Abstract

We describe a simple common-path self-referencing interferometric method requiring no auxiliary optical elements which accurately and directly measures the thermal diffusivity of anisotropic crystals in nonsteady-state conditions. We determine the thermal diffusivity of a lithium niobate crystal as a function of temperature ranging from room temperature up to 500°C.

© 1987 Optical Society of America

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References

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  1. D. Hon, “High Average Power Efficient Second Harmonic Generation,” in Laser Handbook, M. L. Stitch, Ed. (North-Holland, New York, 1979), Vol. 3, pp. 421–484.
  2. R. A. Morgan, F. A. Hopf, “Measurement of the Temperature Tuning Coefficient of Lithium Niobate Using Nonlinear Optical Interferometry,” Appl. Opt. 25, 3011 (1986).
    [CrossRef]
  3. S. E. Gustafsson, A. J. Hamdani, E. Karawacki, “New Method for Measuring Thermal Properties of Transparent Solids,” J. Phys 12, 387 (1979).
  4. D. Malacara, Optical Shop Testing (Wiley, New York, 1978).
  5. C. Kittel, H. Kromer, Thermal Physics (Freeman, San Francisco, 1980).
  6. F. A. Hopf, G. Stegeman, Applied Classical Electrodynamics: Nonlinear Optics, Vol. 2 (Wiley, New York, 1986).
  7. F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).
  8. As quoted inA. Sigrist, R. Balzer, “Untersuchungen zur Bidung von Tracks in Kristallen,” Helv. Phys. Acta 50, 49 (1977).
  9. V. V. Chechkin, “Method of Measuring Thermal Conductivity,” Zavod. Lab. (Indust. Lab.) 46, 146 (Feb.1980).
  10. Yu. N. Venevtsev, S. A. Fedulov, Z. I. Shapiro, V. P. Klyuev, Barium Titanate (Nauka, Moscow, 1973), p.118, in Russian.
  11. V. V. Zhdanova, V. P. Klyuev, V. V. Lemanov, I. A. Smirnov, V. V. Tikhonov, “Thermal Properties of Lithium Niobate Crystals,” Sov. Phys. Solid State 10, 1360 (1968).
  12. The program used is called FAST! Video. Video fringe analysis software tools are available from Phase Shift Technology, Inc., 2601 N. Campbell Ave., Tucson, AZ 85719.
  13. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

1986 (1)

1980 (1)

V. V. Chechkin, “Method of Measuring Thermal Conductivity,” Zavod. Lab. (Indust. Lab.) 46, 146 (Feb.1980).

1979 (1)

S. E. Gustafsson, A. J. Hamdani, E. Karawacki, “New Method for Measuring Thermal Properties of Transparent Solids,” J. Phys 12, 387 (1979).

1977 (1)

As quoted inA. Sigrist, R. Balzer, “Untersuchungen zur Bidung von Tracks in Kristallen,” Helv. Phys. Acta 50, 49 (1977).

1968 (1)

V. V. Zhdanova, V. P. Klyuev, V. V. Lemanov, I. A. Smirnov, V. V. Tikhonov, “Thermal Properties of Lithium Niobate Crystals,” Sov. Phys. Solid State 10, 1360 (1968).

Balzer, R.

As quoted inA. Sigrist, R. Balzer, “Untersuchungen zur Bidung von Tracks in Kristallen,” Helv. Phys. Acta 50, 49 (1977).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Chechkin, V. V.

V. V. Chechkin, “Method of Measuring Thermal Conductivity,” Zavod. Lab. (Indust. Lab.) 46, 146 (Feb.1980).

Fedulov, S. A.

Yu. N. Venevtsev, S. A. Fedulov, Z. I. Shapiro, V. P. Klyuev, Barium Titanate (Nauka, Moscow, 1973), p.118, in Russian.

Gustafsson, S. E.

S. E. Gustafsson, A. J. Hamdani, E. Karawacki, “New Method for Measuring Thermal Properties of Transparent Solids,” J. Phys 12, 387 (1979).

Hamdani, A. J.

S. E. Gustafsson, A. J. Hamdani, E. Karawacki, “New Method for Measuring Thermal Properties of Transparent Solids,” J. Phys 12, 387 (1979).

Hon, D.

D. Hon, “High Average Power Efficient Second Harmonic Generation,” in Laser Handbook, M. L. Stitch, Ed. (North-Holland, New York, 1979), Vol. 3, pp. 421–484.

