JP5361843B2 - Optical anisotropy evaluation method and evaluation apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To evaluate optical anisotropy irrelevantly to a retardation value of a retardation plate and a DC component of transmitted light intensity. <P>SOLUTION: Progressions ä&phiv;<SB POS="POST">P,i</SB>}=äc<SB POS="POST">P</SB>+A<SB POS="POST">P</SB>t<SB POS="POST">i</SB>}, ä&phiv;<SB POS="POST">A,i</SB>}=äc<SB POS="POST">A</SB>+A<SB POS="POST">A</SB>t<SB POS="POST">i</SB>}, and ä&phiv;<SB POS="POST">R,i</SB>}=äc<SB POS="POST">R</SB>+A<SB POS="POST">R</SB>t<SB POS="POST">i</SB>} are calculated from a progression ät<SB POS="POST">i</SB>}=ät<SB POS="POST">0</SB>, t<SB POS="POST">1</SB>, ..., t<SB POS="POST">N</SB>} (unit of t<SB POS="POST">i</SB>; time). Light intensity I<SB POS="POST">i</SB>when angles of a polarizer, an analyzer, and the retardation plate are denoted as &phiv;<SB POS="POST">P,i</SB>, &phiv;<SB POS="POST">A,i</SB>, and &phiv;<SB POS="POST">R,i</SB>specified with (i) is acquired. An amplitude and a phase of at least one component among a component of frequency 2F(A<SB POS="POST">A</SB>-A<SB POS="POST">P</SB>+A<SB POS="POST">R</SB>) and a component of frequency 2F(A<SB POS="POST">A</SB>+A<SB POS="POST">P</SB>-A<SB POS="POST">R</SB>) are found from a plurality of I(t<SB POS="POST">i</SB>)s. Two of amplitudes and phases of at least two components among a component of frequency 2F(A<SB POS="POST">A</SB>-A<SB POS="POST">P</SB>), a component of frequency 2F(A<SB POS="POST">A</SB>+A<SB POS="POST">P</SB>), a component of frequency 2F(A<SB POS="POST">A</SB>+A<SB POS="POST">P</SB>-2A<SB POS="POST">R</SB>), and a component of frequency 2F(A<SB POS="POST">A</SB>-A<SB POS="POST">P</SB>+2A<SB POS="POST">R</SB>) are found from the plurality of I(t<SB POS="POST">i</SB>)s. The magnitude and direction of optical anisotropy of a sample 3 are evaluated based upon the amplitude and phases. <P>COPYRIGHT: (C)2012,JPO&amp;INPIT

Description

  The present invention relates to a method and apparatus for evaluating the optical anisotropy of a sample (for example, a retardation plate or a liquid crystal layer).

  With the expansion of the use of liquid crystal display devices, there is an increasing need to evaluate samples such as retardation plates and liquid crystal layers, that is, samples having optical anisotropy. In order to satisfy this requirement, many evaluation methods that apply ellipsometry techniques that have been used for evaluating optical constants have been developed. Whereas conventional reflective ellipsometry determines the refractive index and film thickness of an optically isotropic sample from the ellipso parameters (phase difference and amplitude ratio of reflected light), the evaluation of a sample having optical anisotropy In order to determine the direction of anisotropy (the direction of slow axis or phase of fast axis) and the magnitude of anisotropy (retardation), a measuring method and an analysis method have been devised in accordance with the purpose.

  Although the rotation analyzer method and the rotation compensator method have an advantage of high speed for modulation measurement, there is a problem that it is difficult to evaluate a sample having small optical anisotropy. On the other hand, as the performance of liquid crystal display devices increases, the optical anisotropy of a member having a small optical anisotropy, such as a TAC (Tri-Acetyl-Cellulose) film that is a supporting substrate of a polarizing plate, is controlled. The need came to be recognized. As a method for evaluating a sample with small optical anisotropy, a phase modulation method using PEM (Photoelastic Modulator) is known. These rotation analyzer method, rotation compensator method, and phase modulation method are terms used in conventional reflection-type ellipsometry, but the analyzer is rotated, the phase difference plate (compensator) is rotated, or the phase is adjusted. Since the method of applying modulation is the same as that used in reflection ellipsometry, it is called by the same name.

  Patent Document 1 discloses a typical rotational analyzer method. By inserting a quarter-wave plate before and after the sample between the polarizer and the analyzer and rotating the analyzer at the angular frequency ω (transmission axis direction θ = ωt), the cos 2ωt in the transmitted light intensity changes. The amplitude of the component is proportional to cos δ. Using this, the retardation δ expressed in units of the angle of the sample can be obtained. Further, by utilizing the fact that the amplitude of the component that changes with sin2ωt is proportional to −sinδsin2φ, the sign information (sign of sinδ) of the main axis directions φ and δ of the sample can be obtained using δ obtained previously. Since the sign information of δ is obtained, it can be determined whether the main axis is a slow axis or a fast axis.

  Patent Document 2 discloses a typical rotation compensator method. A retardation plate of retardation δc is inserted on the polarizer side of the sample between the polarizer and the analyzer, and this retardation plate is rotated at an angular frequency ω (slow axis direction θc = ωt). The transmittance correction coefficient is obtained from the amplitude of the direct current component in the transmitted light intensity and the component that changes at cos4ωt, and the measured transmittance is corrected. Then, the direct current component in the corrected transmittance, cos4ωt component, sin2ωt From the amplitude of the component and the sin4ωt component, the retardation δs expressed in units of the sample angle and the slow axis direction θs of the sample can be obtained. From the direct current component in the transmitted light intensity and the amplitude of the component that changes at cos 4ωt, the retardation δs expressed in the unit of the sample angle and the slow axis direction θs of the sample can be obtained.

  Patent Document 3 discloses a method obtained by modifying the rotation compensator method. A quarter-wave plate is inserted before and after the sample between the polarizer and the analyzer, the polarizer is rotated at an angular frequency ω (transmission axis direction θ = ωt), and the quarter-wave plate on the polarizer side is angular. Rotate at a frequency of 2ω (slow axis direction 2ωt). From the sin 2ωt component, the sin 6ωt component, and the cos 6ωt component, the retardation Δ expressed in units of the angle of the sample and the slow axis direction φ of the sample can be obtained.

  Patent Document 4 discloses a typical phase modulation method. A PEM is inserted on the polarizer side of the sample between the polarizer and the analyzer, and the phase difference of the light incident on the sample is modulated with the frequency f. The amplitude of the component that changes with sin2πft of transmitted light intensity when the transmission axis direction of the analyzer is directed to the reference direction (0 °), and sin2πft of transmitted light intensity when the transmission axis direction of the analyzer is directed to 45 ° From the amplitude of the component that changes, the retardation Δ expressed in units of the sample angle and the slow axis direction θ of the sample can be obtained.

  Hereinafter, the retardation expressed in the unit of the angle of the sample is expressed as δ, and the slow axis direction of the sample is expressed as φ.

JP 11-132940 A JP 2009-236678 A JP 2004-20343 A (Patent No. 3844222) JP 2004-184225 A

  However, in Patent Document 1, the retardation δ of the sample is obtained from cos δ. Therefore, the measurement accuracy is low for a sample having a small δ. Further, it is necessary to normalize the measured transmitted light intensity with the maximum value 1 and the minimum value 0, and it is easily affected by direct current / low frequency noise such as stray light and shot noise in spite of the modulation measurement. Further, the quarter wave plate to be used must strictly have a retardation (wavelength unit) of ¼ of the wavelength of the measurement light, but it is difficult to realize. Even if it can be realized, the retardation of the retardation plate has temperature dependence, and therefore temperature management is necessary for accurate evaluation.

  Since Patent Document 2 uses a method of minimizing the difference between the measured value and the calculated value of the modulation component and the DC component when determining the retardation δ of the sample and the slow axis direction φ of the sample, The measurement accuracy of the DC component determines the evaluation accuracy. The direct current component is easily affected by stray light and the like, and in the sample having a small δ, the direct current component is overwhelmingly larger than the frequency component term, so the measurement accuracy is low in the sample having a small δ. Further, the retardation δc of the retardation plate needs to be known. However, since retardation of an actual retardation plate has temperature dependence, temperature management is necessary for accurate evaluation.

  In Patent Document 3, since the retardation δ of the sample and the slow axis direction φ of the sample can be obtained only by the modulation component in the transmitted light intensity, the measurement accuracy of the DC component as in Patent Document 2 is not affected. Further, since the retardation δ of the sample is obtained from tan δ, it is more advantageous than the above method for a sample having a small δ. However, the two quarter-wave plates to be used must have a retardation (wavelength unit) that is ¼ of the wavelength of the measurement light, but this is difficult to achieve. Even if it can be realized, the retardation of the retardation plate has temperature dependence, and therefore temperature management is necessary for accurate evaluation.

Since Patent Document 4 obtains the retardation δ of a sample from tan δ as in Patent Document 3, it is more advantageous than the methods of Patent Documents 1 and 2 for a sample having a small δ. Since the amplitude of the phase difference of incident light modulated by the PEM can be controlled by the amplitude of the voltage applied to the PEM, it can be arbitrarily set within a practical range. However, it is necessary to normalize the amplitude of the modulation component in the measured transmitted light intensity by the magnitude of the DC component, and the measurement accuracy of the DC component affects the measurement accuracy of the sample (Patent Document 4 describes the standard) However, since the Stokes vector of incident light is given by ^t (1, 0, 0, 0) (t indicates transposition) and the intensity of incident light is normalized to 1, Patent Document 4 In this case, it is necessary to normalize with a direct current component having a magnitude of 1 in Equations 7 and 8 representing transmitted light intensity in FIG. Further, it is known that the temperature of the phase difference amplitude of incident light modulated by the PEM has a large temperature dependence, so that strict temperature adjustment is necessary.

  In summary, the problems in accurately evaluating a sample having a small δ in the prior art are the effects of low-frequency noise such as stray light and shot noise, and the temperature dependence of optical elements used.

  In order to solve these problems, the present invention determines the magnitude and direction of the optical anisotropy of the sample regardless of the retardation value of the retardation plate used and without using the direct current component of the transmitted light intensity. The purpose is to provide technology to evaluate.

The evaluation method according to one aspect of the present invention evaluates the optical anisotropy of the sample by analyzing the light emitted from the monochromatic light source and passing through the polarizer, the retardation plate, the sample, and the analyzer in this order. A _P , A _A , A _R are proportional coefficients (unit: angle · time ⁻¹ ) respectively assigned to the polarizer, the analyzer, and the phase difference plate, and c _P , _Let c _A and c _{R be} constants (units are angles) assigned to the polarizer, the analyzer, and the phase difference plate, respectively, and an arbitrary N + 1 number sequence {t _i } = {t ₀ , t ₁ ,..., T _N } (unit of t _i is time), three sequences {φ _{P, i} } = {c _P + A _p t _i }, {φ _{A, i} } = {c _A + A _A t _{i }, {φ R, i}} = { calculates the _{c R + a R t i}} , for different i all between 0 and N, the phase difference between the polarizer and the analyzer Angle each, phi _P is designated by _{i, i,} phi _{A, i,} when the phi _{R, i,} obtains the light intensity I _i detected by the detector, the sequence {t _i} Is the time sequence in which the elapsed times t _i from the reference time are arranged, and the obtained sequence {I _i } is the light intensity I (t _i ) detected by the detector at the elapsed time t _i from the reference time. Assuming that F is a predetermined coefficient (unit is angle ⁻¹ ), <a> from a plurality of light intensities I (t _i ) corresponding to a plurality of times t _i , a frequency 2F (A _A −A _P + A _R ) And the process of obtaining the amplitude and phase of at least one frequency component of the component of frequency 2F (A _A + A _P −A _R ), and <b> from the plurality of light intensities I (t _i ), a component of the frequency 2F _{(a a} -A _P), a component of the frequency _{2F (a a + a P)} , the frequency _{2F (a a + a P -2A} R And components, and two seek processing of the at least two frequency components amplitude and phase of the component of the frequency _{2F (A A -A P + 2A} R), <c> the processing <a> and < and a process for evaluating the magnitude and direction of the optical anisotropy of the sample based on the amplitude and the phase obtained in b>.

  According to the above aspect, the magnitude and direction of the optical anisotropy of the sample can be evaluated regardless of the retardation value of the retardation plate used and without using the direct current component of the transmitted light intensity. For this reason, a sample having a small retardation can be accurately evaluated even in a bright atmosphere in which stray light is mixed into the detector or in an environment where retardation of the retardation plate cannot be strictly controlled.

It is a schematic diagram which outlines an example of the geometry of an evaluation system. It is a schematic diagram which outlines another example of the geometry of an evaluation system. FIG. 2 is a schematic diagram outlining an evaluation method using the evaluation system in FIG. 1. It is a schematic diagram which outlines the other evaluation methods by the evaluation system of FIG. FIG. 3 is a schematic diagram outlining an evaluation method using the evaluation system in FIG. 2. It is a schematic diagram which outlines the other evaluation methods by the evaluation system of FIG. FIG. 2 is a schematic diagram outlining an evaluation apparatus corresponding to the evaluation system in FIG. 1. FIG. 3 is a schematic diagram outlining an evaluation apparatus corresponding to the evaluation system in FIG. 2. It is a figure which shows the example of a simulation of the output sequence { _Ii } of a detector. FIG. 10 is a diagram illustrating a cos component obtained by performing radix-2 FFT on the output sequence {I _i } of FIG. 9. FIG. 10 is a diagram illustrating a sin component obtained by performing radix-2 FFT on the output sequence {I _i } in FIG. 9. It is an enlarged view of FIG. It is an enlarged view of FIG. It is a figure which shows the example of a simulation of the output sequence {I0 _{, i} } of a detector. It is a figure which shows the example of a simulation of the output sequence { _{I45, i} } of a detector. FIG. 15 is a diagram illustrating a sin component obtained by performing radix-2 FFT on the output string {I _{0, i} } in FIG. 14. It is a figure which shows the sine component obtained by giving radix-2 FFT to the output sequence { _{I45, i} } of FIG.

Embodiment 1 FIG.
In this description, the sine (function) is expressed as sin, the cosine (function) is expressed as cos, the tangent (function) is expressed as tan, and the cotangent (function) is expressed as cot in accordance with a general trigonometric function / triangle ratio notation. Moreover, the circumference is expressed by π. In addition, since the frequency and the angular frequency are only a constant multiple difference, the frequency and the angular frequency may be simply expressed as frequency without being distinguished.

  FIG. 1 shows a schematic diagram of the geometry of the evaluation system. According to the example of FIG. 1, the polarizer 1, the phase difference plate 4, the sample 3, the analyzer 2, and the detector 6 are sequentially arranged on the optical path of the light emitted from the monochromatic light source 5 from the monochromatic light source 5 side. Is arranged. The outgoing light from the monochromatic light source 5 passes through the polarizer 1, the phase difference plate 4, the sample 3, and the analyzer 2 in this order, and is detected by the detector 6.

  When the polarizer 1, the analyzer 2, and the phase difference plate 4 are not distinguished, they are expressed as optical elements. Sample 3 is at least partially plate-shaped, and the plate-shaped portion has optical anisotropy. The plate shape refers to a shape in which two surfaces facing each other and parallel to each other are parallel to each other. It is assumed that the polarizer 1, the analyzer 2, and the analyzer 2 are also plate-shaped.

  It is assumed that light emitted from the monochromatic light source 5 enters the polarizer 1, the phase difference plate 4, the sample 3, and the analyzer 2 perpendicularly. The polarizer 1, the phase difference plate 4, the sample 3, and the analyzer 2 are arranged so that their surfaces are parallel. By placing a stop having an aperture sufficiently smaller than the distance between the monochromatic light source 5 and the detector 6 in front of the detector 6, the light incident on the detector 6 is only the light having the above-described vertical incidence.

  In this description, an orthogonal right-handed coordinate system in which the direction parallel to the light beam traveling from the monochromatic light source 5 toward the detector 6 is taken as the positive direction of the z-axis is referred to as a laboratory coordinate system (see FIG. 1). In this case, the optical path of the emitted light from the monochromatic light source 5 extends in the positive direction of the z axis. The surfaces of the polarizer 1, the phase difference plate 4, the sample 3, and the analyzer 2 (surfaces parallel to each other as described above (so-called main surface) in the plate shape) are optical paths of outgoing light from the monochromatic light source 5. Orthogonal to

  The polarizer 1, the analyzer 2, and the phase difference plate 4 are rotated around the rotation axis parallel to the z axis, in other words, the main surfaces of the polarizer 1, the phase difference plate 4, the sample 3, and the analyzer 2. It is assumed that it can rotate around a rotation axis parallel to the normal direction.

