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Modified total intensity ratio methods for measuring cell gap of twisted nematic liquid crystal cells
Optics Communications 281 (2008) 4560–4565
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Modified total intensity ratio methods for measuring cell gap of twisted nematic liquid crystal cells Yu-Lung Lo *, Tsung-Chih Yu, Li-Shuan Su, Ya-Shan Huang Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan
a r t i c l e
i n f o
Article history: Received 23 November 2006 Received in revised form 26 May 2008 Accepted 4 June 2008
Keywords: Twisted nematic liquid crystal Cell gap Polarization modulation
a b s t r a c t This paper modifies the total intensity ratio method (TIRM) used to measure the cell gap of twisted nematic liquid crystal (TNLC) cells. Compared to the conventional TIRM in which a mechanical mechanism is used to physically rotate the polarizer, the modified TIRM methods presented in this study measure the total intensity ratio using a polarization rotation modulator. Two modified measurement methods are introduced. In the first, the saw-tooth signal applied to the electro-optic (EO) modulator is used as a reference signal in order to determine the polarization state of the measured signal. In the second method, a beam splitter and an additional quarter wave plate are added to the optical configuration. The quarter wave plate is adjusted such that a phase-matching condition is obtained between the reference and measured signals. The experimental results confirm that the modified TIRM approaches yield comparable accuracy to the conventional TIRM. Furthermore, in the proposed approaches, sufficient intensity signals to determine the cell gap can be obtained in just 2 s. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The characteristics of liquid crystal displays (LCDs) have been extensively investigated in the past literatures. The cell gap of an LCD panel has a fundamental influence on its response time. Hence, to improve the image quality, it is essential that the cell gap is accurately controlled during the LCD manufacturing process. Various cell gap measurement techniques have been proposed [1–7]. For example, the phase compensation method [1] uses a phase compensator and calculates the cell gap on the basis of the phase difference. However, this method does not readily lend itself to automation because repeated phase difference measurements are required and it is necessary to use two sources with different wavelengths to resolve the problem caused by multiple solutions. Wu and Xu [2] measured the reflection spectra of a cell at specific orientations to extract the cell gap and twist angle. By taking the ratio of reflected light intensity at two different polarizer angles, Zhu et al. [3] measured the cell gap of the reflective TNLC cell. The spectroscopic ellipsometry method [4] varies the angles of both the polarizer and the analyzer in order to locate the position of null transmission at specific wavelengths. Although this method has the advantage of a simple measurement setup, it cannot be applied to the measurement of small cell
* Corresponding author. Tel.: +886 6 2757575x62123; fax: +886 6 2352973. E-mail address: [email protected] (Y.-L. Lo). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.06.021
gaps. Duran et al. [5] measured cell thickness and twist angle by use of single wavelength light source for the analysis of the output polarization state. The spectral total intensity ratio method (TIRM) [6] uses a spectroscope with a halogen light source to record the transmittance in all the wavelength regions. This method obtains accurate measurements for small cell gaps, but is readily affected by external light sources and involves a complicated integration of the intensity ratio of the transmitted light in two arbitrary wavelength regions. Recently, the single-wavelength TIRM [7] has been proposed as a means of determining the cell gap by measuring the integrated intensity ratio of the transmitted light in two arbitrary polarizer angle regions. Compared with the spectral TIRM technique, the single-wavelength TIRM is more straightforward and provides precise results for both large and small cell gaps. However, this method involves rotating the polarizer using a step motor and is therefore a time consuming process. Furthermore, it is necessary to ensure an absolutely precise positioning of the light spot on the rotating polarizer to eliminate fluctuations in the detected intensity signal caused by alignment errors. Accordingly, the present study develops two modified TIRM approaches in which the rotating polarizer driven by a mechanical step motor is replaced by a polarization rotation modulator [8] based on two quarter-wave plates (QWP) and an E–O modulator driven by a saw-tooth driving signal. The experimental results confirm that the proposed methods not only have comparable accuracy of cell gap measurement to the conventional TIRM, but also reduce the measurement time.
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2. Basic theory of single-wavelength TIRM Fig. 1 presents a schematic illustration of the optical setup used in the conventional single-wavelength TIRM [7]. As shown, the polarizer is rotated from 0° to 180° while the rubbing direction of the TNLC cell and the rotational position of the analyzer are fixed at 0° and 45°, respectively. As described below, the cell gap is then calculated by processing the variation in the intensity signal produced by the photodetector as the polarizer is rotated. The cell gap is measured by integrating the total intensity ratio of the transmitted light in two arbitrary polarizer angle regions [7]. The transmittance, T, of the configuration shown in Fig. 1 is given by
2 cos u T ¼ ðcos c sin cÞM TNLC ð/Þ sin u
ð1Þ
where u is the polarizer angle, c is the analyzer angle, and MTNLC(/) is the Jones matrix of the twisted nematic LC (TNLC) cell. The optical transmittance of the TNLC cell can be expressed by a Jones matrix with elements defined in terms of the twist angle /, cell thickness d, and wavelength-dependent birefringence Dn of the LC material [9], i.e.,
" MTNLC ð/Þ ¼ Rð/Þ
X cos X i C sin / sinX X 2X
/ sinX X
X cos X þ i C sin 2X
# ð2Þ
where R(/) is the rotation matrix, given by
Rð/Þ ¼
cos /
sin /
ð3Þ
sin / cos / qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X ¼ /2 þ ðC=2Þ2
ð4Þ
in which
ð5Þ
In Eq. (5), h is the pre-tilt angle of the TLNC cell and ne and no are the extraordinary and ordinary refractive indices, respectively, of the LC material. As the polarizer is rotated, the intensity of the signal produced by the photodetector varies periodically, as illustrated in Fig. 2. The total intensity of the transmitted light as the polarizer rotates from 0° to 180° is given by
Z
Z
u2
T exp du 6¼
Z
180
Tdu
ð6Þ
u2
T cal du
ð7Þ
u1
where Texp[Tcal] is the measured [calculated] transmitted light intensity. However, as shown in Eq. (8), the measured value of the total intensity ratio, Rt, is in good agreement with the calculated value since the absorption rate is a constant [7].
