Abstract

Rapid calibration of liquid crystal variable retarder (LCVR) devices is critical for successful clinical implementation of a LC-based Mueller matrix imaging system being developed for noninvasisve skin cancer detection. For multispectral implementation of such a system, the effect of wavelength (λ), temperature (T), and voltage (V) on the retardance (δ) required to generate each desired polarization state needs to be clearly understood. Calibration involves quantifying this interdependence such that for a given set of system input variables (λ,T), the appropriate voltage is applied across a LC cell to generate a particular retardance. This paper presents findings that elucidate the dependence of voltage, for a set retardance, on the aforementioned variables for a nematic LC cell:253  mV/100   nm λ-dependence and 10mV/°C T-dependence. Additionally, an empirically derived model is presented that enables initial voltage calibration of retardance for any desired input wavelength within the calibration range of 460905  nm.

© 2007 Optical Society of America

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References

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  1. J. S. Baba, J. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Bio. Med. Opt. 7, 341-349 (2002).
    [CrossRef]
  2. S. Wu, U. Efron, and L. D. Hess, "Birefringence measurements of liquid crystals," Appl. Opt. 23, 3911-3915 (1984).
    [CrossRef] [PubMed]
  3. I. Khoo and S. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, 1993).
  4. A. De Martino, Y. Kim, E. Garcia-Caurel, B. Laude, and D. Drevillon, "Optimized Mueller polarimeter with liquid crystals," Opt. Lett. 28, 616-618 (2003).
    [CrossRef] [PubMed]
  5. E. Compain, S. Poirier, and B. Drevillon, "General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers," Appl. Opt. 38, 3490-3502 (1999).
    [CrossRef]

2003

2002

J. S. Baba, J. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Bio. Med. Opt. 7, 341-349 (2002).
[CrossRef]

1999

1993

I. Khoo and S. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, 1993).

1984

Baba, J. S.

J. S. Baba, J. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Bio. Med. Opt. 7, 341-349 (2002).
[CrossRef]

Cameron, B. D.

J. S. Baba, J. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Bio. Med. Opt. 7, 341-349 (2002).
[CrossRef]

Chung, J.

J. S. Baba, J. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Bio. Med. Opt. 7, 341-349 (2002).
[CrossRef]

Compain, E.

Cote, G. L.

J. S. Baba, J. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Bio. Med. Opt. 7, 341-349 (2002).
[CrossRef]

De Martino, A.

DeLaughter, A. H.

J. S. Baba, J. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Bio. Med. Opt. 7, 341-349 (2002).
[CrossRef]

Drevillon, B.

Drevillon, D.

Efron, U.

Garcia-Caurel, E.

Hess, L. D.

Khoo, I.

I. Khoo and S. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, 1993).

Kim, Y.

Laude, B.

Poirier, S.

Wu, S.

I. Khoo and S. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, 1993).

S. Wu, U. Efron, and L. D. Hess, "Birefringence measurements of liquid crystals," Appl. Opt. 23, 3911-3915 (1984).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Scaled and normalized detected transmitted intensity for λ = 670   nm and T = 29.5 ° C versus voltage for a single E7 liquid crystal cell of thickness 10 .52   μm . Some extrema and midpoints are labeled with the corresponding retardance values.

Fig. 2
Fig. 2

(Color online) Optical set up used to investigate temperature and wavelength effects on the retardance versus voltage relationship of a nematic liquid crystal cell.

Fig. 3
Fig. 3

(Color online) Illustration of the six polarization states of light produced by the polarization generator.

Fig. 4
Fig. 4

(Color online) Representation of a Merck E7 LC cell not drawn to scale.

Fig. 5
Fig. 5

The inset plot dark curve is δ ( V , λ = 670   nm , T = 29.54 ° C ) of the LC based on Wu's phase difference measurement technique; grey curve is the exponential fit between π and 3.5π retardances. The main plot is the actual normalized and scaled transmitted intensity. The dots are experimental data and the solid grey curve is calculated based on the parameters found from the inset grey curve.