  When the optical elements are arranged as described above, the transmission axis directions of the polarizer 1 and the analyzer 2 and the slow axis directions of the phase difference plate 4 and the sample 3 are parallel to the xy plane of FIG. Each axial direction (angle) is specified by an azimuth angle on the xy plane, and a direction from the positive x-axis direction to the positive y-axis direction is defined as a positive angle direction. However, the sign of the angle only needs to be defined uniformly for the optical element and the sample 3, and is not necessarily limited to the right-handed method as described above.

The Stokes vector S ^{out of the} light emitted from the analyzer 2 when the light incident on the polarizer 1 from the monochromatic light source 5 is natural light having unit intensity is expressed by the equation (M) 1).

  A matrix r (ω) representing the rotation of the optical element is defined by equation (2).

The Mueller matrix P (φ _P ) of the polarizer 1 and the Mueller matrix A (φ _A ) of the analyzer 2 are expressed by Expression (3).

Here, φ _P and φ _A are the transmission axis directions of the polarizer 1 and the analyzer 2.

The Mueller matrix R (φ _R , Δ) of the phase difference plate 4 and the Mueller matrix V (φ, δ) of the sample 3 are expressed by Expression (4).

Here, φ and φ _R are the slow axis directions of the sample 3 and the phase difference plate 4, and δ and Δ are phase differences given to the incident light expressed in angular units. Since it is perpendicular incidence, the phase difference given to the incident light is equal to the retardation of the sample 3 or the phase difference plate 4. If the internal structure is uniform, the phase difference is generally expressed as a product value of birefringence and thickness (in length units), or a value multiplied by 2πrad / λ (in angle units). is there. The reading of the units may be freely performed according to a normal method (for example, φ [rad] is φ × 360 / 2π [°]). λ is the wavelength of light emitted from the monochromatic light source 5.

  The Mueller matrix M of the entire optical system is expressed by Equation (5).

Since the Stokes parameter S ₀ represents the intensity of the light, the transmitted light intensity I detected by the detector 6 in the geometry of FIG. 1 can be calculated using the equations (1) to (5), and the result equation (6) Is obtained.

Here, I ₀ is proportional to the intensity of light incident on the detector 6 and is the product of the output coefficient of the detector 6 and the light quantity loss rate of the entire evaluation system. Since I ₀ is proportional to the intensity of the light incident on the detector 6, if the output when the light of intensity “1” is incident in a certain unit system is “I”, the intensity “P” in that unit system. The output when “” light is incident is “P × I”.

Formula (6) is an arrangement in which a monochromatic light source 5, a polarizer 1, a retardation plate 4, a sample 3, an analyzer 2 and a detector 6 are arranged in this order (monochromatic light source 5-polarizer 1-retardation plate 4). -Intensity of transmitted light in Sample 3-Analyzer 2-Detector 6). On the other hand, the transmitted light in the arrangement in which the phase difference plate 4 and the sample 3 are interchanged, that is, the arrangement of the monochromatic light source 5-polarizer 1-sample 3-retardation plate 4-analyzer 2-detector 6 (see FIG. 2). When the intensity I _rev is calculated, Equation (7) is obtained.

Comparing I in equation (6) with I _{rev in} equation (7), it can be seen that only φ _P and φ _A are interchanged. In the following description, the monochromatic light source 5-polarizer 1-retarder plate 4-sample 3-analyzer 2-detector 6 as shown in FIG. When evaluating with the arrangement of light source 5-polarizer 1-sample 3-phase difference plate 4-analyzer 2-detector 6, the description regarding the polarizer 1 and the analyzer 2 may be read. This replacement arrangement will be described in the fifth to eighth embodiments.

  The polarizer 1, the phase difference plate 4, and the analyzer 2 are rotated independently. A certain time is set as a reference time t = 0.

The transmission axis direction φ _P of the polarizer 1 at t = 0 is used as a reference for the angle representing the axial direction (φ _P (t = 0) = 0 °). The rotation frequency of the polarizer 1 is ω _P (φ _P (t) = ω _P t).

An angle difference (initial phase) between the transmission axis direction φ _P of the polarizer 1 and the slow axis direction φ _R of the retardation plate 4 at t = 0 is defined as δ _RP (φ _P (t = 0) = 0 Since it is °, δ _RP = φ _R (t = 0) −φ _P (t = 0) = φ _R (t = 0)). Further, the rotation frequency of the phase difference plate 4 is set to ω _P (φ _R (t) = ω _R t + δ _RP ).

Similarly, the angle difference (initial phase) between the transmission axis direction φ _P of the polarizer 1 and the transmission axis direction φ _A of the analyzer 2 at t = 0 is defined as δ _AP (φ _P (t = 0) = Since it is 0 °, δ _AP = φ _A (t = 0) −φ _P (t = 0) = φ _A (t = 0)). The frequency of rotation of the analyzer 2 is ω _A (φ _A (t) = ω _A t + δ _AP ).

FIG. 1 corresponds to the snapshot at time t = 0. Note that ω _{P and the} like are related to rotation and should be referred to as angular frequencies, but in this description, they are also simply referred to as frequencies following commonly used designations.

  At this time, the time dependency I (t) of the transmitted light intensity detected by the detector 6 is expressed by Expression (8).

According to equation (8), in addition to the DC term I _0/4, it appears the six sections. These terms are in the form of Fcos (δ + ωt), and change periodically with respect to time t with amplitude F, phase δ, and frequency ω, so I (t) is converted to FFT (Fast Fourier Transform) or the like. When the frequency analysis is performed with the above, the phase δ and the amplitude F can be obtained as frequency components of the frequency ω for each term. In the present description, these periodically changing terms other than the DC term are referred to as frequency component terms.

In order to distinguish the frequency component terms in Equation (8), the terms of frequency 2 (ω _A −ω _P ) are described as 1: 2 (AP) terms in order from the top, and the frequency 2 (ω _A + ω _P ) The term is described as a 2: 2 (A + P) term, the term of frequency 2 (ω _A + ω _P −2ω _R ) is described as a 3: 2 (A + P-2R) term, and the frequency 2 (ω _A −ω _P + 2ω _R). the section) 4: 2 (described as a-P + 2R) term, the frequency 2 to the section _{(ω a -ω P + ω R} ) 5: 2 ( described as a-P + R) term, frequency 2 (omega _a + omega The term of ( _P −ω _R ) will be described as a 6: 2 (A + P−R) term.

Since the frequency here is an angular frequency, the international unit system has a unit of rad · s ⁻¹ . In order to convert the frequency into a so-called frequency (unit s ⁻¹ = Hz), it may be divided by 2π [rad]. When describing in other unit systems, the unit may be converted by multiplying by an appropriate coefficient. In other words, generality is not lost even if it is described in an arbitrary unit system.

  A method for obtaining the retardation δ of the sample 3 and the slow axis direction φ of the sample 3 without using the frequency component term (that is, without using the direct current term) and not knowing the retardation Δ of the phase difference plate 4 is known. Is as follows. In order to be able to accurately evaluate even a sample having a small δ, it is assumed in the following description that δ is a small value.

There are four unknown parameters in I (t): the output coefficient I _{0 of the} detector 6, the retardation Δ of the phase difference plate 4, the retardation δ of the sample 3, and the slow axis direction φ of the sample 3. . The measurer can determine the slow axis direction δ _RP of the phase difference plate 4 and the transmission axis direction δ _{AP of the} analyzer 2 at t = 0.

  Since two amounts of phase and amplitude are obtained from one frequency component term, if there are at least two frequency component terms, a maximum of four independent measurement amounts can be taken. However, the phase of the frequency component term does not include any unknown parameters (1: 2 (AP) term and 3: 2 (A + P-2R) term) or only φ (2: 2). (A + P), 4: 2 (A-P + 2R), 5: 2 (A-P + R), 6: 2 (A + P-R)). Therefore, even if different phases are obtained from two different frequency component terms, only information of φ can be obtained. Therefore, even if the two measured amplitudes are different, three unknown parameters remain. Therefore, δ cannot be determined uniquely. That is, in order to evaluate φ and δ, at least three frequency component terms are necessary.

Since it is assumed that [delta] is small, the ^{cos 2 (δ / 2),} sinδ and sin ² (δ / ^2), respectively the order of 1, [delta] and [delta] ^2/4 included in the amplitude of each frequency component term . Therefore, in order to accurately evaluate δ, it is necessary to include at least one of a 5: 2 (A−P + R) term and a 6: 2 (A + P−R) term, which are frequency component terms including sin δ. is there. As described above, since there is only an unknown parameter in the phase of each frequency component term, φ is calculated from one phase of the 5: 2 (A−P + R) term and the 6: 2 (A + P−R) term. Since information can be obtained, the remaining three unknown parameters, I ₀ , Δ, and δ, may be obtained from the amplitude of the frequency component term.

  However, since the amplitudes of the 5: 2 (A−P + R) term and the 6: 2 (A + P−R) term are equal, only two pieces of information on the phase and the amplitude can be obtained from these two terms. Therefore, the amplitudes of two frequency component terms out of the frequency component terms other than the 5: 2 (AP + R) term and the 6: 2 (A + PR) term are necessary.

  In summary, in order to obtain the retardation δ of the sample 3 and the slow axis direction φ of the sample 3 from the time dependency I (t) of the transmitted light intensity detected by the detector 6, <i> 5: The amplitude and phase of at least one frequency component term of 2 (A−P + R) term and 6: 2 (A + P−R) term, <ii> 1: 2 (A−P) term and 2: 2 ( Two of the amplitude and phase of at least two frequency component terms of the (A + P) term, the 3: 2 (A + P-2R) term and the 4: 2 (A-P + 2R) term need to be determined (and thus A total of at least four quantities).

  Looking at equation (8), it appears that <ii> requires only two amplitudes of at least two frequency component terms. However, as will be described later, in terms of mathematical expressions, it is possible to combine the frequencies of different frequency component terms to be equal, and to mix the amplitude and phase information of each frequency component term into the amplitude and phase of the combined frequency component terms. In view of the above, it is necessary to obtain “two of the amplitudes and phases of at least two frequency component terms” as described above. Measuring two frequency component terms that are originally different at the same frequency is equivalent to measuring different frequency component terms simultaneously.

  Evaluation can be performed without using the DC term and using only the frequency component term that depends on the frequency, which is a setting value that can be controlled by the measurer, so that evaluation can be performed without being affected by low-frequency noise such as stray light or thermal noise, or shot noise. Is possible.

As a method for measuring the amplitude and phase of the frequency component term, for example, the polarizer 1, the analyzer 2, and the phase difference plate 4 are continuously rotated at frequencies (ω _A , ω _P , ω _R ) assigned to them. There is a method of generating an output signal from the detector 6 in time series and applying lock-in detection by a lock-in amplifier to the time series signal. Alternatively, by using a digital oscilloscope FFT on the time series signal, a method of taking the time series signal into a computer and performing a Fourier transform such as FFT or DFT (Discrete Fourier Transform), etc. It is also possible to measure amplitude and phase.

When using a detector with a slow response speed such as a CCD (Charge Coupled Device), a certain constant T is prepared instead of continuous rotation, and the polarizer 1, the analyzer 2, and the phase difference plate 4 are angled respectively. ω _A T, ω _P T, ω _R T Rotate. In this state, the output signal of the detector is recorded. By repeating this operation, a time series signal corresponding to the case where the output signal at the time of continuous rotation is sampled at the time interval T can be acquired.

  When using a device equipped with an A / D converter (Analog-Digital Converter) such as a digital oscilloscope as the detector, the output is recorded at a time interval determined by the sampling frequency. A series signal can be acquired. Even when lock-in detection is performed using a PSD (Phase Sensitive Detector) and a low-pass filter, the time constant of the low-pass filter corresponds to the time interval, and an output corresponding to the amplitude and phase obtained by frequency analysis is obtained.

When generalized, it becomes as follows. Proportional coefficients A _P , A _A , A _R and constants c _P , c _A , c _R are assigned to the polarizer 1, the analyzer 2, and the phase difference plate 4, respectively. From an arbitrary number sequence {t _i } = {t ₀ , t ₁ ,..., T _N }, three number sequences {φ _{P, i} } = {c _P + A _P t _i }, {φ _{A, i} } = {c Calculate _A + A _A t _i }, {φ _{R, i} } = {c _R + A _R t _i }. With respect to the set of numbers {t _i , φ _{P, i} , φ _{A, i} , φ _{R, i} } designated by the same subscript i, the polarizer 1 is directed to the angle φ _{A, i} and the analyzer 2 is set to the angle φ _{P , i} is set to a state where the phase difference plate 4 is directed to the angle φ _{R, i,} and the output I _i of the detector 6 in this state is detected. When the angle change of the optical elements 1, 2, and 4 and the detection by the detector 6 are performed for each i (i = 0 to N), an output string {I _i } is obtained. This is regarded as the time dependency I (t) of the output obtained corresponding to the time sequence t = {t _i } in which the times when the time t _{i has} elapsed from the reference time are arranged.

For example, when measurement is performed using an A / D converter in a situation where the polarizer 1 is continuously rotated at the frequency ω _P , the analyzer 2 is at the frequency ω _A , and the phase difference plate 4 is rotated at the frequency ω _R , sampling is performed. If the frequency is f [Hz], {t _i } = {i / f}, {φ _{P, i} } = {c _P + ω _P · i / f}, {φ _{A, i} } = {c _A + ω _A · i / f}, {φ _{R, i} } = {c _R + ω _R · i / f}.

With such generalization, {t _i } need not be a monotonically increasing sequence. However, it is more convenient to perform an analysis such as FFT by setting the minimum value to 0 and using a number sequence that monotonously increases with a constant increase amount. An interpolation method such as spline interpolation may be used to interpolate into a number sequence that monotonously increases with a constant increase amount.

  By the above method, the time dependence I (t) of the output of the detector 6 can be obtained.

The proportionality coefficient is a generalization of the rotation speed of each optical element (it can be applied even if it is not continuous rotation, and in the case of continuous rotation, the proportionality coefficient and the frequency of rotation are equal). Since t _i is regarded as time, it has a unit of time, and since the product of the proportional coefficient and t _i represents an angle, the proportional coefficient has a unit of [angle] × [time] ⁻¹ . For example, when the unit of t _i is s and the unit of the proportional coefficient is rad · s ⁻¹ , the proportional coefficients A _P , A _A , and A _R are obtained when the polarizer 1 has the frequency A _P [rad · s ⁻¹ ]. Thus, the analyzer 2 is rotated at the frequency A _A [rad · s ⁻¹ ], and the phase difference plate 4 is rotated at the frequency A _R [rad · s ⁻¹ ]. In this case, for example, if the frequency unit of the frequency component term of I (t) is s ⁻¹ = Hz, the frequency of the 1: 2 (A−P) term is 2 (A _A −A _P ) / 2π. The other terms are similarly expressed. Using a factor F which depends on the unit system to be used, generally the 2F _(A A -A _P) or the like. In the above case, F = 1 / 2π [rad ⁻¹ ]. When the unit of the proportionality coefficient is [° · s ⁻¹ ], F = 1/360 [° ⁻¹ ].

_{{Φ P, i} = {} c P + A P t i}, {φ A, i} = {c A + A A t i}, {φ R, i} = {c R + A R t i} So, time The axial directions of the optical elements at t = 0 (the polarizer 1 and the analyzer 2 are the transmission axes, and the retardation plate 4 is the slow axis) are c _P , c _A , and c _R , respectively. In the above equation (8) of I (t), the transmission axis direction of the polarizer 1 at t = 0 is used as the reference of the angle representing the axial direction, so that δ _AP appearing in the phase of the frequency component term of equation (8) , Δ _RP δ _AP = φ _A (t = 0) −φ _P (t = 0) = c _A −c _P and δ _RP = φ _R (t = 0) −φ _P (t = 0) = c _R −c _P. Even if 0 is not included in {t _i }, δ _AP and δ _RP can be obtained from the constants c _P , c _A , and c _R by this calculation.

By the above method, δ _AP and δ _RP and the frequency of the frequency component term necessary for evaluation can be obtained from the proportional coefficients A _P , A _A , A _R and the constants c _P , c _A , c _R. Frequency components necessary for evaluation that change at the frequency obtained above by a method such as lock-in detection of the time dependency I (t) of the output of the detector 6 obtained by the above method, or FFT. The amplitude and phase of the term can be measured. By determining the unknown parameters I ₀ , Δ, δ, and φ by an optimization method such as a least square method or a quasi-Newton method so as to reproduce the phase and amplitude of each measured frequency component term, The retardation δ of the sample 3 and the slow axis direction φ of the sample 3 can be evaluated. In addition, since fitting can also be regarded as an optimization problem, fitting is also expressed as an optimization method below. As will be described later, by selecting an appropriate frequency component term, an unknown parameter can be obtained explicitly instead of an implicit method such as an optimization method. The expressions “implicit” and “explicit” are commonly used in mathematics.

