Virus identification apparatus and method.

The present invention relates generally'to particle sorting and identification and more particularly to the use of light scattering to identify viruses in static suspensions. This invention is the result of a contract with the Department of Energy (Contract No. W-7405-ENG-36).

The rapid identification of viruses is of obvious importance in clinical medicine and has been greatly enhanced in recent years. The development of chemiluminescent and enzyme-linked immunoabsorbent assays for the rapid identification of viruses has reduced identification time to 2-4 hours in the most favorable cases. However, identification of microorganisms requires that the cells be isolated and grown in reasonably pure cultures, a process which can take from 16 hours, again in favorable cases, to several weeks. Thus, despite advances in the availability of automated viral identification systems, viral identification still requires on the order of 24 hours since pure cultures must be grown for the current procedures to be used.

A virus is a tiny biological particle whose DNA or RNA exists as an oriented helix which is almost crystalline in nature inside the nucleocapsid. Because of this, such biological macromolecules are asymmetric structures and interact differently with left and right circularly polarized light. Circular intensity differential scattering, which is the differential scattering of left and right circularly polarized light, probes the higher order structure (structure other than the shape of the scattering species) of macromolecular aggregates, and is sensitive to the orientation of such helices relative to the direction of polarization of the incident electromagnetic radiation. The circular intensity differential scattering signal is the amount of light scattered when the incident beam is left circularly polarized minus that Scattered when the incident beam is right circularly polarized, divided by the total amount of light scattered by the object virus. Since the circularly polarized light differentially scattered from a helix into a detector is sensitive to the orientation of the helix with respect to the direction of polarization of the incident light beam, and would be different for different orientations of a single virus, it is desirable to measure the circular intensity differentially scattered signal-as well as any other polarization sensitive signals from , suspensions of the virus of interest. The viruses in a suspension are randomly oriented so that the scattering signals derived therefrom represent a spatial average for all of the virus particles in the path of the light beam. It is fortuitous that according to clinical virologists a clinical virus specimen contains but a single virus type in most of the cases studied.

The circular intensity differential scattering signal can be related to one element of a 4 x 4 matrix called the Mueller matrix which describes the scattering of light from an object at a particular angle and wavelength. All of the information in a beam of electromagnetic radiation is contained in a four element vector called the Stokes vector (I, Q. U, V). I is the intensity of the light in a beam of radiation and is customarily normalized to unity. Q, U and V describe the polarization properties of the light beam. Q is the tendency toward horizontal linear polarization. Its value is +1 for horizontal linearly polarized light and -1 for vertical linearly polarized light. U is the tendency toward linearly polarized light tilted at +45⁰ to the horizontal scattering plane. It has values ranging from +1 (+45°) to -1 (-45). V is the tendency toward right circular polarization. For a right circularly polarized beam. V = +1 and for a left circularly polarized beam. V = -1. For the apparatus of the present invention, the Stokes vectors of the incident and scattered light are manipulated by a series of optical elements, each represented by a 4 x 4 Mueller matrix, in order that the intensity component of this vector, If, for the scattered radiation is made to develop information about the scattering sample which can be extracted by appropriate signal processing. There are ten independent matrix elements which can be determined from the scattering experiments which characterize the scattering particle. Moreover, by utilizing scattering angle and radiation wavelength dependence of the ten parameters, it should be possible to uniquely characterize viruses for rapid and positive identification. It is to be stressed that the present invention permits independent determination of ten parameters for a particular wavelength and scattering angle. In all but one of the references to be evaluated hereinbelow. linear combinations of Mueller matrix elements are obtained. Except for the most fortuitous situations, the number of independent pieces of information which can be derived from such linear combinations is far smaller than the number available. thereby reducing the information available to uniquely characterize the viral particles.

