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References

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  1. H. Schardin, Ergeb. Exakten Naturwiss. 20, 316 (1942).
  2. R. W. Ladenburg, Ed., Physical Measurements in Gas Dynamics and Combustion, (Princeton U. P., Princeton, 1954), Part 1.
  3. H. Wolter, in Handbuch der Physik, S. Fluegge, Ed., Grundlagen der Optik, (Springer, Berlin, 1956) B.24, S. 574.
  4. L. A. Vasiliev, Shadow Methods, (Izdat. Nauka, Moscow, 1968), in Russian.
  5. K. P. Rolff, Dissert. Tech. U. Berlin (1970).
  6. S. Ugniewski, in Proceedings Symposium Electron and You Beam Science and Technology, Eighth International Conference, Seattle, 1978 (Electrochemical Society, Princeton, 1978) p. 71–83.
  7. S. Ugniewski, Comput. Phys. Commun. 14, 155 (1978).
    [CrossRef]
  8. F. Keilmann, (IPP, IV/4, Garching, W. Germany, 1970).
  9. U. Kogelschatz, W. R. Schneider, Appl. Opt. 11, 1822 (1972).
    [CrossRef] [PubMed]
  10. W. Frie, Ann. Phys. (Leipzig) 10, 332 (1963).
  11. O. H. Nestor, H. N. Olsen, SIAM Rev. 2, 200 (1960).
    [CrossRef]

1978 (1)

S. Ugniewski, Comput. Phys. Commun. 14, 155 (1978).
[CrossRef]

1972 (1)

1963 (1)

W. Frie, Ann. Phys. (Leipzig) 10, 332 (1963).

1960 (1)

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

1942 (1)

H. Schardin, Ergeb. Exakten Naturwiss. 20, 316 (1942).

Frie, W.

W. Frie, Ann. Phys. (Leipzig) 10, 332 (1963).

Keilmann, F.

F. Keilmann, (IPP, IV/4, Garching, W. Germany, 1970).

Kogelschatz, U.

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]

Rolff, K. P.

K. P. Rolff, Dissert. Tech. U. Berlin (1970).

Schardin, H.

H. