Abstract

In state-of-the-art laser ultrasonics (LU), the signal-to-noise ratio (SNR) is limited by the shot noise of the detected laser radiation. Further improving the SNR then requires averaging multiple signals or increasing generation and/or detection laser intensities. The former strategy is time consuming and the latter leads to surface damages. For signal-independent limiting noises, Hadamard multiplexing increases the SNR by averaging multiple signals in parallel using a single detector. Here we consider the use of Hadamard multiplexing in LU for the non-contact ultrasonic inspection of materials. By using 31 element Hadamard masks to modulate the spatial intensity distribution of the generation laser beam, the measured SNR is improved by a factor 2.8, in good agreement with the expected multiplexing or Fellgett advantage. In contrast to many other applications of Hadamard multiplexing, the SNR is improved for shot-noise-limited measurements since the shot noise level is independent of the signal in LU. The Hadamard multiplexing of the detection laser beam is also considered but can only lead to a throughput or Jacquinot advantage. However, for pulse-echo LU, the Hadamard multiplexing of both generation and detection laser beams allows using the synthetic aperture focusing technique (SAFT).

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2012 (1)

2006 (1)

P. B. Fellgett, “The nature and origin of multiplex Fourier spectrometry,” Notes Rec. R. Soc.60(1), 91–93 (2006).
[CrossRef]

2002 (1)

2001 (1)

T. W. Murray and S. Krishnaswamy, “Multiplexed interferometer for ultrasonic imaging applications,” Opt. Eng.40(7), 1321–1328 (2001).
[CrossRef]

1999 (1)

T. Kaneta, Y. Yamaguchi, and T. Imasaka, “Hadamard transform capillary electrophoresis,” Anal. Chem.71(23), 5444–5446 (1999).
[CrossRef] [PubMed]

1998 (1)

1995 (1)

J. S. Steckenrider, T. W. Murray, J. W. Wagner, and J. B. Deaton., “Sensitivity enhancement in laser ultrasonics using a versatile laser array system,” J. Acoust. Soc. Am.97(1), 273–279 (1995).
[CrossRef]

1994 (1)

A. Blouin and J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by two-wave mixing in a photorefractive GaAs crystal,” Appl. Phys. Lett.65(8), 932–934 (1994).
[CrossRef]

1993 (2)

M.-H. Noroy, D. Royer, and M. Fink, “The laser-generated ultrasonic phased array: analysis and experiments,” J. Acoust. Soc. Am.94(4), 1934–1943 (1993).
[CrossRef]

J. Yang, N. DeRidder, C. Ume, and J. Jarzynski, “Non-contact optical fibre phased array generation of ultrasound for non-destructive evaluation of materials and processes,” Ultrasonics31(6), 387–394 (1993).
[CrossRef]

1991 (1)

R. K. Ing and J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett.59(25), 3233–3235 (1991).
[CrossRef]

1986 (1)

J.-P. Monchalin, “Optical detection of ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control33(5), 485–499 (1986).
[CrossRef] [PubMed]

1985 (1)

J.-P. Monchalin, “Optical detection of ultrasound at a distance using a confocal Fabry-Perot interferometer,” Appl. Phys. Lett.47(1), 14–16 (1985).
[CrossRef]

1982 (1)

1970 (1)

1969 (1)

1968 (2)

1954 (1)

Aspinall, D.

Blouin, A.

Coufal, H.

Deaton, J. B.

J. S. Steckenrider, T. W. Murray, J. W. Wagner, and J. B. Deaton., “Sensitivity enhancement in laser ultrasonics using a versatile laser array system,” J. Acoust. Soc. Am.97(1), 273–279 (1995).
[CrossRef]

Decker, J. A.

DeRidder, N.

J. Yang, N. DeRidder, C. Ume, and J. Jarzynski, “Non-contact optical fibre phased array generation of ultrasound for non-destructive evaluation of materials and processes,” Ultrasonics31(6), 387–394 (1993).
[CrossRef]

Drolet, D.

Fellgett, P. B.

P. B. Fellgett, “The nature and origin of multiplex Fourier spectrometry,” Notes Rec. R. Soc.60(1), 91–93 (2006).
[CrossRef]

Fine, T.

