Abstract

A combination of a Hartmann-Shack sensor and a standard far-field measurement on one single detector is proposed. The technique is fast and operates without movable parts, thus permitting a compact design. It is not only suited for characterization of the wave-front distribution but may also be considered for determination of the important parameters of beam width, beam divergence, and beam propagation ratio M 2 of partially coherent laser beams. First results indicate that a fairly thorough beam characterization, including spatial coherence, propagation characteristics, and beam quality, can be achieved with this method.

© 2002 Optical Society of America

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References

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  1. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, 2nd ed. (Cambridge U. Press, Cambridge, England, 1994).
  2. M. J. Baastians, “Application of the Wigner distribution function to partially coherent light,” J. Opt. Soc. Am. A 3, 1227–1238 (1986).
    [CrossRef]
  3. B. Eppich, “Measurement of the Wigner distribution function based on the inverse Radon transformation,” in Beam Control, Diagnostics Standards and Propagation, L. W. Austin, A. Giesen, D. H. Leslie, H. Weichel, eds., Proc. SPIE2375, 261–268 (1995).
    [CrossRef]
  4. J. Hartmann, “Bemerkungen über den Bau und die Justierung von Spektrographen,” Z. Instrumentenk. 20, 47–58 (1900).
  5. B. Platt, R. Shack, “Lenticular Hartmann screen,” Opt. Sci. Cent. Newsl. 5, No. 1, 15 (1971).
  6. D. R. Neal, W. J. Alford, J. K. Gruetzner, M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Third International Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., Proc. SPIE2870, 72–82 (1996).
    [CrossRef]
  7. B. Schäfer, K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71, 2663–2668 (2000).
    [CrossRef]
  8. V. Laude, S. Olivier, C. Dirson, J. P. Huignard, “Hartmann wave-front scanner,” Opt. Lett. 24, 1796–1798 (1999).
    [CrossRef]
  9. R. Cubalchini, “Modal wavefront estimation from phase derivative measurement,” J. Opt. Soc. Am. 69, 972–977 (1979).
    [CrossRef]
  10. R. J. Noll, “Phase estimates from slope type wavefront sensors,” J. Opt. Soc. Am. 68, 139–140 (1978).
    [CrossRef]
  11. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1992).
  12. G. Nemes, J. Serna, “Do not use spherical lenses and free spaces to characterize beams: a possible improvement of the ISO/DIS 11146 document,” in Proceedings of the Fourth Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., pp. 29–49 (A. Giesen, Institut fur Strahlwerkzeuge Universität Stuttgart, Munich, Germany, 1997).
  13. International Organization for Standardization, “Lasers and laser-related equipment—Test methods for laser beam parameters—Beam widths, divergence angle and beam propagation factor,” ISO/FDIS 11146, ISO Document ISO/TC 172/SC 9/WG 1 (ISO, Geneva, Switzerland, 1999).
  14. M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, England, 1985).
  15. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
    [CrossRef]

2000 (1)

B. Schäfer, K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71, 2663–2668 (2000).
[CrossRef]

1999 (1)

1986 (1)

1979 (1)

1978 (1)

1971 (1)

B. Platt, R. Shack, “Lenticular Hartmann screen,” Opt. Sci. Cent. Newsl. 5, No. 1, 15 (1971).

1900 (1)

J. Hartmann, “Bemerkungen über den Bau und die Justierung von Spektrographen,” Z. Instrumentenk. 20, 47–58 (1900).

Alford, W. J.

D. R. Neal, W. J. Alford, J. K. Gruetzner, M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Third International Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., Proc. SPIE2870, 72–82 (1996).
[CrossRef]

Baastians, M. J.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, England, 1985).

Cubalchini, R.

Dirson, C.

Eppich, B.

B. Eppich, “Measurement of the Wigner distribution function based on the inverse Radon transformation,” in Beam Control, Diagnostics Standards and Propagation, L. W. Austin, A. Giesen, D. H. Leslie, H. Weichel, eds., Proc. SPIE2375, 261–268 (1995).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1992).

Gruetzner, J. K.

D. R. Neal, W. J. Alford, J. K. Gruetzner, M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Third International Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., Proc. SPIE2870, 72–82 (1996).
[CrossRef]

Hartmann, J.

