目錄
目錄………...……Ⅰ 中文摘要………...………II 英文摘要………...…..III 報告內容
Yu, T.C., *Lo, Y.L., and Huang, R.R., “Determination of azimuthal anchoring strength in twisted nematic liquid crystal cells using heterodyne polarimeter” OPTICS EXPRESS, Vol. 18, No. 20, pp. 21169–21182, 2010 (SCI, EI) (Citation number: 0; Impact factor:
3.880; 3/64 (OPTICS ))
Reference and links ... 21169
1. Introduction ... 21170
2. Basic theory ... 21171
3. Azimuthal anchoring strength measurement for asymmetrical TNLC cells 21172 4. Azimuthal anchoring strength measurement for symmetrical TNLC cells .. 21176
4.1 Basic measurement principle ... 21176
4.2 Experimental setup and results for symmetrical cells ... 21178
5. Conclusions ... 21182
Acknowledgements ... 21182 相關著作……….. IV 計畫成果自評………...VI
中文摘要
本研究中使用共路徑電光調變外差干涉技術發展出一套多功能偏光干涉系統，
用以測量光學非等向性材料之各項參數。此系統已成功應用於葡萄糖溶液之濃度量 測、線性雙折射材料之二維全域量測、高靈敏扭轉向列型液晶厚度之單點及全場量 測、扭轉向列型液晶之單點及全場多參數量測；並以不加外場之方式，成功測量向 列型液晶與polyimide配向膜間之方位角錨定能。本研究以單一架構搭配不同之訊號 處理方式，實現了針對光學非等向性材料之多功能多參數單點及全場量測系統。在
量測方位角錨定能之部分，精度可以達到0.01μJ/m2，已足以應用於包含液晶架構之
生醫檢測。使用此方法量測40% LCT-061153 及60% MJO-42761的混合液晶與 plasma-alignment layer接面之弱方位角錨定能為7.19 μJ/m2。量測對稱之扭轉向列型 液晶時則需要引入基因演算法。由此方法求得polyimide配向膜以及E7液晶間之強方 位角錨定能為160 μJ/m2，polyimide配向膜和MLC-7023液晶間的強方位角錨定能則 為32 μJ/m2。
關鍵詞：偏光外差干涉儀、線性雙折射、主軸角度、相位延遲、扭轉向列型液晶、
Abstract
Two external-field-free methods are presented for measuring the azimuthal anchoring strength in twisted nematic liquid crystal (TNLC) cells. For asymmetrical TNLC samples, the twist angle is derived from the phase of the detected signal in a phase-sensitive heterodyne polarimeter and is then used to calculate the weak anchoring strength directly. The measurement resolution which is found to be about 0.01μJ/m2 makes the present method sensitive enough for the LC-based bio-sensing
application.Using the proposed method, the weak azimuthal anchoring strength of a composite liquid crystal mixture (40% LCT-061153 + 60% MJO-42761) in contact with a plasma-alignment layer is found to be 7.19 μJ/m2. For symmetrical TNLC samples, the liquid crystals are injected into a wedge cell, and the two-dimensional distributions of the twist angle and cell gap are extracted from the detected phase distribution using a genetic algorithm (GA). The azimuthal anchoring strength is then obtained by applying a fitting technique to the twist angle vs. cell gap curve. Utilizing the proposed approach, it is shown that the strong anchoring strength between a rubbed polyimide (PI) alignment layer and E7 liquid crystal is around 160 μJ/m2 while that between a rubbed PI alignment layer and MLC-7023 liquid crystal is approximately 32 μJ/m2.
Keywords：(120.2130) Ellipsometry and polarimetry; (120.3180) Interferometry;
(120.5060) Phase modulation;(120.5050) Phase measurement; (160.3710) Liquid
Determination of azimuthal anchoring strength in twisted nematic liquid crystal cells using
heterodyne polarimeter
Tsung-Chih Yu,1,2,*Yu-Lung Lo,1 and Rei-Rong Huang1
1Department of Mechanical Engineering, National Cheng Kung University, Tainan, 701, Taiwan
2Department of Medical Devices and Opto-Electronics Equipment, Metal Industries Research & Development Centre, Kaohsiung, 821, Taiwan
Abstract: Two external-field-free methods are presented for measuring the azimuthal anchoring strength in twisted nematic liquid crystal (TNLC) cells. For asymmetrical TNLC samples, the twist angle is derived from the phase of the detected signal in a phase-sensitive heterodyne polarimeter and is then used to calculate the weak anchoring strength directly. The measurement resolution which is found to be about 0.01µJ/m2 makes the present method sensitive enough for the LC-based bio-sensing application.
Using the proposed method, the weak azimuthal anchoring strength of a composite liquid crystal mixture (40% LCT-061153 + 60% MJO-42761) in contact with a plasma-alignment layer is found to be 7.19 µJ/m2. For symmetrical TNLC samples, the liquid crystals are injected into a wedge cell, and the two-dimensional distributions of the twist angle and cell gap are extracted from the detected phase distribution using a genetic algorithm (GA). The azimuthal anchoring strength is then obtained by applying a fitting technique to the twist angle vs. cell gap curve. Utilizing the proposed approach, it is shown that the strong anchoring strength between a rubbed polyimide (PI) alignment layer and E7 liquid crystal is around 160 µJ/m2 while that between a rubbed PI alignment layer and MLC-7023 liquid crystal is approximately 32 µJ/m2.
©2010 Optical Society of America
OCIS codes: (120.2130) Ellipsometry and polarimetry; (120.3180) Interferometry; (120.5060) Phase modulation;(120.5050) Phase measurement; (160.3710) Liquid crystals.
