Abstract

Schlieren interferometry is found to be an alternative tool for temperature measurement during thermoplastic laser welding with regard to methods based on thermocouples or optical pyrometers. In fact, these techniques are not easily applied when materials to be processed have reduced thickness, negligible heat conduction, and low emissivity, as is the case of welding high-density polyethylene films with 10.6-μm CO2 laser radiation, even if the method reaches its applicability limit after approximately 1 s of the interaction process. The schlieren method provides the means and the results to probe the thermal variations of the laser-thermoplastic interaction on both the surface and the interface between the sample material and the air.

© 2003 Optical Society of America

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  1. M. R. Barrault, G. R. Jones, F. C. Rodrigues, “Practical arcing environments are plasma diagnostics,” in Proceedings of the Seventh Yugoslav Symposium and Summer School on the Physics of Ionized Gases, V. Vujnovic, ed. (IFIS, Zagrab, Yugoslavia, 1974), Vol. 1, pp. 701–807.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. R. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (Mc-Graw-Hill, New York, 1999).
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    [CrossRef]
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  18. K. Green, M. C. Borrás, P. P. Woskov, G. I. Flores, K. Hadidi, P. Thomas, “Electronic excitation temperatures profiles in an air microwave torch,” Plasma Science and Fusion Center (MIT, Cambridge, Mass., 2001), http://www.psfc.mit.edu/library/01JA/01JA005/01JA005_full.pdf .
  19. P. Ben-Abdallah, M. Sakami, V. Le Dez, J. B. Saulnier, A. Charette, “Optical remote sensing inside an inhomogeneous axisymetric medium: the absorption field measurement,” Appl. Opt. 39, 411–417 (2000).
    [CrossRef]
  20. L. Ciotti, “Inversion of the Abel equation for toroidal density distributions,” Astrophys. Lett. Commun. 40, 85–93 (2000).
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  22. S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, New York, 1996), Chap. 1.
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    [CrossRef] [PubMed]
  24. Zemax—Optical Design Program User’s Guide (Focus Software Inc., Tucson, Ariz., 2001). See Ref. 25.
  25. J. E. Decker, J. R. Pekelsky, “Gauge block calibration by optical interferometry at the National Research Council of Canada,” NRC Internal Report 40002 (NRC, 1997), pp. 6–7.
  26. B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960).

2000 (2)

1999 (2)

B. VanDerWege, C. O’Brien, S. Hochgreb, “Quantitative shearography in axisymmetric gas temperature measurements,” J. Opt. Lasers Eng. 31, 21–39 (1999).
[CrossRef]

A. K. Agrawal, B. W. Albers, D. W. Griffin, “Abel inversion of deflectometric measurements in dynamic flows,” Appl. Opt. 38, 3394–3398 (1999).
[CrossRef]

1997 (1)

1996 (2)

S. Siano, R. Pini, R. Salimbeni, M. Vannini, “A diagnostic set-up for time-resolved imaging of laser-induced ablation,” J. Opt. Lasers Eng. 25, 1–12 (1996).
[CrossRef]

Laboratory for Laser Energetics, “Abel inversion of emission and backlighting images,” LLE Rev. 66, 66–72 (1996), http://www.lle.rochester.edu/pub/review/v66/v66-abel.pdf .

1988 (1)

1981 (1)

1957 (1)

Agrawal, A. K.

Albers, B. W.

Amer, N. M.

Araújo Silva, J.

J. Araújo Silva, A. Fernandes Arriegas, Controlo de qualidade em óptica ocular (M. F. C. R., Lda, Lisbon, 1992).

Barrault, M. R.

M. R. Barrault, G. R. Jones, F. C. Rodrigues, “Practical arcing environments are plasma diagnostics,” in Proceedings of the Seventh Yugoslav Symposium and Summer School on the Physics of Ionized Gases, V. Vujnovic, ed. (IFIS, Zagrab, Yugoslavia, 1974), Vol. 1, pp. 701–807.

Ben-Abdallah, P.

Bialkowski, S. E.

S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, New York, 1996), Chap. 1.

Boccara, A. C.

Boley, B. A.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960).

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (Mc-Graw-Hill, New York, 1999).

Caldeira-Pires, A.

M. Heitor, P. Ferrão, A. Caldeira-Pires, D. Correia, P. Maia, “On the development and implementation of a 3D tomographic sensor on an unconfined laboratory combustion system,” Basic Research in Industrial Technologies—European Research on Advanced Materials Project BE95/1708—Clean Glass Instituto Superior Técnico Technical Report (Instituto Superior Técnico, Lisbon, 1999), http://in3.dem.ist.utl.pt/publications/PAPERS/ifrf_report.pdf .