  Since there is a difference in magnitude between the amplitude and phase values of the frequency component terms, an objective function Q such as Equation (9) is used as the objective function of the optimization method.

Here, p represents the amplitude or phase used for the evaluation, and the subscript j designates the type of the frequency component term and the distinction between the amplitude and the phase. The superscript “measured” indicates a measured value, and “calculated” indicates a calculated value from the parameter to be optimized (for the specific expression, see Expression (8)). By normalizing with p _j ^measured , the magnitude difference is compensated for the amplitude and phase values of the frequency component term.

  According to the above evaluation method, the retardation δ of the sample 3 (that is, the magnitude of the optical anisotropy) is independent of the retardation value of the phase difference plate 4 to be used and without using the direct current component of the transmitted light intensity. The slow axis direction φ (that is, the direction of optical anisotropy) of the sample 3 can be evaluated. Therefore, even in a bright atmosphere where stray light is mixed into the detector 6 or when the retardation Δ of the retardation plate 4 is not strictly managed, the sample 3 having a small δ is accurately detected. Can be evaluated.

  Since the retardation Δ of the phase difference plate 4 to be used is obtained simultaneously with the retardation δ of the sample 3, etc., the value of Δ does not need to be known. It is sufficient to control the ambient temperature so that the retardation of the phase difference plate 4 and the sample 3 does not change during the measurement time. If the temperature control of the sample 3 is possible, the temperature dependence of the retardation δ of the sample 3 can be obtained. Since the evaluation is performed using monochromatic light, if the monochromatic light source 5 is configured to have a variable output wavelength by using, for example, a halogen lamp and a spectroscope, wavelength dependency can be obtained. The retardation Δ of the phase difference plate 4 also has wavelength dependency, but it is not a problem because it is obtained simultaneously with the retardation δ of the sample 3 and the like.

Since at least one frequency component term out of the 5: 2 (A−P + R) term and the 6: 2 (A + P−R) term is necessary, the absolute value of the amplitude of these frequency component terms should be larger. . Therefore, the absolute value of sin Δ is preferably close to 1. That is, Δ is preferably in the vicinity of about π / 2 or a value obtained by adding an integer multiple of π. However, it is only preferable, and may not be strict. If there is one wavelength to be evaluated, a quarter wave plate for that wavelength may be used. Strictly speaking, retardation of a quarter wave plate that can be actually obtained is not a quarter wavelength, but Δ is obtained at the same time as δ and the like, so that there is no problem. The amplitude of other frequency component terms is proportional to cos ² (Δ / 2) or sin ² (Δ / 2) with respect to Δ. If the retardation plate is approximately a quarter-wave plate, the value of cos ² (Δ / 2) and the value of sin ² (Δ / 2) are both about ½. The amplitude of the frequency component term never becomes zero. Also in this respect, it is preferable to use a quarter wave plate as the retardation plate 4.

  Conversely, it is not preferable that the absolute value of sin Δ of the phase difference plate 4 is close to zero. That is, it is not preferable to use a half-wave plate for the wavelength of monochromatic light used for measurement. When evaluating at a plurality of wavelengths using the same retardation plate 4, it is desirable to use a retardation plate that does not become a half-wave plate at all the wavelengths to be measured.

Frequency component term used for evaluation (that is, <i> 5: 2 (A-P + R) term and at least one frequency component term of 6: 2 (A + P-R) term), and <ii> 1: 2 The frequencies of (AP) term, 2: 2 (A + P) term, 3: 2 (A + P-2R) term and 4: 2 (AP + 2R) term) are mutually in phase. Select the rotation frequencies ω _P , ω _A , ω _R (in other words, proportional coefficients A _P , A _A , A _R ) of the optical elements so that they are different and the frequency of the frequency component term used is not zero. There is a need to. The frequency of the frequency component term may be negative because it is expressed by addition / subtraction of the rotation frequency of the optical element. However, since cos (δ−ωt) = cos (−δ + ωt), the sign of the phase is reversed. A positive frequency is considered. Therefore, the difference between the _two frequencies ω ₁ and ω ₂ is that ω ₁ ≠ ± ω ₂ holds. Rotation of the frequency omega _P of specific optical elements, ω _A, ω _R (proportional coefficient _{A P, A A, A R} ) to derive the condition of the two frequencies omega ₁ different need exists, the omega ₂ On the other hand, the condition of ω ₁ = ± ω ₂ may be obtained for all combinations of two frequencies that need to be different, and all negation of the obtained condition may be combined by logical product.

The frequency component term used for evaluation and the frequency component term not used are equal depending on the rotation frequency ω _P , ω _A , ω _R (proportional coefficients A _P , A _A , A _R ) of the optical element. There is a case. When the frequency component term of amplitude F ₁ and phase δ ₁ is equal to the frequency component term of amplitude F ₂ and phase δ ₂ and the frequency is equal to ω, as shown in the following equation (10), Frequency component terms are combined into terms of the same frequency. However, since the original amplitudes F ₁ and F ₂ and phases δ ₁ and δ ₂ are only inherited by the combined terms, the information itself is not lost. That is, in order to be used specifically for the analysis, it is necessary to calculate Equation (10) specifically, but the frequency of the frequency component term used for evaluation is equal to the frequency of the frequency component term not used for evaluation. It does not matter. You should have chosen not to use it, but you just decided to use it.

  By this method, unknown parameter information can be given to the phase of the frequency component term that does not have unknown parameter information. Alternatively, the information of unknown parameters other than φ can be provided in the phase of the frequency component term having only φ information. Further, the information of φ can be provided in the amplitude of the frequency component term that does not have information of φ. However, the information does not increase, and is equivalent to measuring the original two frequency component terms simultaneously.

Here, FIG. 3 shows a schematic diagram outlining the processing in the evaluation method according to the first embodiment. According to the example of FIG. 3, in the process 51, the light intensity detected by the detector 6 (in other words, the output string from the detector 6) I (t _i ) is acquired. In the process 52, frequency components are extracted from the light intensity I (t _i ) for a plurality of times t _i . Although all frequency components are illustrated in FIG. 3 for easy understanding, in the process 52, at least only the frequency components used for evaluation need be acquired. In the process 53, the amplitude and phase of at least one frequency component of the 5: 2 (A−P + R) term and the 6: 2 (A + P−R) term are obtained. In the process 54, at least two frequency components of a 1: 2 (A−P) term, a 2: 2 (A + P) term, a 3: 2 (A + P−2R) term, and a 4: 2 (A−P + 2R) term are used. Find the amplitude and phase of the term. In process 55, the magnitude (retardation δ) and direction (slow axis direction φ) related to the optical anisotropy of the sample 3 are acquired from the amplitude and phase obtained in processes 53 and 54.

Embodiment 2. FIG.
Since the phase of the 2: 2 (A + P) term, 4: 2 (A-P + 2R) term, 5: 2 (A-P + R) term, and 6: 2 (A + P-R) term includes only φ as an unknown parameter, If at least one of these phases can be measured, φ can be obtained explicitly rather than by an implicit method such as an optimization method.

Specifically, 2: 2 (A + P) measurements of sections of the phase and phase1 _2, 4: 2 measurements of the phase of the (A-P + 2R) section and _{phase1 4, 5: 2 (A} -P + R) term If the measured value of the phase is phase ₁₅ and the measured value of the phase of the 6: 2 (A + P−R) term is phase ₁₆ , φ can be obtained using the following equation (11). In Expression (11), it is assumed that the frequency of the frequency component term used for obtaining φ is positive. Therefore, when the frequency of the frequency component term used for obtaining φ is negative, the sign of the phase is reversed, and correction is necessary.

  According to the evaluation method, φ can be positively evaluated from the phase of the frequency component without using an implicit method such as an optimization method. For this reason, the arbitrary nature of setting the objective function for optimization can be eliminated.

Regardless of whether lock-in detection or Fourier transform is used, the phase δ of the frequency component term is the amplitude of the component acos synchronized with cosωt and the amplitude of the component synchronized with sinωt when the frequency of the frequency component term is ω. From asin, a relationship of δ = tan ⁻¹ (asin / acos) is obtained (considering the sign of acos and asin, it is determined where δ is in the first to fourth quadrants). Therefore, if the absolute values of acos and asin are approximately equal, the measurement accuracy will be high (if one is extremely small, the smaller measurement accuracy will be low).

Since the approximate value of φ is often known in advance, the value is set as φ ₀ and is decomposed into φ = φ ₀ + δφ. When the 5: 2 (A−P + R) term and the 6: 2 (A + P−R) term are expanded, the following equation (12) is obtained. For the double sign in equation (12), the upper sign corresponds to the use of the 5: 2 (A-P + R) term, and the lower sign uses the 6: 2 (A + P-R) term. Corresponding to that.

Therefore, when using the 5: 2 (A−P + R) term and the 6: 2 (A + P−R) term, δ _AP and δ _RP are set so that the following equation (13) is satisfied (for example, δ _AP = φ). ₀ and δ _RP = ± π / 8). This is because when δφ is small (φ ₀ is approximately close to the actual direction φ), the amplitudes of the 5: 2 (A−P + R) term and the 6: 2 (A + P−R) term are approximately equal, and the measurement accuracy Because it becomes higher.

  In Expression (13), m is an integer. In addition, for the double sign in equation (13), the upper sign corresponds to using the 5: 2 (AP + R) term, and the lower sign uses the 6: 2 (A + PR) term. Corresponding to that.

Similarly, 2: 2 (A + P ) is used _{δ AP = φ 0/2 +} π / 8 + mπ / 4 with respect to section 4: For 2 (AP + 2R) term δ _RP -δ _AP / 2 = φ ₀ + π / 16 + mπ / 8 may be used. These two conditions can be satisfied simultaneously if δ _RP = 2φ ₀ .

  By evaluating with this method, the unknown parameter φ (or δφ) can be obtained alone with high accuracy. Two or more frequency components of a 2: 2 (A + P) term, a 4: 2 (A-P + 2R) term, a 5: 2 (A-P + R) term, and a 6: 2 (A + P-R) term If φ (or δφ) is obtained separately from the phase of each term and averaged, the accuracy is improved.

  In order to obtain three unknown parameters other than φ, particularly δ, as in the first embodiment, at least one of the <i> 5: 2 (A−P + R) term and the 6: 2 (A + P−R) term. The amplitude and phase of one frequency component term, <ii> 1: 2 (A−P) term, 2: 2 (A + P) term, 3: 2 (A + P−2R) term, and 4: 2 (A−P + 2R) And two of the amplitude and phase of at least two frequency component terms must be determined (thus a total of at least four quantities).

The amplitude and phase of the frequency component term necessary for the evaluation are obtained by a method such as lock-in detection of the time dependency I (t) of the detector output obtained by the method described in the first embodiment or FFT. Can be measured. In order to reproduce the phase and amplitude of each measured frequency component term, the output coefficient I ₀ of the detector, which is an unknown parameter, the retardation Δ of the phase difference plate 4 and the retardation δ of the sample 3 are determined by an optimization method. As a result, the retardation δ of the sample 3 can be evaluated.

  By the above evaluation method, the retardation δ of the sample 3 and the slow axis direction φ of the sample 3 are evaluated regardless of the retardation Δ value of the retardation plate 4 to be used and without using the direct current component of the transmitted light intensity. it can. Therefore, even in a bright atmosphere where stray light is mixed into the detector 6, even when the retardation Δ of the phase difference plate 4 is not strictly managed, a sample having a small δ can be accurately evaluated.

  Since the retardation Δ of the phase difference plate 4 to be used is obtained simultaneously with the retardation δ of the sample 3, etc., the value of Δ does not need to be known. It is sufficient to control the ambient temperature so that the retardation of the phase difference plate 4 and the sample 3 does not change during the measurement time. If the temperature control of the sample 3 is possible, the temperature dependence of the retardation δ of the sample 3 can be obtained. Since the evaluation is performed using monochromatic light, if the monochromatic light source 5 is configured to have a variable output wavelength by using, for example, a halogen lamp and a spectroscope, wavelength dependency can be obtained. The retardation Δ of the phase difference plate 4 also has wavelength dependency, but it is not a problem because it is obtained simultaneously with the retardation δ of the sample 3 and the like.

  As in the first embodiment, the absolute value of sin Δ is preferably close to 1. That is, Δ is preferably in the vicinity of about π / 2 or a value obtained by adding an integer multiple of π. However, it is only preferable, and may not be strict. It is not preferable that the absolute value of sin Δ of the phase difference plate 4 is close to zero. That is, it is not preferable to use a half-wave plate for the wavelength of monochromatic light used for measurement.

Frequency component term used for evaluation (that is, <i> 5: 2 (A-P + R) term and at least one frequency component term of 6: 2 (A + P-R) term), and <ii> 1: 2 The frequencies of (AP) term, 2: 2 (A + P) term, 3: 2 (A + P-2R) term and 4: 2 (AP + 2R) term) are mutually in phase. Select the rotation frequencies ω _P , ω _A , ω _R (in other words, proportional coefficients A _P , A _A , A _R ) of the optical elements so that they are different and the frequency of the frequency component term used is not zero. There is a need to. Also, at least of the 2: 2 (A + P) term, 4: 2 (A-P + 2R) term, 5: 2 (A-P + R) term, and 6: 2 (A + P-R) term used for the evaluation of φ One frequency component term needs to be different from the frequency of a frequency component term not used for evaluation. Here, the fact that the two frequencies ω ₁ and ω ₂ are different means that ω ₁ ≠ ± ω ₂ holds. Specifically, in order to derive the conditions of the rotation frequencies ω _P , ω _A , ω _R (proportional coefficients A _P , A _A , A _R ) of the optical element, the two frequencies ω ₁ , ω ₂ that need to be different are derived. On the other hand, the condition of ω ₁ = ± ω ₂ may be obtained for all combinations of two frequencies that need to be different, and all negation of the obtained condition may be combined by logical product.

Frequency component term used for evaluation (that is, frequency component term of at least one of 5: 2 (AP + R) term and 6: 2 (A + PR) term, and 1: 2 (AP) Frequency used in the evaluation of φ among at least two frequency component terms of the term, 2: 2 (A + P) term, 3: 2 (A + P-2R) term, and 4: 2 (A-P + 2R) term) The frequency of the component term is a frequency component term that is not used for evaluation (that is, the remaining frequency component term of the 5: 2 (A−P + R) term and the 6: 2 (A + P−R) term) and 1: 2 (AP) term, 2: 2 (A + P) term, 3: 2 (A + P-2R) term, and 4: 2 (AP + 2R) term remaining frequency component term) It doesn't matter. When the frequency component term having the amplitude F ₁ and the phase δ _{1 and} the frequency component term having the amplitude F ₂ and the phase δ ₂ and the frequency are equal to ω, two frequencies are obtained as shown in the equation (10). The component terms are combined into terms of the same frequency. However, since the original amplitudes F ₁ and F ₂ and phases δ ₁ and δ ₂ are only inherited by the combined terms, the information itself is not lost.

  The processing in the evaluation method according to the second embodiment is outlined in FIG. 3 as in the first embodiment. However, in the processing 55 according to the second embodiment, the slow axis direction φ of the sample 3 is calculated using a predetermined relational expression instead of the optimization method as described above.

Embodiment 3 FIG.
In the first embodiment, as frequency component terms used for evaluation, <i> at least one frequency component term of 5: 2 (A−P + R) term and 6: 2 (A + P−R) term; ii> at least two frequency component terms of 1: 2 (A−P) term, 2: 2 (A + P) term, 3: 2 (A + P−2R) term, and 4: 2 (A−P + 2R) term; , Said that is necessary.

Here, as the above <ii>, the 1: 2 (AP) term and the 3: 2 (A + P-2R) term are selected. 1: 2 amplitude (A-P) term is ^{_{I 0/4 · cos 2 (}} δ / 2) · cos 2 (Δ / 2), 3: 2 amplitude (A + P-2R) term I ₀ / Since 4 · cos ² (δ / 2) · sin ² (Δ / 2), when the amplitudes of these terms are measured to obtain a ratio, sin ² (Δ / 2) / cos ² (Δ / 2) Is required. When the ratio of the measured amplitude is ratio1 = {3: 2 (A + P-2R) term amplitude} / {1: 2 (A−P) term amplitude}, the retardation of the phase difference plate 4 is obtained from the following equation (14). Δ can be obtained positively. When ratio1 is larger than 1, Δ can be obtained more accurately by using the upper equation, and when ratio1 is smaller than 1, Δ can be obtained more accurately by using the lower equation. When ratio1 is 1, any expression may be used.

  ratio2 = {amplitude of one of frequency component terms of 5: 2 (AP + R) term and 6: 2 (A + PR) term} / {1: 2 (AP) term and 3: 2 (A + P-2R) term and the amplitude of one of the frequency component terms}, and from the measured value of the amplitude, the following equation (15), and Δ obtained by the above equation (14) The retardation δ of the sample 3 can be obtained explicitly. In equation (15), the upper equation is used for the 1: 2 (A−P) term and the lower equation is used for the 3: 2 (A + P−2R) term. Since the amplitude is used to obtain Δ for both the 1: 2 (A−P) term and the 3: 2 (A + P−2R) term, it is necessary to measure the amplitude. Therefore, accuracy is improved by obtaining δ separately using both the upper and lower equations of equation (15) and taking the average.

