JPH02102436A - Birefringence measuring method - Google Patents

Abstract

PURPOSE:To stably measure birefringence characteristics with high accuracy by searching for a couple of the closest values among values of retardation calculated by using results obtained by measuring the relation between the angle of rotation when the coupled body of a sample, a polarizer, and an analyzer is rotated and the intensity of light transmitted through the three bodies as to two different-wavelength light beams. CONSTITUTION:The sample is interposed between the polarizer 3 and analyzer 5 whose polarizing directions cross each other at a constant angle. Then the relation between the angle of rotation when the coupled body of the sample 4, polarizer 3, and analyzer 5 is rotated relatively and the intensity of the light transmitted through the polarizer 3, sample 4, and analyzer 5 is measured as to two light beams. A couple of the closest values are found among many retardation values calculated by using the measurement result as to one wavelength light beam and many retardation values calculated by using the measurement result of the other wavelength light beams. Consequently, one value can be determined unequivocally among the many calculated retardation values.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to an apparatus for measuring W refraction characteristics of various materials.

(Prior art) In optical devices, the birefringence of materials is often a problem (Also, since PlusDeck sheets, etc. become birefringent when stretched, the degree of stretching is detected by the degree of birefringence. In this way, it is necessary to measure the birefringence properties of materials in various cases, but methods such as those using Atsube's refractometer have limitations on the shape of the sample, and the measurement operations are cumbersome. It is difficult to display measurement results in a direct manner.

A sample is sandwiched between a polarizer and an analyzer perpendicular to the polarizer, and white light is incident on the sample, and the interference color exhibited by the transmitted light is observed. The retardation of the sample (ordinary and extraordinary light within the sample) is determined from the interference color chart. There is a method of determining the optical path length difference), but it is an experimental method, has low accuracy, and is difficult to automate. Therefore, methods for automatically measuring birefringence characteristics with higher accuracy have been proposed in Japanese Patent Laid-Open Nos. 60-13245 and 1982-65489. In these methods, linearly polarized light of a single wavelength is made incident on a sample, and the retardation of the sample is determined from the state of the rotationally polarized light transmitted through the sample.

In a sample that causes birefringence, there is a polarization direction of polarized light that exhibits a maximum refractive index for polarized light that travels in a direction perpendicular to the optical axis of the sample, and a polarization direction of polarized light that exhibits a minimum refractive index that is orthogonal to that direction. The maximum refractive index and the minimum refractive index are called the principal refractive index, and are expressed by nl and n2, and when the thickness of the sample is T, the retardation Rt is given by T(r, 1-n2). However, what can be directly determined by the above method is Rt (nl-
n2), but rather the fraction when Rt is divided by the wavelength, that is, the phase difference between the ordinary light and the extraordinary light in the light transmitted through the sample, and this only changes between 0 and 2π, which uniquely determines Rt. I can't. In the above-mentioned Japanese Patent Laid-Open No. 60-13245, Rt is determined by determining T from the attenuation of transmitted light using the light absorption coefficient of the sample. JP-A-52-65489 is applied when the sample is thin and the retardation is about half a wavelength or less.

(Problems to be Solved by the Invention) An object of the present invention is to provide an apparatus that can accurately measure the retardation of a sample with simple operations regardless of the thickness of the sample.

(Means for solving the problem) When a sample is inserted between a polarizer and an analyzer whose polarization directions intersect at a certain angle, and the sample and the polarizer/analyzer combination are rotated relative to each other. The relationship between the rotation angle and the transmitted light intensity of the polarizer, sample, and analyzer is measured for two wavelengths of light, and a large number of retardations are calculated using the above measurement results for one wavelength of light. A set of values that are closest to each other is found from a number of retardation values calculated using the above measurement results for light of one other wavelength.

) Calculating retardation using light of one wavelength is the same as the conventional method. In this case, an infinite number of retardation values are calculated at intervals. If the wavelength used for measurement is different, even if the two principal refractive indices do not change at any wavelength, the wave numbers contained in the sample will differ.
The countless retardation values that can be calculated will also be different, but since the retardation value should be constant regardless of the wavelength, the group of retardation values at the first wavelength and the group of retardation values at the second wavelength are By finding the values closest to each other from a group of retardation values at wavelengths, it is possible to uniquely determine one value from a large number of calculated retardation values.

(Example) FIG. 1 shows an example of the present invention. 1 is a light source, 2 is a filter plate, and two types of monochromatic filters 2a and 2b, which transmit light of different single wavelengths, are attached interchangeably. This allows light of λ2 to be taken out alternately. Reference numeral 3 represents a polarizer, and reference numeral 5 represents an analyzer, both of which can be rotated integrally with their respective polarization directions maintained at a constant angle, parallel to each other in this embodiment, and are rotated by a motor 7. 4 is a sample inserted between the polarizer 3 and the analyzer 5. A photodetector 6 receives the light transmitted through the analyzer 5. A computer 10 receives the output signal of the photodetector 6 and the output signal of the rotation angle detector 8 attached to the motor shaft via an interface 9, processes the data, and controls the motor 7. The results of data processing by computer 10 are displayed on CRT II and recorded by printer 12. A keyboard 13 is used to enter various commands and parameters necessary for data processing into the computer 10.

