Abstract

We study imaging systems designed to assess the smile of laser diode bars (LDBs). The magnification matrix is derived from the required sampling period and the geometries of the LDBs and the charge-coupled device (CCD) array. These image-forming systems present in-plane pure translation invariance, but in the case of anamorphic ones, lack in-plane rotation invariance. It is shown that the smile parameters of the image of the LDB are linked with the smile parameters of the LDB by simple mathematical expressions. The spatial resolution of such optical systems is estimated at approximately 1μm for a mean wavelength of λ800nm. Our results suggest that, with the current state-of-the-art, the formation of imaging methods for LDB smile assessment can be used to assess smile heights 1μm.

© 2009 Optical Society of America

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References

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  1. G. A. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).
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    [CrossRef]
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    [CrossRef]
  4. W. Schulz and R. Poprawe, “Manufacturing with novel high-power diode lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 696-705 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. U. Dürig, D. W. Pohl, and F. Rohner, “Near field optical-scanning microscopy,” J. Appl. Phys. 59, 3318-3327 (1986).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. C. Scholz and M. Belitz, “High resolution near-field analysis of high-power diode lasers,” http://www.ilt.fraunhofer.de/eng/100299.html.
  12. L. Martí-López, J. A. Ramos-de-Campos, and R. A. Martínez-Celorio, “Interferometric method for characterizing the smile of laser diode bars,” Opt. Commun. 275, 359-371 (2007).
    [CrossRef]
  13. M. S. Nixon and A. S. Aguado, Feature Extraction and Image Processing (Newnes, 2002).
  14. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  15. J. L. Hunt, B. G. Nickel, and C. Gigault, “Anamorphic images,” Am. J. Phys. 68, 232-237 (2000).
    [CrossRef]
  16. S. Inoué and R. Oldenbourg, “Microscopes,” in Handbook of Optics: Devices, Measurements and Properties,M. Bass, E. W. Van Stryland, D. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Vol. 2.

2007 (1)

L. Martí-López, J. A. Ramos-de-Campos, and R. A. Martínez-Celorio, “Interferometric method for characterizing the smile of laser diode bars,” Opt. Commun. 275, 359-371 (2007).
[CrossRef]

2006 (1)

2005 (1)

2001 (1)

N. U. Wetter, “Three-fold effective brightness increase of laser diode bar emission by assessment and correction of diode array curvature,” Opt. Laser Technol. 33, 181-187(2001).
[CrossRef]

2000 (3)

H.-G. Treusch, A. Ovtchinnikov, X. He, M. Kanskar, J. Mott, and S. Yang, “High-brightness semiconductor laser sources for materials processing: stacking, beam shaping, and bars,” IEEE J. Sel. Top. Quantum Electron. 6, 601-614(2000).
[CrossRef]

W. Schulz and R. Poprawe, “Manufacturing with novel high-power diode lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 696-705 (2000).
[CrossRef]

J. L. Hunt, B. G. Nickel, and C. Gigault, “Anamorphic images,” Am. J. Phys. 68, 232-237 (2000).
[CrossRef]

1997 (1)

W. D. Herzog, M. S. Ünlü, B. B. Goldberg, G. H. Rodees, and C. Harder, “Beam divergence and waist measurements of laser diodes by near-field scanning optical microscopy,” Appl. Phys. Lett. 70, 688-690 (1997).
[CrossRef]

1992 (1)

E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189-195 (1992).
[CrossRef] [PubMed]

1986 (1)

U. Dürig, D. W. Pohl, and F. Rohner, “Near field optical-scanning microscopy,” J. Appl. Phys. 59, 3318-3327 (1986).
[CrossRef]

Agrawal, G. A.

G. A. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).

Aguado, A. S.

M. S. Nixon and A. S. Aguado, Feature Extraction and Image Processing (Newnes, 2002).

Baker, H. J.

Belitz, M.

C. Scholz and M. Belitz, “High resolution near-field analysis of high-power diode lasers,” http://www.ilt.fraunhofer.de/eng/100299.html.

Betzig, E.

