Abstract

A new scaling law model is presented to rapidly simulate thermal blooming and turbulence effects on high energy laser propagation, producing results approaching the quality normally only available using wave-optics code, but at much faster speed. The model convolves irradiance patterns originating from two distinct scaling law models, one with a proficiency in thermal blooming effects and the other in turbulence. To underscore the power of the new model, results are verified for typical, realistic scenarios by direct comparison with wave optics simulation.

© 2013 OSA

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    [CrossRef] [PubMed]
  2. H. Breaux, W. Evers, R. Sepucha, and C. Whitney, “Algebraic model for cw thermal-blooming effects,” Appl. Opt.18(15), 2638–2644 (1979).
    [CrossRef] [PubMed]
  3. F. G. Gebhardt, “Twenty-five years of thermal blooming: an overview,” Proc. SPIE1221, 2–25 (1990).
    [CrossRef]
  4. R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
    [CrossRef]
  5. N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng.51(10), 104301 (2012).
    [CrossRef]
  6. A. M. Ngwele and M. R. Whiteley, “Scaling Law Modeling of Thermal Blooming in Wave Optics,” MZA Associates Corporation, Dayton, Technical Report NGIT ABL A&AS, 2006.
  7. S. T. Fiorino, R. M. Randall, M. F. Via, and J. L. Burley, “Validation of a UV to RF high spectral resolution atmospheric boundary layer characterization tool,” J. Appl. Meteorol. Climatol. (in review).
  8. S. T. Fiorino, R. M. Randall, R. J. Bartell, A. D. Downs, P. C. Chu, and C. W. Fan, “Climate change: anticipated effects on high-energy laser weapon systems in maritime environments,” J. Appl. Meteorol. Climatol.50(1), 153–166 (2011).
    [CrossRef]
  9. C. L. Leakeas, R. J. Bartell, M. J. Krizo, S. T. Fiorino, S. J. Cusumano, and M. R. Whiteley, “Effects of thermal blooming on systems comprised of tiled subapertures,” Proc. SPIE7685, 267–269 (2010).
    [CrossRef]
  10. M. R. Whiteley, E. P. Magee, and A. M. Ngwele, “Scaling for High Energy Laser and Relay Engagement (SHaRE) User Guide,” MZA Associates, Dayton OH, (2011).
  11. M. R. Whiteley, “Thermal Blooming Modeling in SHaRE,” presented at the DoD High Energy Laser Joint Technology Office Workshop, Air Force Institute of Technology, WPAFB, OH, 9–10 Oct. 2008.
  12. S. C. Coy and B. P. Venet, “WaveTrainTM User Guide” (MZA Associates Corporation, Copyright © 1995 – 2010), http://www.mza.com/doc/wavetrain/wtug/index.htm .
  13. SAIC Final Report, “Analytic Model for Adaptive Optical Compensation of Thermal Blooming (AOTB),” Govt Contract #FA9451–10-D-0250, (2012).
  14. J. D. Barchers, “Linear analysis of thermal blooming compensation instabilities in laser propagation,” J. Opt. Soc. Am. A26(7), 1638–1653 (2009).
    [CrossRef] [PubMed]
  15. R. A. Motes, S. A. Shakir, and R. W. Berdine, “An efficient scalar, non-paraxial beam propagation method,” J. Lightwave Technol.30(1), 4–8 (2012).
    [CrossRef]
  16. B. G. Ward, “Modeling of transient modal instability in fiber amplifiers,” Opt. Express21(10), 12053–12067 (2013).
    [CrossRef]
  17. S. T. Fiorino, R. M. Randall, F. J. Echeverria, R. J. Bartell, M. J. Krizo, and S. J. Cusumano, “Effectiveness assessment of tactical laser engagement scenarios in the lower atmosphere,” J. Aero. Inf. Sys.10(1), 32–38 (2013).

2013 (2)

S. T. Fiorino, R. M. Randall, F. J. Echeverria, R. J. Bartell, M. J. Krizo, and S. J. Cusumano, “Effectiveness assessment of tactical laser engagement scenarios in the lower atmosphere,” J. Aero. Inf. Sys.10(1), 32–38 (2013).

