembly (such as the assembly  220  shown in  FIGS. 1 and 2 ). Polarized light is directed towards the substrate with the polarization set to a specified phase. Step  403  shows that a retarder such as an LCVR set to a phase i*360°/n, specified by the ith step of acquisition and the total number of n acquisitions. In the case where an LCVR is used, the computer is programmed to set the retarder to the selected phases and to record the phase settings. Other embodiments may use other devices or methods for selecting the phase of the polarized light as described above, but in each case the phase settings are saved in or inputted into the processor. Step  405  shows that a two-dimensional intensity image of the light reflected from the substrate is then acquired using a light detection device, such as a charge-coupled detector. The detector typically comprises hundreds to millions of detecting pixels arranged in a two-dimensional array. The term “intensity image” at 405 is intended to mean a set of intensity values for each pixel at each setting of the LCVR. An intensity value for each pixel is then provided to the computer or computer storage device, so the computer or computer storage device stores an intensity image which is an array containing hundreds to millions of intensity values for reflected light at the specified phase, that is, an intensity value for each pixel. As shown by steps  403  and  405 , the LCVR is then set to another phase and another intensity image is acquired and stored. The steps of setting the LCVR and acquiring an intensity image are repeated four times at selected four different phases. While this description speaks of four phase settings, it is understood that more than four phase settings may be used. The phase settings are input to the computer which is programmed to use the settings to control the LCVR. The acquired image intensity data is sent to the computer and stored for use as below. Box  410  then shows that a Fourier transform is performed on the acquired and stored data. The Fourier Transform calculations may be performed by a specially programmed general purpose computer, signal processing hardware, programmable logic devices, or other processing and/or calculating devices which are specially programmed to perform the steps. Note that the Fourier transform is performed on a pixel-by-pixel basis. That is, a Fourier Transform is calculated using the intensity values at each different phase for a pixel to provide a Fourier Transform result for that pixel. The Fourier Transform calculations are performed for every pixel to provide a Fourier Transform result for every pixel in the intensity image. The steps within Box  410  show the calculations that may be used to perform the pixel-by-pixel Fourier Transform by the specially programmed computer. Step  411  shows a cosine calculation applied to the intensity values at a pixel and step  412  shows a sine calculation applied to the intensity values at the same pixel. The cosine results and sine results for the pixel are summed as shown in steps  413  and  414 . The Fourier Transform result for the pixel is shown at step  415  by the arctangent calculation. Note again that these steps are performed for every pixel in the intensity image. The result of the calculations performed at step  415  is an array of values δ0. 
     The specimen testing portion of the procedure is then undertaken, again using the specially programmed computer to perform the following steps, generally the same as the steps with no specimen. Step  501  shows that a specimen is then positioned on the substrate. Similar to steps  403  and  405 , steps  503  and  505  shows that retarder such as an LCVR is used to shift the phase of polarized light directed at the specimen, record the phase settings, and using intensity values for each phase setting, an intensity image is determined for each selected phase. The steps of shifting the phase of the polarized light and acquiring an intensity image are repeated at least four times at the selected four different phases and the intensity images at four different phases are acquired and stored. The four phases may be the same as or different than the phases used in steps  403  and  405 . After the intensity images at several phases are acquired and stored, Box  510  shows that Fourier Transform calculations are performed by the specially programmed computer on a pixel-by-pixel basis for the intensity images acquired with a specimen on the substrate. Steps  511  and  512  show the performance of cosine and sine intensity calculations and steps  513  and  514  show the summation of those results. Step  515  shows a Fourier Transform result for each pixel is obtained by performing an arctangent calculation. The result from step  515  is an array of values δ. Step  610  shows that in the computer, the array of values δ0 is subtracted from the array of values δ to provide a resultant array of values where each value corresponds to a pixel in the two-dimensional detector. This resultant array may be displayed by a display device to show the detected specimen without distortions caused by birefringence in the substrate, as shown by step  620 . The processing system may be configured to provide a user with simple intensity image or may apply other image manipulation techniques to highlight the polarization changes due to the specimen under evaluation. The processing system may also be configured to provide data to other processes or devices for further analysis of the data. 
     In all of the foregoing, and including variations in which the phase changes are accomplished by changing the settings of the polarizer, variable retardation and varying the analyzer, the rules set out in Table 1 above must be observed and the computer is programmed accordingly. 
     As discussed above, the phase change due to the non-birefringent free substrate contributes linearly to the phase change of the combination of the non-birefringent free substrate and the specimen(s). Thus, the phase change due to the non-birefringent free substrate can simply be subtracted from the phase change due to the combination of the non-birefringent free substrate and the specimen(s) to obtain the phase change resulting from the specimen(s) alone. Step  600  represents this subtraction, which is performed by subtracting each pixel of the substrate only phase image  420  from the corresponding pixel in the substrate/specimen(s) phase image  520 . The resultant phase image  620  represents the phase or polarization shifts due to the specimen(s) alone. 