J. Hartmann, “Bemerkungen über den Bau und die Justierung von Spektrographen,” Z. Instrumentenk. 20, 47–58 (1900).

Huignard, J. P.

Laude, V.

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, 2nd ed. (Cambridge U. Press, Cambridge, England, 1994).

Mann, K.

B. Schäfer, K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71, 2663–2668 (2000).
[CrossRef]

Neal, D. R.

D. R. Neal, W. J. Alford, J. K. Gruetzner, M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Third International Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., Proc. SPIE2870, 72–82 (1996).
[CrossRef]

Nemes, G.

G. Nemes, J. Serna, “Do not use spherical lenses and free spaces to characterize beams: a possible improvement of the ISO/DIS 11146 document,” in Proceedings of the Fourth Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., pp. 29–49 (A. Giesen, Institut fur Strahlwerkzeuge Universität Stuttgart, Munich, Germany, 1997).

Noll, R. J.

Olivier, S.

Platt, B.

B. Platt, R. Shack, “Lenticular Hartmann screen,” Opt. Sci. Cent. Newsl. 5, No. 1, 15 (1971).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1992).

Schäfer, B.

B. Schäfer, K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71, 2663–2668 (2000).
[CrossRef]

Serna, J.

G. Nemes, J. Serna, “Do not use spherical lenses and free spaces to characterize beams: a possible improvement of the ISO/DIS 11146 document,” in Proceedings of the Fourth Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., pp. 29–49 (A. Giesen, Institut fur Strahlwerkzeuge Universität Stuttgart, Munich, Germany, 1997).

Shack, R.

B. Platt, R. Shack, “Lenticular Hartmann screen,” Opt. Sci. Cent. Newsl. 5, No. 1, 15 (1971).

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1992).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1992).

Warren, M. E.

D. R. Neal, W. J. Alford, J. K. Gruetzner, M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Third International Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., Proc. SPIE2870, 72–82 (1996).
[CrossRef]

Wolf, E.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, 2nd ed. (Cambridge U. Press, Cambridge, England, 1994).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, England, 1985).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Opt. Sci. Cent. Newsl. (1)

B. Platt, R. Shack, “Lenticular Hartmann screen,” Opt. Sci. Cent. Newsl. 5, No. 1, 15 (1971).

Rev. Sci. Instrum. (1)

B. Schäfer, K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71, 2663–2668 (2000).
[CrossRef]

Z. Instrumentenk. (1)

J. Hartmann, “Bemerkungen über den Bau und die Justierung von Spektrographen,” Z. Instrumentenk. 20, 47–58 (1900).

Other (8)

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, 2nd ed. (Cambridge U. Press, Cambridge, England, 1994).

B. Eppich, “Measurement of the Wigner distribution function based on the inverse Radon transformation,” in Beam Control, Diagnostics Standards and Propagation, L. W. Austin, A. Giesen, D. H. Leslie, H. Weichel, eds., Proc. SPIE2375, 261–268 (1995).
[CrossRef]

D. R. Neal, W. J. Alford, J. K. Gruetzner, M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Third International Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., Proc. SPIE2870, 72–82 (1996).
[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1992).

G. Nemes, J. Serna, “Do not use spherical lenses and free spaces to characterize beams: a possible improvement of the ISO/DIS 11146 document,” in Proceedings of the Fourth Workshop on Laser Beam and Optics Characterization, A. Giesen, M. Morin, eds., pp. 29–49 (A. Giesen, Institut fur Strahlwerkzeuge Universität Stuttgart, Munich, Germany, 1997).

International Organization for Standardization, “Lasers and laser-related equipment—Test methods for laser beam parameters—Beam widths, divergence angle and beam propagation factor,” ISO/FDIS 11146, ISO Document ISO/TC 172/SC 9/WG 1 (ISO, Geneva, Switzerland, 1999).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, England, 1985).

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Principle of a Hartmann-Shack wave-front sensor.

Fig. 2
Fig. 2

Experimental setup for beam parameter determination.

Fig. 3
Fig. 3

Extended Hartmann-Shack system for simultaneous far-field, near-field, and wave-front measurements.