E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189-195 (1992).
[CrossRef] [PubMed]

Brereton, I.

Diehl, R.

R. Diehl, High-Power Diode Lasers: Fundamentals, Technology, Applications (Springer-Verlag, 2000).
[CrossRef]

Dürig, U.

U. Dürig, D. W. Pohl, and F. Rohner, “Near field optical-scanning microscopy,” J. Appl. Phys. 59, 3318-3327 (1986).
[CrossRef]

Dutta, N. K.

G. A. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).

Friese, M. E. J.

Gigault, C.

J. L. Hunt, B. G. Nickel, and C. Gigault, “Anamorphic images,” Am. J. Phys. 68, 232-237 (2000).
[CrossRef]

Goldberg, B. B.

W. D. Herzog, M. S. Ünlü, B. B. Goldberg, G. H. Rodees, and C. Harder, “Beam divergence and waist measurements of laser diodes by near-field scanning optical microscopy,” Appl. Phys. Lett. 70, 688-690 (1997).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Hall, D. R.

Harder, C.

W. D. Herzog, M. S. Ünlü, B. B. Goldberg, G. H. Rodees, and C. Harder, “Beam divergence and waist measurements of laser diodes by near-field scanning optical microscopy,” Appl. Phys. Lett. 70, 688-690 (1997).
[CrossRef]

He, X.

H.-G. Treusch, A. Ovtchinnikov, X. He, M. Kanskar, J. Mott, and S. Yang, “High-brightness semiconductor laser sources for materials processing: stacking, beam shaping, and bars,” IEEE J. Sel. Top. Quantum Electron. 6, 601-614(2000).
[CrossRef]

Heckenberg, N. R.

Herzog, W. D.

W. D. Herzog, M. S. Ünlü, B. B. Goldberg, G. H. Rodees, and C. Harder, “Beam divergence and waist measurements of laser diodes by near-field scanning optical microscopy,” Appl. Phys. Lett. 70, 688-690 (1997).
[CrossRef]

Hunt, J. L.

J. L. Hunt, B. G. Nickel, and C. Gigault, “Anamorphic images,” Am. J. Phys. 68, 232-237 (2000).
[CrossRef]

Inoué, S.

S. Inoué and R. Oldenbourg, “Microscopes,” in Handbook of Optics: Devices, Measurements and Properties,M. Bass, E. W. Van Stryland, D. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Vol. 2.

Kanskar, M.

H.-G. Treusch, A. Ovtchinnikov, X. He, M. Kanskar, J. Mott, and S. Yang, “High-brightness semiconductor laser sources for materials processing: stacking, beam shaping, and bars,” IEEE J. Sel. Top. Quantum Electron. 6, 601-614(2000).
[CrossRef]

Martí-López, L.

L. Martí-López, J. A. Ramos-de-Campos, and R. A. Martínez-Celorio, “Interferometric method for characterizing the smile of laser diode bars,” Opt. Commun. 275, 359-371 (2007).
[CrossRef]

Martínez-Celorio, R. A.

L. Martí-López, J. A. Ramos-de-Campos, and R. A. Martínez-Celorio, “Interferometric method for characterizing the smile of laser diode bars,” Opt. Commun. 275, 359-371 (2007).
[CrossRef]

Monjardin, J. F.

Mott, J.

H.-G. Treusch, A. Ovtchinnikov, X. He, M. Kanskar, J. Mott, and S. Yang, “High-brightness semiconductor laser sources for materials processing: stacking, beam shaping, and bars,” IEEE J. Sel. Top. Quantum Electron. 6, 601-614(2000).
[CrossRef]

Nickel, B. G.

J. L. Hunt, B. G. Nickel, and C. Gigault, “Anamorphic images,” Am. J. Phys. 68, 232-237 (2000).
[CrossRef]

Nixon, M. S.

M. S. Nixon and A. S. Aguado, Feature Extraction and Image Processing (Newnes, 2002).

Nowak, K. M.

Oldenbourg, R.

