JPH04297835A - Method for measuring polarization and polarization measuring device using it - Google Patents

Abstract

PURPOSE:To enable an ellipticity of elliptic polarization and an orientation angle of a longer axis to be calculated at high speed and accurately by obtaining an intensity of output light with a photo detector and then using a specific expression in at least three rotary positions of an analyzer. CONSTITUTION:Light from a light source 1 is guided from a pin hole 5 to a polarizer 6 and an output light passes through an objective lens 7 and is emitted to a sample 8. A transmission light from the sample 8 passes through a lens 9 and an optical fiber 12, is fed to a spectrophotometer 13 for obtaining spectral intensity signal, and then it is calculated by a processing device 14. A standard polarizer 8a with a polarization axis is set in a reference direction and then a polarizer 6 and an analyzer 10 are rotated for matching to the reference direction. The polarizer 8a is removed, a sample 8 is inserted, a direction of a crystal axis of the sample 8 is set in parallel to the reference direction as an x axis. Then, an angle of the ananlyzer 10 is set to 0, 90, and 45 degrees, light intensities I1-I3 are selected by the spectrophotometer 13, and then an ellipticity rho and an orientation angle phi of elliptic polarization are calculated by using expressions I and II.

Description

Detailed Description of the Invention [0001] [Industrial Application Field] The present invention relates to a polarization measurement method and method for measuring the polarization characteristics of light traveling through an anisotropic medium to investigate the properties of the medium. The present invention relates to a polarization measuring device using a polarization measuring device. 2. Description of the Related Art By measuring the polarization state of light traveling through an anisotropic medium such as a liquid crystal or an optical crystal, the direction of the optical axis of the medium, birefringence phase difference, etc. can be determined. As a result, it is possible to know the film thickness of the medium, the optical constants, and further the wavelength dependence of the optical constants by performing the above measurements for each wavelength. Taking liquid crystals as an example, recently, the birefringence properties of liquid crystals have been increasingly evaluated, and measurement of the wavelength dependence of polarization properties has become an important measurement item. More specifically, in super-twist LCDs, coloring due to birefringence is corrected using a retardation film to make black and white and contrast stand out, but in order to achieve accurate correction, it is necessary to Dependencies need to be measured accurately. Conventionally, the following methods have been adopted for measuring polarization characteristics. The classic measurement method is
By arranging a monochromatic light source, polarizer, sample, and analyzer in this order and rotating the analyzer to detect the output light intensity, the polarization characteristics of the light passing through the sample (ellipticity angle χ, azimuth angle φ, etc.) can be determined. (see Figure 11). This method is called the maximum-minimum method. In this maximum-minimum method, it is necessary to rotate the analyzer finely in order to measure the output light intensity, which takes time. In particular, when measuring at multiple wavelengths, the measurement is repeated for each wavelength, which takes an enormous amount of time. Therefore, a method has been proposed that uses a spectrometer and an image sensor to facilitate measurement at multiple wavelengths, and also analyzes polarization characteristics using Stokes parameters and Mueller matrix representation (M.
C. K. Wiltshire and M. R. Le
wis, J. Phys. E: Sci. Instrument
．． 20, 884 (1987)). This method will be referred to as the 4-point method. In this proposed four-point method, the elliptically polarized light transmitted through the sample is received by an analyzer, and the analyzer is fixed at horizontal (0°), vertical (90°), 45°, and 135°, and outputs are obtained respectively. This method measures the spectrum of light intensity. To explain briefly, the Stokes parameter of elliptically polarized light is Σ0
= (S0, S1, S2, S3). Since the Mueller matrix of the analyzer is known as a function of angle, it can be expressed as Pi (i is 0°, 90°, 45
°, 135°. ), the Stokes parameter Σ1 of the light passing through the analyzer is Σ1 = Pi
Σ0, which can be expressed by the above S0 to S3. Therefore, if we measure the intensities I1, I2, I3, and I4 of the light that has passed through the analyzer, we can obtain the Stokes parameter S of the original elliptically polarized light.
0, S1, S2, S3, and S4 can be estimated. On the other hand, the ellipticity angle χ and the azimuth angle φ of the major axis are:
It is known that it can be expressed as a function of S0, S1, S2, and S3. Therefore, by measuring the spectral intensity of the light that has passed through the analyzer, the ellipticity angle χ of the angular wavelength and the azimuth angle φ of the major axis can be determined. When the ellipticity angle χ and the azimuth angle φ of the major axis are expressed in a mathematical formula, the following equation is obtained. The right side of this equation (2) is the intensity I1
, I2, I3, I4 function f(Ii) (i=1,2,3
, 4). Also, from the following equation (3),
The ellipticity ρ can also be found. ρ=tanχ (3) Therefore, the polarization characteristics of the sample and its wavelength dependence can be known. [Problem to be solved by the invention] The four-point method using the Stokes parameter described above uses a spectrometer. Therefore, it is fast, but when measuring the ellipticity ρ, the following errors are introduced because the ellipticity angle χ is first determined and then the ellipticity ρ is determined. ##EQU4## Since cos χ is included in the denominator, when χ is around 90°, that is, when the light is close to linearly polarized light, even if the intensity fluctuation is small, there will be a large measurement error. Therefore, the problem with this method is that for any form of elliptically polarized light, the ellipticity ρ
