Abstract:
A method for determining polarization properties of light from an object uses a detector for detecting the intensity of light incident thereon. A pair of variable retarders are positioned in the optical path with their slow optical axes at a 45° angle to each other, and a polarized light analyzer is also placed in the optical path between the light retarders and the detector. For each of the light retarders, a base retardance level is determined. The base retardance level is such that when each of the light retarders is set at the base retardance thereof and light from an object is circularly polarized, the light analyzer will cause substantial extinction of light from the object that traverses the analyzer and the intensity of light from the object incident on the detector will be substantially zero. Then, the retardance of the light retarders is set at a first retardance level in which the retardance of at least one of said retarders is different from the base retardance thereof and the intensity of light incident on said detector when said light retarders are set at the first retardance level is determined. This procedure is repeated with the retardance of the light retarders set at a second, and different retardance level. The polarization properties of the light is determined from the intensities measured at the different retardance levels.

Description:
FIELD OF INVENTION 
     This invention relates to polarized light and, more particularly, to a polarized light microscope for measuring polarization properties of light and submicroscopic specimen anisotropy. 
     BACKGROUND OF INVENTION 
     The polarized light microscope (&#34;pol-scope&#34;) has the ability to measure submicroscopic molecular arrangements dynamically and non-destructively in living cells and other specimens. For this reason, it has been widely used in the field biological research, as set forth in the publications discussed below, which are incorporated herein by reference. 
     G. Valentin published the first observations on the appearance of parts of organisms between crossed nicols (Valentin, G. 1861. Die Untersuchung der Pflanzen- und der Thiergewebe in polarisiertem Lichte. Leipzig). The use of polarized light microscopy as applied to biology was marked by the numerous observations by W. J. Schmidt on the structure and development of skeletal and cellular components (Schmidt, W. J. 1924. Die Bausteine des Tierkorpers in polarisiertem tichte. Cohen, Bonn.; Schmidt, W. J. 1937. Die Doppelbrechung von Karyoplasma, Ztoplasma und Metaplasma. Borntrager, Berlin). Schmidt inferred the orientation of lipid molecules in membranes from observations in the polarized light microscope, before it was confirmed by X-ray diffraction. By carefully analyzing and eliminating sources of stray light in the polarizing microscope, Swann and Mitchison improved the sensitivity of the instrument considerably. (Swann M. M. and J. M. Mitchison. 1950. Refinements in polarized light microscopy. J. Exp. Biol. 27:226-237) and Inoue (Studies on depolarization of light at microscope lens surfaces. I. The origin of stray light by rotation at the lens surfaces. Exp. Cell Res. 3:199-208 ). With the improved sensitivity Inoue demonstrated the existence of fibers in the mitotic spindle directly in living cells (Inoue, Polarization optical studies of the mitotic spondle. I. The demonstration of spindle fibers in living cells. Chromosoma 5:487-500). 
     The introduction of the polarization rectifier increased the sensitivity further by a factor of 10 (Inoue, S. and W. L. Hyde. 1957. Studies on depolarization of light at microscope lens surfaces II. The simultaneous realization of high resolution and high sensitivity with the polarizing microscope. J. Biophys. Biochem. Cytol. 3:831-838), and led to a landmark study of DNA arrangement in living sperm (Inoue, S. and H. Sato. 1966. Deoxyribonucleic add arrangement in living sperm. In Molecular architecture in cell physiology. T. Nayashi and A. G. SzentGyorgyi, Editor. Prentice Hall, Englewood Cliffs, N.J. 209-248). However, it took Inoue and Sato three man-years to collect and analyze the data taken from three individual sperms with the high resolution, linear polarized light microscope. 