  The amplitude and phase of the frequency component term necessary for the evaluation include lock-in detection of the time dependency I (t) of the output of the detector 6 obtained by the method described in the first embodiment, FFT, etc. It can be measured by the method.

According to the evaluation method, since the optimization method is not used, it is possible to eliminate the arbitraryness of setting the objective function. Since the amplitude of the 1: 2 (A−P) term and the 3: 2 (A + P−2R) term is proportional to cos ² (δ / 2), the amplitude is increased for the sample having a small δ. That is, it is suitable for evaluating a sample having a small δ.

  The slow axis direction φ of the sample 3 is also the method described in Embodiment 2, that is, the 2: 2 (A + P) term, the 4: 2 (A−P + 2R) term, and the 5: 2 (A−P + R) term, It can be obtained explicitly from the phase of at least one frequency component term out of the 6: 2 (A + PR) term (see Equation 11). Two or more frequency components of a 2: 2 (A + P) term, a 4: 2 (A-P + 2R) term, a 5: 2 (A-P + R) term, and a 6: 2 (A + P-R) term If φ (or δφ) is obtained separately from the phase of the term and averaged, the accuracy is improved.

Therefore, both the retardation δ and the slow axis direction φ of the sample 3 can be obtained independently and explicitly. Therefore, since the optimization method is not used for the evaluation of the sample, the arbitraryness of the objective function setting method can be eliminated. As in the second embodiment, it is desirable that the accuracy of the measurement is set to the [delta] _AP and [delta] _RP becomes higher.

  By the above evaluation method, the retardation δ of the sample 3 and the slow axis direction φ of the sample 3 are evaluated regardless of the retardation Δ value of the retardation plate 4 to be used and without using the direct current component of the transmitted light intensity. it can. Therefore, even in a bright atmosphere where stray light is mixed into the detector 6, even when the retardation Δ of the phase difference plate 4 is not strictly managed, a sample having a small δ can be accurately evaluated.

  Since the retardation Δ of the phase difference plate 4 to be used is obtained simultaneously with the retardation δ of the sample 3, etc., the value of Δ does not need to be known. It is sufficient to control the ambient temperature so that the retardation of the phase difference plate 4 and the sample 3 does not change during the measurement time. If the temperature control of the sample 3 is possible, the temperature dependence of the retardation δ of the sample 3 can be obtained. Since the evaluation is performed using monochromatic light, if the monochromatic light source 5 is configured to have a variable output wavelength by using, for example, a halogen lamp and a spectroscope, wavelength dependency can be obtained. The retardation Δ of the phase difference plate 4 also has wavelength dependency, but it is not a problem because it is obtained simultaneously with the retardation δ of the sample 3 and the like.

  As in the first embodiment, the absolute value of sin Δ is preferably close to 1. That is, Δ is preferably in the vicinity of about π / 2 or a value obtained by adding an integer multiple of π. However, it is only preferable, and may not be strict. It is not preferable that the absolute value of sin Δ of the phase difference plate 4 is close to zero. That is, it is not preferable to use a half-wave plate for the wavelength of monochromatic light used for measurement.

Frequency component term used for evaluation (that is, <i> 5: 2 (A-P + R) term and at least one frequency component term of 6: 2 (A + P-R) term), and <ii> 1: 2 The rotation of the optical element is such that the frequencies of the (AP) term and the 3: 2 (A + P-2R) term) are different from each other and the frequency component term used is not zero. Frequency ω _P , ω _A , ω _R (in other words, proportional coefficients A _P , A _A , A _R ) must be selected. The frequency of the frequency component term used for evaluation needs to be different from the frequency of the frequency component term not used for evaluation.

Here, the fact that the two frequencies ω ₁ and ω ₂ are different means that ω ₁ ≠ ± ω ₂ holds. Rotation of the frequency omega _P of specific optical elements, ω _A, ω _R (proportional coefficient _{A P, A A, A R} ) to derive the condition of the two frequencies omega ₁ different need exists, the omega ₂ On the other hand, the condition of ω ₁ = ± ω ₂ may be obtained for all combinations of two frequencies that need to be different, and all negation of the obtained condition may be combined by logical product.

Three frequency component terms are used ({5: 2 (AP + R) term, 1: 2 (AP) term, 3: 2 (A + P-2R) term}, {6: 2 (A + PR)). Term, 1: 2 (A−P) term, 3: 2 (A + P−2R) term}, {5: 2 (A−P + R) term, 6: 2 (A + P−R) term, 1: 2 (A− P), 3: 2 (A + P-2R) term}), the conditions of the rotation frequencies ω _P , ω _A , ω _R of the optical element are specifically written below.

When using the 5: 2 (A−P + R), 1: 2 (A−P), and 3: 2 (A + P−2R) terms, the conditions for the frequencies ω _P , ω _A , and ω _R are as follows: It is given by equation (16). Note that “&” in the expression represents a logical product.

When using the 6: 2 (A + P−R) term, the 1: 2 (A−P) term, and the 3: 2 (A + P−2R) term, the conditions of the frequencies ω _P , ω _A , and ω _R are as follows: It is given by equation (17).

When using the 5: 2 (A-P + R) term, 6: 2 (A + P-R) term, 1: 2 (A-P) term, and 3: 2 (A + P-2R) term, the frequency ω The conditions of _P , ω _A and ω _R are given by the following equation (18).

As described in the first embodiment, since the rotation frequencies ω _P , ω _A , and ω _R of the optical element are proportional to the proportional coefficients A _P , A _A , and A _R , respectively, the equations (16) to (18) Can be read as conditions of proportional coefficients A _P , A _A , A _R.

In any case, ω _P ≠ 0, ω _A ≠ 0, ω _R ≠ 0 and ω _P ≠ ω _A , ω _R ≠ ω _A , ω _R ≠ ω _P, so that the polarizer 1 and the analyzer 2 And the phase difference plate 4 need to be rotated at frequencies different from each other, not 0. There are several other combinations that are prohibited for the rotational frequency of the optical element depending on the combination of frequency component terms used.

For example, ω _A = ω _P / 4, ω _R = 4ω _P , and ω _P ≠ 0 satisfy Expressions (16) to (18). Generalizing the form of ω _A = ω _P / n, ω _R = nω _P , ω _P ≠ 0, n> {1 + √ (3)} to 2.73205, or n <{− √ (2)} to If it is -1.41421, Formula (16)-Formula (18) are satisfy | filled. Note that “√ (3)” represents the square root of 3, and the same applies to “√ (2)”.

  Here, FIG. 4 shows a schematic diagram outlining the process in the evaluation method according to the third embodiment. In the example of FIG. 4, a process 56 is added to the above-described processes 51 to 55 (see FIG. 3). In processing 56, the retardation Δ of the retardation film 4 is calculated by applying the amplitude obtained in processing 54 to a predetermined relational expression. In the process 55 according to the third embodiment, as described above, the amplitude and phase obtained in the processes 53 and 54 and the retardation Δ of the phase difference plate 4 obtained in the process 56 are expressed in a predetermined relational expression. By applying, the retardation δ of the sample 3 is calculated.

Embodiment 4 FIG.
In the first embodiment, as frequency component terms used for evaluation, <i> at least one frequency component term of 5: 2 (A−P + R) term and 6: 2 (A + P−R) term; ii> at least two frequency component terms of 1: 2 (A−P) term, 2: 2 (A + P) term, 3: 2 (A + P−2R) term, and 4: 2 (A−P + 2R) term; , Said that is necessary.

Here, as the above <ii>, the 2: 2 (A + P) term and the 4: 2 (A−P + 2R) term are selected. 2: 2 amplitude (A + P) term is ^{_{I 0/4 · sin 2 (}} δ / 2) · cos 2 (Δ / 2), 4: 2 amplitude (A-P + 2R) term I _0/4 · Since sin ² (δ / 2) · sin ² (Δ / 2), the amplitude of these terms is measured and the ratio is taken to obtain sin ² (Δ / 2) / cos ² (Δ / 2). It is done. When the ratio of the measured amplitude is ratio3 = {4: 2 (A−P + 2R) term amplitude} / {2: 2 (A + P) term amplitude}, the retardation Δ of the phase difference plate 4 is calculated from the following equation (19). You can ask positively. When ratio 3 is greater than 1, Δ can be obtained more accurately by using the upper equation, and when ratio 3 is less than 1, Δ can be obtained more accurately by using the lower equation. When ratio 3 is 1, any expression may be used.

  With respect to the above <i>, ratio4 = {amplitude of one of the frequency component terms of 5: 2 (A−P + R) term and 6: 2 (A + P−R) term} / {2: 2 (A + P) And the amplitude of one of the frequency component terms of the 4: 2 (A-P + 2R) term}, the measured value of the amplitude, the following equation (20), and the equation (19). From this Δ, the retardation δ of the sample 3 can be obtained explicitly. In equation (20), the upper equation is used for the 2: 2 (A + P) term, and the lower equation is used for the 4: 2 (A-P + 2R) term. Since the amplitude is used for obtaining Δ for both the 2: 2 (A + P) term and the 4: 2 (A−P + 2R) term, it is necessary to measure the amplitude. Therefore, the accuracy is improved by obtaining δ separately using both the upper and lower equations of equation (20) and taking the average.

  The amplitude and phase of the frequency component term necessary for the evaluation include lock-in detection of the time dependency I (t) of the output of the detector 6 obtained by the method described in the first embodiment, FFT, etc. It can be measured by the method.

  According to the evaluation method, since the optimization method is not used, it is possible to eliminate the arbitraryness of setting the objective function.

  The slow axis direction φ of the sample 3 is also the method described in Embodiment 2, that is, the 2: 2 (A + P) term, the 4: 2 (A−P + 2R) term, and the 5: 2 (A−P + R) term, It can be obtained explicitly from the phase of at least one frequency component term out of the 6: 2 (A + PR) term (see Equation 11). Two or more frequency components of a 2: 2 (A + P) term, a 4: 2 (A-P + 2R) term, a 5: 2 (A-P + R) term, and a 6: 2 (A + P-R) term If φ (or δφ) is obtained separately from the phase of the term and averaged, the accuracy is improved.

By the above method, both the retardation δ and the slow axis direction φ of the sample 3 can be obtained independently and explicitly. Therefore, since the optimization method is not used for the evaluation of the sample, the arbitraryness of the objective function setting method can be eliminated. As in the second embodiment, it is desirable that the accuracy of the measurement is set to the [delta] _AP and [delta] _RP becomes higher.

  By the above evaluation method, the retardation δ of the sample 3 and the slow axis direction φ of the sample 3 are evaluated regardless of the retardation Δ value of the retardation plate 4 to be used and without using the direct current component of the transmitted light intensity. it can. Therefore, even in a bright atmosphere where stray light is mixed into the detector 6, even when the retardation Δ of the phase difference plate 4 is not strictly managed, a sample having a small δ can be accurately evaluated.

  Since the retardation Δ of the phase difference plate 4 to be used is obtained simultaneously with the retardation δ of the sample 3, etc., the value of Δ does not need to be known. It is sufficient to control the ambient temperature so that the retardation of the phase difference plate 4 and the sample 3 does not change during the measurement time. If the temperature control of the sample 3 is possible, the temperature dependence of the retardation δ of the sample 3 can be obtained. Since the evaluation is performed using monochromatic light, if the monochromatic light source 5 is configured to have a variable output wavelength by using, for example, a halogen lamp and a spectroscope, wavelength dependency can be obtained. The retardation Δ of the phase difference plate 4 also has wavelength dependency, but it is not a problem because it is obtained simultaneously with the retardation δ of the sample 3 and the like.

  As in the first embodiment, the absolute value of sin Δ is preferably close to 1. That is, Δ is preferably in the vicinity of about π / 2 or a value obtained by adding an integer multiple of π. However, it is only preferable, and may not be strict. It is not preferable that the absolute value of sin Δ of the phase difference plate 4 is close to zero. That is, it is not preferable to use a half-wave plate for the wavelength of monochromatic light used for measurement.

A frequency component term used for the evaluation (that is, a frequency component term of at least one of <i> 5: 2 (A−P + R) term and 6: 2 (A + P−R) term), and <ii> 2: 2 The frequency of rotation of the optical element so that the frequencies of the (A + P) term and the 4: 2 (A−P + 2R) term) are different from each other and the frequency of the frequency component term used is not zero. It is necessary to select ω _P , ω _A , ω _R (in other words, proportional coefficients A _P , A _A , A _R ). The frequency of the frequency component term used for evaluation needs to be different from the frequency of the frequency component term not used for evaluation.

Here, the fact that the two frequencies ω ₁ and ω ₂ are different means that ω ₁ ≠ ± ω ₂ holds. Specifically, in order to derive the conditions of the rotation frequencies ω _P , ω _A , ω _R (proportional coefficients A _P , A _A , A _R ) of the optical element, the two frequencies ω ₁ , ω ₂ that need to be different are derived. On the other hand, the condition of ω ₁ = ± ω ₂ may be obtained for all combinations of two frequencies that need to be different, and all negation of the obtained condition may be combined by logical product.

Three frequency component terms are used ({5: 2 (A−P + R) term, 2: 2 (A + P) term, 4: 2 (A−P + 2R) term}, {6: 2 (A + PR) term, 2: 2 (A + P) term, 4: 2 (A-P + 2R) term}, {5: 2 (A-P + R) term, 6: 2 (A + P-R) term, 2: 2 (A + P) term, 4: 2 (AP−2R) term}), the conditions of the optical element rotation frequencies ω _P , ω _A , and ω _R are specifically written below.

When the 5: 2 (A−P + R) term, the 2: 2 (A + P) term, and the 4: 2 (A−P + 2R) term are used, the conditions of the frequencies ω _P , ω _A , and ω _R are as follows: 21). Note that “&” in the expression represents a logical product.

When the 6: 2 (A + P−R) term, the 2: 2 (A + P) term, and the 4: 2 (A−P + 2R) term are used, the conditions of the frequencies ω _P , ω _A , and ω _R are as follows: 22).

When using the 5: 2 (A−P + R) term, 6: 2 (A + P−R) term, 2: 2 (A + P) term, and 4: 2 (A−P + 2R) term, the frequency ω _P , The conditions of ω _A and ω _R are given by the following equation (23).

As described in the first embodiment, the rotation frequencies ω _P , ω _A , and ω _R of the optical element are proportional to the proportional coefficients A _P , A _A , and A _R , respectively. Can be read as conditions of proportional coefficients A _P , A _A , A _R.

In any case, since ω _P ≠ 0, ω _A ≠ 0, and ω _R ≠ 0 are the conditions, it is necessary to rotate all of the polarizer 1, the analyzer 2, and the phase difference plate 4. Since ω _R ≠ ω _P is a condition, it is necessary to rotate the polarizer 1 and the phase difference plate 4 at different frequencies. Further, since −ω _P ≠ ω _A and −ω _R ≠ ω _A are the conditions, it is prohibited to rotate the polarizer 1 and the phase difference plate 4 in the opposite directions at the same absolute frequency as the analyzer 2. The There are several other combinations that are prohibited for the rotational frequency of the optical element depending on the combination of frequency component terms used.

For example, ω _A = ω _P / 4, ω _R = 4ω _P , and ω _P ≠ 0 satisfy Expressions (21) to (23). Generalizing the form of ω _A = ω _P / n, ω _R = nω _P , ω _P ≠ 0, n> {1 + √ (3)} to 2.73205, or n <{− √ (2)} to If it is -1.41421, Formula (21)-Formula (23) are satisfy | filled.

  In addition, the process by the said evaluation method by Embodiment 4 is outlined by FIG. 4 similarly to Embodiment 3. FIG.

