Abstract

An interferometric method of measuring small differences between weak optical absorptions of solutions has been developed using the thermooptic effect. To record the small changes in optical path length ∼λ/200 due to heating, it was necessary to stabilize the fringe pattern with respect to slow thermal drift using a galvanometer-driven compensator plate controlled by a closed feedback loop. Fringe shifts from background absorptions were nulled out to better than 1 part in 400, permitting the measurement of differences in absorptions between two solutions that were 1/100th of background. Using laser powers of 100 mW, absorptions ∼5 × 10−6 cm−1 (base e) could be measured with CCl4 solutions.

© 1982 Optical Society of America

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References

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  1. The absorptivity (α) used here is defined by the equation I = I0 exp(−αl), where l is the path length of the laser beam through the solution.
  2. See, for example, the following articles and references therein: J. R. Whinnery, Acc. Chem. Res. 7, 225 (1974);D. S. Kliger, Acc. Chem. Res. 13, 129 (1980).
    [CrossRef]
  3. J. Stone, J. Opt. Soc. Am. 62, 327 (1972).
    [CrossRef]
  4. J. Stone, Appl. Opt. 12, 1828 (1973);A. Hordvik, Appl. Opt. 16, 2827 (1977).
    [CrossRef] [PubMed]
  5. W. B. Jackson, N. M. Amer, A. C. Boccara, D. Fournier, Appl. Opt. 20, 1333 (1981).
    [CrossRef] [PubMed]
  6. N. J. Dovichi, J. M. Harris, Anal. Chem. 53, 106 (1981).
    [CrossRef]
  7. N. J. Dovichi, J. M. Harris, Anal. Chem. 52, 2338 (1980).
    [CrossRef]
  8. J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
    [CrossRef]
  9. Instruction manual for model 18 benchtop interferometer, Optical Engineering, Santa Rosa, Calif.
  10. The visibility of a fringe pattern is defined to be V = (Imax − Imin)/(Imax + Imin), where Imax and Imin are the intensities at the maxima and minima of the fringe pattern, respectively. The visibility is a maximum (V = 1) when the interfering beams have the same intensities.
  11. Estimates of the fluorescence quantum yield (Φfl) for solutions of I2/CCl4, CoSO4/water, and CoSO4/CH3OH were obtained by comparing the emission intensity from these with that from rhodamine 6G/CH3OH excited with 3.5 mW of the 515-nm Ar-ion laser line. The absorptivity of the solutions was adjusted to 2.8 × 10−4 cm−1. For the value Φfl (rhodamine 6G/CH3OH) = 0.95 our results indicate that Φfl of all three solutions is <0.02, which was the resolution of our comparison method.
  12. R. C. Smith, K. S. Baker, Appl. Opt. 20, 177 (1981).
    [CrossRef] [PubMed]
  13. This absorptivity was measured by comparing the initial slope of d(LIA signal)/dt obtained with CH3OH in one cell of the interferometer (other cell empty) with the slope obtained from a reference sample (water). For t ≪ tcEq. (4) becomes ΔOPL(t) = (αoPlt)[dno(λ,T)/dT]/(8.4πktc) = (αoPlt)/(2.1πω2ζ), where the solvent parameters other than αo are lumped into ζ. Because the LIA signal ∝ ΔOPL(t), we obtain α(CH3OH) = α(water)[ζd (LIA signal)/dt]CH3OH/[ζd(LIA signal)/dt]water. The absorptivity of water at 515 nm was taken to be 3 × 10−4 cm−1 (see Ref. 12).
  14. This equation is similar to that derived by C. Hu, J. R. Whinnery, Appl. Opt. 12, 72 (1973), except for the ρ2 factor, omitted from the latter, and which must be included.Our equation is obtained by S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968), if χ in their Eq. (28) is set equal to k/ρc rather than the thermal conductivity as they state.[See L. Landau, E. M. Liftshitz, Fluid Mechanics (Pergamon, Oxford, 1959), pp. 202–213].
    [CrossRef] [PubMed]
  15. A. D. Fisher, C. Warde, Opt. Lett. 4, 131 (1979).
    [CrossRef] [PubMed]
  16. F. Zernike, J. Opt. Soc. Am. 40, 326 (1950);R. E. Kinzly, Appl. Opt. 6, 137 (1967);L. Sica, Appl. Opt. 12, 2848 (1973).
    [CrossRef] [PubMed]
  17. M. S. Burberry, J. A. Morrell, A. C. Albrecht, R. L. Swofford, J. Chem. Phys. 70, 5522 (1979).
    [CrossRef]
  18. For t ≪ tc both the interferometer and thermal lensing responses are proportional to t/tc = 4tk/ρcω2. Hence for a given solvent the difference in the rate of response of the two techniques is determined in part by ω.
  19. R. B. Green, R. A. Keller, G. G. Luther, P. K. Schenck, J. C. Travis, IEEE J. Quantum Electron. QE-13, 63 (1977).
    [CrossRef]

