GB2254144A - Three-angle polarisation analyser - Google Patents
Three-angle polarisation analyser Download PDFInfo
- Publication number
- GB2254144A GB2254144A GB9206473A GB9206473A GB2254144A GB 2254144 A GB2254144 A GB 2254144A GB 9206473 A GB9206473 A GB 9206473A GB 9206473 A GB9206473 A GB 9206473A GB 2254144 A GB2254144 A GB 2254144A
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- GB
- United Kingdom
- Prior art keywords
- polarized light
- light
- analyzer
- ellipticity
- azimuth
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
- G01N21/21—Polarisation-affecting properties
- G01N21/211—Ellipsometry
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
- G01N21/21—Polarisation-affecting properties
- G01N21/23—Bi-refringence
Description
2254144
-1DESCRIPTION
POLARIZED LIGHT MEASURING METHOD AND APPARATUS The present invention relates to a polarized light measuring method in which the polarization characteristic of light which has passed through an anisotropic medium is measured to analyze the properties of the medium and further relates to a polarized light measuring apparatus using the method.
3y measuring the polarization condition of light which has passed through an anis-otropic medium such as liquid crystals or optical crystals, -'Che optical axis direction, birefringence phase difference, and other properties of the medium can be found. With the above measurement, the layer thickness and optical constant of the medium can be found, and by further carrying out the above-mentioned measurement of light at several points of wavelength, the wavelength dependency can be also found.
Taking liquid crystals as examl5le, recently a 20 growing attention has been paid to the birefringence characteristic of liquid crystals, and therefore the wavelength dependency of light polarization characteristics is currently an important measurement item. More specifically, in supertwist tviDe liquid crystals, possible coloration due to birefringence is 2 compensated with a phase-dif ference film for the purpose of making a monochrome picture and contrast more clear. In order to achieve a correct compensation, the wavelength dependency of the light polarization characteristic must be measured correctly.
Conventionally, the following methods have been used for light polarization characteristic measurement.
According to a classical light polarization characteristic measuring method, a mono-color light source, a polarizer, a specimen, and an analyzer are arranged in the above order, and the analyzer is made to turn to detect the output light intensity, with which the polarization characteristic of light (including such factors as ellipticity angle X and azimuth which shall be referred to in connection with Fig. 11 which has passed through the slpecLmen can be measured. The above-mentioned method is referred to as the maximum- minimum method.
In order to measure the output light intensity according to the maximumminimum method, the analyzer is required to turn finely in Ditches which results in a large time consumption. Particularly for measurement at several points of wavelength, the above-mentioned measurement operation must be repeated at each wavelength, which also results in consuming much time.
In view of the above, there has been developed a method of analyzing light polarization characteristic by means of a Stokes parameter and MUller matrix notation with use of a spectroscope and an image sensor for easy multiple-point wavelength measurement (M.C.K. Wiltshire and M.R. Lewis, J.Phys.E:Sci.Instrum. 20,884(1987)). The above- mentioned method is referred to as the four-point method.
According to the four-point method, ellip-cic polarized light which has passed through a specimen is received by an analyzer where the analyzer is fixed horizontally (0 0), vertically (90 0), at 45, and at 135 to measure the spectrum of output light intensity at each angle.
Describing the four-point method simply, the Stokes parameter of elliptic polarized light is expressed as:
E0 = (SO, Sl, S2, S3) Assuming now that the MUller matrix of an analyzer which is already known to be a function of angle is represented by Pi (i represents an angle of 00, 900, 45', or 135), the Stokes parameter El of light which has passed through the analyzer can be expressed as:
Z' = PiE0 which can be also expressed by SO through S3. Therefore, by measuring the light intensity values Il, 12, 13, and 14 which has passed through the analyzer, the Stoke parameters - 4 SO, Sl, S2, S3, and S4 of the objective elliptic polarized light can be estimated.
Meanwhile, it is found that the ellipticity angle X and the azimuth of the major axis can be expressed as 5 a function of SO, Sl, S2, and S3.
Therefore, by measuring the spectrum intensity of light which has passed through the analyzer, the ellipticity angle X of angular wavelength and the azimuth of the major axis can be found.
The ellipticity angle X and the azimuth of the major axis can be expressed by the numerical expressions as follows: 13 - 14 Il - 12 sin 2% 1-4 (Il 12)2 + (13 - 14)2 1/2 tan 2 (1) (I1 + 12 + 13 + 14)2 The right-hand iDar-c of eauation (2) is assi-uned as a function f (Ii) (i = 1, 2, 3, 4) of the intensity values 11, 12, 13, and 14.
The ellipticity p can be found from the following equation (3).
p = tan X (3) Consequently, the light polarization characteristic and the wavelength dependency of the specimen can be found.
The above-mentioned f our-point method by means of the Stokes parameter permits a rapid analysis for the reason that a spectroscope is used, However, the following error takes place when measuring the ellipticity p because the ellipticity angle X is obtained first and then the ellipticity p is obtained.
1 1 AP = f' (Ii)AIi (4) Cos 2 x 2cos2X Since cos X belongs to the denominator, when X is at around 90, i.e., in the case of light nearly equal to linear polarized light, a great measurement error takes place even if the fluctuation of intensity is small. Therefore, the problem of the four-point method is that high-accuracy measurement of ellipticity p cannot always be achieved for any forms of elliptic polarized light.
Accordingly, it is an object of the present invention to provide a polarized light measuring method which is capable of accurately measuring the ellipticity angle X and the azimuth at a high speed giving a solution to the above- mentioned conventional problems and a polarized light measuring apparatus using the method.
In order to achieve the above-mentioned object, the present invention provides a polarized light measuring method wherein the intensity values 11, -12, and 13 of light output detected by means of a photo detector at least at three rotatory positions of the analyzer are obtained and the ellipticity p and the azimuth of elliptic polarized light emitted from a specimen are calculated according to the following two equations:
tan 2 = (11 + 12 - 2-13)/(12 - II) p = (I1 + 12) - E(I1 + 12 - 2.13)2 + (12 _ Il)2] 1/2 (11 + 12) + [ (I1 + 12 - 2. 13)2 + (12 - Il)2] 112 (6) The present invention also provides a polarized light measuring apparatus comprising a light source, a polarizer for producing a linear polarized light, an analyzer which is rotatable and capable of allowing only polarized light components at a desired angle to pass therethrough, means for disposing a specimen between the polarizer and the analyzer, a photo-detector for detecting the intensity of light output from the analyzer, and calculation means for calculating the ellipticity p and the azimuth of elliptic polarized light which has passed through the specimen based on signals from the photo-detector representing the intensity values Il, 12, and T-3 of light from the analyzer according to the above-mentioned output two equations.
Preferably, a spectroscope is provided ahead of the photo- detector to enable simultaneous measurement at several points of wavelength.
Postulating now that elliptic polarized light as shown in Fig. 2 is tnput to the analyzer, reference axes are X-axis and Y-axis, and the angle between the axis of detection of the analyzer and the X-axis is e, the output light intensity 1 (0) is expressed by the following equation (Malus' law):
i (e) = a2CoS2 ( () _) + b 2S in 2 (e -) (7) wherein represents the angle between X-axis and the ellipse major axis, a represents the length of the major axis, and b represents the length of the minor axis.
As obvious from the equation (7), light intensity at a certain measurement angle e depends on the three variables a, b, and. Therefore, by measuring intensity values Il, 12, and 13 at three selected values of e and forming simultaneous equations for the three intensity values Ilf 12 and 13, the variables a, b, and can be obtained.