     Many of the pioneering studies in polarizing microscopy were associated with special instrumental developments to observe ever finer structural details and measure more rapidly specimen birefringence occurring in e.g. cytoplasmic flow or during rigor to relax transition in vertebrate striated muscle (Taylor, D. L. 1976. Quantitative studies on the polarization optical properties of striated muscle I. Birefringence changes of rabbit psoas muscle in the transition from rigor to relaxes state. J. Cell Biol. 68:497-511). Early automated detection schemes measured the magnitude of specimen birefringence in a single point (spot size 1.3 Micrometer diameter or larger, characteristic time constant 1/10 ms or longer) with an excellent sensitivity of a fraction of an Angstrom of specimen retardance. (Takasaki, H. 1961. Photoelectric measurement of polarized light by means of an ADP polarization modulator. I. Photoelectric Polarimeter, II. Photoelectric elliptic polarimeter. J. Opt. Soc. Am. 51:462-463) (Takasaki, H. 1961. Photoelectric measurement of polarized light by means of an ADP polarization modulator. III. Measurement of linear birefringence, IV. Lens interferometer. J. Opt. Soc. Am. 51:1146-1147); (Allen, R. D., J. Brault and R. D. Moore. 1963. A new method of polarization microscopic analysis I. Scanning with a birefringence detection system. J. Cell Biol. 18:223-235); (Taylor, D. L. and R M. Zeh. 1976. Methods for the measurement of polarization optical properties I. Birefringence. J. Microsc. 108:251-259); (Hiramoto, Y., Y. Hamaguchi, Y. Shoji and S. Shimod. 1981. Quantitative studies on the polarization optical properties of living cells I. Microphotometric birefringence detection system. J. Cell Biol. 89:115-120) However, the low spatial resolution, especially the restriction to a single point or area, and the fixed orientation of the measured birefringence limited the use of these detectors. 
     The restriction of the measurement of optical anisotropy to a single specimen point was overcome by Tinoco and collaborators in a structural study of spermatocyte nuclei, by introducing a scanning stage in their differential polarization microscope (Mickols, W., M. F. Maestre and I. Tinoco Jr. 1987. Differential polarization microscopy of changes in structure in spermatocyte nuclei. Nature 328:452-454; Oldenbourg, R. 1991. Analysis of edge birefringence. Biophys. J. accepted for publication). The optical path in this instrument is similar to a transmission, stage scanning confocal microscope. While the spatial resolution and sensitivity is high, the time required to obtain a complete image is about 45 minutes. 
     The use of video cameras to record images of birefringent specimens with the polarized light microscope was first introduced by Allen and collaborators (Allen, R. D., J. L. Travis, N. S. Allen and Ho Yilmaz. 1981. Video-enhanced contrast polarization (AVEC-POL) microscopy: A new method applied to the detection of birefringence in the motile reticulopodial network Allogromia laticollaris. Cell Motil. 1:275-289) and by Inoue (1981. Video image processing greatly enhances contrast, quality and speed in polarization-based microscopy. J. Cell Biol. 89:346-356). To measure specimen birefringences from recorded images one can use a predetermined calibration curve to relate measured intensities to specimen birefringences in different parts of the image (Schaap, C. J. and A. Forer. 1984. Video digitizer analysis of birefringence along the length of single chromosomal spindle fibres I. Description of the system and general results.]. Cell Sci. 65:21-40). This method is relatively fast, but subject to errors from variations in light intensities that stem from other sources than birefringence, e.g. light scattering or shading. In a study on edge birefringence, Oldenbourg recorded images of a given specimen at several different compensator settings and used the stack of images to compute the specimen birefringences independent of the overall intensity and the background light in different parts of the viewing field. Oldenbourg, R. 1991. Analysis of edge birefringence. Biophys. J. Vol. 60 page 629. 
     With the traditional pol-scope, thus, single images display only those anisotropic structures that have a limited range of orientations with respect to the polarization axes of the microscope. Furthermore, rapid measurements are restricted to a single image point or single area that exhibits uniform birefringence or other form of optical anisotropy, while measurements comparing several image points take an inordinately long time. 
     There remains a need for a pol-scope that will permit data collection and determination of anisotropic structures (e.g., specimen birefringence) irrespective of orientation and over a wide range of magnitude, and that will do so in a short period of time. 
     SUMMARY OF INVENTION 
     The present invention provides for rapid and simultaneous determination of polarization characteristics, e.g., ellipticity and orientation of refractive index ellipses and differential absorbance or reflectivity, in the examination or measurement of structural anisotropies such as birefringence, dichroism and polarized fluorescence. The polarized light microscope (&#34;pol-scope&#34;) of the present invention employes nearly circularly polarized light and a pair of electro-optical modulators whose reference axes are rotated at 45 degrees to each other. A video camera and computer-assisted image analysis system provide fast, and essentially simultaneous, measurements of specimen anisotropy (e.g., retardance magnitude and azimuth) at all points of the image constituting the field of view. 