In "Suspended Organic Particles Monitor Using Circularly Polarized Light," invented by John _W. Liskowitz, U.S. Patent No. 3.612.688, issued on Oct. 12, 1971, the inventor describes the use of circular dichroic absorption to detect organic particles suspended in a fluid. Right circularly polarized light and left circularly polarized light are alternatively passed through the sample and the intensity of -the transmitted intensity of the circularly polarized components (at, ₀° scattering angle) is analyzed. The circular dichroic absorption of the sample is represented by the ratio of the component intensities of the absorbed radiation when starting with right circularly polarized light to that when starting with left circularly polarized light..Although the resulting intensity ratio can be related to components of the Mueller matrix describing the scattering process, the use of circularly polarized light in the manner described by the inventor does not permit evaluation of individual components thereof which as mentioned hereinabove, in general does not permit the , extraction of the individual components but rather linear combinations thereof with the consequent loss of important information in all but the most fortuitous circumstances. Moreover, the linear combinations contain contributions from terms in the Mueller matrix which have nonzero values for optically inactive particles, such terms having their origin in the size and shape of the particle itself and not in the genetic composition of the particle. The use of quarter-wave retarders generates circularly polarized radiation which leads to the linear above-mentioned undesirable combinations of Mueller matrix elements.

In "Testing of Optically Active Substances by Polarized Radiation. invented by Laurence David Barron and Amyand David Buckingham, U.S. Patent No. 3,817,634, issued on June 18, 1974, the inventors disclose the use of alternating right and left circularly polarized radiation to irradiate a sample from which a scattered signal is derived which reflects the nature of the optically active substance contained therein in a similar manner to the invention of Liskowitz, supra. The Barron et al. invention contains, the same limitations found in Liskowitz. except that Barron et al. restrict the angle of observation to be orthogonal to the incident radiation beam and are investigating scattered radiation, not absorbed radiation. No such restriction is required according to the practice of the subject invention. In fact, much additional information can be derived from the angular dependence of the Mueller matrix elements. Barron et al. also disclose the detection of a Raman signal which is produced by the inelastic scattering of the incident radiation, as opposed to the elastic scattering process of the subject invention. Raman signals tend to be quite . weak in the absence of resonance phenomena, and occur at a different wavelength from that of the incident electromagnetic radiation.

Three references by R. M. A. Azzam, "Simulation of Mechanical Rotation by Optical Rotation: Application to the Design of a New Fourier Photopolarimeter," J. Opt. Soc. Am. 68, 518 (1978), "Photopolarimetric Measurement of the Mueller Matrix by Fourier Analysis of a Single Detected Signal," Optics Lett. 2. 1₄8 (1978), and "Polarimeter," U.S. Patent No. 4,306,809, issued on _Dec. 22, 1981, describe a procedure involving Fourier analysis of the detected signals to obtain all ₁₆ components of the Mueller matrix. Two significant points of difference exist between the Azzam invention and the present invention. First, Azzam teaches the Fourier analysis of his scattering data. Since the Fourier series is truncated after the twelfth term according to Azzam's invention, the last few terms, for example, the eighth through twelfth terms, must be approaching zero rapidly in order for the truncation of the series to have meaning. Therefore, to extract several of the Mueller matrix elements, sums and differences of extremely small measurements having noise superimposed thereon must be taken. Since these numbers have decreasing signal-to-noise ratio, the matrix elements derived therefrom are unreliable. This is exactly the difficulty which exists for more direct measurements of linear combinations of the Mueller matrix elements. The present invention substantially avoids this difficulty. Moreover. Azzam restricts the modulation frequencies of the two required retarders to have a ratio of exactly five to one in order that simplifications occur in the Fourier transform mathematics. No such restriction is required for the successful practice of the subject invention.

W. E. Bickel and M. E. Stafford describe the measurement of scattered light from biological systems to yield optical data which can differentiate between species, strains. surface characteristics, etc. in "Polarized Light Scattering from Biological Systems: a Technique for Cell Differentiation," J. Biol. Phys. 9, 53 (1981). Therein the authors disclose that the 10 independent Mueller matrix elements or linear combinations thereof may be determined by combining scattering measurements involving the three possible polarization orientations of input radiation and the three polarization orientations of the scattered radiation plus a measurement of the total intensity. Polarization measarements of the type suggested therein require several different experimental arrangements involving different optical elements and are therefore tedious and time-consuming to achieve. The subject invention requires two configurations of a single experimental apparatus to accomplish the requisite measurements. Bickel et al. describe only one apparatus; one which uses quarter-wave plate retarders for the incident and analyzer optics, and which is therefore only capable of determining linear combinations of Mueller matrix elements - with their inherent loss of significant information. That is, as detailed in a previous paper by Bickel entitled "Application of Polarization Effects in Light Scattering: A New Biophysical Tool." by W. S. Bickel. J. F. Davidson, D. R. Huffman, and R. Kilkson, Proc. Nat. Acad. Sci. U_SA, Biophysics 73, 486 (1976), the coefficient S₃₄, which is a combination of S₁₄, S_34' S₁₁, and S₁₃, is the one obtained from the apparatus described in both references.