Embodiment 5 FIG.
The first to fourth embodiments are evaluation methods in the arrangement of monochromatic light source 5 -polarizer 1 -retardation plate 4 -sample 3 -analyzer 2 -detector 6 as shown in FIG. As described in the first embodiment, the expression (7) of the transmitted light intensity I _{rev in} the arrangement of the monochromatic light source 5-polarizer 1-sample 3-retardation plate 4-analyzer 2-detector 6 is monochromatic. Expression (6) of transmitted light intensity I for the arrangement of light source 5-polarizer 1-retardation plate 4-sample 3-analyzer 2-detector 6, transmission axis direction φ _P of polarizer 1 and analyzer 2 only interchanged in the transmission axis direction phi _a. Therefore, if the description related to the polarizer 1 and the description related to the analyzer 2 described in the first to fourth embodiments are replaced, the monochromatic light source 5 -polarizer 1 -sample 3 -retardation plate 4 -analyzer 2 -It becomes an evaluation method with the arrangement of the detector 6.

  As in the first embodiment, the polarizer 1, the phase difference plate 4, and the analyzer 2 are rotated independently. A certain time is set as a reference time t = 0.

The transmission axis direction φ _P of the polarizer 1 at t = 0 is used as a reference for the angle representing the axial direction (φ _P (t = 0) = 0 °). The rotation frequency of the polarizer 1 is ω _P (φ _P (t) = ω _P t).

An angle difference (initial phase) between the transmission axis direction φ _P of the polarizer 1 and the slow axis direction φ _R of the retardation plate 4 at t = 0 is defined as δ _RP (φ _P (t = 0) = 0 Since it is °, δ _RP = φ _R (t = 0) −φ _P (t = 0) = φ _R (t = 0)). Further, the rotation frequency of the phase difference plate 4 is set to ω _P (φ _R (t) = ω _R t + δ _RP ).

Similarly, the angle difference (initial phase) between the transmission axis direction φ _P of the polarizer 1 and the transmission axis direction φ _A of the analyzer 2 at t = 0 is defined as δ _AP (φ _P (t = 0) = Since it is 0 °, δ _AP = φ _A (t = 0) −φ _P (t = 0) = φ _A (t = 0)). The frequency of rotation of the analyzer 2 is ω _A (φ _A (t) = ω _A t + δ _AP ).

  FIG. 2 corresponds to the snapshot at time t = 0.

  At this time, the time dependency I (t) of the transmitted light intensity detected by the detector 6 is expressed by Expression (24).

Expression (24) can be obtained by changing the following expression (8). That is, in view of the fact that the polarizer 1 and the analyzer 2 are interchanged, ω _A and ω _P are interchanged, and the term in which the sign of ω _A is negative is cos (−x) = cos (x). Is used to correct the sign (in order to unify the notation with Expression (8)), and when the sign of ω _P is negative, the sign of δ _AP is reversed (φ _A (t) = ω _A t + δ (Because the sign of _AP changes), the equation (24) is derived from the equation (8).

1: 2 (AP) term, 2: 2 (A + P) term, 3: 2 (A + P-2R) term, 4: 2 (A-P + 2R) term, and 5 described in the first embodiment : 2 (A-P + R) term and 6: 2 (A + P-R) term are a monochromatic light source 5-polarizer 1-sample 3-retardation plate 4-analyzer 2-detection as shown in FIG. In the arrangement 6, the 1 ′: 2 (A−P) term (frequency 2 (ω _A −ω _P )), 2 ′: 2 (A + P) term (frequency 2 (ω _A + ω _P )), and 3 ': 2 (A + P-2R) term (frequency 2 (ω _A + ω _P -2ω _R )) and 4': 2 (A-P-2R) term (frequency 2 (ω _A -ω _P -2ω _R )) And 5 ′: 2 (A−P−R) term (frequency 2 (ω _A −ω _P −ω _R )) and 6 ′: 2 (A + P−R) term (frequency 2 (ω _A + ω _P −ω _R )). Of the expression (24), only the 4 ′: 2 (AP-2R) term and the 5 ′: 2 (APR) term are different in frequency from the corresponding term in the expression (8).

  As in the first embodiment, the phase of each frequency component term does not include any unknown parameters (1 ′: 2 (A−P) term and 3 ′: 2 (A + P−2R) term), φ (2 ′: 2 (A + P) term, 4 ′: 2 (A−P−2R) term, 5 ′: 2 (A−P−R) term, 6 ′: 2 (A + P−R)) Any of the above). The amplitudes of the 5 ': 2 (APR) term and the 6': 2 (A + PR) term are equal.

Therefore, with respect to the arrangement of the monochromatic light source 5-polarizer 1-sample 3-retardation plate 4-analyzer 2-detector 6 as shown in FIG. 2, the detector 6 uses the method described in the first embodiment. In order to obtain the retardation δ of the sample 3 and the slow axis direction φ of the sample 3 from the time dependence I _rev (t) of the detected transmitted light intensity, <i ′> 5 ′: 2 (A−P− R) and 6 ′: 2 (A + P−R) term and amplitude and phase of at least one frequency component term, <ii ′> 1 ′: 2 (A−P) term and 2 ′: 2 ( It is necessary to obtain two of the amplitude and phase of at least two frequency component terms of the A + P) term, the 3 ′: 2 (A + P−2R) term, and the 4 ′: 2 (A−P−2R) term. There are (thus a total of at least 4 quantities).

  Evaluation can be performed without using the DC term and using only the frequency component term that depends on the frequency, which is a setting value that can be controlled by the measurer, so that evaluation can be performed without being affected by low-frequency noise such as stray light or thermal noise, or shot noise. Is possible.

Necessary for evaluation that changes at the above-mentioned frequency by lock-in detection of the output time dependency I _rev (t) of the output of the detector 6 obtained by the method described in the first embodiment, or FFT. The amplitude and phase of a simple frequency component term can be measured. By determining the unknown parameters I ₀ , Δ, δ, and φ by an optimization method so as to reproduce the phase and amplitude of each measured frequency component term, the retardation δ of the sample 3 and the slow axis direction of the sample 3 are determined. φ can be evaluated.

  According to the above evaluation method, the retardation δ of the sample 3 (that is, the magnitude of the optical anisotropy) is independent of the retardation value of the phase difference plate 4 to be used and without using the direct current component of the transmitted light intensity. The slow axis direction φ (that is, the direction of optical anisotropy) of the sample 3 can be evaluated. Therefore, even in a bright atmosphere where stray light is mixed into the detector 6 or when the retardation Δ of the retardation plate 4 is not strictly managed, the sample 3 having a small δ is accurately detected. Can be evaluated.

  Since the retardation Δ of the phase difference plate 4 to be used is obtained simultaneously with the retardation δ of the sample 3, etc., the value of Δ does not need to be known. It is sufficient to control the ambient temperature so that the retardation of the phase difference plate 4 and the sample 3 does not change during the measurement time. If the temperature control of the sample 3 is possible, the temperature dependence of the retardation δ of the sample 3 can be obtained. Since the evaluation is performed using monochromatic light, if the monochromatic light source 5 is configured to have a variable output wavelength by using, for example, a halogen lamp and a spectroscope, wavelength dependency can be obtained. The retardation Δ of the phase difference plate 4 also has wavelength dependency, but it is not a problem because it is obtained simultaneously with the retardation δ of the sample 3 and the like.

Since at least one frequency component term of the 5 ′: 2 (A−P−R) term and the 6 ′: 2 (A + P−R) term is required, the absolute value of the amplitude of these frequency component terms is Bigger is better. Therefore, the absolute value of sin Δ is preferably close to 1. That is, Δ is preferably in the vicinity of about π / 2 or a value obtained by adding an integer multiple of π. However, it is only preferable, and may not be strict. If there is one wavelength to be evaluated, a quarter wave plate for that wavelength may be used. Strictly speaking, retardation of a quarter wave plate that can be actually obtained is not a quarter wavelength, but Δ is obtained at the same time as δ and the like, so that there is no problem. The amplitude of other frequency component terms is proportional to cos ² (Δ / 2) or sin ² (Δ / 2) with respect to Δ. If the retardation plate is approximately a quarter-wave plate, the value of cos ² (Δ / 2) and the value of sin ² (Δ / 2) are both about ½. The amplitude of the frequency component term never becomes zero. Also in this respect, it is preferable to use a quarter wave plate as the retardation plate 4.

  Conversely, it is not preferable that the absolute value of sin Δ of the phase difference plate 4 is close to zero. That is, it is not preferable to use a half-wave plate for the wavelength of monochromatic light used for measurement. When evaluating at a plurality of wavelengths using the same retardation plate 4, it is desirable to use a retardation plate that does not become a half-wave plate at all the wavelengths to be measured.

Frequency component terms used for evaluation (that is, at least one frequency component term of <i ′> 5 ′: 2 (A−P−R) term and 6 ′: 2 (A + P−R) term) and < Of ii ′> 1 ′: 2 (AP) term, 2 ′: 2 (A + P) term, 3 ′: 2 (A + P-2R) term and 4 ′: 2 (AP-2R) term The frequency of rotation of the optical element ω _P , ω _A , ω _R (proportional if reduced) so that the frequency of at least two frequency component terms) is different from each other and the frequency of the frequency component term used is not zero. The coefficients A _P , A _A , A _R ) need to be selected. The frequency of the frequency component term may be negative because it is expressed by addition / subtraction of the rotation frequency of the optical element. However, since cos (δ−ωt) = cos (−δ + ωt), the sign of the phase is reversed. A positive frequency is considered. Therefore, the difference between the _two frequencies ω ₁ and ω ₂ is that ω ₁ ≠ ± ω ₂ holds. Specifically, in order to derive the conditions of the rotation frequencies ω _P , ω _A , ω _R (proportional coefficients A _P , A _A , A _R ) of the optical element, the two frequencies ω ₁ , ω ₂ that need to be different are derived. On the other hand, the condition of ω ₁ = ± ω ₂ may be obtained for all combinations of two frequencies that need to be different, and all negation of the obtained condition may be combined by logical product.

The frequency component term used for evaluation and the frequency component term not used are equal depending on the rotation frequency ω _P , ω _A , ω _R (proportional coefficients A _P , A _A , A _R ) of the optical element. There is a case. When the frequency component term having the amplitude F ₁ and the phase δ _{1 and} the frequency component term having the amplitude F ₂ and the phase δ ₂ and the frequency are equal to ω, as shown in the above equation (10), Frequency component terms are combined into terms of the same frequency. However, since the original amplitudes F ₁ and F ₂ and phases δ ₁ and δ ₂ are only inherited by the combined terms, the information itself is not lost. That is, in order to be used specifically for the analysis, it is necessary to calculate Equation (10) specifically, but the frequency of the frequency component term used for evaluation is equal to the frequency of the frequency component term not used for evaluation. It does not matter. You should have chosen not to use it, but you just decided to use it.

  By this method, unknown parameter information can be given to the phase of the frequency component term that does not have unknown parameter information. Alternatively, the information of unknown parameters other than φ can be provided in the phase of the frequency component term having only φ information. Further, the information of φ can be provided in the amplitude of the frequency component term that does not have information of φ. However, the information does not increase, and is equivalent to measuring the original two frequency component terms simultaneously.

  Here, FIG. 5 shows a schematic diagram outlining the processing in the evaluation method according to the fifth embodiment. In the example of FIG. 5, processes 61 to 65 correspond to the above-described processes 51 to 55 (see FIG. 3). However, in the process 62, the frequency component according to the fifth embodiment is extracted.

Embodiment 6 FIG.
Even in the arrangement of the monochromatic light source 5-polarizer 1-sample 3-retardation plate 4-analyzer 2-detector 6 as shown in FIG. 2, the 2 ′: 2 (A + P) term is used as in the second embodiment. Since the phase of the 4 ′: 2 (A−P−2R) term, the 5 ′: 2 (A−P−R) term and the 6 ′: 2 (A + P−R) term includes only φ as an unknown parameter, these If at least one of the phases can be measured, φ can be obtained explicitly rather than an implicit method such as an optimization method.

Specifically, the phase measurement value of the 2 ′: 2 (A + P) term is phase 2 _2, and the phase measurement value of the 4 ′: 2 (A−P−2R) term is phase 2 ₄ , 5 ′: 2 ( If the measured value of the phase of the (A−P−R) term is phase 2 ₅ and the measured value of the phase of the 6 ′: 2 (A + P−R) term is phase 2 ₆ , φ is obtained using the following equation (25). be able to. In Expression (25), it is assumed that the frequency of the frequency component term used for obtaining φ is positive. Therefore, when the frequency of the frequency component term used for obtaining φ is negative, the sign of the phase is reversed, and correction is necessary.

  According to the evaluation method, φ can be positively evaluated from the phase of the frequency component without using an implicit method such as an optimization method. For this reason, the arbitrary nature of setting the objective function for optimization can be eliminated.

Regardless of whether lock-in detection or Fourier transform is used, the phase δ of the frequency component term is the amplitude of the component acos synchronized with cosωt and the amplitude of the component synchronized with sinωt when the frequency of the frequency component term is ω. From asin, a relationship of δ = tan ⁻¹ (asin / acos) is obtained (considering the sign of acos and asin, it is determined where δ is in the first to fourth quadrants). Therefore, if the absolute values of acos and asin are approximately equal, the measurement accuracy will be high (if one is extremely small, the smaller measurement accuracy will be low).

Since the approximate value of φ is often known in advance, the value is set as φ ₀ and is decomposed into φ = φ ₀ + δφ. When the 5 ′: 2 (A−P−R) term and the 6 ′: 2 (A + P−R) term are expanded, the following equation (26) is obtained. In addition, about the compound number in Formula (26), the upper code | symbol respond | corresponds to using a 5 ': 2 (APR) term, and the lower code | symbol is 6': 2 (A + PR). Corresponds to using a term.

Therefore, when using the 5 ′: 2 (A−P−R) term and the 6 ′: 2 (A + P−R) term, δ _AP and δ _RP are set so that the following equation (27) holds (for example, It is preferable that δ _AP = ± φ ₀ and δ _RP = π / 8). This is because when δφ is small (φ ₀ is approximately close to the actual direction φ), the amplitudes of the 5 ′: 2 (A−P−R) term and the 6 ′: 2 (A + P−R) term are approximately equal. This is because the accuracy of measurement increases.

  In Expression (27), m is an integer. In addition, for the double sign in formula (27), the upper sign corresponds to using the 5 ′: 2 (A−P−R) term, and the lower code is 6 ′: 2 (A + P−R). Corresponds to using a term.

Similarly, 2 ': 2 (A + P) is used _{δ AP = φ 0/2 +} π / 8 + mπ / 4 with respect to section 4': 2 for the (AP-2R) term δ _RP + δ _AP / 2 = φ ₀ + π / 16 + mπ / 8 may be used. These two conditions can be satisfied simultaneously if δ _RP = 0.

  By evaluating with this method, the unknown parameter φ (or δφ) can be obtained alone with high accuracy. 2 ′: 2 (A + P) term, 4 ′: 2 (A−P−2R) term, 5 ′: 2 (A−P−R) term, and 6 ′: 2 (A + P−R) term If φ (or δφ) is obtained separately from the phases of two or more frequency component terms, and averaged, the accuracy is improved.

  In order to obtain three unknown parameters other than φ, particularly δ, as in the first embodiment, <i ′> 5 ′: 2 (A−P−R) term and 6 ′: 2 (A + P−R) term. And the amplitude and phase of at least one of the frequency component terms, <ii ′> 1 ′: 2 (A−P) term, 2 ′: 2 (A + P) term, and 3 ′: 2 (A + P−2R) term And 4 ': 2 (A-P-2R) terms and two of the amplitude and phase of at least two frequency component terms need to be determined (thus a total of at least four quantities).

The amplitude and phase of the frequency component term necessary for the evaluation by a method such as lock-in detection of the time dependency I _rev (t) of the detector output obtained by the method described in the fifth embodiment or FFT. Can be measured. In order to reproduce the phase and amplitude of each measured frequency component term, the output coefficient I ₀ of the detector, which is an unknown parameter, the retardation Δ of the phase difference plate 4 and the retardation δ of the sample 3 are determined by an optimization method. As a result, the retardation δ of the sample 3 can be evaluated.

  By the above evaluation method, the retardation δ of the sample 3 and the slow axis direction φ of the sample 3 are evaluated regardless of the retardation Δ value of the retardation plate 4 to be used and without using the direct current component of the transmitted light intensity. it can. Therefore, even in a bright atmosphere where stray light is mixed into the detector 6, even when the retardation Δ of the phase difference plate 4 is not strictly managed, a sample having a small δ can be accurately evaluated.

  Since the retardation Δ of the phase difference plate 4 to be used is obtained simultaneously with the retardation δ of the sample 3, etc., the value of Δ does not need to be known. It is sufficient to control the ambient temperature so that the retardation of the phase difference plate 4 and the sample 3 does not change during the measurement time. If the temperature control of the sample 3 is possible, the temperature dependence of the retardation δ of the sample 3 can be obtained. Since the evaluation is performed using monochromatic light, if the monochromatic light source 5 is configured to have a variable output wavelength by using, for example, a halogen lamp and a spectroscope, wavelength dependency can be obtained. The retardation Δ of the phase difference plate 4 also has wavelength dependency, but it is not a problem because it is obtained simultaneously with the retardation δ of the sample 3 and the like.