References and links
1. S. Faetti, and G. C. Mutinati, “Light transmission from a twisted nematic liquid crystal: accurate methods to measure the azimuthal anchoring energy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(2), 026601 (2003).
2. S. Faetti, and G. C. Mutinati, “An improved reflectometric method to measure the azimuthal anchoring energy of nematic liquid crystals,” Eur Phys J E Soft Matter 10(3), 265–279 (2003).
3. G. Barbero, D. Olivero, N. Scaramuzza, G. Strangi, and C. Versace, “Influence of the bias-voltage on the anchoring energy for nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 021713 (2004).
4. T. Akahane, H. Kaneko, and M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35(Part 1, No. 8), 4434–4437 (1996).
5. Y. Zhou, Z. He, and S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
6. Y. Zhou, Z. He, and S. Sato, “Generalized relation theory of torque balance method for azimuthal anchoring measurements,” Jpn. J. Appl. Phys. 38(Part 1, No. 8), 4857–4858 (1999).
7. J. G. Fonseca, and Y. Galerne, “Simple method for measuring the azimuthal anchoring strength of nematic liquid crystals,” Appl. Phys. Lett. 79(18), 2910–2912 (2001).
8. T. Govindaraju, P. J. Bertics, R. T. Raines, and N. L. Abbott, “Using measurements of anchoring energies of liquid crystals on surfaces to quantify proteins captured by immobilized ligands,” J. Am. Chem. Soc. 129(36), 11223–11231 (2007).
9. J. H. Kim, and H. Choi, “Technique for azimuthal anchoring measurement of nematic liquid crystals using magnetic field induced deformation,” Appl. Phys. Lett. 90(10), 101908 (2007).
10. S. Faetti, K. Sakamoto, and K. Usami, “Very strong azimuthal anchoring of nematic liquid crystals on uv- aligned polyimide layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 051704 (2007).
11. T. C. Yu, and Y. L. Lo, “A novel heterodyne polarimeter for the multiple-parameter measurements of twisted nematic liquid crystal cell using a genetic algorithm approach,” J. Lightwave Technol. 25(3), 946–951 (2007).
12. W. L. Lin, T. C. Yu, Y. L. Lo, and J. F. Lin, “A hybrid approach for measuring the parameters of twisted- nematic liquid crystal cells utilizing the Stokes parameter method and a genetic algorithm,” J. Lightwave Technol. 27(18), 4136–4144 (2009).
13. Y. Sato, K. Sato, and T. Uchida, “Relationship between Rubbing Strength and Surface Anchoring of Nematic Liquid Crystal,” Jpn. J. Appl. Phys. 31(Part 2, No. 5A), L579–L581 (1992).
14. P. Yeh, and C. Gu, Optics of liquid crystal displays. New York: John Wiley & Sons, Inc. (1999).
15. S. S. Lin, and Y. D. Lee, “Orientational microgrooves generated by plasma beam irradiation at surface of polymer films to align liquid crystals,” Jpn. J. Appl. Phys. 45(27), 24–28 (2006).
16. T. C. Yu, and Y. L. Lo, “A two-dimentional heterodyne polarimeter for determination of parameters in twisted nematic liquid crystal cells,” J. Lightwave Technol. 27(23), 5500–5507 (2009).
17. Y. L. Lo, H. W. Chih, C. Y. Yeh, and T. C. Yu, “Full-field heterodyne polariscope with an image signal processing method for principal axis and phase retardation measurements,” Appl. Opt. 45(31), 8006–8012 (2006).
18. F. Z. Yang, H. F. Cheng, H. J. Gao, and J. R. Samples, “Determination of the torsional anchoring of a twisted nematic liquid crystal using the half-leaky guided mode technique,” Liq. Cryst. 28(1), 51–57 (2001).
19. S. Faetti, and P. Marianelli, “Strong azimuthal anchoring energy at a nematic-polyimide interface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051708 (2005).
1. Introduction
The physical behavior of liquid crystals (LCs) is largely determined by their surface properties. Of the various surface properties, the surface energy plays a particularly important role in governing the physics of the LCs, and therefore in determining their technical applications. Accordingly, the literature contains many proposals for estimating the anchoring energy of LCs. For example, it has been shown that the azimuthal anchoring energy of nematic LCs can be measured using a torque balance method [1–3]. However, in applying this method, it is necessary to measure the cell parameters (e.g. the cell thickness and the twist angle) with an extremely high degree of precision. Therefore, a requirement exists for more straightforward means of measuring the fundamental properties of LC samples.
In response to this requirement, the literature contains numerous proposals for measuring the azimuthal anchoring strength using either external-field or external-field-free methods.
Akahane et al. [4] minimized the light transmitted through a TNLC cell by rotating both the cell and the analyzer, and then determined the twist angle and the optical retardation of the cell such that the surface azimuthal anchoring strength could be determined using an analytical formulation based on the Jones matrix. In 1997, Zhou et al. [5] presented a method for determining the cell thickness and twist angle of TNLC cells by measuring the Stokes parameters of the transmitted light. In a later study, the same group demonstrated the use of the Stokes parameter method (SPM) in determining the azimuthal anchoring strength in TNLC cells [6]. Fonseca and Galerne [7] proposed a simple method for measuring the azimuthal anchoring strength of nematic LCs by applying a fitting technique to the curve of the cell thickness vs. deviation angle of LC director in a wedge cell at the condition of waveguide regime. In a recent study, Govindaraju et al. [8] used Fonseca’s method to measure the anchoring energy of LC on surfaces in order to quantify different proteins captured by immobilized ligands.