Charette, A.

Ciotti, L.

L. Ciotti, “Inversion of the Abel equation for toroidal density distributions,” Astrophys. Lett. Commun. 40, 85–93 (2000).

Correia, D.

M. Heitor, P. Ferrão, A. Caldeira-Pires, D. Correia, P. Maia, “On the development and implementation of a 3D tomographic sensor on an unconfined laboratory combustion system,” Basic Research in Industrial Technologies—European Research on Advanced Materials Project BE95/1708—Clean Glass Instituto Superior Técnico Technical Report (Instituto Superior Técnico, Lisbon, 1999), http://in3.dem.ist.utl.pt/publications/PAPERS/ifrf_report.pdf .

Decker, J. E.

J. E. Decker, J. R. Pekelsky, “Gauge block calibration by optical interferometry at the National Research Council of Canada,” NRC Internal Report 40002 (NRC, 1997), pp. 6–7.

Fernandes Arriegas, A.

J. Araújo Silva, A. Fernandes Arriegas, Controlo de qualidade em óptica ocular (M. F. C. R., Lda, Lisbon, 1992).

Ferrão, P.

M. Heitor, P. Ferrão, A. Caldeira-Pires, D. Correia, P. Maia, “On the development and implementation of a 3D tomographic sensor on an unconfined laboratory combustion system,” Basic Research in Industrial Technologies—European Research on Advanced Materials Project BE95/1708—Clean Glass Instituto Superior Técnico Technical Report (Instituto Superior Técnico, Lisbon, 1999), http://in3.dem.ist.utl.pt/publications/PAPERS/ifrf_report.pdf .

Fournier, D.

Griffin, D. W.

Gupta, R

Heitor, M.

M. Heitor, P. Ferrão, A. Caldeira-Pires, D. Correia, P. Maia, “On the development and implementation of a 3D tomographic sensor on an unconfined laboratory combustion system,” Basic Research in Industrial Technologies—European Research on Advanced Materials Project BE95/1708—Clean Glass Instituto Superior Técnico Technical Report (Instituto Superior Técnico, Lisbon, 1999), http://in3.dem.ist.utl.pt/publications/PAPERS/ifrf_report.pdf .

Hochgreb, S.

B. VanDerWege, C. O’Brien, S. Hochgreb, “Quantitative shearography in axisymmetric gas temperature measurements,” J. Opt. Lasers Eng. 31, 21–39 (1999).
[CrossRef]

Jackson, W. B.

Jones, G. R.

M. R. Barrault, G. R. Jones, F. C. Rodrigues, “Practical arcing environments are plasma diagnostics,” in Proceedings of the Seventh Yugoslav Symposium and Summer School on the Physics of Ionized Gases, V. Vujnovic, ed. (IFIS, Zagrab, Yugoslavia, 1974), Vol. 1, pp. 701–807.

Le Dez, V.

Maia, P.

M. Heitor, P. Ferrão, A. Caldeira-Pires, D. Correia, P. Maia, “On the development and implementation of a 3D tomographic sensor on an unconfined laboratory combustion system,” Basic Research in Industrial Technologies—European Research on Advanced Materials Project BE95/1708—Clean Glass Instituto Superior Técnico Technical Report (Instituto Superior Técnico, Lisbon, 1999), http://in3.dem.ist.utl.pt/publications/PAPERS/ifrf_report.pdf .

Malacara, Daniel

Daniel Malacara, Optical Shop Testing (Wiley, New York, 1992).

O’Brien, C.

B. VanDerWege, C. O’Brien, S. Hochgreb, “Quantitative shearography in axisymmetric gas temperature measurements,” J. Opt. Lasers Eng. 31, 21–39 (1999).
[CrossRef]

Pekelsky, J. R.

J. E. Decker, J. R. Pekelsky, “Gauge block calibration by optical interferometry at the National Research Council of Canada,” NRC Internal Report 40002 (NRC, 1997), pp. 6–7.

Pini, R.

S. Siano, R. Pini, R. Salimbeni, M. Vannini, “A diagnostic set-up for time-resolved imaging of laser-induced ablation,” J. Opt. Lasers Eng. 25, 1–12 (1996).
[CrossRef]

Rienitz, J.

J. Rienitz, “Schlieren experiment 300 years ago,” in Selected Papers on Schlieren Optics, J. R. Mayer-Arendt, ed., Vol. MS61 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1992), pp. 10–12.

Rodrigues, F. C.

