Abstract

Flash radiography of large hydrodynamic experiments driven by high explosives is a venerable diagnostic technique in use at many laboratories. The size of the radiographic source spot is often quoted as an indication of the resolving power of a particular flash-radiography machine. A variety of techniques for measuring spot size have evolved at the different laboratories, as well as different definitions of spot size. Some definitions are highly dependent on the source spot intensity distributions, and not necessarily well correlated with resolution. The concept of limiting resolution based on bar target measurements is introduced, and shown to be equivalent to the spatial wavenumber at a modulation transfer function value of 5%. This resolution is shown to be better correlated with the full width at half-maximum of the spot intensity distribution than it is with other definitions of spot size.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. J. Boyd, Jr., B. T. Rogers, R. R. Tesche, and Douglas Venable, “PHERMEX—A high-current electron accelerator for use in dynamic radiography,” Rev. Sci. Instrum. 36, 1401–1408(1965).
    [CrossRef]
  2. C. Ekdahl, “Modern electron accelerators for radiography,” IEEE Trans. Plasma Sci. 30, 254–261 (2002).
    [CrossRef]
  3. K. Mueller, “Measurement and characterization of x-ray spot size,” Los Alamos National Laboratory Report LA-UR-89-1886 (August 1989).
  4. D. W. Forster, “Radiographic spot size definitions,” AWE Report HWH/9201/R8 (January 1992).
  5. “Modulation transfer function of screen-film systems,” ICRU Report 41 (International Commission on Radiation Units and Measurements, 1986).
  6. “Military standard photographic lenses,” MIL-STD-150A (U.S. Government Printing Office, 1959), p. 21.
  7. E. Rose and T. Beery, Los Alamos National Laboratory (personal communication, 2006).
  8. T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
    [CrossRef]

2002 (2)

C. Ekdahl, “Modern electron accelerators for radiography,” IEEE Trans. Plasma Sci. 30, 254–261 (2002).
[CrossRef]

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

1965 (1)

T. J. Boyd, Jr., B. T. Rogers, R. R. Tesche, and Douglas Venable, “PHERMEX—A high-current electron accelerator for use in dynamic radiography,” Rev. Sci. Instrum. 36, 1401–1408(1965).
[CrossRef]

Beech, P. F.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Beery, T.

E. Rose and T. Beery, Los Alamos National Laboratory (personal communication, 2006).

Boyd, T. J.

T. J. Boyd, Jr., B. T. Rogers, R. R. Tesche, and Douglas Venable, “PHERMEX—A high-current electron accelerator for use in dynamic radiography,” Rev. Sci. Instrum. 36, 1401–1408(1965).
[CrossRef]

Bryant, T. F.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Clough, S. J.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Cooper, G. M.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Davitt, R.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Edwards, R. D.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Ekdahl, C.

C. Ekdahl, “Modern electron accelerators for radiography,” IEEE Trans. Plasma Sci. 30, 254–261 (2002).
[CrossRef]

Forster, D. W.

D. W. Forster, “Radiographic spot size definitions,” AWE Report HWH/9201/R8 (January 1992).

Goldsack, T. J.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Kenna, N.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Krushelnick, K.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

McLean, J.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Mueller, K.

K. Mueller, “Measurement and characterization of x-ray spot size,” Los Alamos National Laboratory Report LA-UR-89-1886 (August 1989).

Pearce, A. G.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Phillips, M. J.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Pullinger, K. P.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Rogers, B. T.

T. J. Boyd, Jr., B. T. Rogers, R. R. Tesche, and Douglas Venable, “PHERMEX—A high-current electron accelerator for use in dynamic radiography,” Rev. Sci. Instrum. 36, 1401–1408(1965).
[CrossRef]

Rose, E.

E. Rose and T. Beery, Los Alamos National Laboratory (personal communication, 2006).

Short, D. J.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Sinclair, M. A.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Tesche, R. R.

T. J. Boyd, Jr., B. T. Rogers, R. R. Tesche, and Douglas Venable, “PHERMEX—A high-current electron accelerator for use in dynamic radiography,” Rev. Sci. Instrum. 36, 1401–1408(1965).
[CrossRef]

Thomas, K. J.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Threadgold, J. R.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Venable, Douglas

T. J. Boyd, Jr., B. T. Rogers, R. R. Tesche, and Douglas Venable, “PHERMEX—A high-current electron accelerator for use in dynamic radiography,” Rev. Sci. Instrum. 36, 1401–1408(1965).
[CrossRef]

Williamson, M. C.