The external-field-free methods described above provide a convenient means of determining the weak azimuthal anchoring strength in LC cells, but provide less accurate results when applied to LC cells with a strong azimuthal anchoring strength. Accordingly, various external-field methods have been proposed for measuring a wider range of anchoring strengths [9, 10]. However, these methods are theoretically complex and generally involve a time-consuming and complicated experimental procedure. In [11], the present group proposed a simple method for measuring the multiple parameters of a twisted TNLC sample by using a genetic algorithm (GA) to extract the twist angle and cell gap parameters inversely from the intensity ratio and phase of the signal obtained in a heterodyne polarimeter. In a more recent study [12], the same group proposed a hybrid approach based upon the Stokes parameter
method and a GA for enabling the full characterization of a TNLC cell, including the cell thickness, the twist angle, the pre-tilt angle, and the azimuthal angle.
This study proposes two external-field-free methods for measuring the weak and strong anchoring strengths in asymmetrically-aligned and symmetrically-aligned TNLC cells, respectively, using a phase-sensitive heterodyne interferometer. In the case of the asymmetrical TNLC cell, the cell parameters are optimized in such a way that the detected phase signal is rendered sensitive to the twist angle but insensitive to the cell thickness, and the twist angle of the sample is then extracted from the phase of the detected heterodyne signal. The twist angle is then used to calculate the anchoring strength directly. The proposing method is more sensitive than the one utilized by Govindaraju et al. [8] for quantifying proteins captured on surfaces through interactions with immobilized ligands and therefore is suitable for label-free bio-sensing application. For the symmetrical sample, the twist angle and cell gap of a wedge cell incorporating the LCs of interest are extracted from the 2-D phase distribution of the sample using a GA, and the azimuthal anchoring strength is then derived from the twist angle vs. cell gap curve using a fitting technique. The validity of the proposed weak anchoring strength measurement method is demonstrated using an asymmetrically-aligned TNLC cell containing a composite LC mixture of 40% LCT-061153 and 60% MJO-42761. Meanwhile, the validity of the strong anchoring strength measurement method is demonstrated by measuring the anchoring strengths between a rubbed polyimide (PI) layer and E7 liquid crystal and MLC-7023 liquid crystal, respectively.
2. Basic theory
In TNLC display devices, a uniform director alignment is generally obtained using rubbed polymer films. When the rubbing directions on the two substrates in the cell are orientated at an angle to one another, the nematic LCs injected into the cell form a twisted structure as a result of the surface anchoring force. If the surface anchoring energy is weak (and no external field is applied), the twisted structure induces a deviation of the director at the cell surface from the easy axis of the LC alignment layer, and the deviation angle can then be used to estimate the magnitude of the anchoring energy. In practice, the deviation angle is determined by the balance between the elastic power of the twisted LC structure and the torsional effect of the anchoring energy. For the case of a TNLC cell containing nematic LCs doped with a chiral material and having substrates rubbed in anti-parallel or parallel directions, the free energy per unit area is given by the sum of the elastic energy Fb and the surface anchoring energy Fs [13], i.e.
2 ,
b s
F=F + F (1)
( )2
22
0 ,
b 2 t
F K
d φ φ
= − (2)
1 2
sin ( ),
s 2
F = wφ ∆φ (3)
where K22 is the twist elastic constant; d is the cell thickness; φt is the real twist angle; φ0 is the intrinsic pre-twist angle of the sample material and is equal to φ0 = 2πd/p where p is the natural pitch of the material; wφ is the azimuthal anchoring strength, and ∆φ is the deviation of the surface LC director from alignment (rubbing) direction. (Note that for a nematic LC with chiral pitch of p = ∞, φ0 = 0).
In this study, two external-field-free methods are proposed for measuring the azimuthal anchoring strength in TNLC cells. In the first case, the two substrates of the TNLC cell are prepared in the same way such that the LCs are symmetrically aligned. As a result, an identical (strong) azimuthal anchoring strength is obtained at both substrates. In the second case, the two substrates are prepared using different methods such that a strong anchoring
effect is obtained at the lower substrate while a weak anchoring effect is obtained at the upper substrate. Consequently, the LCs are asymmetrically aligned.
In the case of the symmetrical cell, the anchoring strength, wφ, can be obtained by minimizing the free energy, F, with respect to ∆φ [13], i.e.
22 22
2 ( ) 2
sin 2 sin( ),
t t
e t
K K
wφ d d
φ φ
φ φ φ
= =
∆ − (4)
where φe is the twist angle induced by the easy axis of the LC alignment layer. In the case of the asymmetrical cell, the anchorage effect at the lower substrate is so strong relative to that at the upper substrate that the value of wφ at the lower substrate can be approximated as infinity. In other words, no torque-induced deviation of the LC director occurs at the lower substrate. Consequently, the azimuthal anchoring strength at the upper substrate can be obtained as
2 22
sin 2( ).
t
e t
w K
φ d
φ
= φ φ
− (5)
Thus, by measuring the real twist angle φt and the cell thickness d, Eqs. (4) and (5) enable the strong and weak azimuthal anchoring strengths in symmetrically-aligned and asymmetrically-aligned TNLC cells, respectively, to be obtained analytically given a knowledge of the twist elastic constant K22 and the twist angle induced by the easy axis of the LC alignment layer φe.
