Abstract

A fast thermoreflectance impulse response photothermal imager was assembled and tested with several solid materials [quartz, stainless steel, and polyvinylidene difluoride (PVDF)]. The instrument was found to yield quantitative data in agreement with Green’s function theoretical models of time domain heat conduction. The FM chirp laser intensity modulation technique used in these experiments gave wide bandwidth photothermal signals and was found to be only limited by the FFT instrumentation frequency response (100 kHz). Thermal diffusivities were calculated, while thermal lensing and thermoelastic effects were further observed. The imager was thus shown to be capable of replacing pulsed laser devices for truly nondestructive applications with materials with low damage threshold to optical pulses.

© 1988 Optical Society of America

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References

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  1. J. Opsal, A. Rosencwaig, D. L. Willenborg, “Thermal-Wave Detection and Thin-Film Thickness Measurements with Laser Beam Deflection,” Appl. Opt. 22, 3169 (1983).
    [CrossRef] [PubMed]
  2. A. Mandelis, A. Williams, E. K. M. Siu, “Photothermal Wave Imaging of Metal-Oxide-Semiconductor Field Effect Transistor Structures,” J. Appl. Phys. 63, 92 (1988).
    [CrossRef]
  3. A. Rosencwaig, “Thermal Wave Characterization and Inspection of Semiconductor Materials and Devices,” in Photoacoustic and Thermal Wave Phenomena in Semiconductors, A. Mandelis, Ed. (North-Holland, New York, 1987), Chap. 5.
  4. A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980).
  5. A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of Thermal Waves Through Optical Reflectance,” Appl. Phys. Lett. 46, 1013 (1985).
    [CrossRef]
  6. A. Mandelis, J. F. Power, “Frequency-Modulated Impulse Response Photothermal Detection Through Optical Reflectance. 1: Theory,” Appl. Opt. 27, 3397 (1988).
    [CrossRef] [PubMed]
  7. A. Mandelis, “Time-Delay-Domain and Pseudorandom Noise Photoacoustic and Photothermal Wave Processes: A Review of the State of the Art,” IEEE Trans. UFFC-33, 590 (1986).
  8. A. Mandelis, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part I: Theoretical,” Rev. Sci. Instrum. 57, 617 (1986).
    [CrossRef]
  9. A. Mandelis, L. M. L. Borm, J. Tiessinga, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part II: Mirage Effect Spectrometer Design and Performance,” Rev. Sci. Instrum. 57, 622 (1986).
    [CrossRef]
  10. A. Mandelis, L. M. L. Borm, J. Tiessinga, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part III: Mirage Effect Spectrometer Dynamic Range and Comparison to Pseudo-Random-Binary-Sequence (PRBS) Method,” Rev. Sci. Instrum. 57, 630 (1986).
    [CrossRef]
  11. J. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part I: A Theoretical Model,” Rev. Sci. Instrum. 58, 2018 (1987).
    [CrossRef]
  12. J. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part II: Methodology,” Rev. Sci. Instrum. 58, 2024 (1987).
    [CrossRef]
  13. J. F. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part III: Performance and Signal Recovery Techniques,” Rev. Sci. Instrum. 58, 2033 (1987).
    [CrossRef]
  14. KYNAR Piezo Film Technical Manual (Pennwalt Corp., King of Prussia, PA, 1983).
  15. J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, “Long-Transient Effects in Lasers with Inserted Liquid Samples,” J. Appl. Phys. 36, 3 (1965).
    [CrossRef]
  16. H. Biering, O. Z. Pedersen, “System Analysis and Time Delay Spectrometry: Part II,” Bruel Kjaer Tech. Rev. 2, 1 (1983).
  17. C. Hu, J. R. Whinnery, “A New Thermo-Optical Measurement Method and a Comparison with Other Methods,” Appl. Opt. 12, 72 (1973).
    [CrossRef] [PubMed]
  18. Y. S. Touloukian, R. W. Powell, C. Y. Ho, M. C. Nicolaou, Thermal Diffusivity (IFI/Plenum, New York, 1973).