M. R. Barrault, G. R. Jones, F. C. Rodrigues, “Practical arcing environments are plasma diagnostics,” in Proceedings of the Seventh Yugoslav Symposium and Summer School on the Physics of Ionized Gases, V. Vujnovic, ed. (IFIS, Zagrab, Yugoslavia, 1974), Vol. 1, pp. 701–807.

F. C. Rodrigues, “Optical diagnostics—high current arcs,” Ph.D. dissertation (University of Liverpool, Liverpool, UK, 1974).

Sakami, M.

Salimbeni, R.

S. Siano, R. Pini, R. Salimbeni, M. Vannini, “A diagnostic set-up for time-resolved imaging of laser-induced ablation,” J. Opt. Lasers Eng. 25, 1–12 (1996).
[CrossRef]

Saulnier, J. B.

Schreiber, H.

Schwider, J.

Settles, G. S.

G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, Berlin, 2001).
[CrossRef]

Siano, S.

S. Siano, R. Pini, R. Salimbeni, M. Vannini, “A diagnostic set-up for time-resolved imaging of laser-induced ablation,” J. Opt. Lasers Eng. 25, 1–12 (1996).
[CrossRef]

Teixeira, M. R.

M. R. Teixeira, “Processos atómicos em descargas luminescentes de cátodo oco,” Ph.D. dissertation (Universidade de Lisboa, Lisbon, 1983).

Temple, E. B.

VanDerWege, B.

B. VanDerWege, C. O’Brien, S. Hochgreb, “Quantitative shearography in axisymmetric gas temperature measurements,” J. Opt. Lasers Eng. 31, 21–39 (1999).
[CrossRef]

Vannini, M.

S. Siano, R. Pini, R. Salimbeni, M. Vannini, “A diagnostic set-up for time-resolved imaging of laser-induced ablation,” J. Opt. Lasers Eng. 25, 1–12 (1996).
[CrossRef]

Vyas, Reeta

Weiner, J. H.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960).

Appl. Opt. (5)

Astrophys. Lett. Commun. (1)

L. Ciotti, “Inversion of the Abel equation for toroidal density distributions,” Astrophys. Lett. Commun. 40, 85–93 (2000).

J. Opt. Lasers Eng. (2)

S. Siano, R. Pini, R. Salimbeni, M. Vannini, “A diagnostic set-up for time-resolved imaging of laser-induced ablation,” J. Opt. Lasers Eng. 25, 1–12 (1996).
[CrossRef]

B. VanDerWege, C. O’Brien, S. Hochgreb, “Quantitative shearography in axisymmetric gas temperature measurements,” J. Opt. Lasers Eng. 31, 21–39 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

LLE Rev. (1)

Laboratory for Laser Energetics, “Abel inversion of emission and backlighting images,” LLE Rev. 66, 66–72 (1996), http://www.lle.rochester.edu/pub/review/v66/v66-abel.pdf .

Other (16)

S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, New York, 1996), Chap. 1.

M. R. Teixeira, “Processos atómicos em descargas luminescentes de cátodo oco,” Ph.D. dissertation (Universidade de Lisboa, Lisbon, 1983).

M. Heitor, P. Ferrão, A. Caldeira-Pires, D. Correia, P. Maia, “On the development and implementation of a 3D tomographic sensor on an unconfined laboratory combustion system,” Basic Research in Industrial Technologies—European Research on Advanced Materials Project BE95/1708—Clean Glass Instituto Superior Técnico Technical Report (Instituto Superior Técnico, Lisbon, 1999), http://in3.dem.ist.utl.pt/publications/PAPERS/ifrf_report.pdf .

K. Green, M. C. Borrás, P. P. Woskov, G. I. Flores, K. Hadidi, P. Thomas, “Electronic excitation temperatures profiles in an air microwave torch,” Plasma Science and Fusion Center (MIT, Cambridge, Mass., 2001), http://www.psfc.mit.edu/library/01JA/01JA005/01JA005_full.pdf .

M. Pavelek, E. Janotkova, “Interferometric research of heat transfer at air jet from ventilating outlets,” in Proceedings of the Sixth International Symposium Ventilation 2000, S. Hiltumen, ed. (Finnish Institute of Occupational Health, Helsinki, Finland, 2000), Vol. 2, pp. 179–181, http://dt.fme.vutbr.cz/∼pavelek/00fin-m.doc .

M. Pavelek, E. Janotkova, “Research of dynamic temperature fields by means of Mach-Zender interferometer,” in Proceedings of the International Congress of Chemical and Process Engineering, CHISA ’98 (Process Engineering, Prague, Czech Republic, 1998), Vol. 4, paper P1.146, http://dt.fme.vutbr.cz/∼pavelek/98CHISAm.doc .