3. Azimuthal anchoring strength measurement for asymmetrical TNLC cells 3.1 Basic measurement principle
As shown, the light source has the form of a He-Ne laser. The laser beam is passed through a Glan-Thompson polarizer rotated to 0° and is then modulated by an electro-optic modulator (EOM) driven by a saw-tooth waveform signal with an angular frequency ω and with a slow axis oriented at −45° to the x-axis. The light is then passed through the TNLC sample and is incident upon a quarter-wave plate (QWP) whose slow axis is set such that it forms an angle of 45° with that of the EOM. Finally, the light emerging from the QWP is passed through an analyzer (a Glan-Thompson polarizer rotated to −45°) and is incident upon a photo-detector (PD).
Fig. 1. Schematic illustration of heterodyne polarimeter used to measure twist angle of asymmetrical TNLC cell.
The light intensity at the PD, and the electric field vector emerging from the configuration shown in Fig. 1, are given by
/ 4
/ 4
1 1
0 cos sin
2 2 ( )
1 1 0 sin cos
2 2
cos( ) sin( )
cos sin 2 2 1 ,
sin cos 0
sin( ) cos( )
2 2
i i TNLC
E e M
e
t t
i
t t
i
π π
α α
α α φ
ω ω
α α
α α ω ω
− −
−
=
−
−
(6)
where α is the azimuthal angle of the entrance LC director. The Jones matrix of an asymmetrically-aligned TNLC cell can be expressed as [14]
sin sin
cos sin cos 2
( ) ,
sin cos sin sin
cos 2
t
t t
TNLC t
t t
t
i M
i
φ φ φ
φ φ φ φ
Χ Χ
Χ − ⋅Γ ⋅ ⋅
− Χ Χ
= − ⋅ ΧΧ Χ + ⋅ Γ ⋅ Χ Χ
(7)
with
2 2
( / 2) ,
2 /
t
d n φ
π λ
Χ = + Γ
Γ = ∆
(8)
where φt is the twist angle of the LC cell, Γ is the linear retardation, d is the cell gap, and n∆ is the birefringence of the LC material. Therefore, the intensity of the PD output signal is given by
( )
( ) ( )
( )
( )
*
I
2 2 2 2 2 2
A
B
2 2 2
8 2 2 cos 2 8 cos 2 8 8 cos 2
cos 8 cos 2 8 cos 2 cos 2 8 sin 2 sin 2
sin 8 (1 cos 2 ) (1 cos 2 )(8 2 )
DC
t t
t
t
I E E
t
t
φ φ
ω φ α φ α α
ω φ
∝ ⋅
Χ + Γ − Γ Χ + Χ Χ + − Χ
= + ⋅ − Γ + Γ Χ − ΓΧ Χ
+ ⋅ Χ + Χ + − Χ − Γ
( )
( )
2 2
1
cos sin
sin
sin , tan
DC
DC
DC
I A t B t
I A B t
I K t A
B
ω ω
ω σ
ω σ σ −
= + +
= + + +
= + + =
(9)
In other words, the detected heterodyne signal has the form of a sinusoidal signal with the same angular frequency as the EOM driving voltage. As shown in Eq. (9), the detected signal consists of a DC term, IDC, and a modulated term, Ksin(ω σt+ ) . The phase σ of the sinusoidal term can be expressed as a function of the TNLC cell parameters ( , , )α φt d and can be extracted using the phase-lock method. Figures 2(a) and 2(b) illustrate the variation of the phase term in Eq. (9) for twist angles in the range −180° ~180° and retardation values in the range 0 ~2 µm. (Note that the azimuthal angle is assumed to be α = 0°.) It can be seen that the phase, σ, and the twist angle, φt, are linearly related at retardation values of approximately 0.3 µm, 0.9 µm, and 1.5 µm. Furthermore, it is noted that the slope of the linearity at d∆n = 0.3
µm is greater than that at the other retardation values. Thus, in extracting the twist angle from the phase of the heterodyne detected signal, a retardation of around 0.3 µm represents the optimal value in terms of enhancing the measurement resolution. Note that further simulations (results not shown here) reveal that there is no better value of the azimuthal angle than α = 0° when extracting the twist angle from the phase of the detected signal.
Fig. 2. (a) Variation of σ as function of φt and d∆n, (b) alternative view of phase variation shown in (a). (Note that α = 0°).
Figures 3(a) and 3(b) show the variation of σ as a function of the retardation d∆n in the range 0.30 µm to 0.38 µm for twist angles φt ranging from −180° ~180° and a constant azimuthal angle of α = 0. It can be seen from Fig. 3(a) that for a given twist angle, the phase σ is insensitive to the retardation d∆n, i.e. the phase value varies only slightly as the retardation is increased from 0.30 µm to 0.38 µm. Meanwhile, Fig. 3(b), which presents the same results but from a different perspective, gives a clear illustration of the twist angle dependent phase σ performance in the retardation d∆n range 0.30 µm to 0.38 µm. It can be seen from Fig. 3(b) that the rate of change of the phase σ with the twist angle is approximately constant for twist angles in the range −150° ~150°. From inspection, the average sensitivity (i.e. the average slope), ∆σ/∆ , is found to be around 1.2. In the heterodyne polarimeter shown in Fig. 1, φt the phase of the detected signal can be measured with a resolution of 0.1°, and thus it follows that the twist angle can be extracted with a precision of around 0.08°. Thus, the information in Fig. 3(b) provides not only an optimal design of retardation range in 0.3 µm ~0.38 µm and twist angle range in −150° ~150° for the azimuthal anchoring strength measurement but also the measurement performance of the proposing system.
Fig. 3. (a) Variation of σ as function of d∆n in range 0.30µm ~0.38µm for twist angles of φt =
−180° ~180°, (b) alternative view of phase σ variation shown in (a). (Note that α = 0°).