     The present invention can be implemented in different, but closely related ways to determine polarization optical parameters (e.g., birefringence, dichroism, differential reflectivity, polarized fluorescence) of materials as diverse as planetary surfaces in remote sensing, thin films in ellipsometry, geological samples in mineral explorations, metallurgical, plastic, glass, ceramic and crystalline materials in manufacturing and processing control, and biological cell and tissue sample in basic research and clinical applications. 
     The measurement process of the invention as presently implemented results in particularly clear images free of shading and background light over the entire viewing field. The images and measurements document fine structural and molecular organization within a thin optical section of the specimen. The high spatial and temporal resolution of the new pol-scope, together with its ease of use for obtaining quantitative specimen records concurrently for the whole field of view, allows new investigations into the dynamics of macromolecular organization of living cells and other systems. 
     The system of the present invention has the ability to display sequentially the spatial distribution, and rapidly measure the temporal changes in: birefringence due to intra-molecular anisotropy or fine-structural form, and (with some modification to the basic scheme) polarized fluorescence in molecular moiety selectively labeled with reporter dyes, and dichroism exhibited by naturally occurring chromophores. Biological mechanisms and macromolecular phenomena that can be explored taking advantage of these unique capabilities of the invention include: 
     * Regulated assembly and disassembly of microtubules, actin filaments, and other cytoskeletal elements and their role in organelle transport, cell division, cell differentiation. 
     * Functional role and organization of DNA tertiary structure as displayed in decondensing sperm head, polytene chromosomes and chromatin of lower eukaryotes. 
     * Conformational and micro-environmental changes associated with motility and transport functions in myosin, dynein, membrane proteins. 
     * Turnover and functional changes of stacked membrane structures such as in retinal rods and cones, chloroplasts, Golgi bodies. 
     * Spontaneous and induced generation of ordered domains in liquid crystals, polymer solutions and lipid layers, and their Brownian, cyclic, and propagatod fluctuations. 
    
    
     DRAWINGS 
     FIGS. 1-3 schematically illustrate polarizing microscopes embodying the present invention. 
     FIG. 4 illustrates a display of birefringence obtained using the present invention. 
     FIG. 5 is a simplified flow-chart illustrating the sequence of operation of an embodiment of the present invention. 
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
     FIG. 1 illustrates the system of the present invention as built-up in a Nikon Microphot-SA optical microscope stand. As is conventional, the microscope itself includes a mercury arc lamp 10, and a condenser lens 12 and an objective lens 14 (e.g., a 60× 1.4-NA Plan APO objective lens) on opposite sides of a sample stage 15. The light from a sample on the sample stage is directed to a CCD video camera 16 with camera controller 18 (Dage-MTI model CCD-C72). 
     According to this embodiment of the present invention, the light path between the mercury arc lamp 10 and video camera 16 also includes, on the illumination side of the condenser lens 12, an interference filter 20, a linear polarizer 22 (mounted with its axis at 0° to a reference axis), and a pair of variable, liquid crystal, electro-optical retarders 24, 26 with their principal slow axes positioned, respectively, at 45° and 0° to the reference axis. In the optical path on the imaging side of the sample stage 15 and objective lens 14, i.e., between the objective lens and the video camera 16, is a left circular analyzer 28. In the disclosed preferred embodiments, the variable retarders/electro-optic modulators are liquid crystal devices (e.g., obtained from Cambridge Research and Instrumentation, Inc. of Cambridge, Mass.). In other embodiments, other variable retarders/ electro-optic modulators, such as Pockels cells, may also be used. Similarly, other light sources, e.g., incandescent lamps or lasers, may be used in place of mercury vapor lamps; monochromoters or the like may be used in lieu of an interference filter; and a general purpose two-dimensional detector maybe used in lieu of the CCD video camera and associated optics of the preferred embodiments. 
     It will be appreciated that linear polarizer 22 and circular analyzer 28 are located in the same positions in the optical path as are the polarizer and analyzer in a traditional microscope, but that in traditional microscopes a linear analyzer is conventionally used and a sample on sample stage 15 is illuminated with linearly polarized light. Circular polarizers are usually fabricated as a stack of a linear polarizer followed by a quarter wave plate. 
