Abstract

Wavelength modulation imaging (WMI) is capable of determining both spectroscopic and geometrical properties of a target, but the latter is often ignored in spectroscopic studies. This work theoretically and experimentally demonstrates the importance of both in WMI applications. Experiments were performed with an all-digital signal processing approach employing a tunable mid-infrared laser capable of digital wavelength modulation. All three orders of wavelength-derivative images, 0th, 1st, and 2nd are generated simultaneously. Higher order images can reveal or enhance features that are not evident in the 0th order. An example shows a synthetic imaging approach that combines the 2nd order WMI of CO gas with a focal plane array image to allow chemical visualization with minimal background clutter. In another example, fine geometrical features were revealed for a target that has little intrinsic spectroscopic signatures.

© 2004 Optical Society of America

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References

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  1. See for example, R. Grisar, H. Boettner, M. Tacke, and G. Restelli (Eds.), �??Monitoring of gaseous pollutants by tunable diode lasers,�?? in Proceedings of the International Symposium, Freiburg, Germany, 1991, Kluwer Academic Publishers, Dordrecht, The Netherlands (1992).
  2. See for example, P. Werle, �??A review of recent advances in semiconductor laser based gas monitors,�?? Spectrochim. Acta Part A 54, 197-236 (1998).
    [CrossRef]
  3. D. E. Cooper, J. E. van der Laan, R. E. Warren, �??Diode-laser-based lidars: the next generation,�?? in Application of Tunable Diode and Other Infrared Sources for Atmospheric Studies and Industrial Processing Monitoring II, Proc. SPIE 3758, 142-151 (1999).
    [CrossRef]
  4. D. J. Kane, J. A. Siver, �??Real time quantitative 3-D imaging of diffusion flame species,�?? in NASA Conference Publication 10194, 281-286 (1997).
  5. D. S. Bomse, A. C. Stanton, and J. A. Silver, "Frequency modulation and wavelength modulation spectroscopies: comparison of experimental methods using a lead-salt diode laser," Appl. Opt. 31, 718-731 (1992).
    [CrossRef] [PubMed]
  6. C. Peng, H.L. Zhang, H.Q. Le, �??Mid-infrared external-cavity two-segment quantum-cascade laser,�?? Appl. Phys. Lett. 83, 4098-4100 (2003).
    [CrossRef]
  7. P. E. Powers, T.J. Kulp, and R. Kennedy, �??Demonstration of differential backscatter absorption gas imaging,�?? Appl. Opt. 39, 1440-1448 (2000).
    [CrossRef]
  8. T. G. McRae and T. J. Kulp, �??Backscatter absorption gas imaging: a new technique for gas visualization,�?? Appl. Opt. 32, 4037�??4050 (1993).
    [PubMed]
  9. T. J. Kulp, P. Powers, R. Kennedy, and U. B. Goers, �??Development of a pulsed backscatter-absorption gas-imaging and its application to the visualization of natural gas leaks,�?? Appl. Opt. 37, 3912�??3922 (1998).
    [CrossRef]
  10. See for example, E. Wolf, �??Principles and development of diffraction tomography,�?? in Trends in Optics, A. Consortini (Ed.), 83�??110 (Academic, San Diego, Calif., 1996).
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    [CrossRef]
  13. Ibid, Chap. 14, pp. 785-789.
  14. Anatoliy A. Kosterev, Frank K. Tittel, �??Chemical sensors based on quantum cascade lasers,�?? IEEE J. of Quantum Electronics 38, 582-591 (2002).
    [CrossRef]
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    [CrossRef]
  19. D. M. Sonnenfroh, W. T. Rawlins, M. G. Allen, C. Gmachl, F. Capasso, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, �??Application of balanced detection to absorption measurements of trace gases with room-temperature, quasi-cw quantum-cascade lasers�??, Appl. Opt. 40, 812-820 (2001).
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  22. C. Peng, G. P. Luo, H. Q. Le, �??Broadband, continuous, and fine-tune properties of external-cavity thermoelectric-stabilized mid-infrared quantum-cascade lasers,�?? Appl. Opt. 42, 4877-4882 (2003).
    [CrossRef] [PubMed]
  23. G. P. Luo, C. Peng, H. Q. Le, S. S. Pei, H. Lee, W. Y. Hwang, B. Ishang, and J. Zheng, �??Broadly wavelength-tunable external cavity mid-infrared quantum cascade lasers,�?? IEEE J. of Quantum Electron. 38, 486-494 (2002).
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  24. A. Evans, J.S. Yu, J. David, L. Doris, K. Mi, S. Slivken, and M. Razeghi, �??High-temperature high-power continuous-wave operation of buried heterostructure quantum-cascade lasers,�?? Appl. Phys. Lett. 84, 314-316 (2004).
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Appl. Opt. (7)