1988

A. Mandelis, A. Williams, E. K. M. Siu, “Photothermal Wave Imaging of Metal-Oxide-Semiconductor Field Effect Transistor Structures,” J. Appl. Phys. 63, 92 (1988).
[CrossRef]

A. Mandelis, J. F. Power, “Frequency-Modulated Impulse Response Photothermal Detection Through Optical Reflectance. 1: Theory,” Appl. Opt. 27, 3397 (1988).
[CrossRef] [PubMed]

1987

J. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part I: A Theoretical Model,” Rev. Sci. Instrum. 58, 2018 (1987).
[CrossRef]

J. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part II: Methodology,” Rev. Sci. Instrum. 58, 2024 (1987).
[CrossRef]

J. F. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part III: Performance and Signal Recovery Techniques,” Rev. Sci. Instrum. 58, 2033 (1987).
[CrossRef]

1986

A. Mandelis, “Time-Delay-Domain and Pseudorandom Noise Photoacoustic and Photothermal Wave Processes: A Review of the State of the Art,” IEEE Trans. UFFC-33, 590 (1986).

A. Mandelis, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part I: Theoretical,” Rev. Sci. Instrum. 57, 617 (1986).
[CrossRef]

A. Mandelis, L. M. L. Borm, J. Tiessinga, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part II: Mirage Effect Spectrometer Design and Performance,” Rev. Sci. Instrum. 57, 622 (1986).
[CrossRef]

A. Mandelis, L. M. L. Borm, J. Tiessinga, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part III: Mirage Effect Spectrometer Dynamic Range and Comparison to Pseudo-Random-Binary-Sequence (PRBS) Method,” Rev. Sci. Instrum. 57, 630 (1986).
[CrossRef]

1985

A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of Thermal Waves Through Optical Reflectance,” Appl. Phys. Lett. 46, 1013 (1985).
[CrossRef]

1983

J. Opsal, A. Rosencwaig, D. L. Willenborg, “Thermal-Wave Detection and Thin-Film Thickness Measurements with Laser Beam Deflection,” Appl. Opt. 22, 3169 (1983).
[CrossRef] [PubMed]

H. Biering, O. Z. Pedersen, “System Analysis and Time Delay Spectrometry: Part II,” Bruel Kjaer Tech. Rev. 2, 1 (1983).

1973

1965

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, “Long-Transient Effects in Lasers with Inserted Liquid Samples,” J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Biering, H.

H. Biering, O. Z. Pedersen, “System Analysis and Time Delay Spectrometry: Part II,” Bruel Kjaer Tech. Rev. 2, 1 (1983).

Borm, L. M. L.

A. Mandelis, L. M. L. Borm, J. Tiessinga, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part II: Mirage Effect Spectrometer Design and Performance,” Rev. Sci. Instrum. 57, 622 (1986).
[CrossRef]

A. Mandelis, L. M. L. Borm, J. Tiessinga, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part III: Mirage Effect Spectrometer Dynamic Range and Comparison to Pseudo-Random-Binary-Sequence (PRBS) Method,” Rev. Sci. Instrum. 57, 630 (1986).
[CrossRef]

Gordon, J. P.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, “Long-Transient Effects in Lasers with Inserted Liquid Samples,” J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Ho, C. Y.

Y. S. Touloukian, R. W. Powell, C. Y. Ho, M. C. Nicolaou, Thermal Diffusivity (IFI/Plenum, New York, 1973).

Hu, C.

Leite, R. C. C.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, “Long-Transient Effects in Lasers with Inserted Liquid Samples,” J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Mandelis, A.