1981 (3)

1980 (1)

N. J. Dovichi, J. M. Harris, Anal. Chem. 52, 2338 (1980).
[CrossRef]

1979 (2)

M. S. Burberry, J. A. Morrell, A. C. Albrecht, R. L. Swofford, J. Chem. Phys. 70, 5522 (1979).
[CrossRef]

A. D. Fisher, C. Warde, Opt. Lett. 4, 131 (1979).
[CrossRef] [PubMed]

1977 (1)

R. B. Green, R. A. Keller, G. G. Luther, P. K. Schenck, J. C. Travis, IEEE J. Quantum Electron. QE-13, 63 (1977).
[CrossRef]

1974 (1)

See, for example, the following articles and references therein: J. R. Whinnery, Acc. Chem. Res. 7, 225 (1974);D. S. Kliger, Acc. Chem. Res. 13, 129 (1980).
[CrossRef]

1973 (2)

1972 (1)

1965 (1)

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

1950 (1)

Albrecht, A. C.

M. S. Burberry, J. A. Morrell, A. C. Albrecht, R. L. Swofford, J. Chem. Phys. 70, 5522 (1979).
[CrossRef]

Amer, N. M.

Baker, K. S.

Boccara, A. C.

Burberry, M. S.

M. S. Burberry, J. A. Morrell, A. C. Albrecht, R. L. Swofford, J. Chem. Phys. 70, 5522 (1979).
[CrossRef]

Dovichi, N. J.

N. J. Dovichi, J. M. Harris, Anal. Chem. 53, 106 (1981).
[CrossRef]

N. J. Dovichi, J. M. Harris, Anal. Chem. 52, 2338 (1980).
[CrossRef]

Fisher, A. D.

Fournier, D.

Gordon, J. P.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Green, R. B.

R. B. Green, R. A. Keller, G. G. Luther, P. K. Schenck, J. C. Travis, IEEE J. Quantum Electron. QE-13, 63 (1977).
[CrossRef]

Harris, J. M.

N. J. Dovichi, J. M. Harris, Anal. Chem. 53, 106 (1981).
[CrossRef]

N. J. Dovichi, J. M. Harris, Anal. Chem. 52, 2338 (1980).
[CrossRef]

Hu, C.

Jackson, W. B.

Keller, R. A.

R. B. Green, R. A. Keller, G. G. Luther, P. K. Schenck, J. C. Travis, IEEE J. Quantum Electron. QE-13, 63 (1977).
[CrossRef]

Leite, R. C. C.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Luther, G. G.

R. B. Green, R. A. Keller, G. G. Luther, P. K. Schenck, J. C. Travis, IEEE J. Quantum Electron. QE-13, 63 (1977).
[CrossRef]

Moore, R. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Morrell, J. A.

M. S. Burberry, J. A. Morrell, A. C. Albrecht, R. L. Swofford, J. Chem. Phys. 70, 5522 (1979).
[CrossRef]

Porto, S. P. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Schenck, P. K.

R. B. Green, R. A. Keller, G. G. Luther, P. K. Schenck, J. C. Travis, IEEE J. Quantum Electron. QE-13, 63 (1977).
[CrossRef]

Smith, R. C.

Stone, J.

Swofford, R. L.

M. S. Burberry, J. A. Morrell, A. C. Albrecht, R. L. Swofford, J. Chem. Phys. 70, 5522 (1979).
[CrossRef]

Travis, J. C.

R. B. Green, R. A. Keller, G. G. Luther, P. K. Schenck, J. C. Travis, IEEE J. Quantum Electron. QE-13, 63 (1977).
[CrossRef]

Warde, C.

Whinnery, J. R.

Zernike, F.