D. S. Bomse, A. C. Stanton, and J. A. Silver, "Frequency modulation and wavelength modulation spectroscopies: comparison of experimental methods using a lead-salt diode laser," Appl. Opt. 31, 718-731 (1992).
[CrossRef] [PubMed]

T. G. McRae and T. J. Kulp, �??Backscatter absorption gas imaging: a new technique for gas visualization,�?? Appl. Opt. 32, 4037�??4050 (1993).
[PubMed]

T. J. Kulp, P. Powers, R. Kennedy, and U. B. Goers, �??Development of a pulsed backscatter-absorption gas-imaging and its application to the visualization of natural gas leaks,�?? Appl. Opt. 37, 3912�??3922 (1998).
[CrossRef]

P. E. Powers, T.J. Kulp, and R. Kennedy, �??Demonstration of differential backscatter absorption gas imaging,�?? Appl. Opt. 39, 1440-1448 (2000).
[CrossRef]

J. Wang, M. Maiorov, D. S. Baer, D. Z. Garbuzov, J. C. Connolly, and R. K. Hanson, �??In situ combustion measurements of CO with diode-Laser absorption near 2.3 microns,�?? Appl. Opt. 39, 5579�??5589 (2000).
[CrossRef]

D. M. Sonnenfroh, W. T. Rawlins, M. G. Allen, C. Gmachl, F. Capasso, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, �??Application of balanced detection to absorption measurements of trace gases with room-temperature, quasi-cw quantum-cascade lasers�??, Appl. Opt. 40, 812-820 (2001).
[CrossRef]

C. Peng, G. P. Luo, H. Q. Le, �??Broadband, continuous, and fine-tune properties of external-cavity thermoelectric-stabilized mid-infrared quantum-cascade lasers,�?? Appl. Opt. 42, 4877-4882 (2003).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

A. Evans, J.S. Yu, J. David, L. Doris, K. Mi, S. Slivken, and M. Razeghi, �??High-temperature high-power continuous-wave operation of buried heterostructure quantum-cascade lasers,�?? Appl. Phys. Lett. 84, 314-316 (2004).
[CrossRef]

C. Peng, H.L. Zhang, H.Q. Le, �??Mid-infrared external-cavity two-segment quantum-cascade laser,�?? Appl. Phys. Lett. 83, 4098-4100 (2003).
[CrossRef]

IEEE J. of Quantum Electron. (1)

G. P. Luo, C. Peng, H. Q. Le, S. S. Pei, H. Lee, W. Y. Hwang, B. Ishang, and J. Zheng, �??Broadly wavelength-tunable external cavity mid-infrared quantum cascade lasers,�?? IEEE J. of Quantum Electron. 38, 486-494 (2002).
[CrossRef]

IEEE J. of Quantum Electronics (1)

Anatoliy A. Kosterev, Frank K. Tittel, �??Chemical sensors based on quantum cascade lasers,�?? IEEE J. of Quantum Electronics 38, 582-591 (2002).
[CrossRef]

Math. Ann. (1)

Ibid, Chap. 11; and A. Sommerfeld, �??Mathematische theorie der diffraction,�?? Math. Ann. 47, 317-374 (1896).
[CrossRef]

NASA Conference Publication (1)

D. J. Kane, J. A. Siver, �??Real time quantitative 3-D imaging of diffusion flame species,�?? in NASA Conference Publication 10194, 281-286 (1997).