R u4
ne ffi no ; Dn ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h i 2 ne 2 1 þ ðno Þ 1 sin h
Itotal ¼
However, the absolute value of the measured total intensity may be different from the calculated value because of the absorption by the optical elements and the effects of external light. In other words, the measured and calculated transmitted light intensities are related as follows:
u1
and
2pdDn C¼ ; k
Fig. 2. Periodic variation of measured intensity signal as rotation angle of polarizer increases from 0° to 360°.
u
T exp du
u1
T exp du
Rt ¼ R u32
R u4 u
T cal du
u1
T cal du
¼ R u32
ð8Þ
Therefore, as the experimental Rt is equal to the calculated Rt, the theoretical cell gap corresponding to the calculated Rt could be considered as the cell gap of the measured TNLC cell. However, the single-wavelength TIRM described above has a number of disadvantages, principal of which is the requirement to accurately align the light spot on the center of the rotating polarizer. If great care is not taken to ensure an accurate alignment, the intensity of the photodetector signal, which is used to calculate the gap size, will fluctuate, and hence the measurement performance of the optical configuration will be reduced.
0
3. Modified optical configurations for TIRM
Rotating Polarizer (0° → 180° )
TN cell ( 0° )
Analyzer (45°)
He-Ne Laser λ=632.8nm
y
x z Fig. 1. Schematic illustration of conventional TIRM setup.
Photo Detector
To minimize the effects of alignment errors while simultaneously reducing the measurement time, this study proposes two modified TIRM configurations for measuring the cell gap of TNLC cells. In both cases, the mechanical mechanism used in the conventional TIRM to rotate the polarizer is replaced by a polarization rotation modulation system incorporating two QWPs and an EO modulator. In the first modified optical setup, shown schematically in Fig. 3, a saw-tooth signal produced by the function generator is used to drive the EO modulator. In the proposed setup, the direction of the laser light propagation is specified as the +z-direction, while the horizontal direction and the vertical direction are specified as the x- and y-directions, respectively. As shown in Fig. 3, the polarization rotation modulator comprises QWP #1 fixed at 0°, an E–O
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Polarization Rotation Modulator Polarizer
(0°)
QWP #1
(45°)
He-Ne Laser λ=632.8nm
EO Modulator
Y
Function Generator
LC sample
QWP #2
Analyzer (90°)
P.D.
PC with DAQ card
X Z Fig. 3. Schematic illustration of first modified TIRM setup.
modulator fixed at 45°, and QWP #2 fixed at 90°. The E–O modulator is driven by a saw-tooth wave signal with an angular frequency of x = 2p/T (T is the signal period). When the laser light passes through this polarization rotation modulator, a sine wave signal is output from the photodetector. The electric field, Et, of the light incident on the photo-detector can be expressed as
Et ¼ Að90 Þ RðaÞ MTNLC ð/Þ RðaÞ PRðxtÞ Pð0 Þ Einput 0 0 cos a sin a cos a sin a MTNLC ð/Þ ¼ 0 1 sin a cos a sin a cos a ! cosðx2tÞ sinðx2tÞ 1 sinðx2tÞ cosðx2tÞ 0 ð9Þ where PR(xt) is the Jones matrix of the polarization rotation modulator, x is the angular frequency of the saw-tooth driving signal, R(a) and R(a) are the rotation matrices, and a is the rubbing direction of the TNLC cell. The electric field can be derived as
Et ¼
1 ½ðX /Þ 2X C ½cosð2xt 8X
sinð x2t þ / þ XÞ þ ðX /Þ sinðx2t / þ XÞ 2a / þ XÞ cosðxt 2
!
þ 2a þ / þ XÞ ð10Þ
The intensity of the light received at the photodetector can be expressed as
It ¼ jEt j2
ð11Þ
From Eq. (11), it can be inferred that the intensity of the light incident on the photodetector varies periodically as a function of time when the polarization rotation modulator is driven by a saw-tooth wave signal with an angular frequency of x. Specifying Dn, a and the twist angle of the TNLC cell as 0.099, 45° and 90°, respectively, and assuming a driving signal frequency of 1 kHz. Fig. 4 presents the simulated variation of the intensity signal over time for cell gaps of 3.7, 3.9 and 4.2 lm, respectively. It is observed that both the phase and the amplitude of the intensity signal are affected by the cell gap of the TNLC cell. In the conventional TIRM, integrating regions of the detected signal were determined by the angles of the rotating polarizer. However, the corresponding polarizer angles could not be known from the detected signal by using EO modulator. The time regions were therefore used as the integrating regions instead of the angles of the polarizer in the proposed method. Therefore, the intensity ratio defined in Eq. (8) should be written as
Fig. 4. Variation of measured intensity signal over time for different cell gaps.
R t4 t
It dt
t1
It dt
Rt ¼ R t32
ð12Þ
The detected signals obtained with and without the TNLC cell, respectively, are recorded by photo-detector as illustrated in Fig. 5. The trough of the detected signal without TNLC cell is considered as the time origin in the experiment. Deciding time origin, a decision can be made as to the time regions over which the intensity of the measured signal should be integrated in order to calculate the cell gap using the method described in Section 2. As mentioned above, the detected signal without TNLC in the system should be acquired for the set of time origin. This means the detected signals without and with TNLC cell have to be acquired sequentially in each measurement in the configuration of Fig. 3. Accordingly, the second TIRM configuration is developed for simultaneously acquiring the detected signals without and with TNLC cell in which the optical setup of Fig. 3 is extended to the configuration shown in Fig. 6. As shown in Fig. 6, a beam splitter is inserted after the QWP #2. The light transmitted by the beam splitter follows the same optical elements as that shown in Fig. 3. However, the reflected light ray passes through a quarter-wave plate (QWP #3), a second analyzer (Analyzer 2) set at 90° and is incident on a second photodetector (PD #2). The output signal from P.D. #2 is then supplied to the original lock-in amplifier to serve as the reference signal. Note that the function of QWP #3 is to provide an adjustment facility with which to tune the phase of the reference
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3 0.42
The measured signal without TNLC cell.