If one filter 2a is selected in the above-mentioned apparatus, a sample is placed at the position shown in the figure, and the output of the photodetector 6 is displayed in polar coordinates as a function of the rotation angle θ of the integrated polarizer 2 and analyzer 5, the result is as shown in Fig. 2. You will get a graph like this. In this case, linearly polarized light is incident on the sample, but if the sample has birefringence, the light transmitted through the sample is generally elliptically polarized light, and the ratio of the major axis to the minor axis and the direction of the major axis are varies depending on the thickness. Figure 3 shows the refractive index ellipse of the sample. is measured. In FIG. 3, n 1 r02 is the two principal refractive indices, AA' and BB' are the directions of each principal refractive index, and PP' is the direction of the polarizer and analyzer. When the direction PP' of the polarizer or analyzer matches AA' or BB', birefringence does not occur and the incident light passes through the sample and analyzer as is, so AA' as shown in Figure 2. The photodetection output shows a maximum in the direction of and BB'. When PP' is exactly midway between AA' and BB', that is, in the direction QQ' at 45° with respect to AA' and BB', the amplitudes of the components in the AA° direction and BB' direction of the linearly polarized light incident on the sample are They are both equal to l/R of the incident light amplitude A. When the phases of the AA' direction component and the BB' direction component match when passing through the sample, the emitted light is linearly polarized light in the QQ' direction with the same amplitude as the incident light, and the photodetection output is determined by the polarizer analyzer. Alternatively, it is the same as when it is in the BB° direction, and the graph in FIG. 2 becomes a circle. When PP'' is in the QQ'' direction, if the phase difference between the components in the two principal refractive index directions of the light transmitted through the sample is 90°, the amplitude becomes circularly polarized light of AiFi, and the detected light intensity is 1/2 of the maximum. and the phase difference is 180
When the phase difference is 0, the light becomes linearly polarized in a direction orthogonal to that when the phase difference is 0, and is blocked by the analyzer, and the photodetection signal becomes O. In other words, it is 45 degrees from the direction showing the maximum value in the graph of Figure 2.
The phase difference between the transmitted light in the two principal refractive index directions can be determined by the ratio of the photodetection signal value in the direction forming the angle of , and the maximum value of the photodetection signal. By the way, since the object to be measured has two principal refractive indices nl and n2 in principle and two unknowns, it is not possible to determine the two principal refractive indices with only one phase difference data. Therefore, when the second filter 2b was selected and the same measurement as described above was performed, the above-mentioned filter 2a was selected as the phase difference between the two main refractive index direction components of the sample transmitted light when the polarizer and analyzer were in the QQ' direction. Different values are obtained depending on the time. Two wavelengths λ1. obtained by filters 2a and 2b. λ2
If two wavelengths are selected so that the two principal refractive indices can be regarded as the same, then the two principal refractive indices n1. n2
can be found.

If the thickness of the sample is T, the wave number N1 of light with wavelength λ1 in the sample for the refractive index nl is N1=nlXT/λ1 Similarly, the wave number N2 for the refractive index n2 is N2=n2T
/λ1 The phase difference Δ1 of two lights of the same wavelength in the direction of the principal refractive index that are incident in the same phase when the sample exits is △1=2π(Nl-fV2)='i (mt-/nz)
When the direction of the polarizer and analyzer is the QQ' direction in Figure 3, the two principal refractive index direction components of the sample of the incident light have the same phase and the same amplitude, so the output when the phase difference in the output light is Δ1. The amplitude of the emitted light in the QQ' direction is determined as follows.

First, consider the case where the light absorption rate of the sample does not differ depending on the direction of polarization. The light incident on the sample is iii-line polarized light in the QQ' direction, and its amplitude is A. The imaging unit for the component in the principal refractive index n1 direction is AiFi, and the amplitude of the component in the QQ' direction is A/2, and this component is When expressed as (A/2)c, .omega.L, the QQ' direction component of the principal refractive index 02 direction component has a phase delay of .DELTA.1 from the above, so it can be expressed as (A/2) cos (.omega.t-.DELTA.l). For convenience of calculation, the former is (A/2) cos(ωt+Δ1/2
) and write (and the latter is (A/2) cOS (ω - Δ1/2)
8. Therefore, the sample is emitted, and rearranging this becomes M1 Acos-cos ωt ---(O), and the amplitude AQ of the QQ' direction component of the sample emitted light is therefore the photodetection output.The maximum value of the photodetection output is the polarizer, Since it is detected when the analyzer is in the AA' direction or the BB' direction, the maximum and minimum ratio A q / A = R1 is R1 = C1rQ"' =
cc-7” T (/El-”)12) ---(/
)2 λI Similarly, when measuring with light of wavelength λ2, the subscript number is set to 2, and R1 and R2 are actual measured values in equations (1) and (2) above, and λ1
Since ゜λ2 and the sample thickness T are known, (1) ■
n 1 * n 2 is calculated from the formula. In practice, we simply find the ratio of , and then obtain α as the square root of this, and then we want to measure the tardage date T(nl-n2).