Opt. Lett. (4)

Proc. Intl. Symposium, Freiburg, 1991 (1)

See for example, R. Grisar, H. Boettner, M. Tacke, and G. Restelli (Eds.), �??Monitoring of gaseous pollutants by tunable diode lasers,�?? in Proceedings of the International Symposium, Freiburg, Germany, 1991, Kluwer Academic Publishers, Dordrecht, The Netherlands (1992).

Proc. SPIE (2)

D. E. Cooper, J. E. van der Laan, R. E. Warren, �??Diode-laser-based lidars: the next generation,�?? in Application of Tunable Diode and Other Infrared Sources for Atmospheric Studies and Industrial Processing Monitoring II, Proc. SPIE 3758, 142-151 (1999).
[CrossRef]

See for example, Application of tunable diode and other infrared sources for atmospheric studies and industrial processing monitoring II, Proc. SPIE 3758, A. Fried (ed.) (1999).

Spectrochim. Acta Part A (1)

See for example, P. Werle, �??A review of recent advances in semiconductor laser based gas monitors,�?? Spectrochim. Acta Part A 54, 197-236 (1998).
[CrossRef]

Trends in Optics (1)

See for example, E. Wolf, �??Principles and development of diffraction tomography,�?? in Trends in Optics, A. Consortini (Ed.), 83�??110 (Academic, San Diego, Calif., 1996).

Other (3)

M. Born and E. Wolf, Principles of optics, 7th ed., (Cambridge University Press, 1999), Chap. 13.

Ibid, Chap. 14, pp. 785-789.

M. Born and E. Wolf, Principles of optics, 7th ed., (Cambridge University Press, 1999), pp. 64-70.

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Figures (12)

Fig. 1.
Fig. 1.

(a) Scattering imaging with an incident plane wave; and (b) Point-sampled imaging with a focused beam

Fig. 2.
Fig. 2.

Diffraction pattern of a half-obscured Gaussian; (a) linear scale; (b) dB scale. Note the different x-scales. The pattern has two components, the main lobe and the side diffraction fringes, each with different behaviors.

Fig. 3.
Fig. 3.

Left and center: wavelength modulated diffraction patterns as functions of wavelength. The main lobe oscillates vs. wavelength; the diffraction fringes are linear vs. wavelength. Right: Diffracted power (0th order), and the 1st and 2nd wavelength modulated signals are oscillatory functions of wavelength.

Fig. 4.
Fig. 4.

Transmission through an etalon shows modulation in high order wavelength-modulated signals. Left: all-order signals vs. wavelength; Right: 2nd order WMI signal vs. window thickness and wavelength.

Fig. 5.
Fig. 5.

Diffraction patterns in the 0th, 1st, and 2nd wavelength modulated images show increasing spatial frequencies, providing more information on the target geometry.

Fig. 6.
Fig. 6.

Block diagram of the experimental set-up.

Fig. 7.
Fig. 7.

Top row: 2nd order WMI image of CO gas confined in a cell. Bottom row: Corresponding 0th order images, with maximum absorptance ranging from 0.57 to 0.16, 0.05, 0.03, 2.8×10-3, and 0 from left to right.

Fig. 8.
Fig. 8.

(a) 2nd order WMI image of a CO gas cell with 2.8×10-3-absorptance. (b) The same with no gas. (c) Image in (a) subtracted by that in (b); geometrical effects are partially removed. (d) The 3-D plot of image in (c), showing the gas signature in the center. Outer regions have zero-signal average, but with different noise amplitudes.

Fig. 9.
Fig. 9.

(a) Fringes across the gas cell window. Fringes in the 2nd order image have an opposite phase with those in the 0th order, consistent with etalon effects. (b) Spikes on geometrical edges and boundaries in the 2nd order image, consistent with edge diffraction effects of focused beam.

Fig. 10.
Fig. 10.

(a): Left: concept diagram of a combined passive and active imaging system; (b): Right: illustration of synthetic image, obtained by digital combination of CCD visible image with 2nd-order laser-based WMI image.

Fig. 11.
Fig. 11.

(a) A visible image of the target. (b) The three orders WMI images of the target at 4.887 μm.