     It will also be appreciated that, in the illustrated embodiment, the two variable retarders 24, 22 are located in the illumination path between circular polarizer 22 and the condenser lens 12. In other embodiments, the variable retarders may be placed in the imaging path (as shown in FIG. 2), or on opposite sides of the specimen stage 15 (as shown in FIG. 3) instead of entirely in the illuminating path. 
     It will also be appreciated that the embodiments disclosed in FIGS. 1-3 herein employ transmission microscopes in which the illuminating and imaging paths are on opposite sides of the specimen stage. The present invention may also employed in epi-illumination microscopes for measurement of reflective samples. In such epi-illumination microscopes, a single objective lens serves both as a condensor to illuminate the specimen and as an objective to collect the back-scattered light from the speciment and project an image on the video cameras. In these embodiments, a beam splitter, known to be specially designed for reflective polarized light microscopes to minimize polarization abberations, is placed on the side of the objective away from the specimen (i.e., the objecive lens is between the beam splitter and the specimen) to separate the illumination path from the imaging path. 
     As illustrated in connection with the transmission microscope systems of FIGS. 1-3, a pair of variable retarders, a polarizing analyzer, and (depending on the particular embodiment) one or more other polarizing elements, are placed in the illumination and imaging paths. Retarders, analyzers and other polarizing elements of equivalent type are positioned in equivalent positions in the illumination and imaging paths of reflective polarized light microscope systems. Further, the operation of epi-illumination microscope systems embodying the present invention is essentially the same as described hereinafter with respect to the embodiments of FIGS. 1-3 which employ transmission-type microscopes to measure polarized light and specimen optical properties. 
     In all of the disclosed embodiments, each retarder/electro-optic modulator retards, and thus affects the polarization state of light passing through it. The extent to which the polarization state of the light passing through a particular retarder is changed, in both ellipticity and azimuth, can be controlled by varying the voltage applied to the retarder. In the illustrated embodiments, the two retarders are set with their slow axes at 45° to each other; and the pair of retarders together is able to change any elliptically polarized light into any other elliptical polarization (including linear and circular) by changing the retardence levels of individual retarders to appropriate values. 
     Both liquid crystal and Pockel cell retarders are commercially available in precision quality and suitable for imaging purposes. Liquid crystal retarders are made from nematic liquid crystals between optically flat, fused silica substrates with transparent front electrodes suitable for applying a voltage across the liquid crystal material. With a moderate voltage between 0 and 40 V, the liquid crystal reorients and the retardance of the assembly changes in the range from e.g., 1100 nm to 100 nm. With a fixed retarder added in the subtractive position the useful retardance range can be changed to e.g. -500 . . . +500 nm. The typical response time is 40 ms, which is close to the time period of one video frame. Pockels cells, which are made from thin, Z-cut KD*P crystals, have a much faster response time of 1 microsecond. Their retardance is controlled in the desired range by a high voltage between -1000 V and +1000 V. In Pockels cells, the retardance changes linearly with voltage. 
     In the embodiment of FIG. 1, light produced by the mercury arc lamp 10 is first filtered, and a narrow wave band (e.g., 546 mm) is selected and passed, by filter 10. Liquid crystal variable retarders 24, 26 are initially set (i.e., by selection of the voltage applied to each by retarder drive 25) so that retarder 24 acts as a quarter wave (λ/4) plate and retarder 26 acts as a half wave (λ/2) plate. 
     As will be seen, the monochromatic light from filter 20 is linearly polarized. When set as a quarter wave plate, variable retarder 24 causes the linearly polarized light passed through it to become left circularly polarized. When set as a half wave plate, variable retarder 26 causes the left circularly polarized light passed through it to become right circularly polarized. The right circularly polarized light from retarders 26 illuminates a specimen 38 on stage 15, and the light traversing any region of a specimen will be rendered elliptically polarized by any linear birefringence or dichroism of the specimen region traversed. Thus, the image formed by objective lens 14 (assuring specimen birefringence or similar anisotropy) will contain elliptically polarized light. The amount of light from each specimen region that passes through left circular analyzer 28, and the intensity of the light that falls on each detector of the CCD detector array of video camera 16, depends on the extent of ellipticity of the light. 