Next, if the above formula (A) has many combinations, from the formula (1), the cap9〆dan = light T (bar ~ report)... (3) T (n 1-) that satisfies the above formula (3) There are an infinite number of values for n2). Similarly, there are countless values of T (n 1 - n2) that satisfy equations 0 to (b), and equation (4). (3) (4) Both equations hold true at the same time, so within an appropriate range of the countless retardation values mentioned above, the best match (in principle, they match perfectly, but there is a measurement error) (Actually, it is not possible to obtain a perfect match from

For simplicity, the above example assumes that the light absorption rate of the sample does not differ depending on the polarization direction. When the absorption coefficients for polarized light in the direction of the principal refractive index n 1 * n2 are different, the amplitude absorption coefficients al, a
Let the ratio of 2 be a1/a2-α.

In this case, the absorption coefficient equation can be further rearranged by the ratio of the photodetection outputs when the polarizer and analyzer directions are AA' and BB'. Therefore, the above equations (1) and (2) can be transformed into (5) and (6). In the formula, R1, R2, α1. Since α2 is a value found from actual measurements, T(nl-n2) can be determined in the same manner as described above. Here, R1 and R2 are the direction of the principal refractive index rll, that is, the ratio of the photodetection output in the l\A° direction and the photodetection output in the QQ' direction in FIG. 3. This is f because this direction was taken as the reference for the above calculation.

A comparison was made between the method of the present invention and a method using a retardation phase reduction phenomenon using a convesator. Polarized light v! for six samples. The results of determining the retardation of the sample from observation of interference colors using the phase reduction phenomenon of retardation using hemp and Berek compensator and λ1 =
590. Onm, measured by the method of the present invention using light with a wavelength of λ2 = 657.3 nm, retardation < 30
Table 1 shows the results of finding a set of Rts that minimizes the difference between the two retardations in the range of 00 nm.

The six samples were PET (polyethylene terephthalate; 58/μm), FEP (fluorinated polymer; 1
48/μm), PS (polystyrene; 48/μm)
, P P (polypropylene; 28/, um), PS
(Polystyrene: 111/μm), PP (Polypropylene: 28/μm).

From the results in Table ■, the measured values using the Berek Compesator and the measured values using the method of the present invention are very similar, and it is possible to obtain retardation values of 1/2 or more of the measurement wavelength using the method of the present invention. It turns out that it is possible. Regarding measurement accuracy, when using a Berek compensator, due to its characteristics, the larger the Rt, the larger the error, and there are also individual differences among the measurers. On the other hand, in the case of the method of the present invention, the standard deviation of Rt when one sample is continuously measured 20 times is highly accurate, being 0.1 nm or less.

(See next page) N.

Sample ET EP S P S P Sample thickness (μugly) Table! Retardation measurement value (stop) Berek” compentator Method using the method of the present invention λ-590.On-λ-GS7.3rv+50
．． 8 102.4 219.0 41? , 6 623, 7 791.7 48.4 101.2 215, /1 417.7 608, 2 790.4 (Effects of the invention) The method of the present invention is easy to operate and uses human color sense. It is possible to perform stable and highly accurate measurements without including individual differences such as

[Brief explanation of drawings]

Fig. 1 is a block diagram of an example of a device for carrying out the method of the present invention, Fig. 2 is a graphical representation of measurement results for one wavelength, and Fig. 3 is an explanatory diagram of angles, directions, etc. used to explain the method of the present invention. It is. DESCRIPTION OF SYMBOLS 1... Light source, 2a, 2b... Filter, 3... Polarizer, 4... Sample, 5... Analyzer, 6... Photodetector, 7... Motor, 8... ...Rotation angle detector, 9...
Interface, 10... Computer, 11...
・CRT, 12...Printer, 13...Keyboard. Agent Patent Attorney Kosuke Agata

Claims (1)

[Claims] A sample is inserted between a polarizer and an analyzer whose polarization directions intersect at a certain angle, and the rotation angle when the sample and the polarizer/analyzer combination are rotated relative to each other, the polarizer, the sample, The relationship between the three-way transmitted light intensity of the analyzer is measured for two wavelengths of light, and a number of retardation values calculated using the above measurement results for one wavelength of light and the other one wavelength are calculated. A birefringence measurement method characterized by finding a set of values closest to each other from a large number of retardation values calculated using the above measurement results for light.