     Note that while the description above refers to operations being performed on pixels within the intensity images, these pixels may be grouped into locations for processing. That is, the intensity values for multiple pixels may be summed or summed and normalized to produce intensity values for locations within the two-dimensional detector before performing Fourier transforms on the location intensity values to reduce the number of Fourier calculations required. Fourier transform calculations techniques such as a Fast Fourier Transform calculation may also be used to speed the calculation of the Fourier Transform data. 
       FIGS. 5A and 5B  show the steps to obtain the specimen only phase image using the system depicted in  FIGS. 1 and 2 . These steps are performed as above using the specially programmed computer/processor. In  FIG. 5A , step  701  represents placing the non-birefringence substrate into the single reflection assembly  220  of  FIG. 2 . Step  711  represents the measurement of a first intensity image with the two-dimensional detector  233  at an initial phase angle. The phase of light is then changed by performing one or more of the following actions: changing the angle of the linear polarizer  213  as shown in step  713 ; changing the angle of the retarder  215  as shown in step  715 , changing the value of the retarder  215  as shown by step  717 , and changing the angle of the analyzer  231  as shown by step  719 . Step  721  shows the measurement of a second intensity image at the second phase angle. The phase of light is then again changed by performing one or more of the following actions: changing the angle of the linear polarizer  213  as shown in step  723 ; changing the angle of the retarder  215  as shown in step  725 , changing the value of the retarder  215  as shown by step  727 , and changing the angle of the analyzer  231  as shown by step  729 . Step  731  shows the measurement of a third intensity image at the third phase angle. The phase of light is then changed for a third time by performing one or more of the following actions: changing the angle of the linear polarizer  213  as shown in step  733 ; changing the angle of the retarder  215  as shown in step  735 , changing the value of the retarder  215  as shown by step  737 , and changing the angle of the analyzer  231  as shown by step  739 . Step  741  shows the measurement of a fourth intensity image at the fourth phase angle. Step  751  represents the performance of a Fourier Transformation on the measured intensity images to generate an amplitude image and a phase image  761  for the substrate. 
     In  FIG. 5B , step  801  represents placing a specimen or specimens on the non-birefringence substrate into the single reflection assembly  220  of  FIG. 2 . Step  811  represents the measurement of a first intensity image with the two-dimensional detector  233  at an initial phase angle. Note that this initial phase angle or the subsequent angles do not have to be the same as those used to measure the substrate only. The phase of light is then changed by performing one or more of the following actions: changing the angle of the linear polarizer  213  as shown in step  813 ; changing the angle of the retarder  215  as shown in step  815 , changing the value of the retarder  215  as shown by step  817 , and changing the angle of the analyzer  231  as shown by step  819 . Step  821  shows the measurement of a second intensity image at the second phase angle. The phase of light is then again changed by performing one or more of the following actions: changing the angle of the linear polarizer  213  as shown in step  823 ; changing the angle of the retarder  215  as shown in step  825 , changing the value of the retarder  215  as shown by step  827 , and changing the angle of the analyzer  231  as shown by step  829 . Step  831  shows the measurement of a third intensity image at the third phase angle. The phase of light is then changed for a third time by performing one or more of the following actions: changing the angle of the linear polarizer  213  as shown in step  833 ; changing the angle of the retarder  215  as shown in step  835 , changing the value of the retarder  215  as shown by step  837 , and changing the angle of the analyzer  231  as shown by step  839 . Step  841  shows the measurement of a fourth intensity image at the fourth phase angle. Step  851  represents the performance of a Fourier Transformation on the measured intensity images to generate a phase image  861  for the specimen and substrate combination. Step  871  represents the subtraction of the substrate only image  761  from the specimen and substrate phase image  861  to generate a specimen only phase image  881 . 
     The changes in the polarizer, retarder, or analyzer angle or the retardation value should follow the procedures described above. Also, as mentioned above, more than four different phases may be used to generate more than four intensity images for either substrate only images or specimen and substrate images. Also, as discussed above, the intensity images may be based only on pixel values or on values for groups of pixels. The phase images may be represented as two-dimensional matrices or with vectors or other data structures. 