Hopf, F. A.

Karawacki, E.

S. E. Gustafsson, A. J. Hamdani, E. Karawacki, “New Method for Measuring Thermal Properties of Transparent Solids,” J. Phys 12, 387 (1979).

Kittel, C.

C. Kittel, H. Kromer, Thermal Physics (Freeman, San Francisco, 1980).

Klyuev, V. P.

V. V. Zhdanova, V. P. Klyuev, V. V. Lemanov, I. A. Smirnov, V. V. Tikhonov, “Thermal Properties of Lithium Niobate Crystals,” Sov. Phys. Solid State 10, 1360 (1968).

Yu. N. Venevtsev, S. A. Fedulov, Z. I. Shapiro, V. P. Klyuev, Barium Titanate (Nauka, Moscow, 1973), p.118, in Russian.

Kromer, H.

C. Kittel, H. Kromer, Thermal Physics (Freeman, San Francisco, 1980).

Lemanov, V. V.

V. V. Zhdanova, V. P. Klyuev, V. V. Lemanov, I. A. Smirnov, V. V. Tikhonov, “Thermal Properties of Lithium Niobate Crystals,” Sov. Phys. Solid State 10, 1360 (1968).

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Midwinter, J. E.

F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).

Morgan, R. A.

Shapiro, Z. I.

Yu. N. Venevtsev, S. A. Fedulov, Z. I. Shapiro, V. P. Klyuev, Barium Titanate (Nauka, Moscow, 1973), p.118, in Russian.

Sigrist, A.

As quoted inA. Sigrist, R. Balzer, “Untersuchungen zur Bidung von Tracks in Kristallen,” Helv. Phys. Acta 50, 49 (1977).

Smirnov, I. A.

V. V. Zhdanova, V. P. Klyuev, V. V. Lemanov, I. A. Smirnov, V. V. Tikhonov, “Thermal Properties of Lithium Niobate Crystals,” Sov. Phys. Solid State 10, 1360 (1968).

Stegeman, G.

F. A. Hopf, G. Stegeman, Applied Classical Electrodynamics: Nonlinear Optics, Vol. 2 (Wiley, New York, 1986).

Tikhonov, V. V.

V. V. Zhdanova, V. P. Klyuev, V. V. Lemanov, I. A. Smirnov, V. V. Tikhonov, “Thermal Properties of Lithium Niobate Crystals,” Sov. Phys. Solid State 10, 1360 (1968).

Venevtsev, Yu. N.

Yu. N. Venevtsev, S. A. Fedulov, Z. I. Shapiro, V. P. Klyuev, Barium Titanate (Nauka, Moscow, 1973), p.118, in Russian.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Zernike, F.

F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).

Zhdanova, V. V.

V. V. Zhdanova, V. P. Klyuev, V. V. Lemanov, I. A. Smirnov, V. V. Tikhonov, “Thermal Properties of Lithium Niobate Crystals,” Sov. Phys. Solid State 10, 1360 (1968).

Appl. Opt. (1)

Helv. Phys. Acta (1)

As quoted inA. Sigrist, R. Balzer, “Untersuchungen zur Bidung von Tracks in Kristallen,” Helv. Phys. Acta 50, 49 (1977).

J. Phys (1)

S. E. Gustafsson, A. J. Hamdani, E. Karawacki, “New Method for Measuring Thermal Properties of Transparent Solids,” J. Phys 12, 387 (1979).

Sov. Phys. Solid State (1)

V. V. Zhdanova, V. P. Klyuev, V. V. Lemanov, I. A. Smirnov, V. V. Tikhonov, “Thermal Properties of Lithium Niobate Crystals,” Sov. Phys. Solid State 10, 1360 (1968).

Zavod. Lab. (Indust. Lab.) (1)

V. V. Chechkin, “Method of Measuring Thermal Conductivity,” Zavod. Lab. (Indust. Lab.) 46, 146 (Feb.1980).

Other (8)

Yu. N. Venevtsev, S. A. Fedulov, Z. I. Shapiro, V. P. Klyuev, Barium Titanate (Nauka, Moscow, 1973), p.118, in Russian.

The program used is called FAST! Video. Video fringe analysis software tools are available from Phase Shift Technology, Inc., 2601 N. Campbell Ave., Tucson, AZ 85719.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

C. Kittel, H. Kromer, Thermal Physics (Freeman, San Francisco, 1980).

F. A. Hopf, G. Stegeman, Applied Classical Electrodynamics: Nonlinear Optics, Vol. 2 (Wiley, New York, 1986).

F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).