F. C. Rodrigues, “Optical diagnostics—high current arcs,” Ph.D. dissertation (University of Liverpool, Liverpool, UK, 1974).

J. Rienitz, “Schlieren experiment 300 years ago,” in Selected Papers on Schlieren Optics, J. R. Mayer-Arendt, ed., Vol. MS61 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1992), pp. 10–12.

J. Araújo Silva, A. Fernandes Arriegas, Controlo de qualidade em óptica ocular (M. F. C. R., Lda, Lisbon, 1992).

Daniel Malacara, Optical Shop Testing (Wiley, New York, 1992).

G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, Berlin, 2001).
[CrossRef]

R. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (Mc-Graw-Hill, New York, 1999).

M. R. Barrault, G. R. Jones, F. C. Rodrigues, “Practical arcing environments are plasma diagnostics,” in Proceedings of the Seventh Yugoslav Symposium and Summer School on the Physics of Ionized Gases, V. Vujnovic, ed. (IFIS, Zagrab, Yugoslavia, 1974), Vol. 1, pp. 701–807.

Zemax—Optical Design Program User’s Guide (Focus Software Inc., Tucson, Ariz., 2001). See Ref. 25.

J. E. Decker, J. R. Pekelsky, “Gauge block calibration by optical interferometry at the National Research Council of Canada,” NRC Internal Report 40002 (NRC, 1997), pp. 6–7.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960).

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Figures (12)

Fig. 1
Fig. 1

Schematic of lateral shearing interferometry.

Fig. 2
Fig. 2

Schematic of the experimental setup.

Fig. 3
Fig. 3

Example of pattern images registered by the CCD camera at different moments in time (processing started at t = 0 s) during welding of 10-μm-thick samples.

Fig. 4
Fig. 4

Observed parabolic shape of the pattern’s lower limit after the method’s applicability limit was reached.

Fig. 5
Fig. 5

Example of a data sequence as the method is applied: (a) the observed angular deflection, (b) refractive-index gradients obtained by the Abel inversion, and (c) the refractive-index map resulting from integration of former data.

Fig. 6
Fig. 6

Air-temperature distribution measured by the method above the sample at instant t = 0.39 s. Dashed curves, related major and minor errors. Example of welding of 10-μm-thick samples.

Fig. 7
Fig. 7

Average air-temperature distribution measured above the sample at instant t = 0.39 s for both thicknesses considered.

Fig. 8
Fig. 8

Average air-temperature distribution measured above the sample at several instants. Example of welding of 10-μm-thick samples.

Fig. 9
Fig. 9

Time evolution of the thermoplastic’s temperature measured at its surface for welding of (a) 10-μm- and (b) 30-μm-thick samples.

Fig. 10
Fig. 10

Schematic of the experimental setup used for deflection measurements.

Fig. 11
Fig. 11

Predicted deflection for the probe beam at z = 0.5, 1.0, and 1.5 mm for welding of (a) 10-μm- and (b) 30-μm-thick samples. It also shows the best-fit equation for the central point deflection.

Fig. 12
Fig. 12

Probe-beam cross sections: observed before the inspected zone, observed through deflection experiments, and predicted from schlieren interferometry results. Example of welding of 10-μm-thick samples.

Equations (20)

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ddSnrefdδdS=nr, t,
δ=P2A+AF+nFF+FF+FP-P1B+BF+FP+λ2,
δ=h2u2i2Mf+2hn2-sin2i1/2+λ2,
ui=sin2in2-sin2i1/2,
Si=huiM.
dδdi=-hui1-huiMf,
di=-λhui1-huiMf.
di=ΔPΔOP λMh×1ui1-OP2+2OPMf coti02Mf coti0+OP2,
di=- 1ndndzdz
di=- dδndzdz.
diz=2 zR0rdδnrr2-z2dr,
dδnr=-1πrR0diRRR2-r2dR,
δnr=δnrrk,
δnrj=δnrK+k=jKrk+1-rkδnrrk+1.
τac=r/21/2cs,
τt=r2/4k,
nTa=1+nref-1patm1+3.4785×10-3Ta-15,
nref=1+6432.8+2,949,810λp2146λp2-1+25,540λp241λp2-1×10-8.
nTa=1+nref-1patm96,095.43×1+10-80.601-0.00972Tapatm1+0.003661Ta.
Taz, t=T+Tamb-T32zδTt-12zδTt3,

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