2.5
The measured signal with TNLC cell.
2
X: 0.3663 Y: 0.4225
Total intensity ratio
0.4
1.5
Intensity
X: 0.2603 Y: 0.4225
0.41
1 0.5 0
0.39 0.38 0.37 0.36 0.35
-0.5
0.34 0.33
-1 The saw-tooth driving signal -1.5
0
0
0.2
0.4
0.6
0.8
1 1.2 Time (s)
1.4
1.6
1.8
0.1
0.15
0.2
0.25 0.3 dΔ n [ μ m]
signal to that of the measured signal when the TNLC cell is not inserted, i.e., QWP #3 compensates for the non-linear effect of the beam splitter [10]. The electric field of the light incident on P.D. #2 is given by
Er ¼ A2 ð90 Þ Q:W:ðeÞ PRðxtÞ Pð0 Þ Einput ! p 0 0 cos e sin e cos e sin e ei4 0 ¼ p i 0 1 sin e cos e sin e cos e 0 e4 ! x t x t cosð 2 Þ sinð 2 Þ 1 sinðx2tÞ cosðx2tÞ 0 ð13Þ where e is the principal axis angle of QWP #3. Furthermore, the intensity of the light incident on P.D. #2 is expressed as:
1 1 þ cosð2eÞ cosðxt 2eÞ 2 4
0.45
0.5
ð14Þ
From Eq. (14), it is apparent that the phase shift of the reference signal is dependent on the angle of rotation of QWP #3. Therefore, phase matching between the reference signal and the measured signal without TNLC can be obtained by rotating the quarter wave plate. In both optical setups described above, the time origin can be determined by the trough of the reference signal (without TNLC). R 0:4T R 0:6T Fig. 7 shows the total intensity ratio Rt ¼ ð 0:2T It dtÞ=ð 0 It dtÞ as a function of Dn d from 90° TNLC cell with the entrance director angle a of 45°. As can be seen in Fig. 7, the Rt value of 0.4225 corresponds to two extracted d Dn of 0.2063 lm and 0.3663 lm when the measured range of d Dn is from 0 to 0.5 lm. This ambiguity can be solved by changing the integrating regions of Rt. For R 0:4T R 0:5T example, in Fig. 8 while the case that Rt ¼ ð 0:1T It dtÞ=ð 0 It dtÞ, the ratio value of 0.6812 corresponds to two d Dn values of 0.3405 lm and 0.3663 lm. As a result, if the measured values of total intensity ratio in the two sets of integrating ranges of (0–0.6T, 0.2–0.4T) and (0–0.5T, 0.1–0.4T) are 0.4225 and 0.6812,
Polarization Rotation Modulator
( 0° )
QWP #1
L.C. Analyzer sample (90°)
(45°)
EO Modulator
QWP 2
1.
B.S. P.D.
QWP 3 Analyzer
2.
(90°)
Function Generator P.D. 2
Y
0.4
Fig. 7. Total intensity ratio of two integrating time ranges, (0–0.6T) and (0.2–0.4T), for a 90° TNLC cell under the condition of a = 45°.
Polarizer
He-Ne Laser λ=632.8nm
0.35
x 10
Fig. 5. Variation of measured intensity signals with and without inserted TNLC cell and saw-tooth wave reference signal.
It2 ¼ jEt2 j2 ¼
0.05
2 -3
Lock-in Amplifier
X PC
Z Fig. 6. Schematic illustration of second modified TIRM setup.
1
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Y.-L. Lo et al. / Optics Communications 281 (2008) 4560–4565 0.69 0.68 X: 0.3405 Y: 0.6812
X: 0.3663 Y: 0.6812
Total intensity ratio
0.67 0.66 0.65 0.64 0.63 0.62 0.61
0
0.05
0.1
0.15
0.2
0.25 0.3 dΔ n [ μm]
0.35
0.4
0.45
0.5
Fig. 8. Total intensity ratio of two integrating time ranges, (0–0.5T) and (0.1–0.4T), for a 90° TNLC cell under condition of a = 45°.
respectively, the retardation value of the sample can therefore be considered as 0.3663 lm. Furthermore, if we extend the d Dn range as illustrated in Fig. 9, one measured Rt may correspond to two or more d Dn values. Nevertheless, the variations of Rt in the two sets of integrating ranges in Fig. 9 have apparent difference. Therefore the ambiguity in extracting the thickness of TNLC can be solved by changing the integrating ranges as mentioned above even the thickness range is extended. 4. Experimental setup and results To verify the accuracy of the modified TIRM approaches, an experimental study was performed using a empty cell (EHC .Co. Ltd) with a twist angle of 90°, a pre-tilt angle of 1°, and cell gap of 10 lm. The empty cell filled with E7 liquid crystal (Merck Co.), was used as sample A for the measurement. Another TNLC cell with no = 1.483, ne = 1.569 at 632.8 nm wavelength was also used as sample B in the test. The designed values of twist angle / = 90°, cell gap d = 3.7 lm, and pre-tilt angle h ffi 4° in sample B were obtained from the Chi-Mei Optoelectronics Co., Taiwan. The schematic diagram of the system configurations are shown in Figs. 3 and 6.