B. G. Ward, “Modeling of transient modal instability in fiber amplifiers,” Opt. Express21(10), 12053–12067 (2013).
[CrossRef]

2012 (2)

R. A. Motes, S. A. Shakir, and R. W. Berdine, “An efficient scalar, non-paraxial beam propagation method,” J. Lightwave Technol.30(1), 4–8 (2012).
[CrossRef]

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng.51(10), 104301 (2012).
[CrossRef]

2011 (1)

S. T. Fiorino, R. M. Randall, R. J. Bartell, A. D. Downs, P. C. Chu, and C. W. Fan, “Climate change: anticipated effects on high-energy laser weapon systems in maritime environments,” J. Appl. Meteorol. Climatol.50(1), 153–166 (2011).
[CrossRef]

2010 (1)

C. L. Leakeas, R. J. Bartell, M. J. Krizo, S. T. Fiorino, S. J. Cusumano, and M. R. Whiteley, “Effects of thermal blooming on systems comprised of tiled subapertures,” Proc. SPIE7685, 267–269 (2010).
[CrossRef]

2009 (1)

2005 (1)

R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
[CrossRef]

1990 (1)

F. G. Gebhardt, “Twenty-five years of thermal blooming: an overview,” Proc. SPIE1221, 2–25 (1990).
[CrossRef]

1979 (1)

1971 (1)

Barchers, J. D.

Bartell, R. J.

S. T. Fiorino, R. M. Randall, F. J. Echeverria, R. J. Bartell, M. J. Krizo, and S. J. Cusumano, “Effectiveness assessment of tactical laser engagement scenarios in the lower atmosphere,” J. Aero. Inf. Sys.10(1), 32–38 (2013).

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng.51(10), 104301 (2012).
[CrossRef]

S. T. Fiorino, R. M. Randall, R. J. Bartell, A. D. Downs, P. C. Chu, and C. W. Fan, “Climate change: anticipated effects on high-energy laser weapon systems in maritime environments,” J. Appl. Meteorol. Climatol.50(1), 153–166 (2011).
[CrossRef]

C. L. Leakeas, R. J. Bartell, M. J. Krizo, S. T. Fiorino, S. J. Cusumano, and M. R. Whiteley, “Effects of thermal blooming on systems comprised of tiled subapertures,” Proc. SPIE7685, 267–269 (2010).
[CrossRef]

R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
[CrossRef]

Basu, S.

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng.51(10), 104301 (2012).
[CrossRef]

Berdine, R. W.

Breaux, H.

Bunch, D. W.

R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
[CrossRef]

Burley, J. L.

S. T. Fiorino, R. M. Randall, M. F. Via, and J. L. Burley, “Validation of a UV to RF high spectral resolution atmospheric boundary layer characterization tool,” J. Appl. Meteorol. Climatol. (in review).

Chu, P. C.

S. T. Fiorino, R. M. Randall, R. J. Bartell, A. D. Downs, P. C. Chu, and C. W. Fan, “Climate change: anticipated effects on high-energy laser weapon systems in maritime environments,” J. Appl. Meteorol. Climatol.50(1), 153–166 (2011).
[CrossRef]

Cusumano, S. J.

S. T. Fiorino, R. M. Randall, F. J. Echeverria, R. J. Bartell, M. J. Krizo, and S. J. Cusumano, “Effectiveness assessment of tactical laser engagement scenarios in the lower atmosphere,” J. Aero. Inf. Sys.10(1), 32–38 (2013).

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng.51(10), 104301 (2012).
[CrossRef]

C. L. Leakeas, R. J. Bartell, M. J. Krizo, S. T. Fiorino, S. J. Cusumano, and M. R. Whiteley, “Effects of thermal blooming on systems comprised of tiled subapertures,” Proc. SPIE7685, 267–269 (2010).
[CrossRef]

Downs, A. D.

S. T. Fiorino, R. M. Randall, R. J. Bartell, A. D. Downs, P. C. Chu, and C. W. Fan, “Climate change: anticipated effects on high-energy laser weapon systems in maritime environments,” J. Appl. Meteorol. Climatol.50(1), 153–166 (2011).
[CrossRef]

Echeverria, F. J.

S. T. Fiorino, R. M. Randall, F. J. Echeverria, R. J. Bartell, M. J. Krizo, and S. J. Cusumano, “Effectiveness assessment of tactical laser engagement scenarios in the lower atmosphere,” J. Aero. Inf. Sys.10(1), 32–38 (2013).

Evers, W.

Fan, C. W.

S. T. Fiorino, R. M. Randall, R. J. Bartell, A. D. Downs, P. C. Chu, and C. W. Fan, “Climate change: anticipated effects on high-energy laser weapon systems in maritime environments,” J. Appl. Meteorol. Climatol.50(1), 153–166 (2011).
[CrossRef]

Fiorino, S. T.

S. T. Fiorino, R. M. Randall, F. J. Echeverria, R. J. Bartell, M. J. Krizo, and S. J. Cusumano, “Effectiveness assessment of tactical laser engagement scenarios in the lower atmosphere,” J. Aero. Inf. Sys.10(1), 32–38 (2013).