A useful summary of the theoretical background which is relevant to the subject invention may be found in "Measurement of Polarized Light Interactions via the Mueller Matrix," by Randall C. Thompson, Jerold R. Bottiger, and Edward S. Fry. Applied Optics 19, 1323 (1980), the disclosure of which is hereby incorporated by reference herein. Thompson et al. describe a four-modulator photopolarimeter capable of directly and simultaneously determining all sixteen Mueller matrix elements with a single apparatus utilizing light scattering measurements. Of particular importance in this reference is the implication that the use of smaller numbers of polarization modulators permits only the measurement of combinations of matrix elements. Thompson et al. therefore teach away from the present invention which uses two polarization modulators. It should be mentioned at this point that the use of four polarization modulators severely reduces the signal-to-noise ratio of the observed intensities over that for the two modulator configuration. Here the "signal" is the amplitude of the desired frequency component and "noise" is the amplitude of all undesired components. Also of importance in this reference is the choice of the retardance amplitude of 2.40483 radians which makes J (S)= 0. This removes 0 the dc term from the expansion expressions for the Mueller matrix elements, and renders the dc component of If proportional only to the 11 matrix element. The use of only two polarization modulators in two configurations according to the teachings of the present invention to achieve a similar result to that obtained by Thompson et al. with the use of four modulators derives from the fortuitous circumstance that the higher order Bessel function terms appearing in the expressions for the Mueller matrix elements decrease sufficiently rapidly, to permit the desired unique modulation frequency dependence for each Mueller matrix element to be possible as is the case for Thompson et al.

Accordingly, an object of the present invention is to provide an apparatus and method for rapidly characterizing viruses in static suspension.

Additional objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.

To achieve the foregoing and other objects, and in accordance with the purposes of the present invention, as embodied and broadly described herein, the apparatus of this invention may include means for generating collimated, high intensity, substantially monochromatic radiation having a chosen wavelength, a first polarizer for polarizing the monochromatic radiation along a first axis, a first modulator having a first retardance between 1/4-wavelength and 1/2-wavelength of the substantially monochromatic radiation and having a first modulation frequency for generating elliptically polarized radiation from the linearly polarized radiation, means for holding the virus sample and permitting the interaction between the virus sample under investigation and the elliptically polarized radiation to occur, a second modulator having a _\second retardance of between 1/4-wavelength and 1/2-wavelength of the substantially monochromatic radiation and a second modulation frequency for receiving a' portion of the scattered radiation resulting from the interaction of the elliptically polarized incident radiation with the virus sample, a second polarizer for receiving the scattered radiation bearing two modulation frequencies and polarizing this radiation along a second axis, means for quantitatively detecting the radiation passed by the second polarizer where the detecting means is sensitive to the frequencies present in the radiation passed by the second polarizer impressed thereon by the effect of the first and second modulators, and means for identifying and measuring the intensity associated with each individual frequency present in the radiation passed by the second polarizer, whereby the first and second axes and the first and second retardances are chosen such that the dc component of the intensity of the scattered radiation is independent of the polarization of the radiation so that a polarization independent normalization of the total scattered radiation can be achieved, and whereby the measured intensities at each of the frequencies present in the detected radiation have a substantially unique mathematical relationship to a particular Mueller matrix element deriving from the interaction of the incident radiation with both the optical elements of the apparatus and the virus under investigation such that eight independent matrix elements can be extracted from a single polarization configuration of the apparatus, which matrix elements when normalized by the intensity of the total scattered radiation contain information according to the identity of the virus under investigation. Preferably, the first and second polarization modulators include photoelastic modulators. It is also preferred that the first and second retardances are 2.40482 radians. A quarter-wave plate can be inserted between the means for holding the virus sample and the second polarization modulator if the S₂₃ and S₃₂ Mueller matrix elements are to be measured. The scattered radiation passes there-through and interacts therewith to provide the additional information as will be described hereinbelow.