Fig. 4
Fig. 4

Experimental setup for measurement of the spatial coherence.

Fig. 5
Fig. 5

Points of measurement (dots) for the mutual coherence function g within the near-field profile of the KrF excimer laser.

Fig. 6
Fig. 6

Mutual coherence function g of the KrF excimer laser recorded at positions 1(a), 2(b), 3(c), and 4(d) within the beam profile (see Fig. 5).

Fig. 7
Fig. 7

(a) Beam profile of the KrF excimer laser measured in the divergent part of the beam caustic. The satellite peak in the lower part comes in for an intracavity reflection at one electrode of the discharge tube, indicating a slightly misaligned laser resonator. The wave front is represented in wavelength units for the KrF laser (248 nm). (b) Wave front of the KrF excimer laser measured in the divergent part of the beam caustic. Note that the satellite peak propagates in a different direction. The wave front is represented in wavelength units for the KrF laser (248 nm). (c) Near-field beam profile of the diode laser measured approximately 0.5 m behind the source. Near-field wave front of the diode laser measured approximately 0.5 m behind the source.

Fig. 8
Fig. 8

(a) Caustic measurement of the slow axis of the KrF excimer laser according to the ISO 11146 standard. (b) Beam propagation ratio of the KrF excimer laser recorded at three different positions along the beam axis, by use of the caustic measurement and the ordinary Hartmann-Shack sensor.

Fig. 9
Fig. 9

Pattern of a diode laser recorded with the extended Hartmann-Shack system. The far-field branch (left) gives accurate estimates of the beam divergence, whereas the Hartmann-Shack branch (right) delivers beam diameter and wave-front curvature.

Fig. 10
Fig. 10

Fast-axis (vertical) and slow-axis (horizontal) beam caustics of the diode laser according to the ISO 11146 standard.

Tables (3)

Tables Icon

Table 1 Beam Parameters for the Slow (Horizontal) Axis of the KrF Excimer Laser Obtained With Different Experimental Methodsa

Tables Icon

Table 2 Beam Parameters Obtained with Different Methods for the Diode Lasera

Tables Icon

Table 3 Comparison of Different Methods for Laser Beam Characterization Regarding Their Suitability for Determination of Important Beam Parameters

Equations (24)

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Ŝ=w/xw/yij=βij= 1fxc-xryc-yrij.
βx, yx, y; z0=wx, y; z0x, y=k=1L ckz0Pkx, yx, y.
BTC-1B · c-BTC-1 · β=0,
x2= ijxij-x2IijijIij, y2=,
xu= ijβijx-βxxij-xIijijIij,
u2= ijβijx-βx2IijijIij+1k2ijI/xij2Iij4ijIij,
dx=4x2, dy=4y2,
θσx=4u2, θσy=4v2,
Mx2=4πλx2u2-xu2, My2=4πλy2v2-yv2,
τ=0.5uy-vx.
x2z=1Px2Ix, zd2x,
xuz=1Pxβxx, zIx, zd2x,
u2z=-k-2P-1-Ix; z/x24Ix; z-k2Ix; z×βxx; z2d2d2x,
Wx1, y1, x2, y2=Ix1, y1Ix2, y2×gx1, y1, x2, y2×expiαx1, y1, x2, y2,
xiyjukvlz=ik-k+1xiyjksxklsyl ×Wx+ s2, x- s2, zs = 0d2x,
x2z=1Px2Ix, zd2x,
xuz=kP-1x ϕx, zx Ix, zd2x,
u2=-k-2P-1-Ix; z/x24Ix; z-k2Ix; zϕx; zx2+Ix; z2gx, sx=0; zsx2d2x.
ϕx, yx=lims0αx+ sx2, y+ sy2, x- sx2, y- sy2sx.
u2zIHS= u2+1Pk2Ix; z2gx, sx=0; zsx2d2x0.
Lxixjz=1PIx; z× 2gx, sx=0, sy=0; zsxjsxjd2x-1/2
Mx22-Mx2IHS2=8 x2zLxxz2
xijc=kSAijNkijxkijkSAijNkij, yijc=kSAijNkijykijkSAijNkij,
K=Imax-IminImax+Imin,

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