Acc. Chem. Res. (1)

See, for example, the following articles and references therein: J. R. Whinnery, Acc. Chem. Res. 7, 225 (1974);D. S. Kliger, Acc. Chem. Res. 13, 129 (1980).
[CrossRef]

Anal. Chem. (2)

N. J. Dovichi, J. M. Harris, Anal. Chem. 53, 106 (1981).
[CrossRef]

N. J. Dovichi, J. M. Harris, Anal. Chem. 52, 2338 (1980).
[CrossRef]

Appl. Opt. (4)

IEEE J. Quantum Electron. (1)

R. B. Green, R. A. Keller, G. G. Luther, P. K. Schenck, J. C. Travis, IEEE J. Quantum Electron. QE-13, 63 (1977).
[CrossRef]

J. Appl. Phys. (1)

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

J. Chem. Phys. (1)

M. S. Burberry, J. A. Morrell, A. C. Albrecht, R. L. Swofford, J. Chem. Phys. 70, 5522 (1979).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Other (6)

For t ≪ tc both the interferometer and thermal lensing responses are proportional to t/tc = 4tk/ρcω2. Hence for a given solvent the difference in the rate of response of the two techniques is determined in part by ω.

Instruction manual for model 18 benchtop interferometer, Optical Engineering, Santa Rosa, Calif.

The visibility of a fringe pattern is defined to be V = (Imax − Imin)/(Imax + Imin), where Imax and Imin are the intensities at the maxima and minima of the fringe pattern, respectively. The visibility is a maximum (V = 1) when the interfering beams have the same intensities.

Estimates of the fluorescence quantum yield (Φfl) for solutions of I2/CCl4, CoSO4/water, and CoSO4/CH3OH were obtained by comparing the emission intensity from these with that from rhodamine 6G/CH3OH excited with 3.5 mW of the 515-nm Ar-ion laser line. The absorptivity of the solutions was adjusted to 2.8 × 10−4 cm−1. For the value Φfl (rhodamine 6G/CH3OH) = 0.95 our results indicate that Φfl of all three solutions is <0.02, which was the resolution of our comparison method.

This absorptivity was measured by comparing the initial slope of d(LIA signal)/dt obtained with CH3OH in one cell of the interferometer (other cell empty) with the slope obtained from a reference sample (water). For t ≪ tcEq. (4) becomes ΔOPL(t) = (αoPlt)[dno(λ,T)/dT]/(8.4πktc) = (αoPlt)/(2.1πω2ζ), where the solvent parameters other than αo are lumped into ζ. Because the LIA signal ∝ ΔOPL(t), we obtain α(CH3OH) = α(water)[ζd (LIA signal)/dt]CH3OH/[ζd(LIA signal)/dt]water. The absorptivity of water at 515 nm was taken to be 3 × 10−4 cm−1 (see Ref. 12).

The absorptivity (α) used here is defined by the equation I = I0 exp(−αl), where l is the path length of the laser beam through the solution.

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Figures (7)

Fig. 1
Fig. 1

Apparatus used for differential measurements of solvent absorptions: RB is the reference He–Ne beam; PB is the probe He–Ne beam, N is the neutral density filter; M is the mirror to superimpose the heating laser beam on the probe beam; P is the thin glass plate to adjust the heating beam intensity at sample cell (C); W is the wedged quartz window; G is the grating; GC is the galvanometer-driven compensator; MC is the manual compensator for the probe beam; MM is the plane mirror; L is the negative lens; SC is the screen with a small hole in the center, and PD is the photodetector. The folded Jamin interferometer is made from two reflection-coated glass blocks.

Fig. 2
Fig. 2

Stabilization of the probe fringe pattern with respect to drift. The curves represent the LIA signal over a period of 80 sec. The straight horizontal lines are the base lines (0 V). (a) Drift of the probe fringe pattern with the stabilization circuitry off. Drift is ∼−4 V. (b) Drift of the fringes with the stabilization circuitry on. Drift has been reduced by a factor of ∼100.

Fig. 3
Fig. 3

LIA signal vs change of solute absorptivity (αs) for three solvents: water (△); CH3OH (□); CCl4 (○). Solute was added to one cell to produce a differential response. The background absorption for CH3OH was 2.3 × 10−3 cm−1 in each cell. The background absorption for water and CCl4 was provided by the absorption of the pure solvent. The slopes of the least squares fit lines are water (800 ± 1.4%), CH3OH (4550 ± 2.4%), and CCl4 (11300 ± 1.1%).

