Abstract

An apparatus has been designed for real-time and double-exposure holographic interferometry to determine radiation absorbed dose distributions in transparent liquids. The change in refractive index of the liquid due to a temperature rise after irradiation is measured interferometrically. In a cylindrically symmetrical radiation field, the dose distribution can be computed from data supplied by the reconstruction of the holographic interferogram taken as side-view profile of the change in optical pathlength. Relatively inexpensive components such as a low-powered He–Ne laser together with a conventional photographic shutter and low-cost mirrors and lenses were used. The mathematical procedure for unfolding the three-dimensional dose distribtion is described, and an example is given for use with a high-intensity, pulsed, 2-MV electron source.

© 1971 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. International Commission on Radiation Units and Measurements, ICRU Rep. 11 (ICRU, Washington, D.C., 1968).
  2. O. H. Nestor, H. N. Olsen, SIAM Rev. 2, 200 (1960).
    [CrossRef]
  3. M. H. HormanAppl. Opt. 4, 333 (1965).
    [CrossRef]
  4. L. H. Tanner, J. Sci. Instrum. 43, 81 (1966).
    [CrossRef]
  5. B. P. Hildebrand, K. A. Haines, Appl. Opt. 5, 172 (1966).
    [CrossRef] [PubMed]
  6. K. A. Stetson, R. L. Powell, J. Opt. Soc. Amer. 55, 1694 (1965).
    [CrossRef]
  7. L. O. Heflinger, R. F. Wuerker, R. E. Brooks, J. Appl. Phys. 37, 642 (1966).
    [CrossRef]
  8. R. L. Powell, K. A. Stetson, J. Opt. Soc. Amer. 55, 1593 (1965).
    [CrossRef]
  9. R. E. Brooks, Appl. Opt. 6, 1418 (1967).
    [CrossRef] [PubMed]
  10. E. N. Leith, J. Upatnieks, J. Opt. Soc. Amer. 52, 1123 (1962).
    [CrossRef]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 213, 214.
  12. L. W. Tilton, J. K. Taylor, J. Res. Nat. Bur. Stand. 20, 1059 (1938).
  13. Handbook of Chemistry and Physics, 42nd ed. (Chemical Rubber Publ. Co., Cleveland, 1960), p. 2261.
  14. W. L. McLaughlin, Manual for Radiation Dosimetry, Chap. 6, N. W. Holm, R. J. Berry, Eds. (Marcel Dekker, New York, 1970).

1967 (1)

1966 (3)

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, J. Appl. Phys. 37, 642 (1966).
[CrossRef]

L. H. Tanner, J. Sci. Instrum. 43, 81 (1966).
[CrossRef]

B. P. Hildebrand, K. A. Haines, Appl. Opt. 5, 172 (1966).
[CrossRef] [PubMed]

1965 (3)

K. A. Stetson, R. L. Powell, J. Opt. Soc. Amer. 55, 1694 (1965).
[CrossRef]

M. H. HormanAppl. Opt. 4, 333 (1965).
[CrossRef]

R. L. Powell, K. A. Stetson, J. Opt. Soc. Amer. 55, 1593 (1965).
[CrossRef]

1962 (1)

E. N. Leith, J. Upatnieks, J. Opt. Soc. Amer. 52, 1123 (1962).
[CrossRef]

1960 (1)

O. H. Nestor, H. N. Olsen, SIAM Rev. 2, 200 (1960).
[CrossRef]

1938 (1)

L. W. Tilton, J. K. Taylor, J. Res. Nat. Bur. Stand. 20, 1059 (1938).

Brooks, R. E.

R. E. Brooks, Appl. Opt. 6, 1418 (1967).
[CrossRef] [PubMed]

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, J. Appl. Phys. 37, 642 (1966).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 213, 214.

Haines, K. A.

Heflinger, L. O.

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, J. Appl. Phys. 37, 642 (1966).
[CrossRef]

Hildebrand, B. P.

Horman, M. H.

Leith, E. N.

E. N. Leith, J. Upatnieks, J. Opt. Soc. Amer. 52, 1123 (1962).
[CrossRef]

McLaughlin, W. L.

W. L. McLaughlin, Manual for Radiation Dosimetry, Chap. 6, N. W. Holm, R. J. Berry, Eds. (Marcel Dekker, New York, 1970).

Nestor, O. H.

O. H. Nestor, H. N. Olsen, SIAM Rev. 2, 200 (1960).
[CrossRef]

Olsen, H. N.

O. H. Nestor, H. N. Olsen, SIAM Rev. 2, 200 (1960).
[CrossRef]

Powell, R. L.

K. A. Stetson, R. L. Powell, J. Opt. Soc. Amer. 55, 1694 (1965).
[CrossRef]

R. L. Powell, K. A. Stetson, J. Opt. Soc. Amer. 55, 1593 (1965).
[CrossRef]

Stetson, K. A.