A. Mandelis, A. Williams, E. K. M. Siu, “Photothermal Wave Imaging of Metal-Oxide-Semiconductor Field Effect Transistor Structures,” J. Appl. Phys. 63, 92 (1988).
[CrossRef]

A. Mandelis, J. F. Power, “Frequency-Modulated Impulse Response Photothermal Detection Through Optical Reflectance. 1: Theory,” Appl. Opt. 27, 3397 (1988).
[CrossRef] [PubMed]

J. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part II: Methodology,” Rev. Sci. Instrum. 58, 2024 (1987).
[CrossRef]

J. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part I: A Theoretical Model,” Rev. Sci. Instrum. 58, 2018 (1987).
[CrossRef]

J. F. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part III: Performance and Signal Recovery Techniques,” Rev. Sci. Instrum. 58, 2033 (1987).
[CrossRef]

A. Mandelis, L. M. L. Borm, J. Tiessinga, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part II: Mirage Effect Spectrometer Design and Performance,” Rev. Sci. Instrum. 57, 622 (1986).
[CrossRef]

A. Mandelis, “Time-Delay-Domain and Pseudorandom Noise Photoacoustic and Photothermal Wave Processes: A Review of the State of the Art,” IEEE Trans. UFFC-33, 590 (1986).

A. Mandelis, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part I: Theoretical,” Rev. Sci. Instrum. 57, 617 (1986).
[CrossRef]

A. Mandelis, L. M. L. Borm, J. Tiessinga, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part III: Mirage Effect Spectrometer Dynamic Range and Comparison to Pseudo-Random-Binary-Sequence (PRBS) Method,” Rev. Sci. Instrum. 57, 630 (1986).
[CrossRef]

Moore, R. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, “Long-Transient Effects in Lasers with Inserted Liquid Samples,” J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Nicolaou, M. C.

Y. S. Touloukian, R. W. Powell, C. Y. Ho, M. C. Nicolaou, Thermal Diffusivity (IFI/Plenum, New York, 1973).

Opsal, J.

A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of Thermal Waves Through Optical Reflectance,” Appl. Phys. Lett. 46, 1013 (1985).
[CrossRef]

J. Opsal, A. Rosencwaig, D. L. Willenborg, “Thermal-Wave Detection and Thin-Film Thickness Measurements with Laser Beam Deflection,” Appl. Opt. 22, 3169 (1983).
[CrossRef] [PubMed]

Pedersen, O. Z.

H. Biering, O. Z. Pedersen, “System Analysis and Time Delay Spectrometry: Part II,” Bruel Kjaer Tech. Rev. 2, 1 (1983).

Porto, S. P. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, “Long-Transient Effects in Lasers with Inserted Liquid Samples,” J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Powell, R. W.

Y. S. Touloukian, R. W. Powell, C. Y. Ho, M. C. Nicolaou, Thermal Diffusivity (IFI/Plenum, New York, 1973).

Power, J.

J. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part II: Methodology,” Rev. Sci. Instrum. 58, 2024 (1987).
[CrossRef]

J. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part I: A Theoretical Model,” Rev. Sci. Instrum. 58, 2018 (1987).
[CrossRef]

Power, J. F.

A. Mandelis, J. F. Power, “Frequency-Modulated Impulse Response Photothermal Detection Through Optical Reflectance. 1: Theory,” Appl. Opt. 27, 3397 (1988).
[CrossRef] [PubMed]

J. F. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part III: Performance and Signal Recovery Techniques,” Rev. Sci. Instrum. 58, 2033 (1987).
[CrossRef]

Rosencwaig, A.

A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of Thermal Waves Through Optical Reflectance,” Appl. Phys. Lett. 46, 1013 (1985).
[CrossRef]

J. Opsal, A. Rosencwaig, D. L. Willenborg, “Thermal-Wave Detection and Thin-Film Thickness Measurements with Laser Beam Deflection,” Appl. Opt. 22, 3169 (1983).
[CrossRef] [PubMed]

A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980).

A. Rosencwaig, “Thermal Wave Characterization and Inspection of Semiconductor Materials and Devices,” in Photoacoustic and Thermal Wave Phenomena in Semiconductors, A. Mandelis, Ed. (North-Holland, New York, 1987), Chap. 5.

Siu, E. K. M.

