Methods and apparatus for measurement of LC cell parameters
AssigneeThe Hong Kong University of Science and Technology
InventorsHoi-Sing Kwok, Shu-Tuen Tang
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Abstract
Three measuring methods and apparatus for determining the twist angle (φ) and retardation value (dΔn) of any twisted nematic liquid crystal (LC) cell are disclosed. These methods make use of a monochromatic light source such as a laser beam. Twist angle and retardation values an be obtained by data fitting using data obtained by adjusting only the polarizes and the LC cell orientation. No retardation wave-plate is needed.
Claims19
A method of obtaining the twist angle and retardation value of a liquid crystal cell comprising, locating the liquid crystal cell between a first polarizer and a second polarizer serving as an analyzer, providing an input monochromatic light source and means for measuring the light transmitted through the analyzer, and:
- (a) fix the polarizer-analyzer angle α0, at any fixed angle,
- (e) rotate the liquid crystal cell while recording the light transmission,
- (f) note the maximum (K1(α0)+K2) and minimum (K1aα0) values of the transmission from step (b), and
- (g) solve equations K 1 ( α 0 ) = { cos β cos ( φ - α 0 ) + sin β sin ( φ - α 0 ) 1 + r 2 } 2 K 2 = r 2 1 + r 2 sin 2 β
- simultaneously to obtain (φ, dΔn) either graphically or numerically.
A method of obtaining the twist angle and retardation value of a liquid crystal cell comprising, locating the liquid crystal cell between a first polarizer and a second polarizes serving as an analyzer, providing an input monochromatic light source and means for measuring the light transmitted through the analyzer, and:
- (d) fixing the polarizers in the characteristic directions of said cell whereby the angle (Ψ) between said directions is then determined,
- (e) rotate the liquid crystal cell while recording the light transmitted through the analyzer,
- (f) obtain the transmission minimum (1−K2) and then solve equations K 2 = r 2 1 + r 2 sin 2 β φ δ 2 + φ 2 tan δ 2 + φ 2 = tan ( φ - ψ )
- simultaneously to obtain (φ, dΔn) graphically or numerically.
A method of obtaining the twist angle and retardation value of a liquid crystal cell comprising locating said liquid crystal cell between a horizontal polarizer and a Stokesmeter and providing an input source of monochromatic light, and
- (e) rotating the liquid crystal cell while recording the Stokes parameters, and
- (f) obtaining the S1 maximum and minimum and then solve equations K 1 ( α 0 ) = { cos β cos ( φ - α 0 ) + sin β sin ( φ - α 0 ) 1 + r 2 } 2 K 2 = r 2 1 + r 2 sin 2 β
- to obtain (φ, dΔn) through the equation I 11 = 1 + S 1 2 , or
- (g) obtain the S2 maximum and minimum and then solve equations K 2 = r 2 1 + r 2 sin 2 β φ δ 2 + φ 2 tan δ 2 + φ 2 = tan ( φ - ψ )
- to obtain (φ, dΔn) through the equation I 45 = 1 + S 2 2 , or
- (h) obtain the characteristic angle Ψ and the maximum |S3| and then solve the equations φ δ 2 + φ 2 tan δ 2 + φ 2 = tan ( φ - ψ ) S 3 = ± J / cos ( φ - ψ )
- simultaneously to obtain (φ, dΔn).
A method of obtaining the average tilt angle of a liquid crystal cell by a crystal rotation method comprising locating said liquid crystal cell between a horizontal polarizer and a Stokesmeter and providing an input source of monochromatic light, and
- (d) rotating the liquid crystal cell while recording the Stokes parameters,
- (e) measure the retardation maximum against rotation angle to calculate the average tilt angle.
A method of obtaining the characteristic directions of a liquid crystal cell comprising locating the liquid crystal cell between a first polarizer and a second polarizer serving as an analyzer, providing an input monochromatic light source and means for measuring the light transmitted through the analyzer, and:
- (d) aligning the analyzer to be in the same direction as the polarizer,
- (c) rotating the liquid crystal cell to obtain a transmission maximum wherein the input polarizer bisects the two characteristic directions,
- (f) with the polarizer, the bisector and the analyzer aligned in the same orientation rotate the liquid crystal cell and analyzer with a magnitude ratio of 1:2 until maximum transmission is obtained wherein the polarizer and analyzer are in the primary and secondary characterization directions respectively.
A method of obtaining the characteristic directions of a liquid crystal cell comprising locating the liquid crystal cell between a polarizing beam splitter and a polarizer serving as an analyzer, providing an input monochromatic light source and a first photodetector for measuring the light transmitted through the analyzer and a second photodetector for detecting light reflected from the liquid crystal cell, and:
- (a) rotate the liquid crystal cell until the second photodetector measures zero intensity wherein the input polarization is in the primary characteristic direction,
- (f) fix the liquid crystal cell and then rotate the analyzer to obtain a maximum first photodetector reading wherein the analyzer is in the secondary characteristic direction.
A method of obtaining the retardation value of a reflective liquid crystal cell comprising locating the liquid crystal cell between a polarizing beam splitter and a polarizer serving as an analyzer, providing an input monochromatic light source and a first photodetector for measuring the light transmitted through the analyzer and a second photodetector for detecting light reflected from the liquid crystal cell, and:
- (c) rotating the reflective liquid crystal cell until the second photodetector measures zero intensity,
- (d) obtaining the retardation value can be obtained by solving the equation φ δ 2 + φ 2 tan δ 2 + φ 2 = tan 2 α *
- with the twist angle and rubbing direction known in advance.
Dependencies are inferred from the claim text.