*2.11.1. Fast response liquid crystal material*

alize the correction in the whole waveband. The proposed optical set-up is shown in Fig. 22, where a polarized beam splitter (PBS) is used to split the unpolarized light into two linear polarized beams. An unpolarized light can be looked upon as two beams with cross polar‐ ized states. Because the LCWFC can only correct linear polarized light, an unpolarized inci‐ dent light can only be corrected in one polarization direction while the other polarized beam will not be corrected. Therefore, if a PBS is placed following the LCWFC, the light will be split into two linear polarized beams: one corrected beam goes to a camera; the other uncor‐ rected beam is used to measure the distorted wavefront by using a wavefront sensor (WFS). This optical set-up looks like a closed loop AOS, but it is actually an open-loop optical lay‐ out. This LC adaptive optics system must be controlled through the open-loop method [31, 81]. Three dichroic beam splitters (DBSs) are used to acquire different wavebands. A 520– 810 nm waveband is acquired by using a band-pass filter (DBS1). This broadband beam is then divided into two beams by a long-wave pass filter (DBS2). Since DBS2 has a cut-off point of 590 nm, the reflected and transmitted beams of the DBS2 have wavebands of 520– 590 nm and 590–820 nm, respectively. The transmitted beam is then split once more by an‐ other long-wave pass filter (DBS3) whose cut-off point is 690 nm. Through DBS3, the reflect‐ ed and transmitted beams acquire wavebands of 590–690 nm and 690–810 nm, respectively. Thus, the broadband beam of 520–810 nm is divided into three sub-wavebands, each of which can be corrected by an LCWFC. After the correction, three beams are reflected back and received by a camera as a combined beam. Using this method, the light with a wave‐ band of 520–810 nm can be corrected in the whole spectral range with multi-LCWFCs.

86 Adaptive Optics Progress

**Figure 22.** Optical set-up for a broadband correction - PLS represents a point light source, PBS is a polarized beam splitter, DBS means dichroic beam splitter, DBS1 is a band-pass filter, and DBS2 and DBS3 are long-pass filters.

The broadband correction experimental results are shown in Fig. 23. A US Air Force (USAF) resolution target is utilized to evaluate the correction effects in a broad waveband. Firstly, the waveband of 520–590 nm is selected to perform the adaptive correction. After the correc‐ tion, the second element of the fifth group of the USAF target is resolved, with a resolution of 27.9 µm (Fig.23(b)). Considering that the entrance pupil of the optical set-up is 7.7 mm, the diffraction-limited resolution is 26.4 µm for a wavelength of 550 nm. Thus, a near dif‐ In applications of LCWFCs, the response speed is a key parameter. A slow response will sig‐ nificantly decrease the bandwidth of LC AOS. To improve the response speed, dual-fre‐ quency and ferroelectric LCs have been utilized to fabricate the LCWFC [82, 83]. However, there are some shortcomings with these fast materials. The driving voltage of the dual-fre‐ quency LCWFC is high and it is incompatible with the very large scale integrated circuit. The phase modulation of the ferroelectric LCWFC is very slight and it is hard to correct the distortions. Nematic LCs have no such problems. However, its response speed is slow. In this section, we introduce how to improve the response speed of nematic LCs.

For a nematic LC device, the response time of LC can be described by the following equa‐ tions when the LC cell is in parallel-aligned mode [84]:

$$\tau\_{rise} = \frac{\gamma\_1 d^2}{K\_{11} \pi^2 \quad \left(V / V\_{th}\right)^2 - 1} \tag{23}$$

$$
\pi\_{decay} = \frac{\gamma\_1 d^2}{K\_{11}\pi^2} \tag{24}
$$

of its predecessor in considering the additional correlation of the stress tensors with the di‐ rector and the fluxes with the order parameter tensor, except for the autocorrelation of the

Liquid Crystal Wavefront Correctors http://dx.doi.org/10.5772/54265 89

In Fig.24, the RVC of the nematic liquid crystal E7 is shown as a function of temperature. The experimental rotational viscosity decreases with temperature, and similar variations from NZ and F's theoretical methods are also obtained. The calculated NZ and F rotational viscosities are in the same order of magnitude as the experimental values. The larger the number of molecules, the longer the simulation time, and the revised force field for liquid

**Figure 24.** Temperature dependence of the rotational viscosity for E7, ■, the NZ method, ●, the F method, ▲, and the

The birefringence and dielectric anisotropy can be calculated by the Vuks equation and the Maier-Meier theory, respectively, and these calculated values have a good correlation with the experimental data in Ref. 89. In all, these approaches comprise a unique molecular de‐

In order to achieve fast LC material, researchers have synthesized a series of high birefringence LC materials with a linear shape and a long conjugated group. Gauza et al. first synthesized and reported a biphenyl, cyclohexyl- biphenyl isothiocyanato (NCS) LC material in which Δ*n* is 0.2-0.4 and the rotational viscosity is about 10 ms µm-2. The chemical structures are shown in Fig. 25. Moreover, they perform a comparison with a commercial E7 mixture. At 70°C, the *FoM*

crystals is expected to be helpful in improving this prediction.

microscopic stress tensor.

experiment.

sign method for fast response LCs.