S. Inoué and R. Oldenbourg, “Microscopes,” in Handbook of Optics: Devices, Measurements and Properties,M. Bass, E. W. Van Stryland, D. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Vol. 2.

Ovtchinnikov, A.

H.-G. Treusch, A. Ovtchinnikov, X. He, M. Kanskar, J. Mott, and S. Yang, “High-brightness semiconductor laser sources for materials processing: stacking, beam shaping, and bars,” IEEE J. Sel. Top. Quantum Electron. 6, 601-614(2000).
[CrossRef]

Pohl, D. W.

U. Dürig, D. W. Pohl, and F. Rohner, “Near field optical-scanning microscopy,” J. Appl. Phys. 59, 3318-3327 (1986).
[CrossRef]

Poprawe, R.

W. Schulz and R. Poprawe, “Manufacturing with novel high-power diode lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 696-705 (2000).
[CrossRef]

Ramos-de-Campos, J. A.

L. Martí-López, J. A. Ramos-de-Campos, and R. A. Martínez-Celorio, “Interferometric method for characterizing the smile of laser diode bars,” Opt. Commun. 275, 359-371 (2007).
[CrossRef]

Rodees, G. H.

W. D. Herzog, M. S. Ünlü, B. B. Goldberg, G. H. Rodees, and C. Harder, “Beam divergence and waist measurements of laser diodes by near-field scanning optical microscopy,” Appl. Phys. Lett. 70, 688-690 (1997).
[CrossRef]

Rohner, F.

U. Dürig, D. W. Pohl, and F. Rohner, “Near field optical-scanning microscopy,” J. Appl. Phys. 59, 3318-3327 (1986).
[CrossRef]

Rubinsztein-Dunlop, H.

Scholz, C.

C. Scholz and M. Belitz, “High resolution near-field analysis of high-power diode lasers,” http://www.ilt.fraunhofer.de/eng/100299.html.

Schulz, W.

W. Schulz and R. Poprawe, “Manufacturing with novel high-power diode lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 696-705 (2000).
[CrossRef]

Talbot, C. L.

Trautman, J. K.

E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189-195 (1992).
[CrossRef] [PubMed]

Treusch, H.-G.

H.-G. Treusch, A. Ovtchinnikov, X. He, M. Kanskar, J. Mott, and S. Yang, “High-brightness semiconductor laser sources for materials processing: stacking, beam shaping, and bars,” IEEE J. Sel. Top. Quantum Electron. 6, 601-614(2000).
[CrossRef]

Ünlü, M. S.

W. D. Herzog, M. S. Ünlü, B. B. Goldberg, G. H. Rodees, and C. Harder, “Beam divergence and waist measurements of laser diodes by near-field scanning optical microscopy,” Appl. Phys. Lett. 70, 688-690 (1997).
[CrossRef]

Wang, D.

Wetter, N. U.

N. U. Wetter, “Three-fold effective brightness increase of laser diode bar emission by assessment and correction of diode array curvature,” Opt. Laser Technol. 33, 181-187(2001).
[CrossRef]

Yang, S.

H.-G. Treusch, A. Ovtchinnikov, X. He, M. Kanskar, J. Mott, and S. Yang, “High-brightness semiconductor laser sources for materials processing: stacking, beam shaping, and bars,” IEEE J. Sel. Top. Quantum Electron. 6, 601-614(2000).
[CrossRef]

Am. J. Phys. (1)

J. L. Hunt, B. G. Nickel, and C. Gigault, “Anamorphic images,” Am. J. Phys. 68, 232-237 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

W. D. Herzog, M. S. Ünlü, B. B. Goldberg, G. H. Rodees, and C. Harder, “Beam divergence and waist measurements of laser diodes by near-field scanning optical microscopy,” Appl. Phys. Lett. 70, 688-690 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

H.-G. Treusch, A. Ovtchinnikov, X. He, M. Kanskar, J. Mott, and S. Yang, “High-brightness semiconductor laser sources for materials processing: stacking, beam shaping, and bars,” IEEE J. Sel. Top. Quantum Electron. 6, 601-614(2000).
[CrossRef]