     Now referring to  FIGS. 6 through 9 . In  FIGS. 6 and 7  there is shown a slide assembly  900  (see  220  at  FIG. 2 ) having a slide, also referred to as a substrate  901  and a multiwell plate  902  which is securely mounted on the slide. The slide  901  has an upper surface  903  and a lower surface  904 . The multiwell plate  902  is shown transparently and has two rows of wells  905   a  and  905   b . Wells  905   a  and  905   b  are open at the bottom for access to the upper surface  903  of the substrate. The lower or bottom surface  904  of the substrate is configured with a set of grooves defining prismatic surfaces  906  extending the length of the substrate. Referring to  FIG. 8 , there is shown a light beam  907   a  aimed along axis  908   a , at the bottom of the substrate  901 . The beam hits the grooves which define two adjacent prismatic light incident surfaces  906   a  such that the beam passes into the substrate and reflects at the upper surface  903  then extending as an exiting beam of light  907   b  through and out of the substrate  901  along axis  908   b  passing across the grooves which define two prismatic light exiting surfaces  906   b . The surfaces  906   a  and  906   b  are set at selected angles to control the direction of the beam in the substrate to establish an evanescent field at the surface  909 , and in the example illustrated they are normal to the axis  908  of the incoming beam, although they could be at an angle to the beam axis. The area  909  is therefore where specimens can be studied by practice of the invention described herein. In the particular case of  FIG. 8 , the beam or the slide assembly, preferably the latter as shown by the arrow  910 , will be moved so that the beam can be aimed at the second row of wells  905   b .  FIG. 9  shows a substrate (slide)  1004  that has a set of single grooves. The groove aligned with the incoming beam axis  1008   a  defines a prismatic light incident surface  1006   a  and the groove aligned with the exiting beam axis  1008   b . Therefore, an evanescent field is at area  1009  at the surface  1003 . 
     In all cases the angle of entry and exit of the beam must enable formation of an evanescent field. It is well known that at the “critical angle” under Snell&#39;s law an evanescent field is established. Total internal reflection (TIR), where the amount of light available for detection is maximized, is understood to be the preferred condition for selecting the angle. Angles at or more than the critical angle will result in total internal reflection. But total internal reflection is not required for functioning of this system and method herein. In practical application, the equipment may not allow an angle for total internal reflection, or it may not allow for precise setting. Angles less than the critical angle will work, with of course decreasing intensity of the reflected beam as the angles gets further away from the critical angle. Further because of variables in a particular set up, the critical angles may not be exactly known. It has been found that even as little as 10% of the light returning in the reflected beam can give useful results in some set-ups. 
     While the foregoing describes one type of biochip, they come in many forms and it is a rapidly evolving technology. In general it can be appreciated that biochips come to a user in two generic types. One type has the probes or other chemistry already deposited on a surface and the other type permits the user to deposit material onto the surface. The terms “microarray” and micro fluidic array” also define types of biochips. The present invention is understood to apply to any type of biochip that can be implemented for study of material on a surface by single internal reflection of polarized light to determine polarization phase shift caused by the material under study including comparison of phase shift for study of changes in the material that is imaged by sequential reflection measurements and imaging. 
     The foregoing Detailed Description of exemplary embodiments is presented for purposes of illustration and disclosure in accordance with the requirements of the law. It is not intended to be exhaustive nor to limit the invention to the precise form or forms described, but only to enable others skilled in the art to understand how the invention may be suited for a particular use or implementation. The possibility of modifications and variations will be apparent to practitioners skilled in the art. 
     No limitation is intended by the description of exemplary embodiments which may have included tolerances, feature dimensions, specific operating conditions, engineering specifications, or the like, and which may vary between implementations or with changes to the state of the art, and no limitation should be implied therefrom. In particular it is to be understood that the disclosures are not limited to particular compositions or biological systems, which can, of course, vary. This disclosure has been made with respect to the current state of the art, but also contemplates advancements and that adaptations in the future may take into consideration of those advancements, namely in accordance with the then current state of the art. It is intended that the scope of the invention be defined by the Claims as written and equivalents as applicable. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting. Reference to a claim element in the singular is not intended to mean “one and only one” unless explicitly so stated. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the content clearly dictates otherwise. The term “several” includes two or more referents unless the content clearly dictates otherwise. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the disclosure pertains. 
     Moreover, no element, component, nor method or process step in this disclosure is intended to be dedicated to the public regardless of whether the element, component, or step is explicitly recited in the Claims. No claim element herein is to be construed under the provisions of 35 U.S.C. Sec. 112, sixth paragraph, unless the element is expressly recited using the phrase “means for . . . ” and no method or process step herein is to be construed under those provisions unless the step, or steps, are expressly recited using the phrase “comprising step(s) for . . . .” 
     A number of embodiments of the disclosure have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the present disclosure. Accordingly, other embodiments are within the scope of the following claims.