For example, selecting 00, 900, and 450 as e, the following simultaneous equations can be formed.
a 2COS2 + b 2 sin 2 (8) 2 1 2COS2 '12 a sin' + b (9) 8 - 13 = a 2COS2 (45 + b 2Sin 2 (45' (10) The equation (10) is subtracted from the equation (8) as follows:
ii - 13 = a 2 {COS2 _ COS2 (45" + b 2 úsin 2 - sin 2 (45' -)} (11) The equation (10) is subtracted from the equation (9) as f ollows:
12 - 13 = a 2 {sin 2 _ CoS2 (45" + b 2 COS2 - sin1(4511 (12) The equation (11) is added to the equation (12) as follows:
Il - 13 + 12 - 13 = (b 2 - a 2)sin2 (13) The equation (8) is subtracted from the equation (9) as f ollows:
12 - Il = (b 2 - a 2)cos2 (14) From the equations (13) and (14), the following equation can be derived.
tan 2 = (Il + 12 - 2-13)/(12 Il) From the equation (15), the azimuth can be found.
When Il > 12, the ellipticity p is:
p = b/a therefore, the ellipticity p can be obtained f rom the following equation.
(15) (I1 +!2) - [(I1 + 12 - 2. 13)2 + (12 - Il)2] 1/2 (I1 + 12) + E (I1 + 12 - 2. 13)2 + (12 - Il)2]112 ( 16) when the azimuth is:
2 = tan-' (11 + 12 - 2-13)/(12 - Il) When Il < 12, the ellipticity p is:
p = a/b when the calculation result is as same as that of the equation (16). The azimuth is:
2 = tan-' (Il + 12 - 2-13)/(12 - Il) + n When 11 = 12, the azimuth is:
n/4 According to the polarized light measuring method and an apparatus using the method, by merely measuring spectrums at least at three rotatory positions and carrying out calculation in accordance with prescribed equations, the ellipticity p and the azimuth can be obtained with high accuracy.
Furthermore by carrying out measurement with use of a spectro -photometer at several points of wavelength, the wavelength dependency of the ellipticity p and the azimuth can be measured at high speed.
The invention is described further hereinafter, by way of example only, with reference to the accompanying drawings, in which:- Fig. 1 is a graph of light polarization - 10 characteristic in intensity of elliptic polarized light; Fig. 2 is a graph of light polarization characteristic in amplitude of elliptic polarized light; Fig. 3 is a schematic view of a polarized light measuring apparatus in accordance with an embodiment of the present invention; Fig. 4 is a graph of the birefringence characteristic of a polycarbonate phase-contrast film used as a specimen; Fig. 5 is a graph of actual measurement values of ellipticity p at the wavelengths of 450 nm and 550 nm.
Fig. 6 is a graph of actual measurement values in accordance with the conventional maximum-minimum method; Fig. 7 is a graph of actual measurement values in accordance with the conventional four-point method; Fig. 8 is a graph of actual measurement values of azimuth at the wavelengths of 450 nm and 550 nm; Fig. 9 is a graph of actual measurement values of azimuth in accordance with the conventional maximum minimum method; Fig. 10 is a graph of actual measurement values in accordance with the conventional four-noint method; and Fig. 11 is a graph of the characteristic of general elliptic polarized light.
Fig. 3 is a schematic view of a polarized light measuring apparatus in accordance with an embodiment of the present invention.
Light emitted from a light source 1 passes through a pin hole 2 and is reflected on a mirror 3 to be conducted via a lens 4 and a pin hole 5 to a polarizer 6. Light output through the polarizer 6 is applied via an objective lens 7 onto a specimen 8, and light which has passed through the specimen enters into an objective lens 9 to be conducted to an analyzer 10. Light which has passed through the analyzer 10 is converged by means of a lens 11 and input by way of an optical fiber 12 to a spectro-photometer 13. The spectral intensity signal obtained by the spectro -photometer 13 is supplied to a processor 14 in which calculations as described hereinafter are carried out.