For an asymmetrical TNLC cell with a strong anchoring substrate (input surface) and a weak anchoring substrate (output surface), the azimuthal anchoring strength of the weak alignment layer can be calculated from Eq. (5) in Section 2 given a knowledge of the actual twist angle φt, the cell thickness d, the twist elastic constant K22 and the twist angle induced by the easy axis of the LC alignment layer φe. Figure 4 shows the simulation results obtained for the correlation between the real twist angle and the azimuthal anchoring strength of the weak alignment layer in a TNLC cell with parameters of φe = 120°, K22 = 7.35 pN, and d = 3 µm. The results show that for a weak anchoring strength of around 7 µJ/m2, the measurement resolution of the twist angle (i.e. 0.08°) equates to an azimuthal anchoring strength resolution of approximately 0.01 µJ/m2, and the smaller the anchoring strength, the more sensitive the anchoring strength measurement.
Fig. 4. Variation of weak azimuthal anchoring strength wφ with real twist angle φt for asymmetrically-aligned TNLC cell with φe = 120°, K22 = 7.35 pN, and d = 3µm.
3.2 Experimental setup and results for asymmetrical cells
In setting up the heterodyne polarimeter shown in Fig. 1, a frequency stabilized He–Ne laser (Model: SIOS SL 02/2) with an output power of 3 mW was used as the light source and the EOM (Conoptics, Model 370) was driven by a saw-tooth signal with a frequency of 1 kHz.
The phase of the detected signal was acquired using a lock-in amplifier (SR830, Stanford Research Systems Inc.,). The asymmetric TNLC sample was constructed by filling an empty test cell (twist angle φe = 120°, pre-tilt angle 3°, and cell gap 2.91 µm) with a composite LC mixture (K22 = 7.35 pN) comprising 40% LCT-061153 and 60% MJO-42761. The LCs were aligned at the lower substrate via a PI rubbing layer and at the upper substrate by a plasma- alignment layer. In performing the measurement process, the azimuthal angle of the entrance LC director was set to α = 0°. The retardation of the TNLC sample, d∆n, was estimated to be 0.352 µm, i.e. within the optimal range of 0.3 µm ~0.38 µm. The weak azimuthal anchoring strength at the plasma-alignment layer was calculated from Eq. (5) using the method described in Subsection 3.1. Note that prior to the measurement process, the heterodyne signal detected without the TNLC sample in the system was calibrated in order to eliminate the phase effect induced by the EOM.
Figures 5(a) ~5(c) show the correlation between the phase σ and the twist angle for azimuthal angles of α = 0°, 1° and −1°, respectively. Note that the value of α = 0° represents the optimal azimuthal angle, while the values of α = + 1° and −1° are used to investigate the effect of small errors in the optimal azimuthal angle on the calculated value of the anchoring strength. The measured phase σ of the asymmetric TNLC sample is −67.5° ( = 292.5°). In Fig. 5(a), the real twist angle φ is found to be 80.21° at a phase t σ of 292.5°. Substituting this
value of φ into Eq. (5) together with the cell parameters (t φe, ,d K22) provided by the manufacturer, the azimuthal anchoring strength of the weak alignment layer is found to be 7.19 µJ/m2. This result is reasonable since the azimuthal anchoring strength of E7 liquid crystal at a plasma-alignment surface is known to be around 14.8 µJ/m2 [15]. Substituting the twist angle values extracted from Figs. 5(b) and 5(c) into Eq. (5) together with the cell parameters (φe, ,d K22), the azimuthal anchoring strengths of the weak alignment surface in the TNLC cell are found to be 7.13 µJ/m2 and 7.24 µJ/m2, respectively. In other words, an error of 1° in the azimuthal angle results in a deviation of no more than 0.06 µJ/m2 in the calculated value of the weak anchoring strength. Thus, the proposed method provides a robust means of calculating the azimuthal anchoring strength in asymmetrical TNLC cells even when small errors exist in the azimuthal angle setting.
Fig. 5. Correlation between measured phase and extracted twist angle in asymmetrical TNLC cell for azimuthal angles of (a) α = 0°; (b) α = 1°; and (c) α = −1°.
4. Azimuthal anchoring strength measurement for symmetrical TNLC cells 4.1 Basic measurement principle
In symmetrical TNLC cells, the LC director deviates from the easy axis of both substrates, and thus the method described in Subsection 3.1 cannot be used to measure the anchoring strength since the value of α is unknown. Therefore, this section proposes an alternative method for measuring the azimuthal anchoring strength of symmetrical aligned LC samples using a TNLC wedge cell and a genetic algorithm (GA).
Figure 6 shows the simulation results obtained by Eq. (4) for the variation of the twist angle with the cell thickness for known azimuthal anchoring strengths of wφ = 30~150 µJ/m2 at both substrates with φe = 60° and K22 = 6.5 pN in each case. Using the theoretical φt - d curve, the unknown azimuthal anchoring strength of a symmetrically-aligned LC sample can
be obtained simply by fitting the experimental φt - d curve obtained by the GA. Note that the azimuthal strength obtained by fitting the multiple φt - d curves is expected to be more accurate than that obtained when using a sample with a uniform cell gap.
Fig. 6. Simulated twist angle vs. thickness (φt - d) curves for symmetrical TNLC cells with different azimuthal anchoring strengths in the range 30 µJ/m2 (lower) to 150 µJ/m2 (upper).