**2.13. Chemosynthesis of fast response LC materials**

of the NCS mixture has a factor ten higher than that of E7 at 48°C [90].

where γ1 is the rotational viscosity, *V* and *Vth* are turn-on driving and threshold voltage, *K*<sup>11</sup> is the elastic constant and d is the thickness of the LC cell. Generally, the rise time can be decreased by the overdriving method. However the decay time particularly depends upon the intrinsic parameters of LC devices, which are the key factors for response improvement. From Eq. (24), the smaller visco-elastic coefficient (*γ*1/*K*11) and *d* is, the shorter the response time is. However, it is necessary to keep the phase retardation (*d*×Δ*n*) to exceed (or equal) one wavelength for a LCWFC, and then the cell gap can only been reduced to a limited val‐ ue for a constant birefringence (Δ*n*). The higher birefringence of LC materials enables a thin‐ ner cell gap to be used while keeping the same phase retardation and improves the response performance of the LCWFC. Therefore, the LC materials with high Δ*n* and low *γ*1/*K*11 are re‐ quired to have a fast response.

In the study of fast response LC materials, a concept of 'figure-of-merit' (*FoM*) is adopted to evaluate different LC compounds [85], as shown as Eq. (25). A LC material with a high *FoM* value will provide a short response time:

$$Fo\mathbb{M} = \mathbb{K}\_{11} \Delta \mathfrak{n}^2 \;/\ \;/\ \;/\ \;/\ \;\tag{25}$$

#### **2.12. Nematic liquid crystal molecular design**

In practice, some simple empirical rules together with a trial are usually used to help with the molecular design and mixing, such as LC compounds with a tolane and biphenyl group with a large Δ*n* and a moderate *γ*1. Recently, some computer simulation-based theoretical studies have been performed in order to shed light on the connections between macroscopic properties and molecular structure. A notable advantage of simulation is to predict the properties of a nematic LC material with optimal molecular configurations instead of costly and time-consuming experimental synthesis. In the study of fast response LCs, theoretical methods are used to analyse the rotational viscosity and Δn of a specific chemical structure.

In the study of the rotational viscosity (RVC) of nematic liquid crystals, Zhang et al. [86] adopt two statistical-mechanical approaches proposed by Nemtsov-Zakharov (NZ) [87] and Fialkowski (F) [88]. The NZ approach is based on the random walk theory. It is a correction of its predecessor in considering the additional correlation of the stress tensors with the di‐ rector and the fluxes with the order parameter tensor, except for the autocorrelation of the microscopic stress tensor.

For a nematic LC device, the response time of LC can be described by the following equa‐

( )

*d K* g

p

where γ1 is the rotational viscosity, *V* and *Vth* are turn-on driving and threshold voltage, *K*<sup>11</sup> is the elastic constant and d is the thickness of the LC cell. Generally, the rise time can be decreased by the overdriving method. However the decay time particularly depends upon the intrinsic parameters of LC devices, which are the key factors for response improvement. From Eq. (24), the smaller visco-elastic coefficient (*γ*1/*K*11) and *d* is, the shorter the response time is. However, it is necessary to keep the phase retardation (*d*×Δ*n*) to exceed (or equal) one wavelength for a LCWFC, and then the cell gap can only been reduced to a limited val‐ ue for a constant birefringence (Δ*n*). The higher birefringence of LC materials enables a thin‐ ner cell gap to be used while keeping the same phase retardation and improves the response performance of the LCWFC. Therefore, the LC materials with high Δ*n* and low *γ*1/*K*11 are re‐

In the study of fast response LC materials, a concept of 'figure-of-merit' (*FoM*) is adopted to evaluate different LC compounds [85], as shown as Eq. (25). A LC material with a high *FoM*

> 2 11 1 *F M* = D *K no* /

In practice, some simple empirical rules together with a trial are usually used to help with the molecular design and mixing, such as LC compounds with a tolane and biphenyl group with a large Δ*n* and a moderate *γ*1. Recently, some computer simulation-based theoretical studies have been performed in order to shed light on the connections between macroscopic properties and molecular structure. A notable advantage of simulation is to predict the properties of a nematic LC material with optimal molecular configurations instead of costly and time-consuming experimental synthesis. In the study of fast response LCs, theoretical methods are used to analyse the rotational viscosity and Δn of a specific chemical structure.

In the study of the rotational viscosity (RVC) of nematic liquid crystals, Zhang et al. [86] adopt two statistical-mechanical approaches proposed by Nemtsov-Zakharov (NZ) [87] and Fialkowski (F) [88]. The NZ approach is based on the random walk theory. It is a correction

g

*th*


(25)

<sup>=</sup> (24)

2 1 2 2 <sup>11</sup> / 1

*d*

*K VV* g

p

*decay*

t

tions when the LC cell is in parallel-aligned mode [84]:

88 Adaptive Optics Progress

quired to have a fast response.

value will provide a short response time:

**2.12. Nematic liquid crystal molecular design**

*rise*

=

t

In Fig.24, the RVC of the nematic liquid crystal E7 is shown as a function of temperature. The experimental rotational viscosity decreases with temperature, and similar variations from NZ and F's theoretical methods are also obtained. The calculated NZ and F rotational viscosities are in the same order of magnitude as the experimental values. The larger the number of molecules, the longer the simulation time, and the revised force field for liquid crystals is expected to be helpful in improving this prediction.