A. Mandelis, A. Williams, E. K. M. Siu, “Photothermal Wave Imaging of Metal-Oxide-Semiconductor Field Effect Transistor Structures,” J. Appl. Phys. 63, 92 (1988).
[CrossRef]

Smith, W. L.

A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of Thermal Waves Through Optical Reflectance,” Appl. Phys. Lett. 46, 1013 (1985).
[CrossRef]

Tiessinga, J.

A. Mandelis, L. M. L. Borm, J. Tiessinga, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part II: Mirage Effect Spectrometer Design and Performance,” Rev. Sci. Instrum. 57, 622 (1986).
[CrossRef]

A. Mandelis, L. M. L. Borm, J. Tiessinga, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part III: Mirage Effect Spectrometer Dynamic Range and Comparison to Pseudo-Random-Binary-Sequence (PRBS) Method,” Rev. Sci. Instrum. 57, 630 (1986).
[CrossRef]

Touloukian, Y. S.

Y. S. Touloukian, R. W. Powell, C. Y. Ho, M. C. Nicolaou, Thermal Diffusivity (IFI/Plenum, New York, 1973).

Whinnery, J. R.

C. Hu, J. R. Whinnery, “A New Thermo-Optical Measurement Method and a Comparison with Other Methods,” Appl. Opt. 12, 72 (1973).
[CrossRef] [PubMed]

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, “Long-Transient Effects in Lasers with Inserted Liquid Samples,” J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Willenborg, D. L.

A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of Thermal Waves Through Optical Reflectance,” Appl. Phys. Lett. 46, 1013 (1985).
[CrossRef]

J. Opsal, A. Rosencwaig, D. L. Willenborg, “Thermal-Wave Detection and Thin-Film Thickness Measurements with Laser Beam Deflection,” Appl. Opt. 22, 3169 (1983).
[CrossRef] [PubMed]

Williams, A.

A. Mandelis, A. Williams, E. K. M. Siu, “Photothermal Wave Imaging of Metal-Oxide-Semiconductor Field Effect Transistor Structures,” J. Appl. Phys. 63, 92 (1988).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

A. Rosencwaig, J. Opsal, W. L. Smith, D. L. Willenborg, “Detection of Thermal Waves Through Optical Reflectance,” Appl. Phys. Lett. 46, 1013 (1985).
[CrossRef]

Bruel Kjaer Tech. Rev.

H. Biering, O. Z. Pedersen, “System Analysis and Time Delay Spectrometry: Part II,” Bruel Kjaer Tech. Rev. 2, 1 (1983).

IEEE Trans.

A. Mandelis, “Time-Delay-Domain and Pseudorandom Noise Photoacoustic and Photothermal Wave Processes: A Review of the State of the Art,” IEEE Trans. UFFC-33, 590 (1986).

J. Appl. Phys.

A. Mandelis, A. Williams, E. K. M. Siu, “Photothermal Wave Imaging of Metal-Oxide-Semiconductor Field Effect Transistor Structures,” J. Appl. Phys. 63, 92 (1988).
[CrossRef]

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, “Long-Transient Effects in Lasers with Inserted Liquid Samples,” J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Rev. Sci. Instrum.

A. Mandelis, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part I: Theoretical,” Rev. Sci. Instrum. 57, 617 (1986).
[CrossRef]

A. Mandelis, L. M. L. Borm, J. Tiessinga, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part II: Mirage Effect Spectrometer Design and Performance,” Rev. Sci. Instrum. 57, 622 (1986).
[CrossRef]

A. Mandelis, L. M. L. Borm, J. Tiessinga, “Frequency Modulated (FM) Time Delay Photoacoustic and Photothermal Wave Spectroscopies. Technique, Instrumentation and Detection. Part III: Mirage Effect Spectrometer Dynamic Range and Comparison to Pseudo-Random-Binary-Sequence (PRBS) Method,” Rev. Sci. Instrum. 57, 630 (1986).
[CrossRef]

J. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part I: A Theoretical Model,” Rev. Sci. Instrum. 58, 2018 (1987).
[CrossRef]

J. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part II: Methodology,” Rev. Sci. Instrum. 58, 2024 (1987).
[CrossRef]

J. F. Power, A. Mandelis, “Photopyroelectric Thin Film Instrumentation and Impulse Response Detection. Part III: Performance and Signal Recovery Techniques,” Rev. Sci. Instrum. 58, 2033 (1987).
[CrossRef]

Other

KYNAR Piezo Film Technical Manual (Pennwalt Corp., King of Prussia, PA, 1983).

A. Rosencwaig, “Thermal Wave Characterization and Inspection of Semiconductor Materials and Devices,” in Photoacoustic and Thermal Wave Phenomena in Semiconductors, A. Mandelis, Ed. (North-Holland, New York, 1987), Chap. 5.

A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980).

Y. S. Touloukian, R. W. Powell, C. Y. Ho, M. C. Nicolaou, Thermal Diffusivity (IFI/Plenum, New York, 1973).

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Figures (13)

Fig. 1
Fig. 1

Block diagram of wide-bandwidth impulse response photothermal wave instrumentation. X(t) and Y(t) are real-time system input and output waveforms, respectively.

Fig. 2
Fig. 2

Linear FM sweep wavetrains for photothermal (reflectance) response of a semi-infinite quartz sample. Sweep/measurement bandwidth: Δf = 0–100 kHz. Sweep rate, S = 1.25 × 107 Hz/s; window: uniform (a) excitation sweep x(t); (b) response waveform y(t). Averaging N = 1000 records for (a),(b); (c) instantaneous y(t) record with no averaging.

Fig. 3
Fig. 3

Frequency response profiles via (a) point-by-point slow sine sweeps of the sample’s transfer function H(f). Magnitude and phase. (b) FM linear sweep response H(f), magnitude and phase. Frequency span 0–100 kHz. In (a) the sweep rate was 1.1 kHz/s with 50-ms integration period per point. Resolution: 499 Hz. Number of averages = 25. In (b) the sweep rate was 1.25 × 107 Hz/s; window: uniform. Sample was semi-infinite quartz.

Fig. 4
Fig. 4

Transfer function H(f) recorded for a quad cell detector system. Measurements were made with a slow sine sweep from 100 Hz to 100 kHz. The frequency scale was swept point by point with 50-ms integration time per point. Resolution was 499 Hz. Sweep rate: 1.1 kHz/s. (a) Magnitude; (b) phase.

Fig. 5
Fig. 5

Time-domain Gibbs phenomenon observed by truncation of frequency response data: windowing effects on the transfer function H(f) and on the impulse response h(τ). (a) |H(f)| windowed by a function with a gradual cutoff. (b) The same |H(f)| windowed by a function with a sharp rolloff (phase response not shown). (c), (d) Impulse responses corresponding to (a), (b), respectively. Sample was semi-infinite quartz. Data were recovered from a linear FM sweep with Δf = 0–100 kHz, S = 1.25 × 107 Hz/s, and N = 1000 averages.

Fig. 6
Fig. 6

Evaluation of measurement performance: (1) Rxx(τ), (b) Ryy(τ) for semi-infinite quartz sample: Δf = 0–100 kHz; S = 1.25 × 107 Hz/s.

Fig. 7
Fig. 7

Normalized impulse response profiles [h(τ = 0) = 1] for a semi-infinite quartz sample with various values of w0 and w1. Theory vs experiment. Upper curve: (a) w0 = 14 μm, w1 = 12 μm; (b) w0 = 10 μm, w1 = 8 μm; (c) w0 = 8 μm, w1 = 2 μm; (d) w0 = 2 μm, w1 = 6 μm (bottom curve). These results were obtained with linear FM chirp excitation and Δf = 0–100 kHz; S = 1.25 × 107 Hz/s. Theoretical curves, Eq. (6), were fitted assuming that α = 5 × 10−7 m2/s for quartz. Experimental curves are the result of 1000 averages. Beam diameters were estimated independently.