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

IEEE Trans. Plasma Sci. (2)

C. Ekdahl, “Modern electron accelerators for radiography,” IEEE Trans. Plasma Sci. 30, 254–261 (2002).
[CrossRef]

T. J. Goldsack, T. F. Bryant, P. F. Beech, S. J. Clough, G. M. Cooper, R. Davitt, R. D. Edwards, N. Kenna, J. McLean, A. G. Pearce, M. J. Phillips, K. P. Pullinger, D. J. Short, M. A. Sinclair, K. J. Thomas, J. R. Threadgold, M. C. Williamson, and K. Krushelnick, “Multimegavolt multiaxis high-resolution flash x-ray source development for a new hydrodynamics research facility at AWE Aldermaston,” IEEE Trans. Plasma Sci. 30, 239–253 (2002).
[CrossRef]

Rev. Sci. Instrum. (1)

T. J. Boyd, Jr., B. T. Rogers, R. R. Tesche, and Douglas Venable, “PHERMEX—A high-current electron accelerator for use in dynamic radiography,” Rev. Sci. Instrum. 36, 1401–1408(1965).
[CrossRef]

Other (5)

K. Mueller, “Measurement and characterization of x-ray spot size,” Los Alamos National Laboratory Report LA-UR-89-1886 (August 1989).

D. W. Forster, “Radiographic spot size definitions,” AWE Report HWH/9201/R8 (January 1992).

“Modulation transfer function of screen-film systems,” ICRU Report 41 (International Commission on Radiation Units and Measurements, 1986).

“Military standard photographic lenses,” MIL-STD-150A (U.S. Government Printing Office, 1959), p. 21.

E. Rose and T. Beery, Los Alamos National Laboratory (personal communication, 2006).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Comparison of PSFs for source intensity distributions having the same Los Alamos spot size, d LANL = 2.0 mm .

Fig. 2
Fig. 2

Comparison of LSFs for source intensity distributions having the same Los Alamos spot size, d LANL = 2.0 mm .

Fig. 3
Fig. 3

Comparison of MTFs for source intensity distributions having the same Los Alamos spot size, d LANL = 2.0 mm .

Fig. 4
Fig. 4

Comparison of PSFs for source intensity distributions having the same LR, LR = 1.00 lp / mm .

Fig. 5
Fig. 5

Comparison of LSFs for source intensity distributions having the same LR, LR = 1.00 lp / mm .

Fig. 6
Fig. 6

Comparison of MTFs for source intensity distributions having the same LR, LR = 1.00 lp / mm .

Fig. 7
Fig. 7

LSF for the DARHT-I distribution with d LANL = 2.00 mm (solid black curve) compared with that for a quasi-Bennett with d LANL = 0.724 × 2.00 = 1.448 mm (dashed green curve).

Tables (7)

Tables Icon

Table 1 Example Source Distributions

Tables Icon

Table 2 Spot-Size Metrics for the Example Source Distributions

Tables Icon

Table 3 Comparison of Source Spots Having the Same Los Alamos Spot Size

Tables Icon

Table 4 Comparison of Source Spots Having the Same FWHM

Tables Icon

Table 5 Comparison of Source Spots Having the Same AWE Size

Tables Icon

Table 6 Comparison of Source Spots Having the Same Limiting Resolution

Tables Icon

Table 7 Results of Calculation of AWE Spot for a Gaussian PSF

Equations (51)