Figure 7 presents a schematic diagram of the measurement system utilized to measure 2-D parameters distributions from a TNLC cell. As shown, the configuration is modified from the one described in Section 3. A beam expander is used to extend the single-point methodology to full-field measurement and a QWP whose slow axis forms an angle of 45° with that of the EOM was placed at three positions, namely Position 1, Position 2, and Position 3 (see Fig. 7) sequentially in the measurement process. After passing the analyzer, the expanded beam is incident on a CCD triggered by a complex programmable logic device (CPLD) with a phase- shift driver. As the QWP is placed at Position 1, the form of the detected signals I1 consists of a DC term IDC and a modulated term K1sin(ω σt+ 1). Similarly, as the QWP was placed at Position 2 and Position 3, the detected signal can be expressed as I2=IDC+K2sin(ω σt+ 2)
and I3=IDC+K3sin(ω σt+ 3), respectively. In accordance with the method presented in [16], the phase maps of (σ1, σ2, σ3) of heterodyne signals can be carried out as follows
4 2
4 3
2 4
4 2
1,2,3 1,2,3
1 0 1,2,3
1,2,3 1,2,3
( ( ) ( ) )
tan .
( ( ) ( ) )
T T
T T T
T T
I t dt I t dt
I t dt I t dt
σ −
−
=
−
∫ ∫
∫ ∫
(10)
The full-field distributions of the azimuthal angle α, cell thickness d and twist angle φt are extracted using a GA, and the strong azimuthal anchoring strength is then obtained by applying a fitting method to the experimental results for the twist angle vs. cell thickness.
Fig. 7. Schematic illustration of heterodyne polarimeter used to measure parameters of TNLC wedge cell containing symmetrically-aligned LCs.
4.2 Experimental setup and results for symmetrical cells
In the measurement system shown in Fig. 7, empty polyimide-rubbed wedge-shaped cells (provided by LCD&PMR lab, NCTU, Taiwan) with pre-tilt angle of 3° were used as samples for the measurement. The twist angle induced by the easy axis of the LC alignment layer was equal to φe = 60°, and the cell was filled with either E7 liquid crystal (K22 = 6.5 pN, Merck Co.) or MLC-7023 liquid crystal (K22 = 8.25 pN, Merck Co.). The surfaces of the samples are separated by a 20µm spacer, and are not separated by a spacer at the other end. The illuminating light was provided by a frequency-stabilized He-Ne laser (Model: SIOS SL 02/2) with an output power of 3 mW, and the EOM (Conoptics, Model 370) was driven by a saw- tooth signal with a frequency of 1 kHz. In acquiring the intensity images, the exposure time of the 8-bit gray-level CCD (JAI, CV-A11) was set to a quarter period of 0.25 ms. Figure 8 illustrates the interface between the CPLD and the CCD [17]. The control clocks in the CPLD were processed using a cascaded sequence of frequency dividers in an embedded 2 MHz oscillator. Meanwhile, the frequencies of the external trigger signals provided to the function generator and the CCD were set to 1 kHz and 10 Hz, respectively. The phase of the CCD trigger signal was shifted sequentially using a bits / delay controller, and the exposure time, trigger mode and other settings of the CCD were controlled by a computer through IMAQ 1409 and RS-232 interfaces. The mean intensity values of the 30 frames acquired over a 3 second period were then used in computing the phase maps of (σ1, σ2, σ3).
Fig. 8. Block diagram showing interface between CCD and CPLD [16].
Before inserting the sample into the experimental setup, the DC bias of the EOM was adjusted such that the detected signal and the driving signal were in phase (i.e., σinitial =0) in order to eliminate the effect of the phase effect induced by the EOM. Having calibrated the detected signal, the sample was introduced into the measurement system and the QWP was inserted at Position 1 (see Fig. 7). The 2-D phase distribution, σ1, was then obtained from the detected signal. The QWP was then moved to Position 2, and the new 2-D phase distribution, σ2, was obtained. Finally, the QWP was removed from the experimental system, and the corresponding 2-D phase distribution, σ3, was obtained.
Figure 9(a) presents a typical image acquired by the CCD camera of the wedge cell filled with E7 liquid crystals. Note that the diffraction patterns in the image are the result of small particles on the lens surface and interference fringes introduced by the optical components within the interferometer. Figures 9(b)–10(d) show the corresponding 2-D distributions of σ1, σ2, and σ3.
Fig. 9. (a) Typical image acquired by CCD camera of wedge cell containing E7 liquid crystals, (b)~(d): phase distributions σ1 ~σ3 for sample shown in (a).
The measured 2-D phase distributions (σ1, σ2, σ3) were substituted into the GA as the objective values for the error function, and the optimal values ofα , φt, and d (i.e. the parameter values which minimized the error function) were extracted. In Eq. (9), it can be seen that the phase term of the detected signal varies as a function of cos2X. That is, as the cell gap d increases, the term Χ =[φt2+ Γ( / 2) ]2 1/ 2 also increases, and cos2X varies periodically between −1 and 1. Figures 10(a) and 10(b) show the variations of terms A and B in Eq. (9) as a function of d. The periodic properties of A and B lead to a corresponding periodicity in the measured phase distributions. This phenomenon is inevitable, and causes the GA to extract multiple solutions for the TNLC parameters if the search space for the cell
gap parameter is assigned the full range of 0~20 µm. Therefore, in implementing the GA, the TNLC sample parameters ( ,α φt, ) were randomly assigned within the ranges d
0 180
45 65
1 4 , 4 7 , or 7 10 .
t
m d m m d m m d m
α φ
µ µ µ µ µ µ
° ≤ ≤ °
° ≤ ≤ °
≤ ≤ ≤ ≤ ≤ ≤
(11)
Fig. 10. Variations of A and B in Eq. (9) as function of cell gap d.