In a further aspect of the present invention, in accordance with its objects and purposes, the method hereof may include generating substantially monochromatic electromagnetic radiation having a chosen wavelength, linearly polarizing this radiation along a first axis, generating a first modulated elliptically -polarized radiation therefrom which includes the superposition of waves having a phase lag between 1/4- and 1/2-wavelength of the generated radiation and has a first modulation frequency, directing the first elliptically polarized radiation through the static virus suspension to be analyzed permitting the interaction between the elliptically polarized radiation and the static virus suspension to occur, thereby producing scattered radiation containing polarized information related to the virus, generating a second modulated elliptically polarized radiation from a portion of the scattered radiation emitted at a chosen scattering angle, this second elliptically polarized radiation including a superposition of waves having a phase lag between 1/4- and 1/2- wavelength of the generated radiation and having a second modulation frequency, extracting a linearly polarized component of the second elliptically polarized radiation along a second axis, detecting the intensity of this component, the intensity bearing amplitude modulation at frequencies which are linear combinations of the first and _\second modulation frequencies, and extracting the magnitude of the intensity at certain of these frequencies, whereby eight independent Mueller matrix elements can be determined which contain information according to the nature of the virus suspension. The measurements can be repeated at different scattering angles and interrogating radiation wavelengths to provide additional information about the virus. Preferably, a correction for the birefringence of any container holding the viral suspension is made according to the description provided hereinbelow. In the actual identification procedure for an unknown virus, the measured Mueller matrix elements as a function of scattering angle and wavelength are compared with a database comprising many such measurements recorded for known samples.

Benefits and advantages of the present invention include the identification of low concentrations of viruses in static fluid suspension on a timescale which is short compared with current analytical procedures, rendering this important clinical investigation more useful.

The accompanying drawings, which are incorporated in and form a part of the specification, illustrate one embodiment of the present invention and. together with the description, serve to explain the principles of the invention. In the drawings: <ul id="ul0001" list-style="none"><li>Figure 1 shows a schematic representation of the apparatus of the present invention in its most elementary form.</li><li>Figure 2 shows a schematic representation of the detection and measurement portion of the apparatus of the present invention in the configuration used to determine the S₁₄ and 5₃₄ Mueller matrix elements.</li><li>Figure 3 shows the frequency dependence of the elements of the Mueller matrix for a particular choice of polarization modulator retardances and azimuthal angles for the passing axes of the polarizers and the fast axes of the polarization modulators.</li><li>Figure 4 is a graph of S₁₄ as a function of scattering angle at 360 nm for four classes of encephalitis virus vaccines.</li><li>Figure 5 is a graph of S₁₄ as a function of scattering angle at 360 nm for four classes of dengue fever virus vaccines.</li></ul>

The Mueller matrix is a 4 x 4 matrix which describes the polarization sensitive transformation of an incident beam of light into a scattered beam of light by a scattering object such as a virus or suspension of virus particles. Much information concerning the internal structure and shape can be derived about the scattering particles from the simultaneous determination of multiple Mueller matrix elements at specific wavelengths and scattering angles, enough information in many cases to enable discrimination among a wide variety of different viruses of clinical significance. Measurement of a sufficient number of polarization related phenomena to extract the ten independent Mueller matrix elements would be a formidable task involving many experimental configurations and difficult measurements. The present invention overcomes this difficulty by permitting all of the relevant information to be derived from the measurement of a single intensity using a single apparatus.