Fig. 6
Fig. 6

The inset plot dark curve is δ ( V , λ = 633   nm , T = 30.13 ° C ) of the LC based on Wu's phase difference measurement technique; grey curve is the exponential fit between π and 3.5π retardances. The main plot is the actual normalized and scaled transmitted intensity. The dots are experimental data and the solid grey curve is calculated based on the parameters found from the inset grey curve. The functions a ( λ , T ) , b ( λ , T ) , c ( λ , T ) , described in Table 2, were used to generate these empirical curves.

Tables (2)

Tables Icon

Table 1 Temperatures and Wavelengths Used to Determine the Dependence of Birefringence on Voltage Modeled as an Exponential

Tables Icon

Table 2 Variable Order and Coefficients for the Empirical Equations Describing the Three Fit Parameters a

Equations (72)

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( λ , T )
253   mV / 100   nm
10 mV / ° C
460 905   nm
S 0 ,
S 0 ,
1 2 ( 1 sin 2 ( δ / 2 ) + cos 2 ( δ / 2 ) 1 sin 2 ( δ / 2 ) + cos 2 ( δ / 2 ) 0 0 ) = 1 2 ( 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ) . ( 1 0 0 0 0 sin 2 ( δ / 2 ) + cos 2 ( δ / 2 ) 0 sin ( δ ) 0 0 1 0 0 sin ( δ ) 0 cos ( δ ) ) ( 1 1 0 0 ) ,
  1 2 ( 1 + sin 2 ( δ / 2 ) cos 2 ( δ / 2 ) 1 sin 2 ( δ / 2 ) + cos 2 ( δ / 2 ) 0 0 ) = 1 2 ( 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ) . ( 1 0 0 0 0 sin 2 ( δ / 2 ) + cos 2 ( δ / 2 ) 0 sin ( δ ) 0 0 1 0 0 sin ( δ ) 0 cos ( δ ) ) ( 1 1 0 0 ) ,
S 0 , = cos 2 ( δ / 2 ) ,     S 0 , = sin 2 ( δ / 2 ) .
S 0 ,
S 0 ,
S 0 , / S 0 ,
( Δ η )
η o
η e
Δ η ( V , λ , T )
δ ( V , λ , T ) = 2 π l Δ η ( V , λ , T ) λ .
δ ( V )
V th < V < V ( δ = 2.5 λ ; 2 V th )
V ( δ = 2.5 λ ) < V < V ( δ = 0.5 λ ; 4 V th )
V ( δ = 0.5 λ ) < V
V th
δ ( V )
π ( 0.5 λ )
3.5 π ( 1.75 λ )
δ ( V )
( λ , T )
δ = 2 π l λ ( a e b V + c ) .
| I I min | I max I min = cos 2 ( π l λ ( a e b V + c ) ) .
p
M P E = | p p | n .
V ( δ , λ , T )
10   nm
905   nm
2   kHz
10V peak
0V peak
40 ° C
± 300   mV
V ( δ , λ , T )
V ( δ , λ , T )
a ( λ , T )
b ( λ , T )
c ( λ , T )
Measured = 0.9685 × ( Set ) 1.4914
δ ( V )
3.5 π
P ( λ , T ) = n = 1 6 C n λ p n T q n .
P = a
a ( λ , T ) = ( 1.38 e 7 ) λ T ( 3.3434 e 4 ) T 2 + ( 0.017 ) T 1.488 + ( 5.472 e 3 ) λ ( 3.809 e 6 ) λ 2 .
δ ( V )
λ = 460 905   nm
T = 23.66 37.26     ° C
633   nm
30 .13   ° C
δ ( V )
3.5 π
2 π
3 π
50   mV
3 .5 π
± 50   mV
λ = 670   nm
T = 29.5 ° C
10 .52   μm
( V , λ = 670   nm
T = 29.54 ° C
( V , λ = 633   nm
T = 30.13 ° C
a ( λ , T )
b ( λ , T )
c ( λ , T )

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