The problem lies in the inability to measure with high precision. SUMMARY OF THE INVENTION Therefore, an object of the present invention is to solve the above-mentioned technical problems and provide a polarization measurement method that can measure the ellipticity ρ and the azimuth φ quickly and accurately, and a polarization measurement device using the method. That's true. Means for Solving the Problems The polarization measuring method according to claim 1 for achieving the above object is characterized in that the intensity of the output light detected by the photodetector at at least three rotational positions of the analyzer is In this method, I1, I2, and I3 are obtained, and the ellipticity ρ and azimuth φ of the elliptically polarized light emitted from the sample are calculated using the following two equations. tan 2φ=(I1 +I2 −2I3 )/(
I2 - I1 ) (5) [0016] Furthermore, the polarization measuring device according to claim 2 includes a light source, a polarizer that produces linearly polarized light, and a rotatable device that allows only polarized light components at a desired angle to pass through. an analyzer, a sample placed between the polarizer and the analyzer, a photodetector that detects the intensity of the output light from the analyzer, and an intensity I of the output light from the analyzer.
1, I2, I3, and means for calculating the ellipticity ρ and azimuth φ of the elliptically polarized light transmitted through the sample using the above two equations. The polarization measuring device according to a third aspect of the present invention is the polarization measuring device according to the second aspect, which is equipped with a spectrometer before the photodetector so as to be able to measure at multiple wavelengths simultaneously. [Operation] Let us assume that the elliptically polarized light shown in FIG. 2 is incident on the analyzer. The reference axes are the x-axis and the y-axis, and as shown in Figure 1,
If the angle between the detection axis of the analyzer and the x-axis is θ, the output light intensity I(θ) is: I(θ)=a2cos2(θ-φ)+b2si
n2(θ−φ) (7) (
Malus' law). Here, φ is the angle formed by the x-axis and the ellipse major axis ξ, a is the length of the major axis, and b is the length of the minor axis. As can be seen from equation (7), the intensity at a certain measurement angle θ is determined by the three variables a, b, and φ. Therefore, we selected three values of θ and their respective intensities I1, I2,
I3 and these three intensities I1, I2, I3
By setting up simultaneous equations for , it becomes possible to find a, b, and φ. For example, if you choose θ=0°, 90°, 45°,
I1 = a2cos2 φ+b2sin2 φ
(8)
I2 = a2 sin2 φ + b2 cos2 φ
(9
) I3 = a2cos2 (45°-φ)
+b2sin2 (45°−φ) (10
) are created. Subtracting equation (10) from equation (8), I1 - I3 = a2 {cos2
φ−cos2(45°−φ)}
+b2 {sin2φ−sin2(4
5 °−φ)} (11) (9) From equation (10
) subtracting the formula, I2 −I3 = a2 {sin2φ−cos
2(45°−φ)}
+b2 {cos2φ−sin2(45 °−φ
)} (12) is obtained, and equation (11) and (12)
Add the formula and I1 −I3 +I2 −I3
= (b2 - a2 ) sin 2φ (13
)(9) by subtracting equation (8), I2 - I1 = (b2 - a2 ) cos
The formula 2φ (14) is obtained. From equations (13) and (14),
tan 2φ=(I1 +I2 −2I3 )/
(I2 - I1) (15) is obtained, so
This determines the azimuth angle φ. When I1 > I2, the ellipticity ρ is
=b/a, so it can be obtained from the following equation. The azimuth angle φ at this time is 2φ=tan −1 (I1 +I2 −2
I3)/(I2-I1). I1 <I
2, ρ=a/b, but the calculation result is the same as equation (16). The azimuth angle φ is 2φ=tan −1 (I1 +I2 −2
I3 )/(I2 - I1) +π. When I1 = I2, φ=π/4. Embodiments [0024] Hereinafter, embodiments will be explained in detail with reference to the accompanying drawings. FIG. 3 is a schematic diagram showing the polarization measuring device of the present invention. Light emitted from a light source 1 passes through a pinhole 2, is reflected by a mirror 3, and is guided to a polarizer 6 through a lens 4 and a pinhole 5. The output light of the polarizer 6 passes through the objective lens and is irradiated onto the sample, and the transmitted light of the sample enters the objective lens 9 and is guided to the analyzer 10. The transmitted light of the analyzer 10 is focused by a lens, passes through an optical fiber 12, and is input to a spectrophotometer 13. The spectral intensity signal obtained by the spectrophotometer 13 is supplied to a processing device 14, where calculations described below are performed. The light source 1 is, for example, a white light source such as an I2 lamp. Polarizer 6, Analyzer 10
is a linear polarizer using an anisotropic prism such as a Nicol prism or a Glan-Thompson prism, or a Polaroid film. Both can be rotated around the direction in which the light travels. The optical fiber 12 guides the measurement light to the spectrophotometer 13, but also functions as a depolarizer to prevent the light receiving sensitivity of the spectrophotometer 13 from being affected by the polarization state (Japanese Patent Application Laid-Open No. 1999-1-1993). 124
(See Publication No. 723). The spectrophotometer 13 is a known one that combines a dispersive element such as a diffraction grating and an image pickup element. The processing device 14 applies the spectral intensity measured according to the rotation angle of the analyzer 10 to the above-mentioned equations (15) and (16),