By defining the polarization of the radiation incident on the virus sample to be elliptical polarization. choosing the retardances properly, and modulating this polarization before and after its interaction with the virus sample, one can achieve the encoding of the viral -information contained in the Mueller matrix in the frequency dependence of the radiation intensity emerging from the viral sample and its attendant optical system. That is, the intensity can be manipulated to closely approximate the form I(θ,λ,f_ij) = Σ_ija(f_ij)S_ij(θ,λ), where 6 and 'k are the scattering angle and the wavelength of the radiation, respectively, the f_ij are the linear combinations of the two applied polarization modulation frequencies, S_ij(θ,λ) are the Mueller matrix elements, and a(f_ij) are combinations of trigonometric functions each having a unique frequency, f... associated with it. It is an important element of the present invention that a series of measurements of the intensity at each of the frequencies, f_ij, permits the extraction of the individual Mueller matrix elements. That is, S_ij(θ,λ) = I(θ,λ,f_ij)/a(f_ij), for each distinct combination f... Lock-in amplifiers are used to detect the typically small signals at each frequency. Requirements for the intensity of the interrogating radiation are quite modest since the measurements are performed in small cuvettes containing the virus suspension, with no particular time limitations. The measurement procedure is as follows: The clinical specimen is filtered or otherwise prepared so that the small liquid volume remaining contains only virus size particles. The sample is then placed in a cuvette and placed in the path of the interrogating beam which has been suitably prepared as to its polarization. A reference frequency generator is sequentially switched by a computer to the first of eight reference frequencies, each frequency corresponding to a particular Mueller matrix element, and a scattered light intensity measurement made by using a lock-in amplifier tuned to each reference frequency in turn. Measurements are made with a 1 to 3 second time constant, but longer or shorter integration times are possible if the virus concentration is low. The signal corresponding to each selected Mueller matrix element is digitized and compared with Mueller matrix elements previously stored in a database in order to determine the identity of the suspended virus sample under investigation. By performing the measurements in this manner, difficult polarization measurements are avoided, and the individual matrix elements emerge without the need for solving systems of equations with diminutive terms. As mentioned hereinabove, Thompson et al. achieve a similar result..but require the use of four polarization . modulation frequencies. According to the present invention, eight Mueller matrix elements can be determined for each of two choices of the azimuthal angles for the polarizer passing axes and polarization modulator fast axes. Adjustment of the present apparatus from one set of chosen azimuthal angles to the other" does not require any substitution of components but only simple adjustments to the components in place. As will be described hereinbelow, the measurement of the S₃₂ and S₂₃ matrix elements require the insertion of a quarter-wave plate between the sample and the second polarization modulator.

It should be mentioned that the present invention cannot be used for the identification of bacteria. Bacteria in a clinical specimen often represent a very heterogeneous population since many types of bacteria are frequently present. What is required is a flow cytometer in which the bacteria are analyzed one-at-a-time as they ,pass through the focused incident light beam. The DNA in a bacterium is organized in supercoils which are randomly oriented in space. As a result a detector in the flow cytometer would observe the same differential scattering signal regardless of the orientation of the bacterium. Viruses, as oriented particles, cannot readily be analyzed in such a manner.

Turning now to the drawings. Figure 1 is a schematic representation of the apparatus of the present invention in its most basic form. Substantially monochromatic light from a light source such as a laser 10 (argon ion laser operating at between 50 and 250 mW output power) is directed into a first polarizer 12 to insure that a substantial fraction of the transmitted radiation is linearly polarized at a specific angle with respect to the horizontal scattering plane. The emerging beam is then directed to a photoelastic modulator 14 operating at 50 kHz wherein the radiation is elliptically polarized with its handedness alternating left and right at 50 kHz. The radiation emerging from the polarization modulator is then made incident on the sample 16 held in a cylindrical quartz cuvette 50 mm in diameter with 2 mm thick walls. The incident intensity is not modulated by these optical elements. Transmitted radiation is directed into a Rayleigh horn (not shown) to minimize stray scattered light.

The scattered light analyzing and detecting components of the present apparatus are mounted on a computer-controlled rotary stage. The scattering angle, 0, in the horizontal plane is defined relative to the incident radiation, and the acceptance half-angle for the analyzing and detecting components was about 0.5°. Scattered radiation to be observed at a particular scattering angle is passed through a second photoelastic modulator 18 which was operated at 47 kHz. and then directed into a second linear polarizer 20. The emerging light 21 is passed through a wavelength filter (not shown) to remove satellite laser wavelengths and made to impinge on a detector 22 sensitive to the wavelength employed. As will be described in Example II hereinbelow, if direct measurements of the S₂₃ or S₃₂ Mueller matrix elements are desired, a quarter-wave plate (not shown) may be inserted between the sample cuvette and the second p_hotoelastic modulator 18. The retardances of the two modulators 14, 18 were selected to be 2.4048 radians in order to render the total scattered intensity, which is used to normalize the other Mueller matrix elements, independent of the polarization of the scattered light. With the use of two modulators, eight of the Mueller matrix elements can be measured simultaneously; this number being all of the independent matrix elements measurable by any scattering experiments since the remaining matrix elements are derivable therefrom. The two modulation frequencies produce intensity modulation at the photomultiplier tube at several frequencies which are linear combinations of the two input frequencies.