W. Schulz and R. Poprawe, “Manufacturing with novel high-power diode lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 696-705 (2000).
[CrossRef]

J. Appl. Phys. (1)

U. Dürig, D. W. Pohl, and F. Rohner, “Near field optical-scanning microscopy,” J. Appl. Phys. 59, 3318-3327 (1986).
[CrossRef]

Opt. Commun. (1)

L. Martí-López, J. A. Ramos-de-Campos, and R. A. Martínez-Celorio, “Interferometric method for characterizing the smile of laser diode bars,” Opt. Commun. 275, 359-371 (2007).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

N. U. Wetter, “Three-fold effective brightness increase of laser diode bar emission by assessment and correction of diode array curvature,” Opt. Laser Technol. 33, 181-187(2001).
[CrossRef]

Science (1)

E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189-195 (1992).
[CrossRef] [PubMed]

Other (6)

G. A. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).

R. Diehl, High-Power Diode Lasers: Fundamentals, Technology, Applications (Springer-Verlag, 2000).
[CrossRef]

M. S. Nixon and A. S. Aguado, Feature Extraction and Image Processing (Newnes, 2002).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

C. Scholz and M. Belitz, “High resolution near-field analysis of high-power diode lasers,” http://www.ilt.fraunhofer.de/eng/100299.html.

S. Inoué and R. Oldenbourg, “Microscopes,” in Handbook of Optics: Devices, Measurements and Properties,M. Bass, E. W. Van Stryland, D. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Vol. 2.

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Figures (4)

Fig. 1
Fig. 1

Scheme of a LDB smile; each ellipse represents the active zone of a LD.

Fig. 2
Fig. 2

Coordinate system and variables at the output facet of the LDB. Each ellipse represents the active zone of a LD.

Fig. 3
Fig. 3

Block diagram of the setup of the IM for smile assessment: (a) simplified block diagram of the setup and (b) scheme of the CCD array.

Fig. 4
Fig. 4

Image LDB smile variation that is due to rotation for m x = 1 , m y = 10 . (a) Simulated LDB and corresponding image. (b) The same simulated LDB with an in-plane counterclockwise rotation of Δ θ = 5 and the resulting image. Note the change in the SH of the image.

Equations (37)

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SAR = SH L ,
S = 1 N q = 1 N δ q 2 ,
S = 1 N ( b ξ q + d η q ) 2 ,
η = b ξ + d
b = ξ q η q + ξ q η q ξ q 2 ξ q 2 ,
d = η q b ξ q ,
ξ q 2 = 1 N q = 1 N ξ q 2 ,
ξ q = 1 N q = 1 N ξ q ,
η q = 1 N q = 1 N η q ,
ξ q η q = 1 N q = 1 N ξ q η q .
r = Mr ,
M = [ m x 0 0 m y ] ,
Δ r = r 2 r 1
Δ r = r 2 r 1
Δ r = M Δ r .
Δ r new = M ( r 2 + t ) M ( r 1 + t ) .
Δ r new = Δ r .
Δ r = | Δ r | [ cos θ sin θ ] ,
Δ r = M | Δ r | [ cos θ sin θ ] .
| Δ r | = | Δ r | m x 2 cos 2 θ + m y 2 sin 2 θ ,
tan β = m y m x tan θ .
R 0.5 λ NA ,
SH = SH m x 2 cos 2 γ + m y 2 sin 2 γ ,
L = L m x 2 sin 2 γ + m y 2 cos 2 γ ,
SAR = m x 2 cos 2 γ + m y 2 sin 2 γ m x 2 sin 2 γ + m y 2 cos 2 γ SAR ,
SH = | m y | SH ,
L = | m x | L ,
SAR = m y m x SAR .
b = x q y q + x q y q x q 2 y q 2 ,
d = y q b x q ,
x q 2 = 1 N q = 1 N x q 2 ,
x q = 1 N q = 1 N x q ,
y q = 1 N q = 1 N y q ,
x q y q = 1 N q = 1 N x q y q ,
b = m y m x b ,
d = m y d .
S = | m y | S .

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