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng.51(10), 104301 (2012).
[CrossRef]

S. T. Fiorino, R. M. Randall, R. J. Bartell, A. D. Downs, P. C. Chu, and C. W. Fan, “Climate change: anticipated effects on high-energy laser weapon systems in maritime environments,” J. Appl. Meteorol. Climatol.50(1), 153–166 (2011).
[CrossRef]

C. L. Leakeas, R. J. Bartell, M. J. Krizo, S. T. Fiorino, S. J. Cusumano, and M. R. Whiteley, “Effects of thermal blooming on systems comprised of tiled subapertures,” Proc. SPIE7685, 267–269 (2010).
[CrossRef]

R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
[CrossRef]

S. T. Fiorino, R. M. Randall, M. F. Via, and J. L. Burley, “Validation of a UV to RF high spectral resolution atmospheric boundary layer characterization tool,” J. Appl. Meteorol. Climatol. (in review).

Gebhardt, F. G.

F. G. Gebhardt, “Twenty-five years of thermal blooming: an overview,” Proc. SPIE1221, 2–25 (1990).
[CrossRef]

Gravley, L. E.

R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
[CrossRef]

Houleb, M. J.

R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
[CrossRef]

Krizo, M. J.

S. T. Fiorino, R. M. Randall, F. J. Echeverria, R. J. Bartell, M. J. Krizo, and S. J. Cusumano, “Effectiveness assessment of tactical laser engagement scenarios in the lower atmosphere,” J. Aero. Inf. Sys.10(1), 32–38 (2013).

C. L. Leakeas, R. J. Bartell, M. J. Krizo, S. T. Fiorino, S. J. Cusumano, and M. R. Whiteley, “Effects of thermal blooming on systems comprised of tiled subapertures,” Proc. SPIE7685, 267–269 (2010).
[CrossRef]

R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
[CrossRef]

Leakeas, C. L.

C. L. Leakeas, R. J. Bartell, M. J. Krizo, S. T. Fiorino, S. J. Cusumano, and M. R. Whiteley, “Effects of thermal blooming on systems comprised of tiled subapertures,” Proc. SPIE7685, 267–269 (2010).
[CrossRef]

Long, S. N.

R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
[CrossRef]

Manning, Z. P.

R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
[CrossRef]

McCrae, J. E.

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng.51(10), 104301 (2012).
[CrossRef]

Motes, R. A.

Perram, G. P.

R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
[CrossRef]

Randall, R. M.

S. T. Fiorino, R. M. Randall, F. J. Echeverria, R. J. Bartell, M. J. Krizo, and S. J. Cusumano, “Effectiveness assessment of tactical laser engagement scenarios in the lower atmosphere,” J. Aero. Inf. Sys.10(1), 32–38 (2013).

S. T. Fiorino, R. M. Randall, R. J. Bartell, A. D. Downs, P. C. Chu, and C. W. Fan, “Climate change: anticipated effects on high-energy laser weapon systems in maritime environments,” J. Appl. Meteorol. Climatol.50(1), 153–166 (2011).
[CrossRef]

S. T. Fiorino, R. M. Randall, M. F. Via, and J. L. Burley, “Validation of a UV to RF high spectral resolution atmospheric boundary layer characterization tool,” J. Appl. Meteorol. Climatol. (in review).

Rice, C. A.

R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
[CrossRef]

Sepucha, R.

Shakir, S. A.

Van Zandt, N. R.

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng.51(10), 104301 (2012).
[CrossRef]

Via, M. F.

S. T. Fiorino, R. M. Randall, M. F. Via, and J. L. Burley, “Validation of a UV to RF high spectral resolution atmospheric boundary layer characterization tool,” J. Appl. Meteorol. Climatol. (in review).

Ward, B. G.

Whiteley, M. R.

C. L. Leakeas, R. J. Bartell, M. J. Krizo, S. T. Fiorino, S. J. Cusumano, and M. R. Whiteley, “Effects of thermal blooming on systems comprised of tiled subapertures,” Proc. SPIE7685, 267–269 (2010).
[CrossRef]

Whitney, C.

Yura, H. T.

Appl. Opt. (2)

J. Aero. Inf. Sys. (1)

S. T. Fiorino, R. M. Randall, F. J. Echeverria, R. J. Bartell, M. J. Krizo, and S. J. Cusumano, “Effectiveness assessment of tactical laser engagement scenarios in the lower atmosphere,” J. Aero. Inf. Sys.10(1), 32–38 (2013).

J. Appl. Meteorol. Climatol. (2)

S. T. Fiorino, R. M. Randall, M. F. Via, and J. L. Burley, “Validation of a UV to RF high spectral resolution atmospheric boundary layer characterization tool,” J. Appl. Meteorol. Climatol. (in review).