The light source was a frequency stabilized He–Ne laser (Model: SIOS SL 02/2) operating at a wavelength of 632.8 nm. The EO modulator (Conoptics INC. 370) was driven by a saw-tooth wave signal with a frequency of 1 kHz. The detected signals from photo-detectors were acquired by DAQ card. Because of the high modulation frequency of the proposed method, each measurement can be accomplished in 2 s by the second modified configuration. To verify the repeatability and stability of the proposed approaches, the cell gaps of the TNLC samples were measured six times in every 10 min using each optical setup. The experimental results using the first optical configuration are presented in Table 1. It is found that this TIRM measurement method have deviations of ±0.027 lm and ±0.016 lm for sample A and B, respectively. The experimental results obtained by the second optical setup are presented in Table 2. We compared the results with the cell gap values measured by Stokes parameters method [11] and interferometric method as shown in Table 3. When actuating the E–O modulator using a driving frequency of 1 kHz, the electrical signal from the function generator and the photoelectric signal from the photodetector are approximately in-phase. Therefore, there is no more than a slight difference in the experimental results presented in Tables 1 and 2. Though the optical setup of the first measurement configuration is more straightforward than that of the second one, the second one is highly recommended for the high frequency dynamical measurement. The measurement error of the proposed method can be attributed to slight misalignments in the optical setup and manufacturing flaws in the optical components. Hence the more accurate alignment of the optical system, the more precise value of LC parameter would be achieved. In experiment, the twist angle and the pretilt angle were assumed to be specific values. As can be seen in Fig. 10, the deviation of pretilt angle has little influence on the measured results. However, the deviation of twist angle would have more apparent influence on the measurement error than that of pretilt angle. Fig. 11 shows there is slight deviation between the two Rt-d Dn curves Table 1 Experimental results obtained for cell gap using first modified system Sample
A B
Time 1
2
3
4
5
6
Average cell gap (lm)
10.069 3.735
10.124 3.685
10.139 3.723
10.134 3.727
10.075 3.699
10.093 3.725
10.10 ± 0.027 3.72 ± 0.016
0.6
Table 2 Experimental results obtained for cell gap using second modified system
0.5
Sample
2
3
4
5
6
Average cell gap (lm)
10.139 3.717
10.088 3.735
10.068 3.729
10.096 3.741
10.121 3.713
10.113 3.683
10.10 ± 0.020 3.72 ± 0.015
Rt
0.4
Time 1
A B
0.3
0.2
Table 3 Comparison of measured cell gap data
0.1 0
0.5
1
1.5
2
Sample
Designed cell gap value (lm)
Stokes parameters method (lm)
Interferometric method (lm)
Proposed method (lm)
A B
10 3.7
9.70 3.61
9.98 –
10.10 3.72
2.5
dΔ n [μm]
Fig. 9. Total intensity ratio of two sets of integrating time ranges, (dash line: 0–0.5T, 0.1–0.4T) and (solid line: 0–0.5T, 0.1–0.4T).
Y.-L. Lo et al. / Optics Communications 281 (2008) 4560–4565
to the deviation of cell gap about ±0.1 lm for sample A. In most LC display application, however, the retardation value of LC panel is usually the smaller than that of sample A. As for sample B, the retardation value is in the range of 0.35–0.45 lm. The corresponding cell gap deviation is about ±0.05 lm for sample B as the inaccuracy of the twist angle is at the level of ±1°.Therefore, the proposed method has better performance for small cell gap measurement than large one.
0.65 0.6 0.55
Rt
0.5 0.45
5. Conclusions
0.4 0.35 0.3 0.25 0
0.2
0.4
0.6
0.8
1 1.2 dΔ n [μm]
1.4
1.6
1.8
2
Fig. 10. Total intensity ratio of two different pretilt angles, (dot: 8.4°, solid line: 3.4°).
0.65 0.6 0.55
This study has presented and verified the modified TIRM optical configurations for TNLC cell gap measurement. Both configurations replace the mechanical mechanism used to rotate the polarizer in the conventional TIRM with a polarization rotation modulation system incorporating two QWPs and an E–O modulator. In the experimental results, the cell gap measurement deviation about 0.015 lm is obtained. Also, in our investigation, the proposed system has better measurement ability for the TNLC cell with small retardation than with large retardation. Furthermore, compared to the conventional TIRM, which requires several seconds to measure the cell gap, the modified TIRM techniques presented in this paper need only 2 s to acquire the signal and derive the cell gap value. The results of this study indicate that the modified TIRM methods have the potential to carry out on-line TNLC cell gap measurement in the industrial manufacturing of LCDs. Acknowledgements
0.5
Rt
4565
0.45
The current authors would like to acknowledge the financial support of Chi-Mei Optoelectonics (CMO) and also the assistance of Dr. T.S. Lin and Dr. I.L. Ho in the CMO without whom this study could not have been achieved. This research is also partially supported by the National Science Council, Taiwan, under grant NSC96-2628-E-006-005-MY3.
0.4 0.35 0.3 0.25
References 0
0.5
1
1.5
2
2.5
dΔ n [μm]
Fig. 11. Total intensity ratio of two different twist angle, (dash line: 89°, solid line: 90°).