The light source 1 is a white light source such as an 12 (iodine) lamp.
Each of the polarizer 6 and the analyzer 10 comprises, for example, an anisotropic prism such as a Nicol prism or Glan-Thompson prism, or a linear polarizer employing a polaroid film. Each of the polarizer 6 and the analyzer 10 is rotatable around the optical axis.
The optical fiber 12 is to conduct light for measurement to the spectro -photometer 13 while concurrently - 12 serving as a depolarizer for preventing the light-receiving sensitivity of the spectro -photometer from being influenced by the polarization condition reference is directed to the official bulletin of Japanese Unexamined Patent Publication JP-A-124723/1989).
The spectro -photometer 13 is the known unit made by combining a light diverging element such as a diffraction grating with an image pickup element.
The processor 14 is to obtain ellipticity p and azimuth by applying spectral intensity measured in accordance with the rotatory angle of the analyzer 10 to the aforesaid equations (15) and (16). In practice, a personal computer can be used as the processsor 14.
Describing the polarized light measuring method by means of the polarized light measuring apparatus, firstly a reference polarizer 8a having its oolarization axis in a reference direction is set to the apparatus with no specimen loaded, and the polarizer 6 and the analyzer 10 are made to turn to be aligned in the reference direction. Then the reference polarizer 8a is removed and a specimen is loaded with the crystal axis direction of the specimen (now assumed to be known; or if unknown the crystal axis direction shall be measured by appropriate means) set up in parallel with the reference direction, the setup direction being assumed to be the X-axis. Then the angle - 13 of the analyzer 10 is set successively at 00, 900, and 450 to measure the light intensity at each angle.
The following describes the actual measurement results obtained by means of the above-mentioned measuring apparatus.
A polycarbonate phase-contrast film was used as a specimen 8. The wavelength distribution characteristic (relative refractive index difference when the refractive index difference at a wavelength of 550 nm is 1) of the polycarbonate phase-contrast film is known as shown in Fig. 4 (Nitto Technical Information numbered 28, 105 (1980) by Yamamoto and others).
A graph of the actual measurement values of ellipticity p at wavelengths of 450 nm and 550 nm is shown in Fig. 5. The lateral axis of the graph is the azimuth of the incident linear polarized light, i.e., the rotatory angle of the polarizer 6. The mark + is the actual measurement value at the wavelength of 550 nm, while the mark x is the actual measurement value at the wavelength of 450 nm. Theoretical values directly calculated by means of the wavelength distribution characteristic in Fig. 4 are shown by the solid line (550 nm) and the broken line (450 nm).
The actual measurement values accordina to the conventional maximumminimum method is shown in Fig. 6.
- 14 The mark + indicates the actual measurement value at 550 nm, while the mark x indicates the actual measurement value at 450 nm.
The actual measurement values according to the conventional four-point method is shown in Fig. 7. The mark + indicates the actual measurement value at 550 nm, while the mark A indicates the actual measurement value at 450 nm.
The actual measurement values of the azimuth of ellipse at the wavelengths of 450 nm and 550 nm are shown in Fig. 8. The lateral axis of the graph is the azimuth of the incident linear polarized light, i.e., the rotatory angle of the polarizer 6. The mark + is the actual measurement value at the wavelength of 550 nm, and the mark A is the actual measurement value at the wavelength of 450 nm. The theoretical values directly calculated by means of the wavelength distribution characteristic in Fig. 4 are shown by the solid line (550 nm) and the broken line (450 nm).
The actual measurement values according to the conventional maximum-minimum method are shown in Fig. 9, while the actual measurement values according to the conventional four-point method are shown in F-Jg. 10.
Regarding the graphs in Figs. 5 to 1-0, the azimuth is fairly close to the theoretical value in any of the method of the present invention, the conventional maximum-minimum method, and the conventional f our-point method. However, regarding the ellipticity p, the conventional four-point method exhibits significant errors around the angles of 00, 900, and 1800 as obvious in Fig.