     The images produced by the light incident on the detectors of the CCD detector array of video camera 16 are recorded at a regular rate, e.g., 30 frames a second. Between frames, the voltages applied to retarders 24, 26 may be changed, thus causing changes in the ellipticity of the light incident on the specimen and in the intensity of the light incident on the detector array of camera 16. 
     If, as in this embodiment, liquid crystal devices are employed as retarders, at least two frame periods are required per measurement, one for the retarders to settle to the new retardance values and one frame to record the intensities. For good time resolution, the camera 16 should have a high sensitivity and low read-out noise, to reduce the noise of a single frame, and very little lag, to minimize the influence of the reading of one frame on the next. Also, high linearity is desirable between output voltage and light intensity falling on the face plate of the camera. These requirements can be met by a CCD camera such as that described earlier. 
     The detector array of camera 16 is connected to camera control 18 for read out, and for setting camera parameters such as gain and black level. The images from the camera&#39;s detector array are transferred to a video board 30 (e.g., a Scion LC-3 video board with 8 bit resolution) using the conventional RS-170 video standard. In video board 30, the signal is digitized and, converted to a two-dimensional array of integer values representing the intensities in one frame. Array elements (or pixels) are each 8 bit (=1 byte) long to encode intensity values between 0 and 255. Each frame may include as many pixels as there are detector elements in the camera detector array, e.g., 680×480 pixels. Data from fewer detector elements may be processed if desired, principally to increase the speed of operation. If, for example, the number of detector elements from which data is taken is such that one frame includes about 520×480 pixels, about 0.25 Mbyte of memory space is required per frame. 
     From the video board, the data is passed to a desktop computer 32 (e.g., a Macintosh IIx or Quadra 800 computer). The data can then be displayed on monitor 34, and stored in computer memory and/or on a hard or floppy disk. A digital input/output (I/O) card 36 is connected to the desktop computer 32 to control the retarder driver 25. The retarder driver produces the necessary voltages required to set the retarders to desired retardance values. 
     The optical arrangement shown in FIG. 1 is sensitive to the magnitude of the birefringence of specimen 38, and to the orientation of the fast and slow axes of the specimen. Hence the images recorded by camera 16 will reflect the distribution of specimen retardance/birefringence (i.e., the birefringence in the portion of the specimen corresponding to each detector of the camera CCD array) in magnitude and orientation. It will, of course, be recognized that birefringence and retardance are related, and the two terms are often used interchangeably. Birefringence Δn) is an optical property of a specimen, and retardance (R) characterizes the change in polarization of light passing through the specimen. The two are related by: 
     
         R=(Δn)d 
    
     when d is the specimen thickness. 
     FIGS. 2 and 3 illustrate two other embodiments of the invention. As will be seen, each of the systems employs a pair of variable retarders/electro-optic modulators in the optical path, but the arrangement of the retarders, and the selection and arrangement of some of the other elements in the optical paths, differ. In FIGS. 2 and 3, elements that correspond to elements of the embodiment of FIG. 1 are identified using the same reference number, with a differentiating prime (&#39;) or double prime (&#34;) added. 
     In the system of FIG. 2, variable retarders 24&#39; and 26&#39; are mounted between objective lens 14&#39; and left circular analyzer 28&#39; on the imaging side of specimen 38&#39;, rather than on the illuminating side of the specimen as in FIG. 1. Also, in the FIG. 2 embodiment, the only polarizing element between the interference filter 20&#39; and condenser lens 12&#39; is a right circular polarizer 40. In the FIG. 2 system, the variable retarders 24&#39;, 26&#39; are again oriented with their principle slow axes oriented at 45° to each other, but in this embodiment the two axes are at 135° and 90°, respectively, to the reference axis. In the FIG. 2 embodiment, the initial settings of both retarders (e.g., the retardances resulting from the initial voltage levels applied to each of retarders 24&#39;, 26&#39;) have near-zero retardance; rather than the initial voltage and settings being such that the retarders operate at near half-wavelength and quarter-wavelength retardance levels as in the embodiment of FIG. 1. In the general arrangement of FIG. 2, it is also possible to replace circular analyzer 28&#39; with a linear analyzer of appropriate orientation, in which event variable retarders 24&#39; and 26&#39; can be set to near half-wavelength and quarter-wavelength retardance levels to achieve extinction as in the embodiment of FIG. 1. 