S. T. Fiorino, R. M. Randall, R. J. Bartell, A. D. Downs, P. C. Chu, and C. W. Fan, “Climate change: anticipated effects on high-energy laser weapon systems in maritime environments,” J. Appl. Meteorol. Climatol.50(1), 153–166 (2011).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Eng. (1)

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng.51(10), 104301 (2012).
[CrossRef]

Opt. Express (1)

Proc. SPIE (3)

F. G. Gebhardt, “Twenty-five years of thermal blooming: an overview,” Proc. SPIE1221, 2–25 (1990).
[CrossRef]

R. J. Bartell, G. P. Perram, S. T. Fiorino, S. N. Long, M. J. Houleb, C. A. Rice, Z. P. Manning, D. W. Bunch, M. J. Krizo, and L. E. Gravley, “Methodology for comparing worldwide performance of diverse weight-constrained high energy laser systems,” Proc. SPIE5792, 76–87 (2005).
[CrossRef]

C. L. Leakeas, R. J. Bartell, M. J. Krizo, S. T. Fiorino, S. J. Cusumano, and M. R. Whiteley, “Effects of thermal blooming on systems comprised of tiled subapertures,” Proc. SPIE7685, 267–269 (2010).
[CrossRef]

Other (5)

M. R. Whiteley, E. P. Magee, and A. M. Ngwele, “Scaling for High Energy Laser and Relay Engagement (SHaRE) User Guide,” MZA Associates, Dayton OH, (2011).

M. R. Whiteley, “Thermal Blooming Modeling in SHaRE,” presented at the DoD High Energy Laser Joint Technology Office Workshop, Air Force Institute of Technology, WPAFB, OH, 9–10 Oct. 2008.

S. C. Coy and B. P. Venet, “WaveTrainTM User Guide” (MZA Associates Corporation, Copyright © 1995 – 2010), http://www.mza.com/doc/wavetrain/wtug/index.htm .

SAIC Final Report, “Analytic Model for Adaptive Optical Compensation of Thermal Blooming (AOTB),” Govt Contract #FA9451–10-D-0250, (2012).

A. M. Ngwele and M. R. Whiteley, “Scaling Law Modeling of Thermal Blooming in Wave Optics,” MZA Associates Corporation, Dayton, Technical Report NGIT ABL A&AS, 2006.

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Figures (5)

Fig. 1
Fig. 1

Wave optics (a) and HELEEOS (b) far-field irradiance patterns for a 7.5 km slant path, air to surface engagement exclusive of thermal blooming effects. The center- to outer-most calibration rings about the central propagation axis in this and subsequent figures have arbitrarily sized diameters to represent the diffraction-limit, 5-cm and 10-cm, respectively. Note: HELEEOS’ Gaussian scaling law approximation matches wave optics very well.

Fig. 2
Fig. 2

A comparison of wave optics (a) and AOTB (b) far-field irradiance patterns for the 7.5 km slant path, air-to-surface engagement. Since the two methods model thermal blooming differently, the minor differences in the irradiance patterns are expected.

Fig. 3
Fig. 3

A comparison of wave optics (a), HELEEOS – AOTB (b), and pre-convolution, legacy HELEEOS (c) far-field patterns for 7.5 km slant path, air to surface laser engagement showing good correlation between HELEEOS – AOTB and wave optics.

Fig. 4
Fig. 4

Wave optics generated far-field irradiance patterns: turbulence-only effects (a); thermal blooming-only effects (b); their convolution (c); and turbulence and thermal blooming effects (d). The comparison of (c) and (d) shows the convolution step is able to reproduce total effects from constituent contributions quite well.

Fig. 5
Fig. 5

The irradiance profiles for the wave optics (a-d) and HELEEOS – AOTB (e-h) results with S2S, S2A, A2S, and A2A scenario pairs presented top to bottom, respectively. The general shapes of the spots in each row match well.

Tables (4)

Tables Icon

Table 1 Comparison of simulation run times using wave optics and HELEEOS – AOTB for realistic 5 km range scenarios.

Tables Icon

Table 2 Scenarios1 used to verify convolved scaling law model technique.

Tables Icon

Table 3 PIB values from wave optics and HELEEOS – AOTB for 5 and 10 cm diameter buckets and all four scenarios. The error column compares the scaling law to wave optics, which is considered truth.

Tables Icon

Table 4 A comparison of peak irradiance and centroid tilt values between wave optics and the proposed scaling law model.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

g( x,y )= E peak exp[ 0.5( x 2 / σ x 2 + y 2 / σ y 2 ) ]
{ g( x,y )h( x,y ) }={ g( x,y ) }{ h( x,y ) }
g( x,y )h( x,y )=2π E peak σ x σ y exp[ 2 π 2 ( σ x 2 f x 2 + σ y 2 f y 2 ) ] ×{ h( x,y ) }exp[ j2π( f x x+ f y y ) ]d f x d f y

Metrics