Figures 11(a)–11(c) present the cell parameter distributions obtained from the GA for the E7 wedge cell, while Figs. 12(a)–12(c) present the equivalent results for the MLC-7023 wedge cell. Finally, Figs. 13(a) and 13(b) show the azimuthal anchoring energies of the E7 and MLC-7023 wedge cells, respectively, obtained by fitting the cell thickness and twist angle data presented in Figs. 11 and 12. The anchoring strengths of the E7 and MLC-7023 cells are found to be 160 µJ/m2 and 32 µJ/m2, respectively, and are therefore consistent with the values presented in previous studies [18,19]. For example, in [18], the azimuthal anchoring energy of E7 liquid crystal on a rubbed PI alignment layer was found to be 58 µJ/m2, while in [19], the azimuthal anchoring energy of 5CB liquid crystal on a rubbed PI layer was found to be 330 µJ/m2. Thus, even though the experimental values obtained for the azimuthal anchoring energies of E7 and MLC-7023 liquid crystal are different from the values presented in the literature, they are still within a reasonable range.
Fig. 11. Cell parameter distributions of E7 wedge cell: (a) azimuthal angle, (b) twist angle (φe
= 60° ± 2°), and (c) cell gap (1.8 µm ~4.5 µm).
Fig. 12. Cell parameter distributions of MLC-7023 wedge cell: (a) azimuthal angle, (b) twist angle (φe = −60° ± 2°), and (c) cell gap (7.3µm ~9.5 µm).
Fig. 13. Variation of twist angle with cell thickness and fitted values of azimuthal anchoring strength for: (a) E7 wedge cell, and (b) MLC-7023 wedge cell.
5. Conclusions
This study has demonstrated the use of a phase-sensitive heterodyne interferometer in determining the azimuthal anchoring strengths of asymmetrical and symmetrical TNLC cells.
For the case of asymmetrical TNLC cells, the twist angle of the cell is extracted from the phase of the detected heterodyne signal and is then used to compute the weak azimuthal anchoring strength directly. It’s not necessary to rotate the optical elements during measurement, and the resolution 0.01µJ/m2 is better than the standard error 0.3µJ/m2 obtained by Govindaraju et al. [8] for quantifying proteins captured on surfaces through interactions with immobilized ligands. The present method thus may provide a more straightforward and more sensitive way for the future bio-sensing applications. For symmetrical TNLC samples, the LC is inserted into a wedge cell and the correlation between the twist angle and the cell gap is extracted from the recorded phase measurements using a genetic algorithm (GA). A fitting technique is then applied to the twist angle vs. cell gap measurements in order to determine the corresponding value of the strong azimuthal anchoring strength. Unlike the method presented in ref [7], this method can be used as the sample is not in the waveguide regime. The experimental results have shown that the weak azimuthal anchoring strength of a composite liquid crystal mixture (40% LCT-061153 + 60% MJO-42761) on a plasma- alignment layer is equal to 7.19 µJ/m2. Meanwhile, it has been shown that the strong azimuthal anchoring strengths of E7 liquid crystal and MLC-7023 liquid crystal on rubbed polyimide alignment substrates are equal to 160 µJ/m2 and 32 µJ/m2, respectively. The azimuthal anchoring strengths obtained in this study are in good general agreement with the results presented in the literature, and thus the validity of the proposed approach is confirmed.
The phase-sensitive measurement methods proposed in this study not only eliminate the effects of intensity variations, but also minimize the influence of energy absorption at the optical elements within the measurement system. Moreover, the common-path configuration and heterodyne scheme reduce the effects of environmental perturbations and improve the SNR of the detected signal. As a result, the resolution of the measurement results is significantly improved. Finally, the use of a wedge cell in determining the azimuthal anchoring strength of symmetrical TNLC samples yields a more accurate estimate of the anchoring strength than that obtained using a sample with a uniform cell gap.
Acknowledgements
The authors gratefully acknowledge the financial support provided to this study by MIRDC (Metal Industries Research & Development Centre), Taiwan, and the National Science Council of Taiwan under Grant No. NSC96-2628-E-006-005-MY3.
相關著作 1. 期刊論文
(1) Yu, T.C., Shan, H., Pham, T.T.H., and *Lo, Y.L., “Full-Field and Full-Range Sequential Measurement of Slow Axis Angle and Phase Retardation of Linear Birefringent Materials,” Applied Optics, 2009. (SCI, EI) (CN: 0; IF: 1.763; 18/64 (OPTICS)).
(2) Lin, W.L., Yu, T.C., *Lo, Y.L., and Lin, J.F., “A hybrid approach for measuring the parameters of twisted-nematic liquid crystal cells utilizing the Stokes parameter method and a genetic algorithm,” JOURNAL OF LIGHTWAVE TECHNOLOGY , 2009 (SCI, EI) (CN: 0 ; IF: 2.736 ; 19/227 (ENGINEERING, ELECTRICAL &
ELECTRONIC)))
(3) Yu, T.C. and *Lo, Y.L., “A two-dimentional heterodyne polarimeter for determination of cell parameter for twisted nematic liquid crystal cell,” Accepted by IEEE Journal of Lightwave Technology 2009 (SCI, EI) (CN:0 ; IF: 2.196; 19/227 (ENGINEERING, ELECTRICAL & ELECTRONIC)).