The ellipticity ρ and the azimuth φ are determined using a personal computer. To explain the polarization measurement method using a polarization measuring device, first, with the sample removed, set the standard polarizer 8a with the polarization axis in a certain reference direction, and rotate the polarizer 6 and analyzer 10. to align with the reference direction. Then, remove the standard polarizer 8a, insert the sample, and set the direction of the crystal axis of the sample (assumed to be known. If unknown, measure with an appropriate method) parallel to the reference direction, and set this as the x-axis. do. Next, set the angle of the analyzer 10 to 0°,
Measure the light intensity by setting at 90° and 45°. Next, actual measurement results obtained using the above-mentioned measuring device will be introduced. For sample 8, a polycarbonate retardation film was used. It is known that the wavelength dispersion characteristics (relative refractive index difference when the refractive index difference at a wavelength of 550 nm is 1) of this polycarbonate retardation film are as shown in Figure 4 (Yamamoto et al., Nitto Giho, 28, 105
(1980)). Ellipticity ρ at wavelengths of 450 nm and 550 nm
A graph of the actual measured values is shown in FIG. The horizontal axis of the graph is the azimuth angle of the incident linearly polarized light, that is, the rotation angle of the polarizer 6. The + mark is an actual value measured at 550 nm, and the x mark is an actual value measured at 450 nm. In addition, the theoretical values directly calculated using the wavelength dispersion characteristics in Figure 4 are shown as the solid line (550 nm),
Indicated by a broken line (450 nm). In addition, the actual measured values using the conventional maximum-minimum method are shown in FIG.
Shown below. The + mark is an actual value measured at 550 nm, and the x mark is an actual value measured at 450 nm. Figure 7 shows the actual measured values using the 4-point method. The + mark is an actual value measured at 550 nm, and the △ mark is an actual value measured at 450 nm. Next, FIG. 8 shows a graph of actually measured values of the azimuth angle φ of the ellipse at wavelengths of 450 nm and 550 nm. The horizontal axis of the graph is the azimuth angle of the incident linearly polarized light, that is, the rotation angle of the polarizer 6. + mark is actual measurement value at 550nm, △ mark is 450n
This is an actual measured value at m. In addition, the theoretical values directly calculated using the wavelength dispersion characteristics in Figure 4 are shown for the solid line (550 nm) and the broken line (4
50 nm). Further, the actual measured values of the azimuth angle φ using the conventional maximum-min method are shown in FIG. 9, and the actual measured values using the 4-point method are shown in FIG. Looking at the graphs in Figures 5 to 10 above, the azimuth angle φ is
The method of the present invention, the conventional maximum-minimum method, and the conventional 4-point method all agree well with the theoretical values. However, regarding the ellipticity ρ, in the conventional four-point method, as can be seen from FIG. 7, errors are noticeable near 0°, 90°, and 180°. The method of the present invention and the conventional maximum-minimum method have small errors (FIGS. 5 and 6). Therefore, in order to accurately evaluate the measurement accuracy of the ellipticity ρ, the average relative deviation δ1 from the theoretically calculated value of the ellipticity ρ is defined as follows. In this formula, ρe
x is an actual value, and ρth is a theoretical value. Table 1 shows the results of determining the average relative deviation δ1 using the method of the present invention, the conventional maximum-minimum method, and the conventional 4-point method using this equation. [Table 1] According to Table 1, in the method of the present invention and the conventional maximum-minimum method, the average relative deviation δ1 is relatively small, but in the 4-point method, the average relative deviation δ1 is large. Ori,
What was inferred from the graph is confirmed. Also,
Table 2 shows the results of determining the average error δ2 from the theoretically calculated value of the ellipse azimuth angle φ. Table 2 shows that the method of the present invention, the conventional maximum-minimum method, and the 4-point method all measure with almost the same accuracy. As described above, by measuring the intensity at the three rotational positions of the analyzer, the ellipticity ρ and the ellipse azimuth φ can be directly determined by applying a simple formula. The determined values are sufficiently accurate compared to conventional methods, and since measurements only need to be made at three rotational positions, the measurement time can be shortened. Furthermore, if a spectrometer is connected to measure the spectral intensity, measurements at multiple wavelengths can be completed in one measurement. It should be noted that the present invention is not limited to the above-mentioned embodiments. For example, when using a liquid crystal that has polarization characteristics in advance as a sample, or when using a light source whose polarization characteristics are known from the beginning, When using , it is also possible to omit the polarizer that creates linearly polarized light. Various other changes can be made without departing from the gist of the invention. Effects of the Invention As described above, according to the polarization measuring method of the present invention and the polarization measuring device using the method, at least 3
The ellipticity ρ and the azimuth angle φ can be determined with sufficiently high accuracy by simply measuring the spectrum at two rotational positions and calculating by applying it to a predetermined formula. Furthermore, if a spectrophotometer is used to perform measurements at multiple wavelength points, the wavelength dependence of the ellipticity ρ and the azimuthal angle φ can be measured at high speed.

[Brief explanation of the drawing]

FIG. 1 is a graph showing intensity polarization characteristics of elliptically polarized light.

FIG. 2 is a graph showing amplitude polarization characteristics of elliptically polarized light.

FIG. 3 is a schematic diagram showing an embodiment of the polarization measuring device of the present invention.

FIG. 4 is a graph showing the birefringence characteristics of a polycarbonate retardation film used as a sample.

FIG. 5 is a graph of actually measured values of ellipticity ρ at wavelengths of 450 nm and 550 nm.

FIG. 6 is a graph of actually measured values using the conventional maximum-minimum method.

FIG. 7 is a graph showing actual measured values using the conventional 4-point method.

FIG. 8 is a graph of actually measured values of the azimuth angle φ of an ellipse at wavelengths of 450 nm and 550 nm.

FIG. 9 is a graph of actually measured values of the azimuth angle φ using the conventional maximum-minimum method.

FIG. 10 is a graph of actual measured values using the 4-point method.

FIG. 11 is a diagram showing the characteristics of general elliptically polarized light.

[Explanation of symbols]

1 Light source 6 Polarizer 8 Sample 10 Analyzer 13 Spectrophotometer 14 Processing equipment

Claims (3)

[Claims] 1. A polarization measuring device comprising: a rotatable analyzer that allows only a polarized component at a desired angle to pass among the light emitted from a sample; and a photodetector that detects the intensity of the output light from the analyzer. Intensities I1, I2, of the output light detected by the photodetector at at least three rotational positions of the analyzer using
I3 is calculated and the ellipticity ρ determined by the length of the major axis and the length of the minor axis of the elliptically polarized light emitted from the sample is calculated using the following two formulas.
and a polarization measurement method characterized by calculating the azimuth angle φ of the long axis of the elliptically polarized light. tan 2φ=(I1 +I2 −2I3 )/(I2
-I1) [Math. 1] [Claim 2] A light source, a polarizer that produces linearly polarized light,
a rotatable analyzer that allows only polarized light components at a desired angle to pass; a photodetector that detects the intensity of output light from the analyzer;
A sample is placed between a polarizer and an analyzer, and based on the detection signals of the photodetector representing the intensities I1, I2, I3 of the output light detected by the photodetector at at least three rotational positions of the analyzer. , means for calculating the length and short axis of the major axis of the elliptically polarized light transmitted through the sample, the ellipticity ρ determined by the length, and the azimuth angle φ of the major axis of the elliptically polarized light using the following two equations. A polarization measurement device using a distinctive polarization measurement method. tan 2φ=(I1 +I2 −2I3 )/(I2
-I1) [Math. 2] 3. A polarization measuring device using the polarization measuring method according to claim 2, further comprising a spectrometer upstream of the photodetector to enable simultaneous measurement at multiple wavelengths.