Figure 2 shows a block diagram of the electronic circuitry used for measuring S₁₄ and s₃₄ Mueller matrix elements. Photomultiplier tube 22 is powered by a high voltage power supply 30. Power amplifier 26 both increases the amplitude of the signal 24 from the photomultiplier in order to drive the lock-in amplifiers 32, 34, and is part of a feedback loop 26, 28, 30 for maintaining the anode current of the photomultiplier constant by controlling the high voltage bias on the photomultiplier tube as the scattering angle is changed. This effectively normalizes all of the matrix elements _"to 'the total scattered intensity. Computer 42 drives a rotary stage 44 which changes the scattering angle observed by the analyzing optics, receives the signals generated by the lock-in amplifiers (only two signals in the situation described), and compares the normalized results with those stored in database 44 in order to identify the virus in the suspension. An oscillator 36 operating at 50 kHz provides the reference frequency for one lock-in amplifier 32, while a second oscillator 38 operating at 47 kHz drives a frequency multiplier/filter chain 40 which provides a 44 kHz reference frequency to the second phase lock-in amplifier. The choice of this reference frequency will become apparent in the discussion which follows. It should be mentioned at this point that the number of lock-in amplifiers employed is a function of the number of desired independent Mueller matrix elements. That is, since each Mueller matrix element occurs at a distinct frequency and each lock-in amplifier is electrically referenced to a single frequency, the simultaneous measurement of eight Mueller matrix elements for a chosen set of polarizer passing axes and polarization modulator fast axes will require eight phase-sensitive detectors. Determination of the Mueller matrix elements as a function of wavelength and scattering angle for many viral suspensions will provide a databa-se from which unknown viral suspensions will be able to be compared in order to quickly identify the unknown viral sample.

Having generally described the invention, the following specific examples are given as a further illustration thereof.

EXAMPLE I

If the azimuthal angle, γ, is defined as being positive in a clockwise manner measured from the horizontal scattering plane in which the scattering angle 6 is defined and looking into the beam of radiation incident on the sample under investigation, and the azimuthal angle of the passing axis of each of the polarizers is +45° while that for the fast axis for each of the polarization modulators is +90°, the measurable matrix elements of the Mueller matrix are shown in Fig. 3. The numbers in parentheses are the frequencies in kilohertz at which each matrix element is determined. The dashes in some of the parentheses indicate that there is no contribution from that particular matrix element. With the polarizer passing axes set at +90°. and the modulator fast axes set at +45°, however, row 3- and column ₃ are missing. S₁₁ is the total scattering intensity and appears as a dc component at zero frequency. S₁₄ is the circular intensity differential scattering term, I_L- I_R, and appears at 50 kHz. The other polarization sensitive element of particular interest is S34 which appears at 44 kHz. With row 3 and column 3 missing instead of row 2 and column 2, S24 appears at 44 kHz instead of S₃₄. The results for several virus vaccines are shown in Figs. 4 and 5. Figure 4 shows plots of S14 for four types of encephalitis virus vaccines as a function of scattering angle at 360 nm. The plot for VEE (TC-83) is denoted by "a", "b" is the plot for SLE (TBH-28), "c" is the plot for WEE (Fleming) and "d" is the plot for EEE. Figure 5 shows plots of S₁₄ for four types of dengue fever virus vaccines as a function of scattering angle at 360 nm. As in Fig. 4, the four viral types are readily distinguishable at 30o scattering angle within the experimental variation indicated by the error bars. The 'plot for Dengue Type 1 (Hawaii) is denoted by "a", "b" is the plot for Dengue Type 2 (New Guinea), "c" is the plot for Dengue Type 3 (H879), and "d" id the plot for Dengue Type 4 (H24L). The St. Louis Encephalitis Virus is difficult to distinguish from Dengue Fever Virus serologically. The circular intensity differential scattering spectra for the vaccine preparations are, however, very different. Clearly, to obtain additional information about each virus, especially those which have similar scattering angle or wavelength plots for particular matrix element, other Mueller matrix elements would be measured.