D. Hon, “High Average Power Efficient Second Harmonic Generation,” in Laser Handbook, M. L. Stitch, Ed. (North-Holland, New York, 1979), Vol. 3, pp. 421–484.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental configuration used to measure the thermal diffusivity of lithium niobate. Note that two slightly different configurations were used. First, to collect data with the 1-D CCD array and OMA a collimating lens L1 is necessary. Also it aids in the accuracy and alignment to have a slit which is parallel to the appropriate crystal axis and CCD array. Second, to collect data with a TV camera, L1 is not necessary if the crystal is properly imaged (and magnified) into the camera.

Fig. 2
Fig. 2

Illustrations of interference fringes from this experiment. (a) Reference fringes as seen in the crystal plane before heating (OPD0). Note that perfectly straight parallel reference fringes were not required. (b) Interference fringes after the crystal has been irradiated with the CO2 heat pulse deviating the fringes from their unperturbed positions. (c) The 1-D CCD array scan of the reference fringes at t0 (solid line) and superimposed are the perturbed fringes at a later time t1 (dotted line). The intensity in arbitrary units is plotted vs the distance along the y direction.

Fig. 3
Fig. 3

Data (denoted by circles) and the resulting quadratic fit [see Eq. (17)] computed from a least-squares regression. The curvature determines the parameter 4Dyt for a given time t after the pulse.

Fig. 4
Fig. 4

Thermal diffusivity of lithium niobate as a function of temperature as determined using the RSI. (The dashes connecting the data points are for visual guidance.)

Fig. 5
Fig. 5

(a) Perturbed phase distribution (ΔOPD) at a given time following the CO2 laser heat pulse. This is also simply proportional to the temperature distribution. The data were determined by fitting fringe data to Zernike polynomials after irradiating the crystal with a heat impulse (OPD1) and subsequently subtracting out the reference phase (OPD0). (b) The x and y profiles of OPD1 (denoted by dots) and their corresponding fits to a 2-D Gaussian (solid line).

Equations (19)

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OPD = 2 n d + 2 n y tan θ = m λ ,
OPD 0 = 2 n d + 2 n y tan θ + f ( x , y ) .
OPD 1 = OPD 0 + 2 d n T δ T + 2 n d T δ T ,
OPD 1 = OPD 0 + c δ T ( x , y , t ) ,
c 2 d ( n T + n α ) .
Δ OPD = c δ T ( x , y , t ) .
δ T ( x , y , t ) t = ( D x 2 x 2 + D y 2 y 2 ) δ T ( x , y , t ) + S ( x , y , t ) R ( x , y , t ) ,
δ T ( x , y , t ) t = ( D x 2 x 2 + D y 2 y 2 ) δ T ( x , y , t ) .
δ T ( x , y , t ) = C 4 π ( D x D y ) 1 / 2 t exp [ ( x x 0 ) 2 4 D x t ] exp [ ( y y 0 ) 2 4 D y t ] ,
Δ OPD = C t exp [ ( x x 0 ) 2 4 D x t ] exp [ ( y y 0 ) 2 4 D y t ] ,
β ( n s , e n f , o ) T ,
Δ n = Δ n 0 + β δ T ( x , y , t ) ,
OPD 0 = 2 n d + 2 n tan θ y + f ( x , y ) = m 0 λ .
OPD ( t 1 ) 1 = OPD 0 + C t 1 exp [ ( x x 0 ) 2 4 D x t 1 ] × exp [ ( y y 0 ) 2 4 D y t 1 ] = m 1 λ .
Δ OPD ( t 1 ) = C t 1 exp [ ( y y 0 ) 2 4 D y t 1 ] = ( m 1 m 0 ) λ .
Δ OPD ( t 2 ) = C t 2 exp [ ( y y 0 ) 2 4 D y t 2 ] = ( m 2 m 0 ) λ .
ln ( Δ m 1 , 2 ) = ln ( C t 1 , 2 ) 1 4 D y t 1 , 2 ( y y 0 ) 2 .
ln ( Δ m 1 , 2 ) = A 1 , 2 + B 1 , 2 y + C 1 , 2 y 2 ,
D y = 1 C 1 1 C 2 4 Δ t .

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