Fig. 4
Fig. 4

Comparison of LIA signals with the apparatus in nondifferential [(a) and (c)] and differential (b) configurations. (a) One cell contains pure CH3OH and the other cell contains a CoSO4/CH3OH solution having α(515 nm) = 2.3 × 10−3 cm−1. (b) Both cells contain the CoSO4/CH3OH solution with α(515 nm) = 2.3 × 10−3 cm−1. (c) The solutions in (a) are interchanged between the two cells. The initial spike on each curve indicates the start of heating of the solutions by unblocking the Ar-ion laser beam. Heating lasts for 10 sec.

Fig. 5
Fig. 5

Comparison of measurements made with the apparatus in differential (○) and nondifferential (□) configurations. In both cases the background absorption was 2.3 × 10−3 cm−1. The solute absorptivity (αs) added to one cell to increase the absorption above the background level is plotted on the abscissa.

Fig. 6
Fig. 6

Demonstration that the smallest absorptivity measurable with the interferometer is ∼5 × 10−6 cm−1. The solution was I2/CCl4 and the laser power was 100 mW.

Fig. 7
Fig. 7

Fringe stabilization circuitry. The operational amplifier (op-amp) sums the dc error and reference voltages to the galvanometer. In our apparatus the op-amp enclosed by the dashed circle was replaced by the electronics from a commercial galvanometer system which served the same purpose. Here GC is the galvanometer-driven compensator; MM is the plane mirror; L is the negative lens; SC is the screen with a small hole in the center; PD is the photodiode; LIA is the lock-in amplifier; and RB and PB are, respectively, reference and probe He–Ne laser beams inside one arm of the interferometer.

Tables (1)

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Table I Experimental and Calculated Parameters of Some Pure Solvents

Equations (17)

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Δ OPL ( r , t ) = l d n 0 ( λ , T ) = l d n 0 ( λ , T ) d T Δ T ( r , t ) ,
Δ T ( r , t ) = ( α o + α s ) P 16.8 π k [ ln ( 1 + 2 t / t c ) 2 ( r / ω ) 2 1 + t c / 2 t ] ,
t c = ω 2 ρ c / 4 k
Δ OPL ( r , t ) = Δ OPL ( t ) = l d n 0 ( λ , T ) d T ( α o + α s ) P 16.8 π k × ln ( 1 + 2 t / t c ) r ~ 0 .
δ Δ OPL ( t ) = l P 16.8 π k d n 0 ( λ , T ) d T ln ( 1 + 2 t / t c ) ( α s α s ) = β P Δ α ,
β = l 16.8 π k d n 0 ( λ , T ) d T ln ( 1 + 2 t / t c ) and Δ α = α s α s .
I ( t ) = 2 I 0 [ 1 + cos Φ ( t ) ] ,
ϕ 2 ( t ) = 2 π λ δ Δ OPL ( t ) .
ϕ ( θ ) = 2 π λ { d cos θ t [ n 1 cos ( θ θ t ) ] + d ( 1 n 1 ) } ,
ϕ 3 ( t ) = [ ϕ ( θ 0 ) ϕ ( θ ) ] .
θ ( t ) = θ 0 + Δ θ sin ( 2 π f t )
I ( t ) = 2 I 0 { 1 + cos [ π + ϕ 2 ( t ) + ϕ 3 ( t ) ] } ,
V ( t ) = V 0 { 1 + cos [ π + ϕ 2 ( t ) + ϕ 3 ( t ) ] } .
f ( t ) = H ( τ / 2 t ) H ( t τ / 2 ) , 0 < t < τ .
D ( t ) 0 τ f ( t ) V ( t ) d t = 0 τ f ( t ) { [ π + ϕ 2 ( t ) ] cos ϕ 3 ( t ) sin [ π + ϕ 2 ( t ) ] sin ϕ 3 ( t ) } d t = cos ϕ 2 ( t ) 0 τ f ( t ) cos ϕ 3 ( t ) d t + sin ϕ 2 ( t ) 0 τ f ( t ) sin ϕ 3 ( t ) d t = I 1 cos ϕ 2 ( t ) + I 2 sin ϕ 2 ( t ) .
D ( 10 sec ) ( 2.47 × 10 7 ) cos ϕ 2 ( 10 sec ) ( 6.34 × 10 4 ) × sin ϕ 2 ( 10 sec ) .
D ( 10 sec ) Δ α

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