     The embodiment of FIG. 3 includes a pair of variable electro-optic retarders 24&#34;, 26&#34; positioned with their slow axes at 45° to each other and at 45° and 0° respectively to the reference axis. One of the retarders is mounted in the illuminating path, between linear polarizer 22&#34; and condenser lens 12&#34;; the other is in the imaging path on the other side of specimen 38&#34;, between objective lens 14&#34; and linear analyzer 42. At their initial settings, both retarders act as quarter wave plates. Linear polarizer 22&#34; is positioned with its main axis at 90° to the reference axis; the axis of linear analyzer 42 is at 45° to the reference axis. The system of FIG. 3 does not include any fixed wave plate in its optical path, and thus can be used to measure optical parameters at different wave lengths simply changing interference filter 20&#34; so that it produces monochromatic light of the desired wavelength, and adjusting the linear retarders to provide quarter wavelength retardance at the selected wavelength. 
     It will be seen that, in all three disclosed embodiments, the light incident on and illuminating the samples 38, 38&#39;, 38&#34; will be circularly polarized when the variable retarders are at their initial settings, and will be elliptically polarized if a slightly different voltage is applied to the retarders so that they provide a retardence somewhat different (e.g., slightly more or slightly less) than that produced at the initial settings. It will also be seen that, in each embodiment, the analyzer 28, 28&#39;, 42&#34; on the imaging side of the specimen 38, 38&#39;, 38&#34; is chosen such that no light will pass through it if the variable retarders are at their initial settings and any specimen in the optical path has zero retardance. Additionally, in each embodiment the variable retarders are positioned with their slow axes mutually oriented at 45° to each other, and that the retardances of the two can be varied independently depending on the voltage applied by the retarder drive. 
     This present invention permits the retardance (magnitude and azimuth) introduced by the specimen, regardless of orientation, to be compensated for by varying a specific voltage applied to one or both of the variable retarders. For any given linear specimen retardance or birefringence, there is a unique setting (and retardance value) of each of the variable retarders will cause the intensity of the beam passed through the output analyzer 28, 28&#39;, 42 to be at a minimum, or at extinction. These two retardance values (one for each of the variable retarders) can be obtained without rotating either retarder, any polarizer, or the specimen. Instead, only the voltages applied to the variable retarders are adjusted until minimum intensity or extinction is reached. 
     With the system of the present invention, it is also possible to determine the orientation and magnitude of specimen retardance without having to determine variable retardance settings that result in minimum intensity (or extinction) fo the light passing through analyzer 28, 28&#39;, 42. This capability is particularly important when the retardance of a specimen is not uniform over the entire viewing field. 
     Thus, according to the preferred practice of the present invention, the intensity of the light passing analyzer 28, 28&#39;42 is measured at a plurality of predetermined settings of the variable retarders. Typically, four intensity measurements are made. When the retardance of the specimen is relatively large, i.e. is more than about the wavelength of the light, two sets of images (each including four images) are taken, one set using light of one wavelength and the other with a different wavelength light, and the same four variable retarder settings are used for each set of images. The retardance (magnitude and/or orientation) of the specimen is determined based on the measured (typically four) light intensities, and the known retardance values of the variable retarders corresponding to each intensity measurement. 
     The following description describes the four-image procedure typically used in determining specimen birefringence of less than about the wavelength of the illuminating light, and particularly the manner in which the magnitude and azimuth of the birefringence or retardance are determined when the birefringence is not more than about 1/25 of the wavelength, in the preferred embodiment not more than about 20 nanometers. The described procedure is essentially repeated when the birefringence is large and a second set of images is taken with a larger wavelength light. 
     In the preferred practice of the invention, one light intensity image is taken with the variable retarders at their initial settings, and the three other intensity images are taken with the retarders at different, predetermined and mutually independent retarder settings. The differences in retardance between the initial setting and the other predetermined settings are typically chosen to be larger than, or about the same magnitude as, the maximum retardance expected to be measured in the specimen. 
     For each region of the specimen in the field of camera view (e.g., for each region light from which is incident on a detector of the detector array, or for each region corresponding to a pixel of the display), the specimen region anisotropy is produced and displayed (or otherwise recorded or output) based on the intensity of the four images corresponding to that region. 