with twist angles of 90° and 89°. As can be seen in the figure, the larger value of retardation is, the more apparent deviation can be observed. The maximum deviation of d Dn which is about ±0.025 lm in the large retardation ranges of 2–2.5 lm corresponds
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
A. Lien, H. Takano, J. Appl. Phys. 69 (1991) 1304. S.T. Wu, G. Xu, IEEE Trans. Electron. Dev. 47 (2000) 2290. X. Zhu, W.K. Choi, S.T. Wu, IEEE Trans. Electron. Dev. 49 (2002) 1863. S.T. Tang, H.S. Kwok, J. Appl. Phys. 89 (2001) 80. V. Duran, J. Lancis, E. Tajahuerce, J. Appl. Phys. 97 (2005) 043101. J.S. Gwag, S.H. Lee, K.Y. Han, J.C. Kim, T.H. Yoon, J. Appl. Phys. 41 (2002) L79. J.S. Gwag, K.H. Park, G.D. Lee, T.H. Yoon, J.C. Kim, J. Appl. Phys. 43 (2004) L30. Y.L. Lo, T.C. Yu, Opt. Commun. 259 (2006) 40. P. Yeh, C. Gu, Optics of Liquid Crystal Displays, 121, Wiley, New York, 2000. Y.L. Lo, J.F. Lin, S.Y. Lee, Appl. Opt. 43 (2004) 6248. Y. Zhou, Z. He, S. Sato, J. Appl. Phys. 36 (1997) 2760.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Modified total intensity ratio methods for measuring cell gap of twisted nematic liquid crystal cells Yu-Lung Lo *, Tsung-Chih Yu, Li-Shuan Su, Ya-Shan Huang Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan
a r t i c l e
i n f o
Article history: Received 23 November 2006 Received in revised form 26 May 2008 Accepted 4 June 2008
Keywords: Twisted nematic liquid crystal Cell gap Polarization modulation
a b s t r a c t This paper modifies the total intensity ratio method (TIRM) used to measure the cell gap of twisted nematic liquid crystal (TNLC) cells. Compared to the conventional TIRM in which a mechanical mechanism is used to physically rotate the polarizer, the modified TIRM methods presented in this study measure the total intensity ratio using a polarization rotation modulator. Two modified measurement methods are introduced. In the first, the saw-tooth signal applied to the electro-optic (EO) modulator is used as a reference signal in order to determine the polarization state of the measured signal. In the second method, a beam splitter and an additional quarter wave plate are added to the optical configuration. The quarter wave plate is adjusted such that a phase-matching condition is obtained between the reference and measured signals. The experimental results confirm that the modified TIRM approaches yield comparable accuracy to the conventional TIRM. Furthermore, in the proposed approaches, sufficient intensity signals to determine the cell gap can be obtained in just 2 s. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The characteristics of liquid crystal displays (LCDs) have been extensively investigated in the past literatures. The cell gap of an LCD panel has a fundamental influence on its response time. Hence, to improve the image quality, it is essential that the cell gap is accurately controlled during the LCD manufacturing process. Various cell gap measurement techniques have been proposed [1–7]. For example, the phase compensation method [1] uses a phase compensator and calculates the cell gap on the basis of the phase difference. However, this method does not readily lend itself to automation because repeated phase difference measurements are required and it is necessary to use two sources with different wavelengths to resolve the problem caused by multiple solutions. Wu and Xu [2] measured the reflection spectra of a cell at specific orientations to extract the cell gap and twist angle. By taking the ratio of reflected light intensity at two different polarizer angles, Zhu et al. [3] measured the cell gap of the reflective TNLC cell. The spectroscopic ellipsometry method [4] varies the angles of both the polarizer and the analyzer in order to locate the position of null transmission at specific wavelengths. Although this method has the advantage of a simple measurement setup, it cannot be applied to the measurement of small cell
* Corresponding author. Tel.: +886 6 2757575x62123; fax: +886 6 2352973. E-mail address: [email protected] (Y.-L. Lo). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.06.021
gaps. Duran et al. [5] measured cell thickness and twist angle by use of single wavelength light source for the analysis of the output polarization state. The spectral total intensity ratio method (TIRM) [6] uses a spectroscope with a halogen light source to record the transmittance in all the wavelength regions. This method obtains accurate measurements for small cell gaps, but is readily affected by external light sources and involves a complicated integration of the intensity ratio of the transmitted light in two arbitrary wavelength regions. Recently, the single-wavelength TIRM [7] has been proposed as a means of determining the cell gap by measuring the integrated intensity ratio of the transmitted light in two arbitrary polarizer angle regions. Compared with the spectral TIRM technique, the single-wavelength TIRM is more straightforward and provides precise results for both large and small cell gaps. However, this method involves rotating the polarizer using a step motor and is therefore a time consuming process. Furthermore, it is necessary to ensure an absolutely precise positioning of the light spot on the rotating polarizer to eliminate fluctuations in the detected intensity signal caused by alignment errors. Accordingly, the present study develops two modified TIRM approaches in which the rotating polarizer driven by a mechanical step motor is replaced by a polarization rotation modulator [8] based on two quarter-wave plates (QWP) and an E–O modulator driven by a saw-tooth driving signal. The experimental results confirm that the proposed methods not only have comparable accuracy of cell gap measurement to the conventional TIRM, but also reduce the measurement time.
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2. Basic theory of single-wavelength TIRM Fig. 1 presents a schematic illustration of the optical setup used in the conventional single-wavelength TIRM [7]. As shown, the polarizer is rotated from 0° to 180° while the rubbing direction of the TNLC cell and the rotational position of the analyzer are fixed at 0° and 45°, respectively. As described below, the cell gap is then calculated by processing the variation in the intensity signal produced by the photodetector as the polarizer is rotated. The cell gap is measured by integrating the total intensity ratio of the transmitted light in two arbitrary polarizer angle regions [7]. The transmittance, T, of the configuration shown in Fig. 1 is given by
2 cos u T ¼ ðcos c sin cÞM TNLC ð/Þ sin u
ð1Þ
where u is the polarizer angle, c is the analyzer angle, and MTNLC(/) is the Jones matrix of the twisted nematic LC (TNLC) cell. The optical transmittance of the TNLC cell can be expressed by a Jones matrix with elements defined in terms of the twist angle /, cell thickness d, and wavelength-dependent birefringence Dn of the LC material [9], i.e.,
" MTNLC ð/Þ ¼ Rð/Þ
X cos X i C sin / sinX X 2X
/ sinX X
X cos X þ i C sin 2X
# ð2Þ
where R(/) is the rotation matrix, given by
Rð/Þ ¼
cos /
sin /
ð3Þ
sin / cos / qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X ¼ /2 þ ðC=2Þ2
ð4Þ
in which
ð5Þ
In Eq. (5), h is the pre-tilt angle of the TLNC cell and ne and no are the extraordinary and ordinary refractive indices, respectively, of the LC material. As the polarizer is rotated, the intensity of the signal produced by the photodetector varies periodically, as illustrated in Fig. 2. The total intensity of the transmitted light as the polarizer rotates from 0° to 180° is given by
Z
Z
u2
T exp du 6¼
Z
180
Tdu
ð6Þ
u2
T cal du
ð7Þ
u1
where Texp[Tcal] is the measured [calculated] transmitted light intensity. However, as shown in Eq. (8), the measured value of the total intensity ratio, Rt, is in good agreement with the calculated value since the absorption rate is a constant [7].