Fink, M.

M.-H. Noroy, D. Royer, and M. Fink, “The laser-generated ultrasonic phased array: analysis and experiments,” J. Acoust. Soc. Am.94(4), 1934–1943 (1993).
[CrossRef]

Fomitchov, P.

Fredman, M. L.

Grainger, J. F.

Harwit, M.

Harwitt, M. O.

Ibbett, R. N.

Imasaka, T.

T. Kaneta, Y. Yamaguchi, and T. Imasaka, “Hadamard transform capillary electrophoresis,” Anal. Chem.71(23), 5444–5446 (1999).
[CrossRef] [PubMed]

Ing, R. K.

R. K. Ing and J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett.59(25), 3233–3235 (1991).
[CrossRef]

Jacquinot, P.

Jarzynski, J.

J. Yang, N. DeRidder, C. Ume, and J. Jarzynski, “Non-contact optical fibre phased array generation of ultrasound for non-destructive evaluation of materials and processes,” Ultrasonics31(6), 387–394 (1993).
[CrossRef]

Kaneta, T.

T. Kaneta, Y. Yamaguchi, and T. Imasaka, “Hadamard transform capillary electrophoresis,” Anal. Chem.71(23), 5444–5446 (1999).
[CrossRef] [PubMed]

Krishnaswamy, S.

Lévesque, D.

Moller, U.

Monchalin, J.-P.

G. Rousseau, A. Blouin, and J.-P. Monchalin, “Non-contact photoacoustic tomography and ultrasonography for tissue imaging,” Biomed. Opt. Express3(1), 16–25 (2012).
[CrossRef] [PubMed]

A. Blouin, D. Lévesque, C. Néron, D. Drolet, and J.-P. Monchalin, “Improved resolution and signal-to-noise ratio in laser-ultrasonics by SAFT processing,” Opt. Express2(13), 531–539 (1998).
[CrossRef] [PubMed]

A. Blouin and J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by two-wave mixing in a photorefractive GaAs crystal,” Appl. Phys. Lett.65(8), 932–934 (1994).
[CrossRef]

R. K. Ing and J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett.59(25), 3233–3235 (1991).
[CrossRef]

J.-P. Monchalin, “Optical detection of ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control33(5), 485–499 (1986).
[CrossRef] [PubMed]

J.-P. Monchalin, “Optical detection of ultrasound at a distance using a confocal Fabry-Perot interferometer,” Appl. Phys. Lett.47(1), 14–16 (1985).
[CrossRef]

Murray, T. W.

P. Fomitchov, T. W. Murray, and S. Krishnaswamy, “Intrinsic fiber-optic ultrasonic sensor array using multiplexed two-wave mixing interferometry,” Appl. Opt.41(7), 1262–1266 (2002).
[CrossRef] [PubMed]

T. W. Murray and S. Krishnaswamy, “Multiplexed interferometer for ultrasonic imaging applications,” Opt. Eng.40(7), 1321–1328 (2001).
[CrossRef]

J. S. Steckenrider, T. W. Murray, J. W. Wagner, and J. B. Deaton., “Sensitivity enhancement in laser ultrasonics using a versatile laser array system,” J. Acoust. Soc. Am.97(1), 273–279 (1995).
[CrossRef]

Nelson, E. D.

Néron, C.

Noroy, M.-H.

M.-H. Noroy, D. Royer, and M. Fink, “The laser-generated ultrasonic phased array: analysis and experiments,” J. Acoust. Soc. Am.94(4), 1934–1943 (1993).
[CrossRef]

Phillips, P. G.

Rousseau, G.

Royer, D.

M.-H. Noroy, D. Royer, and M. Fink, “The laser-generated ultrasonic phased array: analysis and experiments,” J. Acoust. Soc. Am.94(4), 1934–1943 (1993).
[CrossRef]

Schneider, S.

Sloane, N. J. A.

Steckenrider, J. S.

J. S. Steckenrider, T. W. Murray, J. W. Wagner, and J. B. Deaton., “Sensitivity enhancement in laser ultrasonics using a versatile laser array system,” J. Acoust. Soc. Am.97(1), 273–279 (1995).
[CrossRef]

Ume, C.