     Typically, the analysis of data from the four images produces two outputs, one representing the magnitude of the specimen retardance and the other of its orientation (i.e., the orientation of the slow axes). The image displayed on computer monitor 34, 34&#39;, 34&#34; shows the data for each pixel in the field of view. The two complete images, typically 680×480 pixels, can be displayed separately, or they can be combined to show both retardance and orientation in each pixel. 
     FIG. 4 shows the retardance magnitude and orientation of an aster prepared from clam oocytes. The magnitude of the retardance is represented by the gray scale, and ranges between 0 (black) and 3.2 (white) nanometers. The orientation (0° to 180° ) of the retardance in the region corresponding to each pixel is indicated by the black lines which point (from the reference circle at one end of the line) in the direction of the azimuth. In FIG. 4, the azimuths are displayed on regular grid points, at a much lower resolution than that which the detectors at camera 16 would permit, to reduce the complexity of the display. The camera data permits a display of 680×480 image points, and has a sensitivity of 0.4 nanometers of specimen retardance. The display of FIG. 4 is an array of 256×240 pixels. 
     The display of FIG. 4 was enabled by the discovery that a simple and definite relationship exists between retardances of the two variable retarders and the orientation (ρ, measured in degrees) and magnitude (R, measured in nanometers) of specimen retardance. In instances in which the specimen retardance is less than about 1/25 of the wavelength of the light, the relationship, with only a small degree of error, can be expressed as: ##EQU1## where αm in  and β min  are the differences between retardances of the two variable retarders at which minimum intensity is obtained, and the initial values of the variable retarders. 
     As indicated above, the values of α min  and β min  can be obtained directly, by employing a feedback loop and adjusting the voltages applied to the variable retarders until minimum intensity (or extinction) is obtained. If the specimen birefringence/retardance is small (e.g., in the illustrated embodiments is less than about 20 nm ) the values of α min  and β min  may be obtained from the relationship: 
     
         I.sub.i =I.sub.o [(α.sub.i -α.sub.min).sup.2 +(β.sub.i -β.sub.min).sup.2 ]+I.sub.min                        (3) 
    
     where I i  is the measured intensity, I o  is the total intensity measured with compensation settings that result in maximum transmission and I min  is the background intensity detected even at perfect compensation. The remaining terms of the relationship, α i  and β i , are the offsets introduced into the variable retarders. 
     Three of the terms in the relationship, I i , α i  and β i  are known; four terms, I o , I min , α min  and β min , are not. The four unknowns can be determined when measuring the intensity I i  for four different retardances (e.g., α i , β i ) settings. Typically, the retardances are chosen so that each of α i  and β i  are either O, X, or -X; X being a retardance between 0 and about 20 nm, and in most work to-date preferably about 16 nm; and the intensity is measured at: 
     
         (α.sub.1 =O; β.sub.1 =O) (α.sub.2 =X, β.sub.2 =O) (α.sub.3 =O, β.sub.3 =X), (α.sub.4 =O; β.sub.4 -X). 
    
     The values of αm in , β min  required to determine specimen retardance and azimuth are then found based on the four measured intensities I 1 , I 2 , I 3 , I 4  as follows: ##EQU2## It will be noted that the denominators of the two expressions (4) and (5) are the same, and that α min  and β min  are independent of both I o  and I i . The thus determined values of α min  and β min  may be used in expressions (1) and (2) to determine specimen retardance magnitude R and orientation ρ. Alternatively, α min  and β min  in expressions (1) and (2) may be replaced by the right side of expressions (4) and (5) and R and ρ may be determined directly from the measured intensities: ##EQU3## 
     The CCD array of camera 16 measures the intensity of light incident on each detector, i.e., for the region of the specimen corresponding to each detector element in the array. Equations (6) and (7) allow determination of the specimen retardance and azimuth for each such region of the specimen using the four intensity values measured. The intensity values are stored in four frame buffers of the video card or in computer memory. The actual computation of specimen retardances for each picture element with expressions (6) and (7) can be accomplished by using either specialized digital hardware, or specialized software controlling general purpose computer hardware. The first approach requires one or more computer boards providing several frame buffers, e.g., look up tables (INVERSE . . . ) and arithmetic functions (ADD, . . . ) or equivalent hardware, to compute the resultant images R and from the initial images I 1 , I 2 , I 3  and I 4 . The second approach, which in general is slower than the hardware implementation but more flexible, requires specialized software, such as the NIH Image program described below and the program of Appendix A. 