  As in the fifth embodiment, the absolute value of sin Δ is preferably close to 1. That is, Δ is preferably in the vicinity of about π / 2 or a value obtained by adding an integer multiple of π. However, it is only preferable, and may not be strict. It is not preferable that the absolute value of sin Δ of the phase difference plate 4 is close to zero. That is, it is not preferable to use a half-wave plate for the wavelength of monochromatic light used for measurement.

Frequency component terms used for evaluation (that is, at least one frequency component term of <i ′> 5 ′: 2 (A−P−R) term and 6 ′: 2 (A + P−R) term) and < Of ii ′> 1 ′: 2 (AP) term, 2 ′: 2 (A + P) term, 3 ′: 2 (A + P-2R) term and 4 ′: 2 (AP-2R) term The frequency of rotation of the optical element ω _P , ω _A , ω _R (in other words proportional) so that the frequency of at least two frequency component terms is different from each other and the frequency of the frequency component term used is not zero. The coefficients A _P , A _A , A _R ) need to be selected. In addition, 2 ′: 2 (A + P) term, 4 ′: 2 (A−P−2R) term, 5 ′: 2 (A−P−R) term and 6 ′: 2 (A + P−) are used for evaluating φ. At least one frequency component term of the (R) term needs to be different from the frequency of the frequency component term not used for the evaluation. Here, the fact that the two frequencies ω ₁ and ω ₂ are different means that ω ₁ ≠ ± ω ₂ holds. Specifically, in order to derive the conditions of the rotation frequencies ω _P , ω _A , ω _R (proportional coefficients A _P , A _A , A _R ) of the optical element, the two frequencies ω ₁ , ω ₂ that need to be different are derived. On the other hand, the condition of ω ₁ = ± ω ₂ may be obtained for all combinations of two frequencies that need to be different, and all negation of the obtained condition may be combined by logical product.

Frequency component terms used for evaluation (that is, at least one frequency component term of 5 ′: 2 (A−P−R) term and 6 ′: 2 (A + P−R) term), and 1 ′: 2 ( (A−P) term, 2 ′: 2 (A + P) term, 3 ′: 2 (A + P−2R) term and 4 ′: 2 (A−P−2R) term). Among them, the frequency of the frequency component term that is not used for the evaluation of φ is the frequency component term that is not used for the evaluation (that is, the remaining of the 5: 2 (A−P + R) term and the 6: 2 (A + P−R) term). Frequency component term and the remaining frequency of 1: 2 (AP) term, 2: 2 (A + P) term, 3: 2 (A + P-2R) term, and 4: 2 (AP + 2R) term It may be equal to the frequency of the component term). When the frequency component term having the amplitude F ₁ and the phase δ _{1 and} the frequency component term having the amplitude F ₂ and the phase δ ₂ and the frequency are equal to ω, two frequencies are obtained as shown in the equation (10). The component terms are combined into terms of the same frequency. However, since the original amplitudes F ₁ and F ₂ and phases δ ₁ and δ ₂ are only inherited by the combined terms, the information itself is not lost. You should have chosen not to use it.

  The processing in the above evaluation method according to the sixth embodiment is outlined in FIG. 5 as in the fifth embodiment. However, in the processing 65 according to the sixth embodiment, the slow axis direction φ of the sample 3 is calculated using a predetermined relational expression instead of the optimization method as described above.

Embodiment 7 FIG.
At least three frequency components used for the evaluation described in the fifth embodiment even in the arrangement of the monochromatic light source 5-polarizer 1-sample 3-retardation plate 4-analyzer 2-detector 6 as shown in FIG. A term (ie, <i ′> 5 ′: 2 (A−P−R)) and at least one frequency component term of 6 ′: 2 (A + P−R), and <ii ′> 1 ′ : 2 (AP) term, 2 ': 2 (A + P) term, 3': 2 (A + P-2R) term and 4 ': 2 (AP-2R) term, at least two frequency components As for <ii ′>, the 1 ′: 2 (A−P) term and the 3 ′: 2 (A + P−2R) term can be selected as <ii ′> above.

1 ': 2 amplitude (A-P) term is ^{_{I 0/4 · cos 2 (}} δ / 2) · cos 2 (Δ / 2), 3': 2 (A + P-2R) amplitude term I _Since 0/4 · cos ² (δ / 2) · sin ² (Δ / 2), when the amplitudes of these terms are measured to obtain a ratio, sin ² (Δ / 2) / cos ² (Δ / 2) is required. When the ratio of the measured amplitude is ratio5 = {3 ′: 2 (A + P−2R) term amplitude} / {1 ′: 2 (A−P) term amplitude}, the phase difference plate 4 is obtained from the following equation (28). The retardation Δ of can be obtained explicitly. When ratio 5 is larger than 1, Δ can be obtained more accurately by using the upper equation, and when ratio 5 is smaller than 1, Δ can be obtained more accurately by using the lower equation. When ratio 5 is 1, any expression may be used.

  With respect to the above <i ′>, ratio6 = {amplitude of one frequency component term out of 5 ′: 2 (A−PR) term and 6 ′: 2 (A + PR) term} / {1 ': 2 (A−P) term and 3 ′: 2 (A + P−2R) term, amplitude of any one of frequency component terms}, and the measured value of the amplitude and the following equation (29): From the Δ obtained by the above equation (28), the retardation δ of the sample 3 can be obtained explicitly. In equation (29), the upper equation is used for the 1 ': 2 (A-P) term, and the lower equation is used for the 3': 2 (A + P-2R) term. Since the amplitude is used to obtain Δ for both the 1 ′: 2 (A−P) term and the 3 ′: 2 (A + P−2R) term, it is necessary to measure the amplitude. Therefore, accuracy is improved by obtaining δ separately using both the upper and lower equations of Equation (29) and taking the average.

For the amplitude and phase of the frequency component term necessary for the evaluation, lock-in detection is performed on the time dependency I _rev (t) of the output of the detector 6 obtained by the method described in the fifth embodiment, or FFT is performed. It can be measured by the method.

According to the evaluation method, since the optimization method is not used, it is possible to eliminate the arbitraryness of setting the objective function. Since the amplitudes of the 1 ′: 2 (A−P) term and the 3 ′: 2 (A + P−2R) term are proportional to cos ² (δ / 2), the amplitude of the sample having a small δ increases. That is, it is suitable for evaluating a sample having a small δ.

  The slow axis direction φ of the sample 3 is also the method described in the second embodiment, that is, the 2 ′: 2 (A + P) term, the 4 ′: 2 (A−P-2R) term, and the 5 ′: 2 (A−). From the phase of at least one frequency component term out of the (P−R) term and the 6 ′: 2 (A + P−R) term, it can be obtained explicitly (see Equation 25). 2 ′: 2 (A + P) term, 4 ′: 2 (A−P−2R) term, 5 ′: 2 (A−P−R) term, and 6 ′: 2 (A + P−R) term If φ (or δφ) is separately obtained and averaged from the phases of two or more frequency component terms, the accuracy is improved.

Therefore, both the retardation δ and the slow axis direction φ of the sample 3 can be obtained independently and explicitly. Therefore, since the optimization method is not used for the evaluation of the sample, the arbitraryness of the objective function setting method can be eliminated. As in the sixth embodiment, it is desirable that the accuracy of the measurement is set to the [delta] _AP and [delta] _RP becomes higher.

  By the above evaluation method, the retardation δ of the sample 3 and the slow axis direction φ of the sample 3 are evaluated regardless of the retardation Δ value of the retardation plate 4 to be used and without using the direct current component of the transmitted light intensity. it can. Therefore, even in a bright atmosphere where stray light is mixed into the detector 6, even when the retardation Δ of the phase difference plate 4 is not strictly managed, a sample having a small δ can be accurately evaluated.

  Since the retardation Δ of the phase difference plate 4 to be used is obtained simultaneously with the retardation δ of the sample 3, etc., the value of Δ does not need to be known. It is sufficient to control the ambient temperature so that the retardation of the phase difference plate 4 and the sample 3 does not change during the measurement time. If the temperature control of the sample 3 is possible, the temperature dependence of the retardation δ of the sample 3 can be obtained. Since the evaluation is performed using monochromatic light, if the monochromatic light source 5 is configured to have a variable output wavelength by using, for example, a halogen lamp and a spectroscope, wavelength dependency can be obtained. The retardation Δ of the phase difference plate 4 also has wavelength dependency, but it is not a problem because it is obtained simultaneously with the retardation δ of the sample 3 and the like.

  As in the first embodiment, the absolute value of sin Δ is preferably close to 1. That is, Δ is preferably in the vicinity of about π / 2 or a value obtained by adding an integer multiple of π. However, it is only preferable, and may not be strict. It is not preferable that the absolute value of sin Δ of the phase difference plate 4 is close to zero. That is, it is not preferable to use a half-wave plate for the wavelength of monochromatic light used for measurement.

Frequency component terms used for evaluation (that is, at least one frequency component term of <i ′> 5 ′: 2 (A−P−R) term and 6 ′: 2 (A + P−R) term) and < ii ′> 1 ′: the frequency of the 2 (AP) term and the frequency component term of 3 ′: 2 (A + P−2R)) are different from each other, and the frequency component term used is zero. In order to avoid this, it is necessary to select the rotation frequencies ω _P , ω _A , ω _R (in other words, proportional coefficients A _P , A _A , A _R ) of the optical element. The frequency of the frequency component term used for evaluation needs to be different from the frequency of the frequency component term not used for evaluation.

Here, the fact that the two frequencies ω ₁ and ω ₂ are different means that ω ₁ ≠ ± ω ₂ holds. Rotation of the frequency omega _P of specific optical elements, ω _A, ω _R (proportional coefficient _{A P, A A, A R} ) to derive the condition of the two frequencies omega ₁ different need exists, the omega ₂ On the other hand, the condition of ω ₁ = ± ω ₂ may be obtained for all combinations of two frequencies that need to be different, and all negation of the obtained condition may be combined by logical product.

Three frequency component terms are used ({5 ′: 2 (A−P−R) term, 1 ′: 2 (A−P) term, 3 ′: 2 (A + P−2R) term}), {6 ′: 2 (A + P−R) term, 1 ′: 2 (A−P) term, 3 ′: 2 (A + P−2R) term}, {5 ′: 2 (APR) term, 6 ′: 2 ( A + P−R) term, 1 ′: 2 (A−P) term, 3 ′: 2 (A + P−2R) term}), the following are specific rotation frequencies ω _P , ω _A , Write down the condition of ω _R.

When using the 5 ′: 2 (APR) term, the 1 ′: 2 (AP) term, and the 3 ′: 2 (A + P-2R) term, the frequencies ω _P , ω _A , ω The condition of _R is given by the following equation (30). Note that “&” in the expression represents a logical product.

When using the 6 ′: 2 (A + P−R) term, the 1 ′: 2 (A−P) term, and the 3 ′: 2 (A + P−2R) term, the frequencies ω _P , ω _A and ω _R The condition is given by the following equation (31).

5 ′: 2 (A−P−R) term, 6 ′: 2 (A + P−R) term, 1 ′: 2 (A−P) term and 3 ′: 2 (A + P−2R) term When used, the conditions of the frequencies ω _P , ω _A and ω _R are given by the following equation (32).

As described in the first embodiment, the rotation frequencies ω _P , ω _A , and ω _R of the optical element are proportional to the proportional coefficients A _P , A _A , and A _R , respectively. Can be read as conditions of proportional coefficients A _P , A _A , A _R.

In any case, ω _P ≠ 0, ω _A ≠ 0, ω _R ≠ 0 and ω _P ≠ ω _A , ω _R ≠ ω _A , ω _R ≠ ω _P, so that the polarizer 1 and the analyzer 2 And the phase difference plate 4 need to be rotated at frequencies different from each other, not 0. There are several other combinations that are prohibited for the rotational frequency of the optical element depending on the combination of frequency component terms used.

For example, ω _A = ω _P / 4, ω _R = 4ω _P , and ω _P ≠ 0 satisfy Expressions (30) to (32). Generalizing the form of ω _A = ω _P / n, ω _R = nω _P , ω _P ≠ 0, n> {1 + √ (3)} to 2.73205, or n <{− √ (2)} to If it is -1.41421, Formula (30)-Formula (32) are satisfy | filled.

  Here, FIG. 6 shows a schematic diagram outlining the processing in the evaluation method according to the seventh embodiment. In the example of FIG. 6, a process 66 is added to the above-described processes 61 to 65 (see FIG. 5). In process 66, the retardation Δ of the phase difference plate 4 is calculated by applying the amplitude obtained in process 64 to a predetermined relational expression. In the process 65 according to the seventh embodiment, as described above, the amplitude and phase obtained in the processes 63 and 64 and the retardation Δ of the phase difference plate 4 obtained in the process 66 are set in a predetermined relational expression. By applying, the retardation δ of the sample 3 is calculated.

Embodiment 8 FIG.
At least three frequency components used for the evaluation described in the fifth embodiment even in the arrangement of the monochromatic light source 5-polarizer 1-sample 3-retardation plate 4-analyzer 2-detector 6 as shown in FIG. A term (i.e., <i ′> 5 ′: 2 (A−P−R)) and a frequency component term of at least one of 6 ′: 2 (A + P−R) and <ii ′> 1 ′: 2 (AP) term, 2 ': 2 (A + P) term, 3': 2 (A + P-2R) term and 4 ': 2 (AP-2R) term, at least two frequency component terms ), The 2 ′: 2 (A + P) term and the 4 ′: 2 (A−P−2R) term can be selected as <ii ′> as in the fourth embodiment.

2 ': 2 amplitude (A + P) term is ^{_{I 0/4 · sin 2 (}} δ / 2) · cos 2 (Δ / 2), 4': 2 amplitude (A-P-2R) section I _Since 0/4 · sin ² (δ / 2) · sin ² (Δ / 2), the amplitudes of these terms are measured to obtain a ratio of sin ² (Δ / 2) / cos ² (Δ / 2) is required. When the ratio of the measured amplitude is ratio7 = {4 ′: 2 (A−P−2R) term amplitude} / {2 ′: 2 (A + P) term amplitude}, the phase difference plate 4 is obtained from the following equation (33). The retardation Δ of can be obtained explicitly. When ratio 7 is larger than 1, Δ can be obtained more accurately by using the upper equation, and when ratio 7 is smaller than 1, Δ can be obtained more accurately by using the lower equation. When ratio 7 is 1, any expression may be used.

  With respect to the above <i ′>, ratio8 = {amplitude of one of the frequency component terms of the 5 ′: 2 (A−P−R) term and the 6 ′: 2 (A + P−R) term} / {2 ': 2 (A + P) term and 4': 2 (AP-2R) term amplitude of any one of the frequency component terms}, the measured value of the amplitude and the following equation (34) Then, from the Δ obtained by the above equation (33), the retardation δ of the sample 3 can be obtained explicitly. In equation (34), the upper equation is used for the 2 ': 2 (A + P) term, and the lower equation is used for the 4': 2 (AP-2R) term. Since the amplitude is used to obtain Δ for both the 2 ′: 2 (A + P) term and the 4 ′: 2 (AP-2R) term, it is necessary to measure the amplitude. Therefore, accuracy is improved by obtaining δ separately using both the upper and lower equations of Equation (34) and taking the average thereof.

For the amplitude and phase of the frequency component term necessary for the evaluation, lock-in detection is performed on the time dependency I _rev (t) of the output of the detector 6 obtained by the method described in the fifth embodiment, or FFT is performed. It can be measured by the method.

  According to the evaluation method, since the optimization method is not used, it is possible to eliminate the arbitraryness of setting the objective function.

  The slow axis direction φ of the sample 3 is also the method described in the second embodiment, that is, the 2 ′: 2 (A + P) term, the 4 ′: 2 (A−P-2R) term, and the 5 ′: 2 (A−). From the phase of at least one frequency component term out of the (P−R) term and the 6 ′: 2 (A + P−R) term, it can be obtained explicitly (see Equation 25). 2 ′: 2 (A + P) term, 4 ′: 2 (A−P−2R) term, 5 ′: 2 (A−P−R) term, and 6 ′: 2 (A + P−R) term If φ (or δφ) is separately obtained and averaged from the phases of two or more frequency component terms, the accuracy is improved.

By the above method, both the retardation δ and the slow axis direction φ of the sample 3 can be obtained independently and explicitly. Therefore, since the optimization method is not used for the evaluation of the sample, the arbitraryness of the objective function setting method can be eliminated. As in the sixth embodiment, it is desirable that the accuracy of the measurement is set to the [delta] _AP and [delta] _RP becomes higher.