(4) Chen, P.C., *Lo, Y.L., Yu, T.C., Lin, J.F., and Yang, T.T., “Measurement of linear birefringence and diattenuation properties of optical samples using polarimeter and Stokes parameters,” OSA, Optics Express, 2009 (SCI, EI) (Citation number: 0;
Impact factor: 3.880; 3/64 (OPTICS)).
(5) Yu, T.C., *Lo, Y.L., and Huang, R.R., “Determination of azimuthal anchoring strength in twisted nematic liquid crystal cells using heterodyne polarimeter” OPTICS EXPRESS, Vol. 18, No. 20, pp. 21169–21182, 2010 (SCI, EI) (Citation number: 0;
Impact factor: 3.880; 3/64 (OPTICS )).
2. 研討會論文:
(1) Tsung-Chih Yu and Yu-Lung Lo, ”New Heterodyne Polarimeter for Full-Field Cell Gap Determination of Twisted-Nematic Liquid-Crystal Cell,” Optics and Photonics Taiwan, 2007.
(2) Yu, T.C. and Lo, Y.L., “New imaging polariscope for the full-field measurement of twisted-nematic liquid-crystal thickness,” Society of Experimental Mechanics Annual conference, Springfield, Massachusetts USA, 2007.
(3) Yu, T.C. and Lo, Y.L., “New imaging polariscope for two-dimensional cell gap determination of twisted-nematic liquid-crystal cell,” International Conference on
(4) Yu, T.C. and *Lo, Y.L., “A two-dimensional heterodyne polarimeter for the determination of cell parameters in twisted nematic liquid crystal cell,” The 25th National Conference on Mechanical Engineering, 2008
(5) *Yu-Lung Lo, Hsu Shan, and Tsung-Chih Yu, “Full-Field Measurements in the Principal Axis and Phase Retardation of Linear Birefringence Materials in Full-Scale Range,” The International Conference on Experimental Mechanics, Nan-Jing China, 2008 (ICEM 2008)
(6) *Lo, Y.L. and Chu C.S., “Highly-sensitive optical fiber oxygen sensor bsed on Pt(II) complex and dye entrapped core-shell silica particles embedded in sol-gel matrix”
submitted to Optics and Photonics Taiwan (台灣光電科技研討會), 2009.
(7) Chen, P.C., *Lo, Y.L., Yu, T.C., Lin, J.F., and Yang, T.T., ”Measurement of linear birefringence and diattenuation properties of optical samples using polarimeter and Stokes parameters,” Submitted to OPT 2009.
(8) Chen, P.C., *Lo, Y.L., Yu, T.C., Lin, J.F., and Yang, T.T., ”Measurement of linear birefringence and diattenuation properties of optical samples using polarimeter and Stokes parameters,” Submitted to CSME 26th, 2009.
(9) Hsu Shan, Tsung-Chih Yu and *Yu-Lung Lo, “Imaging Polariscope for the Characterization of Linear Birefringence Materials in Full-scale Range of Phase Retardation and Principal Axis,” Society of Experimental Mechanics Annual conference, Albuquerque, New Mexico USA, 2009.
(10) Ruei-Ron Huang, Tsung-Chih Yu, and *Yu-Lung Lo, "A phase-sensitive heterodyne polariscope for determination of azimuthal anchoring strength in twisted nematic liquid crystal cell," Accepted by 中國機械工程學會, 第二十六屆全國學術研討會, 2009.
3. 博士論文
“偏極化外差干涉儀於光學非等向性材料特性分析之研究”, 尤崇智, 國立成功大學 機械工程學系博士論文, 2009.
4. 其它
(1) 尤崇智、羅裕龍, “多參數量測扭轉向列型液晶之新型外差偏光儀”, 成大研發快 訊第九卷第六期, 2009
(2) 羅裕龍*, 陳鐵城, 李永春,“探討利用奈米壓印製造LCD產業次世代配向層技 術”, 成大研發快訊第十六卷第四期, 2010.
計畫成果自評
本研究計畫確認了以共路徑電光調變外差干涉技術進行單點及全場量測線性雙 折射材料及扭轉型液晶盒參數的可行性。光學外差式偏光架構對於相位量測具有高 度靈敏性，而所得的各參數與設計值十分接近。本系統除了可快速的得到液晶盒厚 度之分佈，可用於對於液晶線上製程檢測，亦可穩定的同時量測扭轉向列型液晶的 方位角、扭轉角及液晶盒厚及方位角錨定能等參數，對於光學非等向性材料之特性 分析提供有力之工具。
藉由光學外差共路徑干涉的量測架構，可降低環境擾動對於訊號的影響，並改 善訊噪比(signal-to-noise ratio)。以外差干涉訊號的相位及強度比作為多目標基因演 算法中的目標值，可找出最適合的基因(即液晶參數)來對應到所要之目標值，此方 法用於量測扭轉向列型液晶盒的入射液晶導軸方位角、扭轉角以及液晶盒厚度之精 度甚高；而以外差訊號之二維相位分佈作為目標值，更可同時求出液晶盒的入射液 晶導軸方位角、扭轉角以及液晶盒厚度之二維分佈。研究中更進一步以楔型液晶盒 為樣本，量測其扭轉角及厚度分布，進而求出液晶與 polyimide 之方位角錨定能，
此方法毋須外加電場或磁場，待測樣本亦不需符合 waveguiding regime 之特殊條件。
本計畫所發展的量測技術對國內的面板產業將有明顯助益，且可向更多領域擴 展延伸，拓展其應用範圍。研究成果亦有多篇論文被 Optics Express 等光學領域頂尖 國際期刊接受。因此，國科會所支持本計畫所得技術與衍生之研究成果相當豐碩。