R. L. Powell, K. A. Stetson, J. Opt. Soc. Amer. 55, 1593 (1965).
[CrossRef]

K. A. Stetson, R. L. Powell, J. Opt. Soc. Amer. 55, 1694 (1965).
[CrossRef]

Tanner, L. H.

L. H. Tanner, J. Sci. Instrum. 43, 81 (1966).
[CrossRef]

Taylor, J. K.

L. W. Tilton, J. K. Taylor, J. Res. Nat. Bur. Stand. 20, 1059 (1938).

Tilton, L. W.

L. W. Tilton, J. K. Taylor, J. Res. Nat. Bur. Stand. 20, 1059 (1938).

Upatnieks, J.

E. N. Leith, J. Upatnieks, J. Opt. Soc. Amer. 52, 1123 (1962).
[CrossRef]

Wuerker, R. F.

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, J. Appl. Phys. 37, 642 (1966).
[CrossRef]

Appl. Opt. (3)

J. Appl. Phys. (1)

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, J. Appl. Phys. 37, 642 (1966).
[CrossRef]

J. Opt. Soc. Amer. (3)

R. L. Powell, K. A. Stetson, J. Opt. Soc. Amer. 55, 1593 (1965).
[CrossRef]

K. A. Stetson, R. L. Powell, J. Opt. Soc. Amer. 55, 1694 (1965).
[CrossRef]

E. N. Leith, J. Upatnieks, J. Opt. Soc. Amer. 52, 1123 (1962).
[CrossRef]

J. Res. Nat. Bur. Stand. (1)

L. W. Tilton, J. K. Taylor, J. Res. Nat. Bur. Stand. 20, 1059 (1938).

J. Sci. Instrum. (1)

L. H. Tanner, J. Sci. Instrum. 43, 81 (1966).
[CrossRef]

SIAM Rev. (1)

O. H. Nestor, H. N. Olsen, SIAM Rev. 2, 200 (1960).
[CrossRef]

Other (4)

International Commission on Radiation Units and Measurements, ICRU Rep. 11 (ICRU, Washington, D.C., 1968).

Handbook of Chemistry and Physics, 42nd ed. (Chemical Rubber Publ. Co., Cleveland, 1960), p. 2261.

W. L. McLaughlin, Manual for Radiation Dosimetry, Chap. 6, N. W. Holm, R. J. Berry, Eds. (Marcel Dekker, New York, 1970).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 213, 214.

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

Model of isodose map, with z axis representing the electron beam axis intersected by equally spaced planes zn.

Fig. 2
Fig. 2

Light wavefront passing the cell in a zn plane: (a) unirradiated; (b) irradiated (showing the circular isodose curves and the distorted wavefront); and (c) change in optical pathlength Δs caused by electron beam irradiation as depicted by interference between the wavefronts in (a) and (b).

Fig. 3
Fig. 3

General view of object and reference beams in the holographic interferometer.

Fig. 4
Fig. 4

Detailed view of the holographic interferometer: L0, L1, L2, L3, lenses; P, pinhole; IS, iris shutter; M1, M2, M3, M4, plane front-surface mirrors; BS, beam splitter; C, irradiation cell; CM, corner mirror; HP, holographic plate; S, screen with a small hole; and PP, photographic plate.

Fig. 5
Fig. 5

Arrangement for superimposing of reference and object beams on the holographic plate.

Fig. 6
Fig. 6

Holographically reconstructed interferogram of the pulsed electron beam energy deposition in water.

Fig. 7
Fig. 7

Absorbed dose distribution in a semi-infinite water volume, in a plane containing the pulsed electron beam axis, as calculated from an interferogram as shown in Fig. 6.

Equations (17)

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

D = D ( z , r ) .
s = n x ,
s = n ( x ) d x .
Δ s = Δ n ( x ) d x .
Δ s ( z , y ) = 2 0 ( R 2 - y 2 ) 1 2 Δ n ( z , r ) d x ,
Δ s ( z , y ) = 2 y R Δ n ( z , r ) r d r ( r 2 - y 2 ) 1 2 .
Δ n ( r , z n ) = - 2 λ π δ j = k M - 1 B k , j Δ s * ( y j , z n ) ,
k = r / δ ,
δ = y i + 1 - y i ,
M = R / δ ,
Δ s ( z n , y ) = λ Δ s * ( z n , y ) .
B k , j = A k , j - 1 - A k , j             for             j > k ,
= - A k , j             for             j = k ,
A k , j = [ ( j + 1 ) 2 - k 2 ] 1 2 - ( j 2 - k 2 ) 1 2 2 j + 1 .
D ( z n , T ) = Δ T ( z n , r ) c .
x = λ / sin θ ,
sin θ = d / f , θ d / f ,

Metrics