J. Yang, N. DeRidder, C. Ume, and J. Jarzynski, “Non-contact optical fibre phased array generation of ultrasound for non-destructive evaluation of materials and processes,” Ultrasonics31(6), 387–394 (1993).
[CrossRef]

Wagner, J. W.

J. S. Steckenrider, T. W. Murray, J. W. Wagner, and J. B. Deaton., “Sensitivity enhancement in laser ultrasonics using a versatile laser array system,” J. Acoust. Soc. Am.97(1), 273–279 (1995).
[CrossRef]

Yamaguchi, Y.

T. Kaneta, Y. Yamaguchi, and T. Imasaka, “Hadamard transform capillary electrophoresis,” Anal. Chem.71(23), 5444–5446 (1999).
[CrossRef] [PubMed]

Yang, J.

J. Yang, N. DeRidder, C. Ume, and J. Jarzynski, “Non-contact optical fibre phased array generation of ultrasound for non-destructive evaluation of materials and processes,” Ultrasonics31(6), 387–394 (1993).
[CrossRef]

Anal. Chem. (1)

T. Kaneta, Y. Yamaguchi, and T. Imasaka, “Hadamard transform capillary electrophoresis,” Anal. Chem.71(23), 5444–5446 (1999).
[CrossRef] [PubMed]

Appl. Opt. (5)

Appl. Phys. Lett. (3)

J.-P. Monchalin, “Optical detection of ultrasound at a distance using a confocal Fabry-Perot interferometer,” Appl. Phys. Lett.47(1), 14–16 (1985).
[CrossRef]

R. K. Ing and J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett.59(25), 3233–3235 (1991).
[CrossRef]

A. Blouin and J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by two-wave mixing in a photorefractive GaAs crystal,” Appl. Phys. Lett.65(8), 932–934 (1994).
[CrossRef]

Biomed. Opt. Express (1)

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

J.-P. Monchalin, “Optical detection of ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control33(5), 485–499 (1986).
[CrossRef] [PubMed]

J. Acoust. Soc. Am. (2)

M.-H. Noroy, D. Royer, and M. Fink, “The laser-generated ultrasonic phased array: analysis and experiments,” J. Acoust. Soc. Am.94(4), 1934–1943 (1993).
[CrossRef]

J. S. Steckenrider, T. W. Murray, J. W. Wagner, and J. B. Deaton., “Sensitivity enhancement in laser ultrasonics using a versatile laser array system,” J. Acoust. Soc. Am.97(1), 273–279 (1995).
[CrossRef]

J. Opt. Soc. Am. (2)

Notes Rec. R. Soc. (1)

P. B. Fellgett, “The nature and origin of multiplex Fourier spectrometry,” Notes Rec. R. Soc.60(1), 91–93 (2006).
[CrossRef]

Opt. Eng. (1)

T. W. Murray and S. Krishnaswamy, “Multiplexed interferometer for ultrasonic imaging applications,” Opt. Eng.40(7), 1321–1328 (2001).
[CrossRef]

Opt. Express (1)

Ultrasonics (1)

J. Yang, N. DeRidder, C. Ume, and J. Jarzynski, “Non-contact optical fibre phased array generation of ultrasound for non-destructive evaluation of materials and processes,” Ultrasonics31(6), 387–394 (1993).
[CrossRef]

Other (5)

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic Press, New York, NY, 1979).

L. Wei, J. Xu, and S. Zhang, “Application of two-dimensional Hadamard transform to photoacoustic microscopy,” IEEE 1986 Ultrasonics Symposium Proceedings, pp. 501–504.

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, Hoboken, NJ, 2007).

American National Standard for the Safe Use of Lasers ANSI Z136.1–2007 (Laser Institute of America, Orlando, Florida, 2007).

C. B. Scruby and L. E. Drain, Laser Ultrasonics: Techniques and Applications (Adam Hilger, Bristol, UK, 1990).

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Figures (15)

Fig. 1
Fig. 1

(a) Bit sequence of 2N − 1 = 61 elements defining the augmented Hadamard mask with the corresponding schematic representation of opaque (gray squares) and transparent (empty squares) elements. (b) Schematic representation of the augmented mask (gray) in front of the N = 31 element wide vertical aperture (black blades).

Fig. 2
Fig. 2

Schematic diagrams illustrating elementary measurements (a) in spectroscopy and (b) in LU and Hadamard-multiplexed measurements (c) in spectroscopy and (d) in LU.

Fig. 3
Fig. 3

Temporal profile of the detection laser pulse. The green line represents the arrival time of the generation laser pulse.

Fig. 4
Fig. 4

Measured spatial intensity distributions at the exit of the augmented mask followed by the limiting aperture. Size of square elements: 100 µm × 100 µm.

Fig. 5
Fig. 5

Schematic diagrams of scanning setups used for the spatial multiplexing of (a) the generation laser beam, (b) the detection laser beam, and (c) both detection and generation laser beams. All components are described in the text.

Fig. 6
Fig. 6

Schematic diagram of the generation beam shaper GBS. Components are described in the text. Lenses L1,2 are not present in the DBS which is otherwise identical to the GBS.

Fig. 7
Fig. 7

(a) Hadamard B-scan, (b) corresponding retrieved B-scan, and (c) elementary B-scan. The averaging number was 16 for both, Hadamard and elementary measurements. Each graph on the lower row shows the central A-scan (between white arrows) of the corresponding B-scan. Green line: generation laser pulse. L and S stand for longitudinal and shear waves.

Fig. 8
Fig. 8

(a) Rms noise of A-scans in Fig. 7 normalized to the average rms noise of elementary A-scans (green line): elementary A-scans (green dots), Hadamard A-scans (black dots) and retrieved A-scans (red dots). Each horizontal line gives the average value of corresponding series of dots (same color).

Fig. 9
Fig. 9

PSFs obtained (a) by Hadamard multiplexing of the generation laser beam and (b) by elementary measurements for averaging numbers indicated in parenthesis. Horizontal and vertical profiles passing through each PSF are shown, respectively, on the top and left sides of each image.

Fig. 10
Fig. 10

(a) Hadamard B-scan, (b) corresponding retrieved B-scan, and (c) elementary B-scan. The averaging number was 16 for both, Hadamard and elementary measurements. Each graph on the lower row shows the central A-scan (between white arrows) of the corresponding B-scan. Green line: generation laser pulse. L and S stand for longitudinal and shear waves.

Fig. 11
Fig. 11

(a) Rms noise of A-scans in Fig. 10 normalized to the average rms noise of elementary A-scans (green line): elementary A-scans (green dots), Hadamard A-scans (black dots) and retrieved A-scans (red dots). Each horizontal line gives the average value of corresponding series of dots (same color).

Fig. 12
Fig. 12

PSFs obtained (a) by Hadamard multiplexing of the detection laser beam and (b) by elementary measurements for averaging numbers shown in parenthesis. Horizontal and vertical profiles passing through each PSF are shown, respectively, on the top and left sides of each image.

Fig. 13
Fig. 13

Schematic diagram (side view) of the aluminum plate specimen with a step on the back side. GB, generation laser beam; R, Rayleigh waves; S, shear wave; L, longitudinal wave. The region of interest (ROI: dotted box) is 1.86 mm wide by 0.9 mm deep. Dimensions are in mm.

Fig. 14
Fig. 14

(a) Left: B-scan image retrieved from Hadamard measurements. Right: Corresponding A-scan at x = 0.5 mm (between arrows) (b) Left: B-scan image obtained from elementary measurements. Right: Corresponding A-scan at x = 0.5 mm (between arrows). For each image (curve), the amplitude scale is adjusted above the red line by an attenuation factor given in the red box.

Fig. 15
Fig. 15

(a) Left: B-scan images retrieved from Hadamard measurements. Right: Corresponding SAFT images. (b) Left: B-scan images obtained from elementary measurements. Right: Corresponding SAFT images. In (a) and (b), averaging numbers are: 1 (upper row), 4 (middle row), and 16 (lower row).

Tables (1)

Tables Icon

Table 1 Multiplexing or Fellgett advantage F. Approximate values are valid for large N.

Equations (3)

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r = M 1 h =e+ M 1 n h
σ r = N K σ h
F SNR r SNR e = r/ σ r e/ σ e = σ e σ r = K N σ e σ h

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