7. There are small errors in the method ol- the present invention and the conventional maximum-minimum method (refer to Figs. 5 and 6).
In order to estimate the measurement accuracy of ellipticity p, an average relative deviation 81 from the theoretical calculation value of ellipticity p is defined as follows:
E [Pex(E)i) - Pth( E)i)] 2 i 61 r P2(ei) i wherein p,, is the actual measurement value and p,h is the theoretical value.
According to the above equation, the resulting values of the average relative deviation 81 obtained in accordance with the method of the present invention, the conventional maximum-minimum method, and the conventional four-point method are shown in Table 1.
Table 1
1 Maximum- Invention Four-point minimum 450 nm 8.2% 10.1% 21.6% 550 nm 6.4% 5.2% 11.7% According to Table 1, the average relative deviation 6, is comparatively small in the cases of the method of the present invention and the conventional maximum-minimum method, however, the average relative deviation 81 is great in the case of the conventional four- point method, which substantiates the estimation on the graph.
The resulting values of average deviation 8. obtained from the elliptic azimuth are shown in Table 2.
Table 2
Maximum- Four-point minimum Invention 450 nm 1.07(deg.) 1.20(deg.) 0.97(deg.) 550 nm 3.65(deg.) 3.80(deg.) 3.75(deg.) According to Table 2, it is found that measurement was carried out with the same accuracy in any of the method of the present invention, the conventional maximum-minimum method, and the conventional four-point method.
As described above, by measuring light intensity at three rotatory positions of the analyzer and putting the obtained values to simple equations, ellipticity p and azimuth can be directly obtained. The obtained values are accurate enough in comparison with any conventional method, and the fact that measurement at only three rotatory positions is required results in reducing the time for measurement. When spectral intensity is measured with the use of a spectroscope, only one-time measurement can achieve measurement at several points of wavelength.
It is noted that the present invention is not limited to the abovementioned embodiment. For example, when a substance such as a liquid crystal having a polarization characteristic is selected to be a specimen, or when a light source whose polarization characteristic is already known is used, the polarizer for forming linear polarized light can be eliminated.
-.1 18- CLADNIS A polarized light measuring method using a polarized light measuring apparatus provided with an analyzer which is rotatable and capable of allowing only a polarized light component at a desired angle of light emitted from a specimen to pass therethrough and a photo- detector for detecting the intensity of light output from said analyzer, said polarized light measuring method comprising the steps of obtaining the intensity values Il, 12, and 13 of output light detected by means of said photo-detector at least at three rotatory positions of said analyzer, and calculating ellipticity p depending on the major length and the minor length of elliptic polarized light emitted from said specimen and azimuth of the major axis of the elliptic polarized light in accordance with the following two equations: tan 2 = (Il + 12 - 2-13)/(12 - Il) (Il + 12) [(Il + 12 - 2-1:3)2 + (12 - Il)2] 1/2 P)2 + -1)2jl/2 (11 + 12) + [(Il + 12 - 2-13 (12 -.L 2. A polarized light measuring apparatus comprising:
light source, polarizer for producing linear polarized light, an analyzer which is rotatable and capable of allowing only a polarized light component at a desired angle pass therethrough, a photo-detector for detecting the intensity of light output from said analyzer, and calculation means for calculating ellipticity p and azimuth angle depending on the major lencrth and the minor length of elliptic polarized light emitted from a specimen arranged between said polarizer and said analyzer based on a signal from said photo-detector representing each of intensity values 11, 12, and 13 of output light detected by means of said photo detector at least at three rotatory positions of said analyzer in accordance with the following two equations:
tan 2 = (Il + 12 - 2- 13)/(12 - Il) and (Il + 12) - [(Il + 12 - 2-13)2 + (12 - I l) 2] 1/2 (Il + 12) + [(Il + 12 - 2-13)2 + (12 - Il)2] 1/2
Claims (1)
- 3. A polarized light measuring apparatus as claimed in Claim 2, wherein aspectroscope is provided ahead of said photo-detector to enable simultaneous measurement of polarized light at several points of wavelength.-20 1 4. A polarized light measuring method subS-Lant-4allv as hereinbefore described with reference to Figure 'I Of Lhe accompanying drawings.5. A polarized light measuring apparatus substantially as hereinbefore described with reference to and as illustrated in Figure 3 of the accompanying drawings.