Fig. 12.
Fig. 12.

The three orders WMI images after being processed. The 2nd order image has enhanced features such as sharp edges and fringes not evident in the 0th order image. Some dye spots indicated by the dashed circles at the bottom of the three images are more visible in the 1st and 2nd than the 0th order image.

Equations (20)

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U ( λ ; r ) = e i k 0 . r + k 2 4 π V [ ε ( λ ; r ) 1 ] U ( λ ; r ' ) e ik r r ' r r ' d r '
A ( k 0 ) U ( λ ; r ) d k 0 = A ( k 0 ) e i k 0 r d k 0 + V d r ' k 2 4 π A ( k 0 ) [ ε ( λ ; r ) 1 ] U ( λ , r ' ) e i k r r ' r r ' d k 0
λ U ( λ ; r ) λ = 2 U ( λ ; r ) ( i k 0 r 2 ) e i k 0 r
+ k 2 4 π V [ ε ( λ ; r ' ) 1 ] [ λ U ( λ , r ' ) λ i k r r ' ] e i k r r ' r r ' d r '
k 2 V ε ( λ , r ' ) λ U ( λ , r ' ) e i k r r ' r r ' d r '
I ij ( 0 ) ( λ ) = 1 4 [ S ij ( λ Δ λ ) + S ij ( λ ; 1 ) + S i j ( λ + Δ λ ) + S i j ( λ ; 2 ) ]
I ij ( 1 ) ( λ ) = 1 2 [ S ij ( λ Δ λ ) + S ij ( λ ; 1 ) + S i j ( λ + Δ λ ) + S i j ( λ ; 2 ) ]
I ij ( 2 ) ( λ ) = S ij ( λ Δ λ ) S ij ( λ ; 1 ) + S i j ( λ + Δ λ ) S i j ( λ ; 2 )
σ 2 [ 1 N e i 2 πmp / N S m ] = 1 N m = 0 N 1 e i 2 πmp / N | 2 σ 2 [ S m ] = σ 2 [ S ]
σ 2 [ I ( 0 ) , I ( 1 ) , or I ( 2 ) ] = { 1 / 4 , 1 , or 4 } σ 2 [ S ] ,
E TE = e i ( k x x + k z z ) + 1 1 k x / k ( μ + k x / k ) 1 + μ e ik ( z 1 μ 2 )
E TE = A ( k x ) e i ( k x x + k z z ) d k x + 1 exp ( ik ( z 1 μ 2 ) ) 1 + μ A ( k x ) k 2 k k x ( + k x ) dk x
E TE = 1 2 e ikr sin ( θ + α ) { 1 erf [ e i 3 π / 4 2 kr cos ( θ + α 2 π 4 ) ] }
1 2 e ikr sin ( θ α ) { 1 erf [ e i 3 π / 4 2 kr cos ( θ α 2 + π 4 ) ] }
I ( 0 ) = T e ikL 1 R e 2 ikL 2 where T = 4 n e α L / 2 ( n + 1 ) 2 ; R = ( n 1 ) 2 ( n + 1 ) 2 e α L ;
I ( 1 ) = 4 Δ λ λ kLRT 2 sin 2 kL ( 1 + R 2 2 R cos 2 kL ) 2
I ( 1 ) = 8 ( Δ λ λ ) 2 kLRT 2 ( 1 + R 2 2 R cos 2 kL ) 2 [ 4 kLR sin 2 2 kL 1 + R 2 2 R cos 2 kL k L cos 2 kL sin 2 kL ]
I ( 0 ) = 4 F 0 2 ; Where : F 0 = v J 1 ( η ) / η u J 1 ( ξ ) / ξ
I ( 1 ) Δ λ I λ = 2 Δ λ λ I ( 0 ) 8 Δ λ λ F 0 F 1 ; Where F 1 = u J 2 ( ξ ) v J 2 ( η ) .
I ( 2 ) Δ λ 2 2 I λ 2 = 3 Δ λ λ I ( 1 ) + 8 Δ λ 2 λ 2 [ F 1 2 F 0 F 2 ] ; Where F 2 = v η J 1 ( η ) u ξ J 1 ( ξ )

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