R u4
ne ffi no ; Dn ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h i 2 ne 2 1 þ ðno Þ 1 sin h
Itotal ¼
However, the absolute value of the measured total intensity may be different from the calculated value because of the absorption by the optical elements and the effects of external light. In other words, the measured and calculated transmitted light intensities are related as follows:
u1
and
2pdDn C¼ ; k
Fig. 2. Periodic variation of measured intensity signal as rotation angle of polarizer increases from 0° to 360°.
u
T exp du
u1
T exp du
Rt ¼ R u32
R u4 u
T cal du
u1
T cal du
¼ R u32
ð8Þ
Therefore, as the experimental Rt is equal to the calculated Rt, the theoretical cell gap corresponding to the calculated Rt could be considered as the cell gap of the measured TNLC cell. However, the single-wavelength TIRM described above has a number of disadvantages, principal of which is the requirement to accurately align the light spot on the center of the rotating polarizer. If great care is not taken to ensure an accurate alignment, the intensity of the photodetector signal, which is used to calculate the gap size, will fluctuate, and hence the measurement performance of the optical configuration will be reduced.
0
3. Modified optical configurations for TIRM
Rotating Polarizer (0° → 180° )
TN cell ( 0° )
Analyzer (45°)
He-Ne Laser λ=632.8nm
y
x z Fig. 1. Schematic illustration of conventional TIRM setup.
Photo Detector
To minimize the effects of alignment errors while simultaneously reducing the measurement time, this study proposes two modified TIRM configurations for measuring the cell gap of TNLC cells. In both cases, the mechanical mechanism used in the conventional TIRM to rotate the polarizer is replaced by a polarization rotation modulation system incorporating two QWPs and an EO modulator. In the first modified optical setup, shown schematically in Fig. 3, a saw-tooth signal produced by the function generator is used to drive the EO modulator. In the proposed setup, the direction of the laser light propagation is specified as the +z-direction, while the horizontal direction and the vertical direction are specified as the x- and y-directions, respectively. As shown in Fig. 3, the polarization rotation modulator comprises QWP #1 fixed at 0°, an E–O
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Y.-L. Lo et al. / Optics Communications 281 (2008) 4560–4565
Polarization Rotation Modulator Polarizer
(0°)
QWP #1
(45°)
He-Ne Laser λ=632.8nm
EO Modulator
Y
Function Generator
LC sample
QWP #2
Analyzer (90°)
P.D.
PC with DAQ card
X Z Fig. 3. Schematic illustration of first modified TIRM setup.
modulator fixed at 45°, and QWP #2 fixed at 90°. The E–O modulator is driven by a saw-tooth wave signal with an angular frequency of x = 2p/T (T is the signal period). When the laser light passes through this polarization rotation modulator, a sine wave signal is output from the photodetector. The electric field, Et, of the light incident on the photo-detector can be expressed as
Et ¼ Að90 Þ RðaÞ MTNLC ð/Þ RðaÞ PRðxtÞ Pð0 Þ Einput 0 0 cos a sin a cos a sin a MTNLC ð/Þ ¼ 0 1 sin a cos a sin a cos a ! cosðx2tÞ sinðx2tÞ 1 sinðx2tÞ cosðx2tÞ 0 ð9Þ where PR(xt) is the Jones matrix of the polarization rotation modulator, x is the angular frequency of the saw-tooth driving signal, R(a) and R(a) are the rotation matrices, and a is the rubbing direction of the TNLC cell. The electric field can be derived as
Et ¼
1 ½ðX /Þ 2X C ½cosð2xt 8X
sinð x2t þ / þ XÞ þ ðX /Þ sinðx2t / þ XÞ 2a / þ XÞ cosðxt 2
!
þ 2a þ / þ XÞ ð10Þ
The intensity of the light received at the photodetector can be expressed as
It ¼ jEt j2
ð11Þ
From Eq. (11), it can be inferred that the intensity of the light incident on the photodetector varies periodically as a function of time when the polarization rotation modulator is driven by a saw-tooth wave signal with an angular frequency of x. Specifying Dn, a and the twist angle of the TNLC cell as 0.099, 45° and 90°, respectively, and assuming a driving signal frequency of 1 kHz. Fig. 4 presents the simulated variation of the intensity signal over time for cell gaps of 3.7, 3.9 and 4.2 lm, respectively. It is observed that both the phase and the amplitude of the intensity signal are affected by the cell gap of the TNLC cell. In the conventional TIRM, integrating regions of the detected signal were determined by the angles of the rotating polarizer. However, the corresponding polarizer angles could not be known from the detected signal by using EO modulator. The time regions were therefore used as the integrating regions instead of the angles of the polarizer in the proposed method. Therefore, the intensity ratio defined in Eq. (8) should be written as
Fig. 4. Variation of measured intensity signal over time for different cell gaps.