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP6330791A JPH04297835A (en) | 1991-03-27 | 1991-03-27 | Method for measuring polarization and polarization measuring device using it |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| GB9206473D0 GB9206473D0 (en) | 1992-05-06 |
| GB2254144A true GB2254144A (en) | 1992-09-30 |
Family
ID=13225505
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| GB9206473A Withdrawn GB2254144A (en) | 1991-03-27 | 1992-03-25 | Three-angle polarisation analyser |
Country Status (3)
| Country | Link |
|---|---|
| JP (1) | JPH04297835A (en) |
| DE (1) | DE4209537A1 (en) |
| GB (1) | GB2254144A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5606418A (en) * | 1993-04-01 | 1997-02-25 | High Yield Technology, Inc. | Quasi bright field particle sensor |
| US5764209A (en) * | 1992-03-16 | 1998-06-09 | Photon Dynamics, Inc. | Flat panel display inspection system |
| CN102914368A (en) * | 2011-08-05 | 2013-02-06 | 精工爱普生株式会社 | Polarization state measurement apparatus and polarization state measurement method |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2008216325A (en) * | 2007-02-28 | 2008-09-18 | Nitto Denko Corp | Compensating layer optical characteristic evaluation method and compensating layer optical characteristics evaluation system |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4030836A (en) * | 1975-10-28 | 1977-06-21 | The United States Of America As Represented By The Secretary Of The Air Force | Method for mapping surfaces with respect to ellipsometric parameters |
| EP0249235A2 (en) * | 1986-06-13 | 1987-12-16 | Nippon Kokan Kabushiki Kaisha | Film thickness-measuring apparatus using linearly polarized light |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS5663223A (en) * | 1979-10-26 | 1981-05-29 | Mizojiri Kogaku Kogyosho:Kk | Automatic ellipsometry system |
| JPH068755B2 (en) * | 1985-07-29 | 1994-02-02 | 日本電信電話株式会社 | Polarization degree measuring method and device |
-
1991
- 1991-03-27 JP JP6330791A patent/JPH04297835A/en active Pending
-
1992
- 1992-03-24 DE DE19924209537 patent/DE4209537A1/en not_active Withdrawn
- 1992-03-25 GB GB9206473A patent/GB2254144A/en not_active Withdrawn
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4030836A (en) * | 1975-10-28 | 1977-06-21 | The United States Of America As Represented By The Secretary Of The Air Force | Method for mapping surfaces with respect to ellipsometric parameters |
| EP0249235A2 (en) * | 1986-06-13 | 1987-12-16 | Nippon Kokan Kabushiki Kaisha | Film thickness-measuring apparatus using linearly polarized light |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5764209A (en) * | 1992-03-16 | 1998-06-09 | Photon Dynamics, Inc. | Flat panel display inspection system |
| US5606418A (en) * | 1993-04-01 | 1997-02-25 | High Yield Technology, Inc. | Quasi bright field particle sensor |
| CN102914368A (en) * | 2011-08-05 | 2013-02-06 | 精工爱普生株式会社 | Polarization state measurement apparatus and polarization state measurement method |
Also Published As
| Publication number | Publication date |
|---|---|
| DE4209537A1 (en) | 1992-10-01 |
| GB9206473D0 (en) | 1992-05-06 |
| JPH04297835A (en) | 1992-10-21 |
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