Each of the Mueller matrix elements is calibrated by rotating the detector to 0° scattering angle and replacing the sample cuvette with various combinations of optical elements whose Mueller matrices are known. For example. S14 and S₃₄ are calibrated by inserting a 488 nm quarter-wave plate with its fast axis at 0° followed by a polarizer. The polarizer is rotated in steps through azimuthal angles ranging from 0° to 180°. S₁₄ behaves as the sine of twice the azimuthal angle and S₃₄ behaves as the sine squared of twice the azimuthal angle. The lock-in amplifier gain corrections for S₁₄ and S₃₄ can thereby be determined and stored in the computer for use in obtaining a set of Mueller matrix elements which is representative of a particular virus. A similar procedure is followed for the remaining matrix elements. These calibrations also enable the determination of the correct phase offsets between the reference and signal waveforms.

EXAMPLE II

Example I describes the extraction of fourteen out of the sixteen Mueller matrix elements in two measurements of eight matrix elements each, ten of which are independent. The additional matrix elements might be useful for investigating the measurement precision but could be obtained by appropriate combinations of the measured elements. In this regard, the S₂₃ and S32 matrix elements, which cannot be obtained in the manner described hereinabove, are extracted according to the following procedure if these elements are desired: <ul id="ul0002" list-style="none"><li>With the azimuthal angle, γ, of the passing axis for each of the first and second polarizers is set at 9₀°, the fast axis of each of the first and second polarization modulator set at 45°. and that for the elements ₂₁, ₄₁, 12. 22, 42, 14. 24 and 44 are determined, as described in Example I and will hereinafter be designated as _I configuration. Moreover, if the azimuthal angle for the passing axis for each of the polarizers is 45°, and that for the fast axis for each of the polarization modulators is 90°, the matrix elements 31, 41, 13, 33, 43, 14, 34, 44 are determined, which will hereinafter be designated as configuration II. If a quarter-wave plate having its fast axis oriented at 0° azimuthal angle is inserted between the sample cuvette. and the second polarization modulator, and if the remaining azimuthal angles are arranged according to configuration I, matrix elements 21, 31. 12, 22, 32, 14, 24, and 34, can be determined. Similarly, if the azimuthal angle of the fast axis of the quarter-wave plate is set at 45° while the remaining azimuthal angles are arranged according to configuration II, matrix elements 21, 31. 13, 23, 33, 14, 24, and 34 can be determined. It should be mentioned at this point that S₁₁, the polarization independent scattered intensity related matrix element is always _'determined if anything at all is to be measured.</li></ul>

Ideally, the cuvette should exhibit no strain birefringence at either the light input or output locations. A strain of less than 10 nm of retardance at a specified wavelength per centimeter of cuvette light transmitting material is considered strain free in the optics industry. s₁₄ is affected only by strain at the input location, while S₃₄ is affected equally by strain at both the input and output locations. Strain at the input location causes S₁₂ and s₁₃ to have contributions at the same frequency as that for S₁₄. Since S₁₂ can be as large as -1 (at 90° scattering angle), this represents a potentially severe problem for extracting independent Mueller matrix elements. Modeling studies indicate, however, that for cuvette input light transmitting material strains as large as 24.4 nm/cm, an s₁₂ value of -0.5, and an S14 value of 0.001, the contribution at 50 kHz from S₁₄ is twice as large as that from S₁₂, and the S12 contribution does not change as the S14 value varies over a wide range. This calculation was performed for the situation where the azimuthal angle for the passing axis of each of the polarizers was +45°, that for the fast axis for each of the polarization modulators was +90°. and the fast axis for the strain was +45° with respect to the horizontal scattering plane. The modeling calculations also indicate that if a set of measurements is performed for both choices of azimuthal angle described hereinabove, the degree of strain and the orientation of its fast axis at each of the input and output locations will be able to be determined. Once these four numbers are determined, each Mueller matrix element can be appropriately corrected. That is, the two chosen azimuthal angle configurations can give rise to fourteen pieces of information: ten independent Mueller matrix elements, and the four required degree of strain parameters.

The foregoing description of the preferred embodiment of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiment was chosen and described in order to best explain the principles of the invention and its practical application to thereby enable others skilled in the art to best utilize the invention in various embodiments and with various modifications as are suited to the particular.use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto.