JP3136569B2 - Method for measuring retardation of birefringent material - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring the retardation of a birefringent material, and more particularly to a method for accurately measuring the retardation when a sample is thick and the order of the retardation is high.

[0002]

2. Description of the Related Art In general, the measurement of retardation is obtained by placing a polarizer and an analyzer in a parallel Nicol state, rotating a sample between them, and calculating from the relationship between the intensity of transmitted light and the rotation angle of the sample. . In this case, the wavelength of the light used for the measurement is a single wavelength. Retardation is the phase difference angle between the ordinary ray and the extraordinary ray that are incident on the sample in phase, when the sample is emitted.
Generally represented by 2nπ + φ, where n is the order, 0, 1,
The value of n, which is the value of 2..., Increases as the sample becomes thicker. However, the change width of the transmitted light intensity when the sample is rotated varies depending on φ, and φ is directly obtained, and there is no method for directly obtaining n.

Therefore, conventionally, the retardation, that is, φ, has been obtained for each of the two wavelengths of light, and the order 1,
The sample thickness in each order was calculated backward while changing the order of 2, 3,..., And the actual order was determined as the order when the sample thickness calculated for light of two wavelengths best matched. However, in this method, the difference Δ in retardation due to light of two wavelengths is up to 2π, and the difference in retardation is 2πm + Δ ′ (m is 1, 2, 3,.
π), the integer m cannot be determined, so that the only practical application is that the retardation order n is 20
The rank was the limit. Moreover, even when the retardation is 20 or more and the above-mentioned m is 1, 2,..., There is a risk that m = 0 and the order is determined.

[0004]

As described above, it is possible to solve the problem that the measurement of the retardation becomes difficult when the order of the retardation increases.

[0005]

When the apparent retardation of a sample for light of one wavelength is 0 (the transmitted light pattern is a circle), light of another wavelength close to the wavelength of the light is obtained. It utilizes the relationship that exists between the apparent retardation of the sample with respect to the light and the order of the retardation of the sample with respect to the one wavelength of light. So that the retardation of the sample and the phase plate together is an integral multiple of 2π,
In this state, using light of another wavelength close to the above-mentioned wavelength, the sample and the polarizing plate are relatively rotated between the two polarizing plates arranged in parallel Nicols, and the maximum and minimum of the transmitted light intensity at that time. Is applied to the relationship between the degree of retardation prepared in advance and this difference to determine the degree of retardation of the sample.

[0006]

When two wavelengths are used, the order n when the difference in retardation at each wavelength becomes 2π (that is, when the order difference becomes 1) depends on the wavelength ratio of the two wavelengths used. The higher the order, the greater the order. However, when the wavelength difference is reduced, the accuracy of determining the order is reduced. The present invention avoids this decrease in order determination accuracy by inserting a phase plate. In FIG. 3A, x and y indicate the optical axes of the sample, and I indicates the amplitude vector of linearly polarized light whose polarization direction incident on the sample forms 45 degrees with the optical axis. In the sample, this light travels in two directions of linearly polarized light Ix and Iy. Considering now Iy, the light incident on the light receiving element 3 is such that the polarizers 3 and 4 are at 45 degrees with respect to the optical axis, so that the I direction component Iyy of Iy and the Ix of Ix whose phase is shifted by an angle φ therefrom In the direction component Ixx, the sum of these two vectors is the amplitude of the light incident on the light receiving element 3, so the amplitude Is of this light is In ² = Iyy ² + Ixx ² + 2Iyy'IxxCOSφ Is ² with reference to FIG. 3B. it is proportional to the output of the light receiving element 3, the light receiving element output when the incident light and the optical axis of the sample in the same direction of polarization is I ^2. In addition, Ixx, because Iyy are respectively ^{1/2, Is 2 = I 2/} 2 + I 2/2 · cosφ I 2 -Is 2 = (1-cosφ) I 2/2 ...... (1) above (1) The equation is the difference between the maximum value and the minimum value of the flower shape of FIG.
Considering a value C obtained by dividing the difference between the maximum diameter Do and the minimum diameter D of the flower shape of the figure by the maximum diameter in order to eliminate I and the like in the above equation, 2C = 1−cos φ (2) It is a value measured directly. The value of D is 0
And Do. The sine waveform A shown in FIG. 4 is shown when the change in D is illustrated by taking the retardation R = cos (2πn + φ) on the horizontal axis. The order n increases by one for each cycle of this waveform. When a similar curve is drawn for light having slightly different wavelengths, FIG.
And the period is slightly different. Obtaining D for light of wavelength λ ′ by superimposing a phase plate so that the apparent retardation for light of wavelength λ is 0 means that the waveform A has a maximum in FIG. By obtaining D by the light having the wavelength λ ′ at the time of taking the value, this is represented by the points a′b′c.
Is to find the value of When the values of D in a'b'c... Of the waveform B are connected, a curve as shown by C in FIG. 4 is obtained, and the curve decreases monotonically as the order increases, and the curves A and B overlap with just opposite phases. It becomes Io by the order, and then turns to monotonic increase. Since the actual measured value of D changes depending on the measurement conditions (such as a change in the intensity of the light source), it is actually better to use D / Do. That is, the value of D / Do is a function of the order n, and the order at which D / Do becomes 0 is determined by the wavelengths of the two wavelengths of light. Therefore, if the relationship between D / Do and n is determined in advance, D / Do is obtained. Can be determined from actual measurement to determine n.

The relationship between D / Do and the order n is as follows. Now, let the two wavelengths be λ and λ ′, and let the refractive indexes of the two optical principal axes of the sample be ν and ν ′. The wavelength λ of this refractive index,
The difference due to λ ′ can be ignored since the difference between λ and λ ′ is small.
Assuming that the thickness when the pattern first becomes a circle by increasing the thickness gradually from 0 with the light having the wavelength λ is S, then S (ν−ν ′) = λ (3) The retardation δ of light is δ = 2πS (ν−ν ′) / λ ′ = 2π + e When the thickness of the sample is an integral multiple of S, the retardation due to light of wavelength λ is apparently 0 and the order is n. The retardation for light of wavelength λ ′ is nδ, which is 2πn + m
e, but the apparent retardation is ne.
This ne becomes 2π when the curve C of FIG. 4 draws one cycle. Assuming that n at this time is no, from 2πnoS (ν−ν ′) / λ ′ = 2πno + noe = 2π (no + 1), using equation (3), noλ / λ ′ = no + 1. (4) where no is determined only by the wavelength, and when λ and λ ′ are close, no has a large order.
Even in a place where the order n is large, n can be determined from the actually measured value of D / Do. When n is determined, the retardation of the sample is obtained by adding the order n to the apparent retardation obtained from the actual measurement.

[0008]

FIG. 1 shows an example of an apparatus for executing the method of the present invention. In the figure, 1 is a light source for white light, 2 is a filter holding plate, and 5
There are provided various types of filters F1 to F5, one of which is inserted into the optical path from the light source 1 to the light receiving element 3. One filter is turned by turning the holding plate 2. Selected. Among these filters, F1 is a bandpass filter that transmits light of a wavelength whose retardation is to be measured, and F2 to F5 are filters that transmit a plurality of lights selected such that the transmission wavelength difference from F1 increases in order from F2 to F5. It is. Polarizing plates 4 and 5 are arranged so that their polarization directions are parallel to each other, and are connected to pulleys 8 and 9 fixed on one axis via belts 6 and 7, and both polarizers are integrated by a motor 10. Is rotated. The sample S is placed between the polarizers 4 and 5. With this configuration, the filters F1 to F
5, light having a wavelength selected by passing through the polarizer A, the sample 3, and the polarizer 5, is incident on the light receiving element 3, and is measured.
The photometric output is taken into the data processing computer 11, subjected to data processing, and the result is displayed on the display device 12. Reference numeral 13 denotes a phase plate which is disposed between the polarizing plate 4 and the sample S so as to be able to freely enter and exit, and a Babinet Soleil compensator is used so that its own retardation is variable, but it is expensive. Therefore, a plurality of plates having known retardations and slightly different values from each other may be provided so as to be exchangeable in a turret type like the filters F1 to F5.

The operation and use of the above device will be described. First, the filter F1 for selecting the light of the measurement reference wavelength is positioned on the measurement optical path, and the upper and lower polarizers 4 and 5 are rotated while the phase plate 13 is retracted from the measurement optical path, and the intensity change of the transmitted light is measured. Then, the relationship data between the rotation angles of the polarizing plates 4 and 5 and the transmitted light intensity is fetched. This relationship generally shows a flower shape as shown in FIG. Next, the phase plate 13 is advanced onto the measurement optical path, and the transmitted light intensity and the polarization
5 is measured, and the retardation of the phase plate 13 is changed so that the transmitted light intensity is constant irrespective of the rotation angle, that is, the flower shape of FIG. In this case, the retardation of the phase plate 13 need not be known. After the above preparatory measurement is completed, the phase plate 13 is left as it is, the filter is changed to F2, the polarizing plates 4 and 5 are rotated, the transmitted light intensity is measured, and the maximum D in the flower shape of FIG.
The ratio of o to the minimum D is determined as D / Do. FIG. 4 is a graph showing the relationship between the order determined in advance for the transmitted light of the filter F1 and the transmitted light of the filter F2 using the value of D / Do and D / Do.
The order n of the retardation is determined from C. In the first measurement (the filter F1 and no phase plate), the retardation of the sample S is determined in the formula (1) of the fifth paragraph in the range of 0 to 2π. And n + δ
Is the retardation of sample S.

In order to improve the accuracy of the measurement, the filters F3 to F3
The same measurement as above may be performed for F5 to obtain four values for n, and one majority may be determined by majority decision. In the above embodiment, the accuracy when the retardation of the sample S and the phase plate 13 combined with the reference wavelength by the filter F1 is set to 0 is related to the measurement accuracy. A half-wave plate for the reference wavelength light is prepared separately from the phase plate 13, and the retardation when the sample S is combined with the phase plate 13 and the half-wave plate is π, that is, the polarization plate 4 When the half-wave plate is retracted so that the transmitted light intensity when rotating 5 changes between 0 and the maximum, the retardation of the sample S and the phase plate 13 together becomes 0. And
The phase plate 13 can be adjusted with higher sensitivity than when a polar coordinate record of transmitted light intensity is found to be a circle.

As the order of the retardation increases, the interference of the extraordinary extraordinary light becomes blurred due to the spread of the wavelength of the monochromatic light used, and the transmitted light when the polarizers 4 and 5 are rotated. The change in the intensity becomes smaller, and the apparent retardation becomes smaller. Therefore, it is desirable that the light source used has high monochromaticity. As a light source, it is better to use a discharge tube and select some bright line light with a filter than to select light of a continuous spectrum light source with a filter. For example, bright lines 450.1, 462.4, and 4 of a xenon discharge tube are preferable.
67.1 nm is available. Now, when the 462.4 emission line is used together with the 462.4 emission line as a reference, no in the expression (4) described in paragraph 6 is about 100, and the measurement can be performed up to the 50th order.

[0012]

According to the present invention, the polarization retardation of a relatively thick optically anisotropic material can be measured relatively easily and accurately.

[Brief description of the drawings]

FIG. 1 is a perspective view of an example of an apparatus for performing the method of the present invention.

FIG. 2 is a graph of a measurement result obtained by the above device.

FIG. 3 is a diagram showing a relationship between a polarization vector and an optical axis of a sample.

FIG. 4 is a graph illustrating the operation of the present invention.

[Explanation of symbols]

 Reference Signs List 1 light source 2 filter holding plate 3 light receiving element 4, 5 polarizing plate 13 phase plate F1 to F5 filter

──────────────────────────────────────────────────続 き Continuation of the front page (72) Inventor Kyoji Imagawa 4-3-1 Jokoji, Amagasaki City Kanzaki Paper Co., Ltd. Kanzaki Mill Co., Ltd. (56) References JP-A-64-35244 (JP, A) JP-A Heihei 3-218441 (JP, A) JP-A-3-218442 (JP, A) JP-A-58-35425 (JP, A) (58) Fields investigated (Int. Cl. ⁷ , DB name) G01N 21/00 -21/61 G01J 4/00-4/04

Claims (1)

(57) [Claims] 1. A sample and a phase plate are superposed on each other, and the retardation of the sample and the phase plate for light of one wavelength is 2
In this state, light of another wavelength close to the above-mentioned wavelength is used, and in this state, the two polarizing plates that maintain the polarization direction in a fixed relationship and the sample between them are relatively positioned. It is characterized by determining the order of the retardation of the sample by applying the difference between the maximum and the minimum of the transmitted light intensity at that time to the relationship between the order of the retardation prepared in advance and this difference. Method for measuring retardation of birefringent material.