  By the above evaluation method, the retardation δ of the sample 3 and the slow axis direction φ of the sample 3 are evaluated regardless of the retardation Δ value of the retardation plate 4 to be used and without using the direct current component of the transmitted light intensity. it can. Therefore, even in a bright atmosphere where stray light is mixed into the detector 6, even when the retardation Δ of the phase difference plate 4 is not strictly managed, a sample having a small δ can be accurately evaluated.

  Since the retardation Δ of the phase difference plate 4 to be used is obtained simultaneously with the retardation δ of the sample 3, etc., the value of Δ does not need to be known. It is sufficient to control the ambient temperature so that the retardation of the phase difference plate 4 and the sample 3 does not change during the measurement time. If the temperature control of the sample 3 is possible, the temperature dependence of the retardation δ of the sample 3 can be obtained. Since the evaluation is performed using monochromatic light, if the monochromatic light source 5 is configured to have a variable output wavelength by using, for example, a halogen lamp and a spectroscope, wavelength dependency can be obtained. The retardation Δ of the phase difference plate 4 also has wavelength dependency, but it is not a problem because it is obtained simultaneously with the retardation δ of the sample 3 and the like.

  As in the first embodiment, the absolute value of sin Δ is preferably close to 1. That is, Δ is preferably in the vicinity of about π / 2 or a value obtained by adding an integer multiple of π. However, it is only preferable, and may not be strict. It is not preferable that the absolute value of sin Δ of the phase difference plate 4 is close to zero. That is, it is not preferable to use a half-wave plate for the wavelength of monochromatic light used for measurement.

Frequency component terms used for evaluation (that is, at least one frequency component term of <i ′> 5 ′: 2 (A−P−R) term and 6 ′: 2 (A + P−R) term) and < ii '>2': the frequency of the 2 (A + P) term and the frequency component term of the 4 ': 2 (AP-2R) term) are different from each other, and the frequency of the frequency component term used is zero. In order to avoid this, it is necessary to select the rotation frequencies ω _P , ω _A , ω _R (in other words, proportional coefficients A _P , A _A , A _R ) of the optical element. The frequency of the frequency component term used for evaluation needs to be different from the frequency of the frequency component term not used for evaluation.

Here, the fact that the two frequencies ω ₁ and ω ₂ are different means that ω ₁ ≠ ± ω ₂ holds. Rotation of the frequency omega _P of specific optical elements, ω _A, ω _R (proportional coefficient _{A P, A A, A R} ) to derive the condition of the two frequencies omega ₁ different need exists, the omega ₂ On the other hand, the condition of ω ₁ = ± ω ₂ may be obtained for all combinations of two frequencies that need to be different, and all negation of the obtained condition may be combined by logical product.

Three frequency component terms are used ({5 ′: 2 (A−P−R) term, 2 ′: 2 (A + P) term, 4 ′: 2 (A−P−2R) term}), {6 ′: 2 (A + P−R) term, 2 ′: 2 (A + P) term, 4 ′: 2 (A−P−2R) term}, {5 ′: 2 (A−P−R) term, 6 ′: 2 ( A + P−R) term, 2 ′: 2 (A + P) term, 4 ′: 2 (A−P−2R) term}), and the following are specific rotation frequencies ω _P , ω _A , Write down the condition of ω _R.

When using the 5 ′: 2 (A−P−R) term, the 2 ′: 2 (A + P) term, and the 4 ′: 2 (A−P−2R) term, the frequencies ω _P , ω _A , ω The condition of _R is given by the following equation (35). Note that “&” in the expression represents a logical product.

When using the 6 ′: 2 (A + P−R) term, the 2 ′: 2 (A + P) term, and the 4 ′: 2 (A−P−2R) term, the frequencies ω _P , ω _A and ω _R The condition is given by the following equation (36).

5 ′: 2 (A−P−R) term, 6 ′: 2 (A + P−R) term, 2 ′: 2 (A + P) term and 4 ′: 2 (A−P−2R) term When used, the conditions of the frequencies ω _P , ω _A and ω _R are given by the following equation (37).

As described in the first embodiment, the rotation frequencies ω _P , ω _A , and ω _R of the optical element are proportional to the proportional coefficients A _P , A _A , and A _R , respectively. Can be read as conditions of proportional coefficients A _P , A _A , A _R.

In any case, since ω _P ≠ 0, ω _A ≠ 0, and ω _R ≠ 0 are the conditions, it is necessary to rotate all of the polarizer 1, the analyzer 2, and the phase difference plate 4. Since ω _R ≠ ω _A is a condition, the analyzer 2 and the phase difference plate 4 need to be rotated at different frequencies. Further, since −ω _P ≠ ω _A and −ω _R ≠ ω _P are the conditions, it is prohibited to rotate the analyzer 2 and the phase difference plate 4 in the opposite directions at the same absolute frequency as the polarizer 1. The There are several other combinations that are prohibited for the rotational frequency of the optical element depending on the combination of frequency component terms used.

For example, ω _A = ω _P / 4, ω _R = 4ω _P , and ω _P ≠ 0 satisfy Expressions (35) to (37). Generalizing the form of ω _A = ω _P / n, ω _R = nω _P , ω _P ≠ 0, n> {1 + √ (3)} to 2.73205, or n <{− √ (2)} to If it is -1.41421, Formula (35)-Formula (37) are satisfy | filled.

  The processing in the above evaluation method according to the eighth embodiment is outlined in FIG. 6 as in the seventh embodiment.

Embodiment 9 FIG.
FIG. 7 is a schematic diagram outlining the evaluation device 21 corresponding to the evaluation system of FIG. In the evaluation apparatus 21 illustrated in FIG. 7, the monochromatic light source 5, the polarizer 1, the phase difference plate 4, the analyzer 2, and the detector 6 are arranged as described above.

  That is, the emitted light is transmitted onto the optical path of the emitted light from the monochromatic light source 5 (more specifically, the light emitted from the light source 5 and passed through the polarizer 1, the phase difference plate 4, the sample 3, and the analyzer 2). The detector 6 is arranged in a detectable state. The polarizer 1 is disposed between the light source 5 and the detector 6 on the optical path. The analyzer 2 is disposed between the polarizer 1 and the detector 6 on the optical path. The phase difference plate 4 is disposed between the polarizer 1 and the analyzer 2 on the optical path.

  The monochromatic light source 5 is a light source that emits monochromatic light. The wavelength of the monochromatic light does not need to be strictly a single wavelength, and may have a wavelength width such that the wavelength dependency of retardation of the phase difference plate 4 or the sample 3 can be ignored. As the monochromatic light source 5, a laser can be used, and light close to monochromatic light can be obtained. A light source that emits light in a certain wavelength region such as a halogen lamp may be combined with an optical device or optical element having wavelength selectivity such as a spectroscope or an interference filter. According to such an example, light having a wavelength width of about several nm can be obtained. When a depolarization plate is used in combination, natural light can be obtained even if a polarization component is mixed in the light emitted from the light source 5.

  The polarizer 1 and the analyzer 2 are optical elements that extract linearly polarized light in the transmission axis direction from incident light. An extinction ratio of about 10,000: 1 or more is readily available. A polarizing prism such as a Glan-Thompson prism can be used as the polarizer 1 and the analyzer 2. A plate-like polarizing plate such as a polarizing filter may be used.

  The phase difference plate 4 is an element that gives a phase difference equal to retardation to vertically incident light. More broadly defined, it is an element that gives a constant phase difference to incident light. In this evaluation method and this evaluation apparatus, the constant phase difference does not need to be known, but as described in Embodiment 1 or the like, the phase difference is approximately ¼ wavelength of the wavelength of the monochromatic light used for the evaluation. The retardation plate 4 giving (wavelength unit) is preferable. A quartz wave plate can be used for the phase difference plate 4. A stretched resin film may be used.

  The polarizer 1, the analyzer 2, and the phase difference plate 4 are arranged so as to be orthogonal to the optical path. Further, as described in the first embodiment, these optical elements 1, 2, and 4 have a direction parallel to the normal direction of each main surface (in other words, a direction parallel to the optical path) and a rotation axis direction. It is arranged so as to be rotatable. The optical elements 1, 2, and 4 can be rotated manually, for example. In the example of FIG. 7, the optical elements 1, 2, and 4 are provided with rotating mechanisms 11, 12, and 14, respectively.

  The rotation mechanisms 11, 12, and 14 have a mechanism for at least knowing the frequency of rotation and the angle of the object to be rotated at a specific time. For example, a rotation mechanism using a rotation motor such as a stepping motor can be used. A device for reading the rotation angle (for example, a device such as an encoder) is preferably attached. After obtaining the angle of the rotation target before the rotation, the rotation angle may be obtained using the rotation frequency.

  The detector 6 is an element that converts the intensity of light incident on the detector 6 into an output signal having a magnitude depending on the intensity. As the detector 6, a detector (for example, a photomultiplier tube, a photodiode, or the like) that can obtain an output that linearly responds to incident light intensity can be used. If the calibration curve for the incident light intensity is known, the linear response may not be exact, and a detector that responds monotonously (or decreases) to the incident light intensity may be used. Since this evaluation method and this evaluation apparatus can be used even in the presence of stray light, low-frequency noise such as thermal noise, and shot noise, a mechanism for blocking stray light and cooling the detector is not essential. If accessory devices such as a power source are necessary for the detector 6, they are used.

  The evaluation device 21 further includes a sample support 13 for supporting the sample 3. Although the shape of the support 13 is not particularly limited, the support 13 is configured to be able to support the sample 3 so as to be orthogonal to the optical path. In the evaluation apparatus 21 in FIG. 7 corresponding to the evaluation system in FIG. 1, the support 13 is configured such that the sample 3 is supported between the phase difference plate 4 and the analyzer 2 on the optical path. The support 13 may be configured such that the sample 3 is supported between the polarizer 1 and the phase difference plate 4 on the optical path as in the evaluation apparatus 22 of FIG. 8 corresponding to the evaluation system 2. . Alternatively, the support 13 is configured such that the sample 3 can be disposed at both the position between the phase difference plate 4 and the analyzer 2 and the position between the polarizer 1 and the phase difference plate 4. Either one of the positions may be selectively used.

  As described above, the polarizer 1, the phase difference plate 4, the sample 3, and the analyzer 2 are arranged so that the emitted light from the monochromatic light source 5 enters perpendicularly and the principal surfaces are parallel to each other. Placed in. When a light source that emits highly directional light, such as a laser, is used as the monochromatic light source 5, the light source 5 is arranged so that the emitted light is perpendicularly incident on the surface of the polarizer 1. Light emitted from the light source 5 may be guided by a mirror or the like to form an optical path. Further, instead of a light source that emits highly directional light such as a laser, an aperture having an opening sufficiently smaller than the distance between the monochromatic light source 5 and the detector 6 may be placed in front of the detector 6. Or you may give directivity to the emitted light from the monochromatic light source 5 using a plano-convex lens and a collimator.

  The evaluation device 21 further has a processing means 19. The processing means 19 performs various processes (calculation, control, etc.) in the evaluation device 21 or functions as various means corresponding to the various processes. Various functions realized by the processing means 19 may be provided by software (in other words, program processing by a microcomputer), may be provided by hardware, or provided by a combination of software and hardware. May be.

  The processing unit 19 includes, for example, a receiving unit (A / D converter or the like) that receives the output of the detector 6, an analyzing unit that analyzes a signal generated by the receiving unit by the method of Embodiments 1 to 8, and the polarizer 1. A rotation control means for controlling the rotation of the analyzer 2 and the phase difference plate 4 is included. For example, the analysis means and the rotation control means can be combined with a microcomputer.

  The support 13 preferably has a guide or the like indicating the direction in which the sample 3 is installed. Moreover, it is preferable that the support 13 has a rotation mechanism like the polarizer 1 and the like.

  The evaluation devices 21 and 22 exhibit the above various effects by performing the analysis of the first to eighth embodiments.

  In addition, it is not limited to the illustration of the evaluation apparatuses 21 and 22, The element, apparatus, etc. which can implement | achieve the required function are employable.

Embodiment 10 FIG.
In the tenth embodiment, a simulation result of evaluation will be described. As an arrangement of the optical elements, an arrangement of a monochromatic light source 5-a polarizer 1-a phase difference plate 4-a sample 3-an analyzer 2-a detector 6 was used (see FIG. 1). The evaluation method used was the method described in the third embodiment. Evaluation was performed using the following procedures ST1 to ST11.

<Procedure ST1>
Set various parameter values.
Measurement wavelength λ = 546 nm,
Sample 3 slow axis direction φ = φ ₀ + δφ, direction assumed by the operator φ ₀ = 90 ° (= 6.283 rad), deviation from φ ₀ δφ = 0.856 ° (= 0.01494 rad), phase difference δ = 0.457nm (= 0.00526rad),
Polarizer 1 frequency ω _P = 2 Hz (= 12.57 rad · s ⁻¹ ),
Initial phase δ _RP = −22.5 ° (= −0.3927 rad) of phase difference plate 4, phase difference Δ = 140 nm (= 2πΔ / λ = 1.611 rad), frequency ω _R = 8 Hz (= 50.27 rad · s ⁻¹ ),
Initial phase of analyzer 2 δ _AP = 90 ° (= 6.283 rad), angular velocity ω _A = 0.5 Hz (= 1.571 rad),
Detector 6 output coefficient I ₀ = 1,
Data capture time 8 s, number of capture points N + 1 = 4096 pts, capture interval ΔT = 1.93 mS.

<Procedure ST2>
i = 0.

<Procedure ST3>
Using the set value, I _i ^cal = I (t _i ) of transmitted light intensity at time t _i = iΔT is calculated using equation (8).

<Procedure ST4>
i 1 increases by until i> N Repeat steps ST3, obtain a calculation output sequence consisting of (N + 1) _{^{I i cal {I i cal}}} .

<Procedure ST5>
A normal noise with a standard deviation of 0.1% is added to {I _i ^cal } and a simulated component of stray light obtained by adding a normal noise with a standard deviation of 0.1% to 2% of I ₀ , and an output sequence from the detector 6 Obtain the simulation value of {I _i }.

<Procedure ST6>
The obtained {I _i } is subjected to a radix-2 FFT to obtain a sin component (asin) and a cos component (acos) of each frequency component term, and a phase (tan ⁻¹ (asin / acos)) and amplitude ((asin ² + acos ² ) ^1/2 ).

<Procedure ST7>
The slow axis direction φ of the sample 3 is obtained from the phases of the 5: 2 (A−P + R) term and the 6: 2 (A + P−R) term, and the deviation δφ is obtained by subtracting the assumed direction φ ₀ . Then, an average value δφ _ave of both deviations δφ is obtained.

<Procedure ST8>
Retardation (DELTA) of the phase difference plate 4 is calculated | required from the amplitude of 1: 2 (AP) term and 3: 2 (A + P-2R) term.

<Procedure ST9>
One of the 5: 2 (A-P + R) term amplitude and the 6: 2 (A + P-R) term amplitude, 1: 2 (A-P) term amplitude and the 3: 2 (A + P-2R) term The retardation δ of the sample 3 is obtained for each of all the combinations (4 types) based on one of the amplitudes. Then, an average value δ _ave thereof is obtained.

<Procedure ST10>
The above steps ST2 to ST9 are repeated 10 times with the same set value.

  Here, the normal noise is noise whose probability distribution of intensity is normal distribution, the average is 0, and the standard deviation is the value shown in the procedure ST5.

FIG. 9 illustrates simulation values of the output sequence {I _i }. FIGS. 10 and 11 show a cosine component and a sin component, respectively, obtained by performing radix-2 FFT on the output sequence {I _i } in FIG. 9. Further, enlarged views of FIGS. 10 and 11 are shown in FIGS. 12 and 13, respectively. 5: 2 (A-P + R) term frequency 13 Hz, 6: 2 (A + P-R) term frequency 11 Hz, 1: 2 (A-P) term frequency 3 Hz, 3: The signal is obtained at 27 Hz which is the frequency of the 2 (A + P-2R) term.

Table 1 shows 10 sets of δφ _ave , δ _ave , Δ obtained in the above steps ST2 to ST9 repeated 10 times in the above step ST10, and shows the average value and standard deviation in the 10 sets.

<Comparative example>
As a comparative example, the following procedures ST21 to ST31 were used, and a phase modulation method simulation using a PEM disclosed in Patent Document 4 was performed. As the arrangement of the optical elements, the arrangement of monochromatic light source-polarizer-PEM-sample-analyzer-detector was used. The simulation set values for the sample, measurement wavelength, and noise were set to be the same as the values according to the tenth embodiment.