Fig. 8
Fig. 8

Thermal blooming observed at the surface of a semi-infinite sample. Impulse response profile for thermal lens with expected 3-D theoretical response superimposed. Measurements were made with sweep rate, S = 12.5 Hz/s and Δf = 0–100 Hz.

Fig. 9
Fig. 9

Ray traces showing schematic of probe beam refraction and thermal lens formation above the sample surface in the gas phase: (A) Defocusing: forms of dark annulus in the probe beam center; (B) collimation: forms a bright spot at the center of the probe beam.

Fig. 10
Fig. 10

Effect of spatial filtering of probe beam on the form of recovered thermal lens response: (a) response recovered with the center of annulus sampled; (b) response recovered with the rim of the annulus sampled; (c) response recovered with beam edge sampled. All measurements were made with a frequency sweep from 0 to 100 Hz at 12.5 Hz/s. Sample throughout was an oxidized Si wafer.

Fig. 11
Fig. 11

Power dependence of (a), (b) thermal lens and (c) thermoreflectance signals. (a) Power dependence for the thermal lens effect was plotted as the peak value of the impulse response h(τ = 0) vs the modulated laser power level. Sample was semi-infinite quartz. (b) Impulse responses recovered at various incident beam powers for a semi-infinite sample of stainless steel. (a), (b) Measurements were made with linear FM sweeps from 0 to 100 Hz at 1.25 Hz/s and N = 10 sweeps. (c) Power dependence of reflectivity signal for semi-infinite quartz measured at the peak of impulse response h(τ = 0). These measurements were made with a linear FM sweep from 0 to 100 kHz at 1.25 × 107 Hz/s and N = 1000.

Fig. 12
Fig. 12

Experimental transfer function |Hexp(f)| for semi-infinite quartz and theoretical fit |Hth(f)|. The latter involves a superposition of a purely thermal response component and a constant thermoelastic baseline x: (a) w0 = 2 μm, w1 = 7 μm; N = 500 averages; (b) w0 = 14 μm, w1 = 12 μm; N = 1000 averages. α = 5 × 10−7 m2/s.

Fig. 13
Fig. 13

Experimental frequency and corresponding impulse response measurements made with (a) pump and probe beams concentrically aligned; (b) probe beam offset from pump beam with rb > w1. The sample was semi-infinite quartz excited with a linear frequency sweep from 0 to 100 kHz at 1.25 × 107 Hz/s and N = 300 averages; (c), (d) impulse responses corresponding to (a), (b) measurements.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

Δ R = R - R 0 = ( R T ) T = T 0 Δ T ,
Δ T = T ( r , z = 0 , t ) - T 0 ,
h ( t ) = 0 0 2 π T ( r ¯ , z = 0 , t ) exp ( - r 2 / w 1 2 ) r d r d θ ,
T ( r ¯ , z = 0 , t ) = A ( 4 α t + w 0 2 ) t 1 / 2 exp [ - 1 ( r - r b ) 2 4 α t + w 0 2 ] ,
A 0 = P 0 w 0 2 α 3 / 2 2 π 3 / 2 ,
h ( t ) = A 0 τ 0 2 ( t + τ 1 ) t 1 / 2 exp [ - r b 2 4 α ( t + τ 1 ) ] ,
τ 1 1 4 α ( w 1 2 + w 0 2 ) ;             τ 0 w 1 2 4 α .
h ( τ ) = A 0 w 1 2 8 α ( τ + τ 1 ) τ 1 / 2 ,
( T 1 t 1 / 2 )
τ d = w 1 2 6 α ,
H th ( 100 ) kHz H th ( 500 Hz ) = H exp ( 100 kHz ) - x H exp ( 500 Hz ) - x ,
H th ( 100 kHz ) Norm = H exp ( 100 kHz ) - x 1 - x .
w 1 2 4 α             or             w 0 2 4 α

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