Abstract

The performance of a fiber-optic laser beam delivery system strongly depends on the fiber and the optics used to image the fiber face on the workpiece. We have compared off-the-shelf homogenous (BK7) and GRADIUM (axial-gradient) singlets to determine what improvement the GRADIUM offers in practice to the typical laser user. The realized benefit for this application, although significant, is much smaller than would be realized by a conventional imaging application. The figure of merit for laser-based materials processing is the 86% energy-enclosure radius, which is not directly supported by commercial ray-tracing software. Therefore empirical rules of thumb are presented to understand when GRADIUM (or any other well-corrected optics) will yield meaningful improvements to the beam delivery system.

© 1997 Optical Society of America

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References

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  1. C. J. Nonhof, Material Processing with Nd Lasers (Electrochemical Publications, Ayr, Scotland, 1988), p. 182.
  2. K. H. Leong, B. V. Hunter, “High-power fiberoptic laser beam delivery moves forward,” Ind. Laser Rev. 11, 7–12 (1996).
  3. B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Laser Materials Processing: New Developments in Laser Sources and Applications, W. Duley, K. Shibata, R. Poprawe, eds., Proc. ICALEO81E, 173–182 (1996).
  4. P. J. Sands, “Third-order aberrations of inhomogeneous lenses,” J. Opt. Soc. Am. 60, 1436–1443 (1970); “Inhomogeneous lenses II. Chromatic paraxial aberrations,” J. Opt. Soc. Am. 61, 777–783 (1971); “Inhomogeneous lenses III. Paraxial optics,” J. Opt. Soc. Am. 61, 879–885 (1971); “Inhomogeneous lenses IV. Aberrations of lenses with axial index distributions,” J. Opt. Soc. Am. 61, 1086–1091 (1971); “Inhomogeneous lenses V. Chromatic paraxial aberrations of lenses with axial or cylindrical index distributions,” J. Opt. Soc. Am. 61, 1495–1500 (1971); “Inhomogeneous lenses VI. Derivatives of paraxial coefficients,” J. Opt. Soc. Am. 63, 1210–1216 (1973).
    [CrossRef]
  5. P. K. Manhart, K. R. Castle, M. C. Ruda, T. W. Stuhlinger, “Advantages of non-linear axial gradients in optical design,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 379–388 (1993).
    [CrossRef]
  6. R. J. Pagano, K. Perkins, P. K. Manhart, “Axial gradient-index lenses come of age,” Laser Focus World 31, 191–196 (1995).
  7. R. D. Jones, T. R. Scott, “Laser-beam analysis pinpoints critical parameters,” Laser Focus World 29, 123–130 (1993).

1996 (1)

K. H. Leong, B. V. Hunter, “High-power fiberoptic laser beam delivery moves forward,” Ind. Laser Rev. 11, 7–12 (1996).

1995 (1)

R. J. Pagano, K. Perkins, P. K. Manhart, “Axial gradient-index lenses come of age,” Laser Focus World 31, 191–196 (1995).

1993 (1)

R. D. Jones, T. R. Scott, “Laser-beam analysis pinpoints critical parameters,” Laser Focus World 29, 123–130 (1993).

1970 (1)

Castle, K. R.

P. K. Manhart, K. R. Castle, M. C. Ruda, T. W. Stuhlinger, “Advantages of non-linear axial gradients in optical design,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 379–388 (1993).
[CrossRef]

Glesias, R. D.

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Laser Materials Processing: New Developments in Laser Sources and Applications, W. Duley, K. Shibata, R. Poprawe, eds., Proc. ICALEO81E, 173–182 (1996).

Golden, J. F.

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Laser Materials Processing: New Developments in Laser Sources and Applications, W. Duley, K. Shibata, R. Poprawe, eds., Proc. ICALEO81E, 173–182 (1996).

Hunter, B. V.

K. H. Leong, B. V. Hunter, “High-power fiberoptic laser beam delivery moves forward,” Ind. Laser Rev. 11, 7–12 (1996).

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Laser Materials Processing: New Developments in Laser Sources and Applications, W. Duley, K. Shibata, R. Poprawe, eds., Proc. ICALEO81E, 173–182 (1996).

Jones, R. D.

R. D. Jones, T. R. Scott, “Laser-beam analysis pinpoints critical parameters,” Laser Focus World 29, 123–130 (1993).

Laverty, P. J.

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Laser Materials Processing: New Developments in Laser Sources and Applications, W. Duley, K. Shibata, R. Poprawe, eds., Proc. ICALEO81E, 173–182 (1996).

Leong, K. H.

K. H. Leong, B. V. Hunter, “High-power fiberoptic laser beam delivery moves forward,” Ind. Laser Rev. 11, 7–12 (1996).

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Laser Materials Processing: New Developments in Laser Sources and Applications, W. Duley, K. Shibata, R. Poprawe, eds., Proc. ICALEO81E, 173–182 (1996).