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

C = max ( I f ) min ( I f ) max ( I f ) + min ( I f ) ,
PSF ( x , y ) d x d y = 1
0 PSF ( r ) 2 π r d r = 1
PSF ( x , y ) = I ( x , y ) / I TOTAL .
LSF ( x ) = + PSF ( x , y ) d y .
LSF ( x ) = 2 x r PSF ( r ) r 2 x 2 d r .
PSF ( r ) = 1 π r d LSF / d x x 2 r 2 d x .
ESF ( x ) = x LSF ( x ) d x .
MTF ( ν x , ν y ) = | H ( ν x , ν y ) | ,
H ( ν x , ν y ) = d x PSF ( x , y ) exp [ 2 π j ( ν x x + ν y y ) ] d y .
MTF ( ν x , 0 ) = | H ( ν x , 0 ) | = | d x PSF ( x , y ) exp [ 2 π j ( ν x x ) ] d y | .
MTF ( ν x , 0 ) = | LSF ( x ) exp [ 2 π j ( ν x x ) ] d x | .
x = r cos ( θ ) , y = r sin ( θ ) , 2 π ν x = k cos ( φ ) , 2 π ν y = k sin ( φ ) .
2 π ( ν x x + ν y y ) = k r ( cos ( θ ) cos ( φ ) + sin ( θ ) sin ( φ ) ) = k r cos ( θ φ ) ,
H ( k , φ ) = 0 PSF ( r ) r d r 0 2 π exp [ j k r cos ( θ φ ) ] d θ = 0 PSF ( r ) r d r 0 2 π exp [ j k r cos ( ϑ ) ] d ϑ = 2 0 PSF ( r ) r d r 0 π cos ( k r cos ( ϑ ) ) d ϑ ,
MTF ( k ) = H ( k ) = 2 π 0 PSF ( r ) J 0 ( k r ) r d r .
PSF ( r ) = 1 2 π 0 MTF ( k ) J 0 ( k r ) k d k .
Im = Raw dark Flat dark ,
d AWE = 2.47541 Δ x .
d LANL = 0.70508 / ν 1 / 2 = 4.4301 / k 1 / 2 .
PSF ( r ) = 1 π a 2 r a = 0 r > a ,
LSF ( x ) = 2 π a 2 a 2 x 2 ,
ESF ( x ) = 1 π a 2 [ x a 2 x 2 + a 2 sin 1 ( x / a ) + π a 2 / 2 ] .
MTF ( k ) = 2 π 0 a J 0 ( r ) r d r = 2 | J 1 ( k a ) | k a .
k 1 / 2 a = 2.21508937 ,
d LANL = 4.43017874 / k 1 / 2 .
PSF ( r ) = 1 π a 2 exp ( r 2 / a 2 ) .
FWHM = 2 a ln 2 = 1.6651092 a
a = FWHM 2 ln 2 = 0.6005613     FWHM .
MTF ( k ) = 2 a 2 0 exp ( r 2 / a 2 ) J 0 ( k r ) r d r = exp ( k 2 a 2 / 4 ) .
k 1 / 2 a = 2 π ν 1 / 2 a = 2 ln 2 ,
LSF ( x ) = 1 a π exp ( x 2 / a 2 ) ,
ESF ( x ) = 1 2 [ erf ( x / a ) + 1 ] .
ESF ( x ) = q @ erf ( x / a ) = 2 q 1
d AWE = 2.082 a .
ν LR = ln 20 π a = 0.55094 / a .
PSF ( r ) = 1 π a 2 1 [ 1 + ( r / a ) 2 ] 2 .
FWHM = 2 2 1 a = 1.2872 a .
MTF ( k ) = 2 a 2 0 r [ 1 + ( r / a ) 2 ] 2 J 0 ( k r ) d r = k a K 1 ( k a ) .
LSF ( x ) = a 2 2 ( a 2 + x 2 ) 3 / 2 ,
ESF ( x ) = 1 2 [ x a 2 + x 2 + 1 ] .
d AWE ( 25 75 ) = 2.85836 a .
PSF ( r ) = 1 2 π a 2 1 [ 1 + ( r / a ) 2 ] 3 / 2 .
FWHM = 2 2 2 / 3 1 a = 1.5328 a .
MTF ( k ) = 1 a 2 0 r [ 1 + ( r / a ) 2 ] 3 / 2 J 0 ( k r ) d r = e k a
LSF ( x ) = a π ( a 2 + x 2 ) ,
ESF ( x ) = 1 π tan 1 ( x / a ) + 1 2 .
LSF ( x ) = A 2 a e | x | / a + 1 A 2 q a e | x | / ( q a ) ,
MTF ( k ) = A 1 + ( k a ) 2 + 1 A 1 + ( k q a ) 2 .
PSF ( r ) = A 2 π a 2 K 0 ( r / a ) + 1 A 2 π q 2 a 2 K 0 ( r / ( q a ) ) ,
ESF ( x ) = A 2 e x / a + 1 A 2 e x / ( q a ) x 0 = A 2 [ 2 e x / a ] + 1 A 2 [ 2 e x / ( q a ) ] x 0 .

Metrics