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Intracavity measurement of liquid crystal layer thickness by wavelength tuning of an external cavity laser diode

Yu-Ping Lan, Yea-Feng Lin, Yu-Tai Li, Ru-Pin Pan, Chao-Kuei Lee, and Ci-Ling Pan

Open Access Open Access

Abstract

The gap of a planar-aligned liquid crystal (LC) cell is measured by a novel method: Monitoring the change in output wavelength of an external-cavity diode laser by varying the voltage driving the LC cell placed in the laser cavity. This method is particularly suitable for measurement of LC cells of small phase retardation. Measurement errors of ±0.5 % and ±0.6 % for 9.6-μm and 4.25-μm cells with phase retardations of 1.63 μm and 0.20 μm respectively are demonstrated.

©2005 Optical Society of America

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Figures (3)
Fig. 1.
Fig. 1. The schematic diagram for LC cell gap measurement. LD: laser diode; Obj: Objective, LC: liquid crystal, λ-meter: wavelength meter.

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Fig. 2.
Fig. 2. (a) Output wavelength of the laser and (b) transmittance of the LC cell (9.6 μm) through crossed polarizers as a function of the driving root-mean square (rms) voltage of the LC cell.

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Fig. 3.
Fig. 3. (a) Output wavelength of the laser and (b) transmittance of the LC cell (4.25 μm) through crossed polarizers as a function of the driving root-mean-square (rms) voltage of the LC cell.

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Tables (2)

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Table 1. Results of LC layer thickness measurement

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Table 2. Error sources for LC layer thickness measurement by the present method

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Equations (9)

Equations on this page are rendered with MathJax. Learn more.

n eff ( θ ) = [ sin ⁡ 2 ( θ ) n e + cos ⁡ 2 ( θ ) n o ] − 1 2 ,
ΔΦ = k ∫ 0 d [ n eff ( z ) − n 0 ] dz ,
Δ Φ max = 2 π λ ( n e − n o ) d .
Δ l l = − Δ λ λ ,
δd ≈ ∣ δ ( Δ λ ) Δ λ ∣ ∙ d .
δd = 1 Δ n ∣ δf ∣ f .
δd = ∣ δl ∣ d l .
δd = Δ λ λ ℓ δ ( Δ n ) ( Δ n ) 2 = d Δ n δ ( Δ n )
δd = ∣ d tan ⁡ θ · δθ ∣ .

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