R t4 t
It dt
t1
It dt
Rt ¼ R t32
ð12Þ
The detected signals obtained with and without the TNLC cell, respectively, are recorded by photo-detector as illustrated in Fig. 5. The trough of the detected signal without TNLC cell is considered as the time origin in the experiment. Deciding time origin, a decision can be made as to the time regions over which the intensity of the measured signal should be integrated in order to calculate the cell gap using the method described in Section 2. As mentioned above, the detected signal without TNLC in the system should be acquired for the set of time origin. This means the detected signals without and with TNLC cell have to be acquired sequentially in each measurement in the configuration of Fig. 3. Accordingly, the second TIRM configuration is developed for simultaneously acquiring the detected signals without and with TNLC cell in which the optical setup of Fig. 3 is extended to the configuration shown in Fig. 6. As shown in Fig. 6, a beam splitter is inserted after the QWP #2. The light transmitted by the beam splitter follows the same optical elements as that shown in Fig. 3. However, the reflected light ray passes through a quarter-wave plate (QWP #3), a second analyzer (Analyzer 2) set at 90° and is incident on a second photodetector (PD #2). The output signal from P.D. #2 is then supplied to the original lock-in amplifier to serve as the reference signal. Note that the function of QWP #3 is to provide an adjustment facility with which to tune the phase of the reference
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Y.-L. Lo et al. / Optics Communications 281 (2008) 4560–4565
3 0.42
The measured signal without TNLC cell.
2.5
The measured signal with TNLC cell.
2
X: 0.3663 Y: 0.4225
Total intensity ratio
0.4
1.5
Intensity
X: 0.2603 Y: 0.4225
0.41
1 0.5 0
0.39 0.38 0.37 0.36 0.35
-0.5
0.34 0.33
-1 The saw-tooth driving signal -1.5
0
0
0.2
0.4
0.6
0.8
1 1.2 Time (s)
1.4
1.6
1.8
0.1
0.15
0.2
0.25 0.3 dΔ n [ μ m]
signal to that of the measured signal when the TNLC cell is not inserted, i.e., QWP #3 compensates for the non-linear effect of the beam splitter [10]. The electric field of the light incident on P.D. #2 is given by
Er ¼ A2 ð90 Þ Q:W:ðeÞ PRðxtÞ Pð0 Þ Einput ! p 0 0 cos e sin e cos e sin e ei4 0 ¼ p i 0 1 sin e cos e sin e cos e 0 e4 ! x t x t cosð 2 Þ sinð 2 Þ 1 sinðx2tÞ cosðx2tÞ 0 ð13Þ where e is the principal axis angle of QWP #3. Furthermore, the intensity of the light incident on P.D. #2 is expressed as:
1 1 þ cosð2eÞ cosðxt 2eÞ 2 4
0.45
0.5
ð14Þ
From Eq. (14), it is apparent that the phase shift of the reference signal is dependent on the angle of rotation of QWP #3. Therefore, phase matching between the reference signal and the measured signal without TNLC can be obtained by rotating the quarter wave plate. In both optical setups described above, the time origin can be determined by the trough of the reference signal (without TNLC). R 0:4T R 0:6T Fig. 7 shows the total intensity ratio Rt ¼ ð 0:2T It dtÞ=ð 0 It dtÞ as a function of Dn d from 90° TNLC cell with the entrance director angle a of 45°. As can be seen in Fig. 7, the Rt value of 0.4225 corresponds to two extracted d Dn of 0.2063 lm and 0.3663 lm when the measured range of d Dn is from 0 to 0.5 lm. This ambiguity can be solved by changing the integrating regions of Rt. For R 0:4T R 0:5T example, in Fig. 8 while the case that Rt ¼ ð 0:1T It dtÞ=ð 0 It dtÞ, the ratio value of 0.6812 corresponds to two d Dn values of 0.3405 lm and 0.3663 lm. As a result, if the measured values of total intensity ratio in the two sets of integrating ranges of (0–0.6T, 0.2–0.4T) and (0–0.5T, 0.1–0.4T) are 0.4225 and 0.6812,
Polarization Rotation Modulator
( 0° )
QWP #1
L.C. Analyzer sample (90°)
(45°)
EO Modulator
QWP 2
1.
B.S. P.D.
QWP 3 Analyzer
2.
(90°)
Function Generator P.D. 2
Y
0.4
Fig. 7. Total intensity ratio of two integrating time ranges, (0–0.6T) and (0.2–0.4T), for a 90° TNLC cell under the condition of a = 45°.
Polarizer
He-Ne Laser λ=632.8nm
0.35
x 10
Fig. 5. Variation of measured intensity signals with and without inserted TNLC cell and saw-tooth wave reference signal.
It2 ¼ jEt2 j2 ¼
0.05
2 -3
Lock-in Amplifier
X PC
Z Fig. 6. Schematic illustration of second modified TIRM setup.
1
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Y.-L. Lo et al. / Optics Communications 281 (2008) 4560–4565 0.69 0.68 X: 0.3405 Y: 0.6812
X: 0.3663 Y: 0.6812
Total intensity ratio
0.67 0.66 0.65 0.64 0.63 0.62 0.61
0
0.05
0.1
0.15
0.2
0.25 0.3 dΔ n [ μm]
0.35
0.4
0.45
0.5
Fig. 8. Total intensity ratio of two integrating time ranges, (0–0.5T) and (0.1–0.4T), for a 90° TNLC cell under condition of a = 45°.
respectively, the retardation value of the sample can therefore be considered as 0.3663 lm. Furthermore, if we extend the d Dn range as illustrated in Fig. 9, one measured Rt may correspond to two or more d Dn values. Nevertheless, the variations of Rt in the two sets of integrating ranges in Fig. 9 have apparent difference. Therefore the ambiguity in extracting the thickness of TNLC can be solved by changing the integrating ranges as mentioned above even the thickness range is extended. 4. Experimental setup and results To verify the accuracy of the modified TIRM approaches, an experimental study was performed using a empty cell (EHC .Co. Ltd) with a twist angle of 90°, a pre-tilt angle of 1°, and cell gap of 10 lm. The empty cell filled with E7 liquid crystal (Merck Co.), was used as sample A for the measurement. Another TNLC cell with no = 1.483, ne = 1.569 at 632.8 nm wavelength was also used as sample B in the test. The designed values of twist angle / = 90°, cell gap d = 3.7 lm, and pre-tilt angle h ffi 4° in sample B were obtained from the Chi-Mei Optoelectronics Co., Taiwan. The schematic diagram of the system configurations are shown in Figs. 3 and 6.