<Procedure ST21>
Set various parameter values.
Measurement wavelength λ = 546 nm,
Sample slow axis direction φ = φ ₀ + δφ, direction assumed by the operator φ ₀ = 90 ° (= 6.283 rad), deviation from φ ₀ δφ = 0.856 ° (= 0.01494 rad), phase difference δ = 0.457nm (= 0.00526rad),
PEM frequency f = 50 kHz, slow axis direction 0 °, amplitude of phase difference given to transmitted light Δ ₀ = 137.8 ° (2.40483 rad, zeroth-order first kind Bessel function zero J ₀ (Δ ₀ ) = 0) ,
Polarizer transmission axis direction 45 °,
Detector output coefficient I ₀ = 1,
Data acquisition time 2.56 ms, number of acquisition points N + 1 = 4096 pts, acquisition interval ΔT = 0.625 μs.

<Procedure ST22>
i = 0.

<Procedure ST23>
The transmission axis direction φ _A of the analyzer is set to 0 °, and the transmitted light intensity I _{0, i} ^cal = I _PEM (t _i , 0 °) at time t _i = iΔT using the set value is expressed by equation (38) Calculate with

<Procedure ST24>
With the transmission axis direction φ _A of the analyzer being −45 °, using the set value, the transmitted light intensity I _{45, i} ^cal = I _PEM (t _i , 45 °) at time t _i = iΔT is expressed by the equation (38 )

<Procedure ST25>
i 1 increases with i> N to become until Repeat steps ST23, ST24, and (N + 1) I _0, calculated output sequence consisting of ^{_{I cal {I 0, I cal}} }, N + 1 pieces of I _{45, I} ^cal A calculation output sequence {I _{45, I} ^cal } consisting of is obtained.

<Procedure ST26>
Simulating stray light by adding normal noise with a standard deviation of 0.1% to each of {I _{0, I} ^cal } and {I _{45, I} ^cal }, and normal noise with a standard deviation of 0.1% added to 2% of I ₀ The simulation value of the output sequence {I _{0, I} }, {I _{45, I} } from the detector is obtained by adding the components.

<Procedure ST27>
The obtained {I _{0, I} } is subjected to radix-2 FFT to calculate the magnitude of the direct current term aDC0 and the amplitude asin0 of the sin component of the frequency component of frequency f to obtain the ratio ratio0 = asin0 / aDC0.

<Procedure ST28>
The obtained {I _{45, I} } is subjected to radix-2 FFT to calculate the magnitude aDC45 of the DC term and the amplitude asin45 of the sine component of the frequency component of the frequency f to obtain the ratio ratio45 = asin45 / aDC45.

<Procedure ST29>
φ = 1/2 · tan a phi calculated by ^{-1 (ratio0} / ^ratio45), obtaining .delta..phi from δφ = φ-φ _0.

<Procedure ST30>
δ is obtained by δ = sin ⁻¹ ((ratio 0 ² / ratio 45 ² ) ^1/2 / J ₁ (Δ ₀ )). J _n (x) is an nth-order first-type Bessel function.

<Procedure ST31>
The above steps ST22 to ST30 are repeated 10 times with the same set value.

FIG. 14 and FIG. 15 illustrate simulation values of the output sequences {I _{0, i} } and {I _{45, i} }, respectively. FIGS. 16 and 17 show sin components obtained by performing radix-2 FFT on {I _{0, i} } in FIG. 14 and {I _{45, i} } in FIG. 15, respectively. A signal is seen at f = 50 kHz = 50000 Hz.

  Table 2 shows 10 sets of δφ and δ obtained in the above steps ST22 to ST30 by repeating 10 times in the above step ST31, and shows the average value and standard deviation in the 10 sets.

“(Average value−set value) / set value” in the fourth row of Tables 1 and 2 indicates how much the set value can be reproduced by the evaluation result obtained by each evaluation method. The -7.58% of δ of the phase modulation method (Table 2) is larger than -0.003% of δ _ave of the evaluation method (Table 1) according to the tenth embodiment, and the set value is reproduced by the phase modulation method. It may not be possible. For the sake of clarity, a t-test was performed with a null hypothesis that “the average value is equal to the set value 0.457 nm”. Table 3 shows the obtained P values. The P value represents the probability that data to be tested is obtained when the null hypothesis is assumed to be correct. If P <α when the significance level is α, the null hypothesis is rejected, and it can be concluded that the null hypothesis is not correct at the 1-α significance level.

  Looking at Table 3, the result of the phase modulation method is sufficiently smaller than 0.01. This indicates that the null hypothesis that “the set value and the average value are equal” at a significance level of 99% or more can be concluded that the result of the phase modulation method is not correct. The P value of the evaluation method according to the tenth embodiment is sufficiently larger than 0.05 and 0.01, which are values of the significance level α that are usually used for rejecting the null hypothesis. This concludes that the null hypothesis cannot be rejected.

The cause of this difference is that the evaluation method according to the tenth embodiment does not use a DC term, whereas the phase modulation method needs to take a ratio with the size of the DC term in steps ST27 and ST28. The DC term is susceptible to low frequency noise such as stray light and thermal noise. Furthermore, in the case of the phase modulation method using the PEM as a trial, the temperature dependence of the amplitude Δ ₀ of the phase difference given to the transmitted light by the PEM is large. In the comparative example, the zero point (J ₀ (Δ ₀ ) = 0) of the first-order Bessel function of the 0th order is accurately set, but if this changes, two items of the direct current term of the transmitted light intensity I _PEM (Equation (38) Since the second term on the right side is not 0, the measurement is further affected. Therefore, according to the evaluation method according to the tenth embodiment that does not use a DC term, high accuracy can be obtained.

10 times the average value 0.772 ° of .delta..phi _ave methods evaluation according to a tenth embodiment (Table 1), even for 10 times average 0.820 ° of .delta..phi phase modulation method (Table 2), "Setting The null hypothesis that the value is equal to the value 0.856 ° was made, and t-test was performed. Table 4 shows the obtained P values.

  According to Table 4, it can be concluded that the null hypothesis cannot be rejected because it is sufficiently larger than 0.05 and 0.01 which are the values of the significance level α normally used for rejecting the null hypothesis. Further, a null hypothesis that “the 10-time average values obtained by the evaluation method according to the tenth embodiment and the phase modulation method are equal” was established, and t-test was performed. As a result, P = 0.379 was obtained. . This is also sufficiently larger than 0.05 and 0.01, which are values of the significance level α normally used for rejecting the null hypothesis. That is, it can be concluded that the set values are reproduced in the same manner as in the evaluation method according to the tenth embodiment and the phase modulation method.

  FIG. 16 shows that the phase modulation method has a larger influence of noise. This is because the set value of φ is close to 90 °, and thus the amplitude of the frequency component term of sin 2πft in the phase modulation method is reduced (see equation (38)). However, the obtained standard deviation appears to be substantially equal between the evaluation method according to the tenth embodiment and the phase modulation method.

  In order to compare the influence of the normal noise of 0.1% between the evaluation method according to the tenth embodiment and the phase modulation method, “standard deviation of 10 results obtained by simulation of 10 times measurement (accurately, dispersion) The F-test was performed with the null hypothesis that “the evaluation method is equal to the phase modulation method”. Table 5 shows the obtained P values.

  If the variance ratio (ratio of variance of 10 results obtained by the two methods) is greater than the F boundary value and the P value is less than the significance level α, the null hypothesis is rejected and the significance level of 1-α It can be concluded that the null hypothesis is not correct. In Table 5, the F boundary value was calculated at α = 0.05. From the obtained results, it can be concluded that the null hypothesis cannot be rejected because both the deviation δφ and retardation δ of the slow axis are dispersion ratio <F boundary value and P> α = 0.05. That is, it can be said that both the evaluation method according to the tenth embodiment and the phase modulation method can obtain the same standard deviation in the repeated evaluation, in other words, can be evaluated with the same repeated accuracy.

  From the above, the evaluation method according to the tenth embodiment can be evaluated with the same degree of repetition accuracy as the phase modulation method, which is a conventional evaluation method, and is a DC term such as mixing of stray light, which is a problem of the conventional evaluation method. It can be said that highly accurate evaluation is possible even under an environment that affects

  DESCRIPTION OF SYMBOLS 1 Polarizer, 2 Analyzer, 3 Sample, 4 Phase difference plate, 5 Light source, 6 Detector, 11, 12, 14 Rotation mechanism, 13 Support tool, 19 Processing means, 21,22 Evaluation apparatus, 51-56,61 ~ 66 treatment.

Claims (9)

A method for evaluating the optical anisotropy of the sample by analyzing light emitted from a monochromatic light source and passing through a polarizer, a retardation plate, a sample, and an analyzer in this order,
A _P , A _A , and A _R are proportional coefficients (unit: angle · time ⁻¹ ) respectively assigned to the polarizer, the analyzer, and the phase difference plate, and c _P , c _A , and c _R are Constants (units are angles) respectively assigned to the polarizer, the analyzer, and the retardation plate, and an arbitrary N + 1 number sequence {t _i } = {t ₀ , t ₁ ,..., T _N } (Unit of t _i is time) three sequences {φ _{P, i} } = {c _P + A _p t _i }, {φ _{A, i} } = {c _A + A _A t _i }, {φ _{R, i} } = {c _R + A _R t _i }, and for all i different from 0 to N, the angles of the polarizer, the analyzer, and the retardation plate are respectively designated by i. The light intensity I _i detected by the detector when φ _{P, i} , φ _{A, i} , φ _{R, i} is obtained, and the sequence {t _i } is used as the elapsed time t _i from the reference time. Considered as a time sequence The deemed acquired sequence {I _i} is detected by the detector at the elapsed time t _i from the reference time the light intensity I and (t _i), and the F and predetermined coefficient (unit angle ^-1) If
<a> From a plurality of light intensities I (t _i ) corresponding to a plurality of times t _i , a component of frequency 2F (A _A −A _P + A _R ) and a component of frequency 2 F (A _A + A _P −A _R ) Processing for determining the amplitude and phase of at least one frequency component of
<B> From the plurality of light intensities I (t _i ), a component of frequency 2F (A _A −A _P ), a component of frequency 2F (A _A + A _P ), and a frequency 2F (A _A + A _P −2A _R ) And a process for obtaining two of the amplitude and phase of at least two frequency components of the component of frequency 2F (A _A -A _P + 2A _R );
<C> Evaluation of optical anisotropy comprising: processing for evaluating the magnitude and direction of the optical anisotropy of the sample based on the amplitude and the phase obtained in the processing <a> and <b> Method. The method for evaluating optical anisotropy according to claim 1,
The process <c>
<C1> and component of the frequency _{2F (A A + A P)} , a component of the frequency _{2F (A A -A P + 2A} R), a component of the frequency _{2F (A A -A P + A} R), the frequency An optical anisotropy evaluation method including a process of obtaining a slow axis direction of the sample from the phase of at least one frequency component of 2F (A _A + A _P −A _R ). The method for evaluating optical anisotropy according to claim 1,
<D> a process for obtaining retardation of the retardation plate from the amplitude of the component of the frequency 2F (A _A -A _P ) and the component of the frequency 2F (A _A + A _P -2A _R );
The process <c>
<C2> and the amplitude of one of the frequency components of said frequency _{2F (A A -A P + A} R) component and the frequency _{2F (A A + A P -A} R) components of the frequency 2F The amplitude of any one frequency component of the component of (A _A -A _P ) and the component of the frequency 2F (A _A + A _P -2A _R ), and the position obtained in the processing <d>. A method for evaluating optical anisotropy, comprising a process of obtaining retardation of the sample from the retardation of the retardation plate. The method for evaluating optical anisotropy according to claim 1,
<E> further comprising a process for obtaining retardation of the retardation plate from the amplitude of the component of the frequency 2F (A _A + A _P ) and the component of the frequency 2F (A _A −A _P + 2A _R ),
The process <c>
<C3> and the amplitude of one of the frequency components of said frequency _{2F (A A -A P + A} R) component and the frequency _{2F (A A + A P -A} R) components of the frequency 2F The amplitude of any one frequency component of the component (A _A + A _P ) and the component of the frequency 2F (A _A −A _P + 2A _R ), and the phase difference obtained in the processing <d> A method for evaluating optical anisotropy, comprising a process of obtaining retardation of the sample from the retardation of the plate. A method for evaluating the optical anisotropy of the sample by analyzing light emitted from a monochromatic light source and passing through a polarizer, a sample, a retardation plate, and an analyzer in this order,
A _P , A _A , and A _R are proportional coefficients (unit: angle · time ⁻¹ ) respectively assigned to the polarizer, the analyzer, and the phase difference plate, and c _P , c _A , and c _R are Constants (units are angles) respectively assigned to the polarizer, the analyzer, and the retardation plate, and an arbitrary N + 1 number sequence {t _i } = {t ₀ , t ₁ ,..., T _N } (Unit of t _i is time) three sequences {φ _{P, i} } = {c _P + A _p t _i }, {φ _{A, i} } = {c _A + A _A t _i }, {φ _{R, i} } = {c _R + A _R t _i }, and for all i different from 0 to N, the angles of the polarizer, the analyzer, and the retardation plate are respectively designated by i. The light intensity I _i detected by the detector when φ _{P, i} , φ _{A, i} , φ _{R, i} is obtained, and the sequence {t _i } is used as the elapsed time t _i from the reference time. Considered as a time sequence The deemed acquired sequence {I _i} is detected by the detector at the elapsed time t _i from the reference time the light intensity I and (t _i), and the F and predetermined coefficient (unit angle ^-1) If
<a> From a plurality of light intensities I (t _i ) corresponding to a plurality of times t _i , a component of frequency 2F (A _A −A _P −A _R ) and a component of frequency 2F (A _A + A _P −A _R ) A process for obtaining the amplitude and phase of at least one frequency component of
<B> From the plurality of light intensities I (t _i ), a component of frequency 2F (A _A −A _P ), a component of frequency 2F (A _A + A _P ), and a frequency 2F (A _A + A _P −2A _R ) And a process for obtaining two of the amplitude and phase of at least two frequency components of the component of frequency 2F (A _A -A _P -2A _R ),
<C> Evaluation of optical anisotropy comprising: processing for evaluating the magnitude and direction of the optical anisotropy of the sample based on the amplitude and the phase obtained in the processing <a> and <b> Method. The method for evaluating optical anisotropy according to claim 5,
The process <c>
<C1> a component of the frequency 2F (A _A + A _P ), a component of the frequency 2F (A _A −A _P −2A _R ), a component of the frequency 2F (A _A −A _P −A _R ), from at least one frequency component of the phase, the evaluation method of the optical anisotropy includes processing for obtaining the slow axis direction of the sample of the component of the frequency _{2F (a a + a P -A} R). The method for evaluating optical anisotropy according to claim 5,
<D> a process for obtaining retardation of the retardation plate from the amplitude of the component of the frequency 2F (A _A -A _P ) and the component of the frequency 2F (A _A + A _P -2A _R );
The process <c>
<C2> and the amplitude of any one frequency component of the component of the frequency _{2F (A A -A P -A R} ) component and the frequency _{2F (A A + A P -A} R), the frequency The amplitude of any one frequency component of the component of 2F (A _A -A _P ) and the component of the frequency 2F (A _A + A _P -2A _R ), and the above-described processing <d> A method for evaluating optical anisotropy, comprising a process for obtaining retardation of the sample from the retardation of the retardation plate. The method for evaluating optical anisotropy according to claim 5,
<E> a process for obtaining retardation of the retardation plate from the amplitude of the component of the frequency 2F (A _A + A _P ) and the component of the frequency 2F (A _A −A _P −2A _R );
The process <c>
<C3> and the amplitude of any one frequency component of the component of the frequency _{2F (A A -A P -A R} ) component and the frequency _{2F (A A + A P -A} R), the frequency The amplitude of any one of the components of 2F (A _A + A _P ) and the component of frequency 2F (A _A −A _P −2A _R ) and the processing <d> A method for evaluating optical anisotropy, comprising a process for obtaining retardation of the sample from the retardation of the retardation plate. A monochromatic light source;
A detector arranged to detect the emitted light on an optical path of the emitted light from the monochromatic light source;
A polarizer disposed on the optical path between the monochromatic light source and the detector;
An analyzer disposed on the optical path between the polarizer and the detector;
A retardation plate disposed between the polarizer and the analyzer on the optical path;
A sample support configured to be able to support a sample between at least one of the retardation plate and the analyzer and between the polarizer and the retardation plate on the optical path;
Processing means,
The polarizer, the analyzer, the retardation plate, and the sample are arranged to be orthogonal to the optical path,
The polarizer, the analyzer, and the phase difference plate are rotatably arranged with a direction parallel to the optical path as a rotation axis direction,
The processing means performs a process of evaluating the magnitude and direction of the optical anisotropy of the sample according to the evaluation method according to any one of claims 1 to 8.
Optical anisotropy evaluation device.

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