     When the magnitude of the specimen birefringence and retardance is more than about 1/25 of the wavelength, the results provided by the particular relationships set forth above may not be sufficiently accurate for many scientific purposes, and the relationships between specimen retardence and that of the variable retarders will be better expressed by other equations. 
     System accuracy can also be increased by compensating for background effects. This is accomplished by taking a set of four intensity measurements with no specimen present, determining the background values of α min-b  and β min-b  in the absence of a specimen, and then correcting the values of α min  and β min  determined from the four intensity measurements by substracting the background values from them, i.e.: 
     
         α.sub.min-c =α.sub.min-m -α.sub.min-b 
    
     and 
     
         β.sub.min-c =β.sub.min-m -β.sub.min-b 
    
     where subscripts &#34;-b&#34; represent background measurements, and subscripts &#34;-m&#34; represent measurements taken with the specimen in position, and &#34;-c&#34; are the corrected values. These corrected values may then be substituted for α min  and β min  in relationships (1), (2), (4), and (5) and corrected values of the magnitude and orientation of the specimen retardance obtained from corrected relationships (1) and (2). 
     The operational sequence of the systems of FIGS. 1-3, under the control of computer 34, is generally as shown in FIG. 5. The computer software used is NIH Image, a public domain program known available from NIH at NIH computer address &#34;anonymous ftp zippy.nimh.nih.gov&#34;, modified by addition of a program the source code of which is attached as Appendix A. The program used in the illustrated systems permits the four images used to determine retardance to be captured in a total of 0.33 seconds (if only a single image is taken at each of the retarder voltage settings), or in 1.27 seconds (if eight frames are taken at each set of voltages and averaged). 
     The data for each of the four images I i , R, and is stored in a respective frame buffer. Any image I i  may be displayed. R and may also be displayed, either separately or, as shown in FIG. 4, together. 
     OTHER EMBODIMENTS 
     It is know that high extinction of linear polarized light in a microscope can be realized with the addition of a polarization rectifier to the optical path; the polarization rectifier removes the polarization distortion introduced by the curved lens surfaces especially of high numerical aperture lenses. It has been found that circular polarized light can also be modified. For linear polarized light, without rectification, the distortion pattern of the polarization results in four bright quadrants, observed in the back aperture of the objective or condenser lens. With circular polarized light, a radially symmetric intensity increase form the center outward is observed. Both patterns are induced by the radially symmetric linear &#34;dichroism&#34; (differential transmission) of curved lens surfaces. The linear rectifier consists of two parts, a zero power lens which has an equivalent linear dichroism as, e.g., the condenser lens, and a half wave plate to flip the rotation of polarization induced by the zero- power lens. When using circular polarized light, a second half-wave plate is added with its fast axis rotated by 45° with respect to the first wave plate. This combination of two half wave plates acts as a 90°  rotator for elliptical polarization. The rectification then works as follows: Circular polarized light first enters the zero power lens and emerges elliptically polarized, with the long axes oriented radially outward in the aperture. After the light passes through the two half wave plates, the polarization is rotated by 90° and the short axes of the polarization ellipses now point in the radial direction. When the light continues through the regular lens system, e.g., the condenser, it emerges with circular polarization and the analyzer blocks most of the light. This enables good extinction, which increases the sensitivity of the pol-scope of the present invention. 
     The optical set-up and measurement systems described above are sensitive not only to linear birefringence, but also to linear dichroism in the specimen. To distinguish between the two forms of optical anisotropy, measurements at different illumination wavelengths should be performed; dichroism is strongly wavelength dependent, while birefringence is only weakly dependent on wavelength. To accomplish this, the above-described systems may be modified as described above. 
     The above systems are also suitable for measuring the polarization in specimen fluorescence. The combination of retarders and circular polarizer in the imaging path of the microscope can be used to analyze any polarization state of the light emitted by the specimen. When the microscope is operated in the transmission mode, the excitation light would be polarized and effectively blocked by the analyzer. In addition, excellent barrier filters are available for transmission fluorescence microscopy. 
     These and other embodiments will be within the scope of the following claims: ##SPC1##