**Figure 24.** Temperature dependence of the rotational viscosity for E7, ■, the NZ method, ●, the F method, ▲, and the experiment.

The birefringence and dielectric anisotropy can be calculated by the Vuks equation and the Maier-Meier theory, respectively, and these calculated values have a good correlation with the experimental data in Ref. 89. In all, these approaches comprise a unique molecular de‐ sign method for fast response LCs.

#### **2.13. Chemosynthesis of fast response LC materials**

In order to achieve fast LC material, researchers have synthesized a series of high birefringence LC materials with a linear shape and a long conjugated group. Gauza et al. first synthesized and reported a biphenyl, cyclohexyl- biphenyl isothiocyanato (NCS) LC material in which Δ*n* is 0.2-0.4 and the rotational viscosity is about 10 ms µm-2. The chemical structures are shown in Fig. 25. Moreover, they perform a comparison with a commercial E7 mixture. At 70°C, the *FoM* of the NCS mixture has a factor ten higher than that of E7 at 48°C [90].

**Figure 25.** Chemical structures of biphenyl, cyclohexyl- biphenyl isothiocyanato LC materials.

In 2006, Gauza [91] provided one type of NCS LC material with unsaturated groups. The LC chemical structures are shown in Fig. 26: the final two NCS LC mixtures show a Δn value of 0.25 and 0.35; a viscosity factor of about 6 ms µm-2; *FoM* values of 10.1 and 18.7 µm<sup>2</sup> s-1. The response speed of such a LC material can be as low as 640 µs with a LC thickness of 2 µm at 35°C.

**Figure 27.** The synthesis of isothiocyanato compounds using Suzuki coupling.

performance [93], the chemical structures are shown in Fig. 28:

**Figure 28.** Chemical structures of NCS LC materials with high birefringence.

In Gauza et al., in subsequent research, a series of fluro-substituted NCS LC materials with a Δ*n* up to 0.5 at room temperature was developed, and some of them show better response

Liquid Crystal Wavefront Correctors http://dx.doi.org/10.5772/54265 91

In the research of isothiocyanate tolane LC compounds, Peng et al. prepared a NCS LC compound via an electronation reaction. The reaction route is shown in Fig. 29. Com‐

**Figure 26.** Chemical structures of NCS LC materials with unsaturated groups.

The high birefringence isothiocyanato LC with a tolane or terphenyl group can usually be synthesized via a couple reaction; the chemical reaction route was shown in Fig. 27 [92]:

**Figure 27.** The synthesis of isothiocyanato compounds using Suzuki coupling.

**Figure 25.** Chemical structures of biphenyl, cyclohexyl- biphenyl isothiocyanato LC materials.

90 Adaptive Optics Progress

and 0.35; a viscosity factor of about 6 ms µm-2; *FoM* values of 10.1 and 18.7 µm<sup>2</sup>

**Figure 26.** Chemical structures of NCS LC materials with unsaturated groups.

speed of such a LC material can be as low as 640 µs with a LC thickness of 2 µm at 35°C.

In 2006, Gauza [91] provided one type of NCS LC material with unsaturated groups. The LC chemical structures are shown in Fig. 26: the final two NCS LC mixtures show a Δn value of 0.25

The high birefringence isothiocyanato LC with a tolane or terphenyl group can usually be synthesized via a couple reaction; the chemical reaction route was shown in Fig. 27 [92]:

s-1. The response

In Gauza et al., in subsequent research, a series of fluro-substituted NCS LC materials with a Δ*n* up to 0.5 at room temperature was developed, and some of them show better response performance [93], the chemical structures are shown in Fig. 28:

**Figure 28.** Chemical structures of NCS LC materials with high birefringence.

In the research of isothiocyanate tolane LC compounds, Peng et al. prepared a NCS LC compound via an electronation reaction. The reaction route is shown in Fig. 29. Com‐ pared to the conventional couple reaction method, this synthesis route improves the total reaction yield [94].

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**Figure 29.** The synthesis of isothiocyanato tolane LC compound using electronation reaction.

It has rarely been reported that LCs with a very low rotational viscosity were mixed to high Δ*n* LCs in order to improve response performance. However, Peng et al. introduce a type of difluorooxymethylene-bridged (CF2 O) LCs with a very low rotational viscosity so as to im‐ prove the response performance of NCS LCs. The chemical structure is shown in Fig. 30. When the material was mixed to NCS LCs with a high Δ*n*, the visco-elastic coefficient of mixture decreased noticeably, the LC mixture approximately maintained high birefringence, and the *FoM* value increased from 14.8 to 16.9 µm2 s-1 at 7% concentration [95].

**Figure 30.** Chemical structure of difluorooxymethylene- bridged LC compound.