Manhart, P. K.

R. J. Pagano, K. Perkins, P. K. Manhart, “Axial gradient-index lenses come of age,” Laser Focus World 31, 191–196 (1995).

P. K. Manhart, K. R. Castle, M. C. Ruda, T. W. Stuhlinger, “Advantages of non-linear axial gradients in optical design,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 379–388 (1993).
[CrossRef]

Miller, C. B.

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Laser Materials Processing: New Developments in Laser Sources and Applications, W. Duley, K. Shibata, R. Poprawe, eds., Proc. ICALEO81E, 173–182 (1996).

Nonhof, C. J.

C. J. Nonhof, Material Processing with Nd Lasers (Electrochemical Publications, Ayr, Scotland, 1988), p. 182.

Pagano, R. J.

R. J. Pagano, K. Perkins, P. K. Manhart, “Axial gradient-index lenses come of age,” Laser Focus World 31, 191–196 (1995).

Perkins, K.

R. J. Pagano, K. Perkins, P. K. Manhart, “Axial gradient-index lenses come of age,” Laser Focus World 31, 191–196 (1995).

Ruda, M. C.

P. K. Manhart, K. R. Castle, M. C. Ruda, T. W. Stuhlinger, “Advantages of non-linear axial gradients in optical design,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 379–388 (1993).
[CrossRef]

Sands, P. J.

Scott, T. R.

R. D. Jones, T. R. Scott, “Laser-beam analysis pinpoints critical parameters,” Laser Focus World 29, 123–130 (1993).

Stuhlinger, T. W.

P. K. Manhart, K. R. Castle, M. C. Ruda, T. W. Stuhlinger, “Advantages of non-linear axial gradients in optical design,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 379–388 (1993).
[CrossRef]

Ind. Laser Rev. (1)

K. H. Leong, B. V. Hunter, “High-power fiberoptic laser beam delivery moves forward,” Ind. Laser Rev. 11, 7–12 (1996).

J. Opt. Soc. Am. (1)

Laser Focus World (2)

R. J. Pagano, K. Perkins, P. K. Manhart, “Axial gradient-index lenses come of age,” Laser Focus World 31, 191–196 (1995).

R. D. Jones, T. R. Scott, “Laser-beam analysis pinpoints critical parameters,” Laser Focus World 29, 123–130 (1993).

Other (3)

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Laser Materials Processing: New Developments in Laser Sources and Applications, W. Duley, K. Shibata, R. Poprawe, eds., Proc. ICALEO81E, 173–182 (1996).

P. K. Manhart, K. R. Castle, M. C. Ruda, T. W. Stuhlinger, “Advantages of non-linear axial gradients in optical design,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 379–388 (1993).
[CrossRef]

C. J. Nonhof, Material Processing with Nd Lasers (Electrochemical Publications, Ayr, Scotland, 1988), p. 182.

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Figures (9)

Fig. 1
Fig. 1

Diagram of the equipment used to profile the focused beams from the optics head with fixed positions for the lenses; BFL, back focal length.

Fig. 2
Fig. 2

Axial refractive-index profiles for G4SF. The crosses mark the refractive indices of the front and back surfaces of the 132-mm lens.

Fig. 3
Fig. 3

Comparison of the rms relative aberration (at r 86 focus) versus the increase in the r 86 radius for the lens combinations used in this study.

Fig. 4
Fig. 4

Cross-sectional irradiance profiles of a focused spot from BK7 127–65 and GRADIUM 132–65 lens combinations, showing the sharper edge of the image generated with the GRADIUM lenses. Both profiles are at the same scale; the horizontal line in the Y section shows the 86% radius irradiance.

Fig. 5
Fig. 5

Plot of wasted energy as a function of the irradiance threshold for the BK7 127–65 and GRADIUM 132–65 combinations presented in Fig. 4.

Fig. 6
Fig. 6

Energy enclosure versus radius for the BK7 127–65 and GRADIUM 132–56 combinations shown in Fig. 4. Calculated results for these lenses (zemax BK7 and zemax GRADIUM), when Gaussian pupil apodization is used, are given for comparison.

Fig. 7
Fig. 7

86% and 100% enclosure radii for the BK7 127–BK7 65 and GRADIUM 132–65 lens combinations. The approximate positions of the paraxial, rms, and geometrical foci are indicated. BFL, back focal length.

Fig. 8
Fig. 8

86% radii for the BK7 and GRADIUM lens combinations versus paraxial magnification. Using GRADIUM lenses results in improved performance when fast lenses are used.

Fig. 9
Fig. 9

100% spot sizes for all combinations of BK7 and GRADIUM lenses tested.

Tables (1)

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Table 1 Summary of Calculated and Measured Parameters for the BK7 127–65 and GRADIUM 132–65 Lenses (|m| = 0.5)a

Equations (2)

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r image   = m r source + r blur ,
r blur r   = max m r source - r ,   r min   for   r     m r source ,

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