The light source was a frequency stabilized He–Ne laser (Model: SIOS SL 02/2) operating at a wavelength of 632.8 nm. The EO modulator (Conoptics INC. 370) was driven by a saw-tooth wave signal with a frequency of 1 kHz. The detected signals from photo-detectors were acquired by DAQ card. Because of the high modulation frequency of the proposed method, each measurement can be accomplished in 2 s by the second modified configuration. To verify the repeatability and stability of the proposed approaches, the cell gaps of the TNLC samples were measured six times in every 10 min using each optical setup. The experimental results using the first optical configuration are presented in Table 1. It is found that this TIRM measurement method have deviations of ±0.027 lm and ±0.016 lm for sample A and B, respectively. The experimental results obtained by the second optical setup are presented in Table 2. We compared the results with the cell gap values measured by Stokes parameters method [11] and interferometric method as shown in Table 3. When actuating the E–O modulator using a driving frequency of 1 kHz, the electrical signal from the function generator and the photoelectric signal from the photodetector are approximately in-phase. Therefore, there is no more than a slight difference in the experimental results presented in Tables 1 and 2. Though the optical setup of the first measurement configuration is more straightforward than that of the second one, the second one is highly recommended for the high frequency dynamical measurement. The measurement error of the proposed method can be attributed to slight misalignments in the optical setup and manufacturing flaws in the optical components. Hence the more accurate alignment of the optical system, the more precise value of LC parameter would be achieved. In experiment, the twist angle and the pretilt angle were assumed to be specific values. As can be seen in Fig. 10, the deviation of pretilt angle has little influence on the measured results. However, the deviation of twist angle would have more apparent influence on the measurement error than that of pretilt angle. Fig. 11 shows there is slight deviation between the two Rt-d Dn curves Table 1 Experimental results obtained for cell gap using first modified system Sample
A B
Time 1
2
3
4
5
6
Average cell gap (lm)
10.069 3.735
10.124 3.685
10.139 3.723
10.134 3.727
10.075 3.699
10.093 3.725
10.10 ± 0.027 3.72 ± 0.016
0.6
Table 2 Experimental results obtained for cell gap using second modified system
0.5
Sample
2
3
4
5
6
Average cell gap (lm)
10.139 3.717
10.088 3.735
10.068 3.729
10.096 3.741
10.121 3.713
10.113 3.683
10.10 ± 0.020 3.72 ± 0.015
Rt
0.4
Time 1
A B
0.3
0.2
Table 3 Comparison of measured cell gap data
0.1 0
0.5
1
1.5
2
Sample
Designed cell gap value (lm)
Stokes parameters method (lm)
Interferometric method (lm)
Proposed method (lm)
A B
10 3.7
9.70 3.61
9.98 –
10.10 3.72
2.5
dΔ n [μm]
Fig. 9. Total intensity ratio of two sets of integrating time ranges, (dash line: 0–0.5T, 0.1–0.4T) and (solid line: 0–0.5T, 0.1–0.4T).
Y.-L. Lo et al. / Optics Communications 281 (2008) 4560–4565
to the deviation of cell gap about ±0.1 lm for sample A. In most LC display application, however, the retardation value of LC panel is usually the smaller than that of sample A. As for sample B, the retardation value is in the range of 0.35–0.45 lm. The corresponding cell gap deviation is about ±0.05 lm for sample B as the inaccuracy of the twist angle is at the level of ±1°.Therefore, the proposed method has better performance for small cell gap measurement than large one.
0.65 0.6 0.55
Rt
0.5 0.45
5. Conclusions
0.4 0.35 0.3 0.25 0
0.2
0.4
0.6
0.8
1 1.2 dΔ n [μm]
1.4
1.6
1.8
2
Fig. 10. Total intensity ratio of two different pretilt angles, (dot: 8.4°, solid line: 3.4°).
0.65 0.6 0.55
This study has presented and verified the modified TIRM optical configurations for TNLC cell gap measurement. Both configurations replace the mechanical mechanism used to rotate the polarizer in the conventional TIRM with a polarization rotation modulation system incorporating two QWPs and an E–O modulator. In the experimental results, the cell gap measurement deviation about 0.015 lm is obtained. Also, in our investigation, the proposed system has better measurement ability for the TNLC cell with small retardation than with large retardation. Furthermore, compared to the conventional TIRM, which requires several seconds to measure the cell gap, the modified TIRM techniques presented in this paper need only 2 s to acquire the signal and derive the cell gap value. The results of this study indicate that the modified TIRM methods have the potential to carry out on-line TNLC cell gap measurement in the industrial manufacturing of LCDs. Acknowledgements
0.5
Rt
4565
0.45
The current authors would like to acknowledge the financial support of Chi-Mei Optoelectonics (CMO) and also the assistance of Dr. T.S. Lin and Dr. I.L. Ho in the CMO without whom this study could not have been achieved. This research is also partially supported by the National Science Council, Taiwan, under grant NSC96-2628-E-006-005-MY3.
0.4 0.35 0.3 0.25
References 0
0.5
1
1.5
2
2.5
dΔ n [μm]
Fig. 11. Total intensity ratio of two different twist angle, (dash line: 89°, solid line: 90°).
with twist angles of 90° and 89°. As can be seen in the figure, the larger value of retardation is, the more apparent deviation can be observed. The maximum deviation of d Dn which is about ±0.025 lm in the large retardation ranges of 2–2.5 lm corresponds
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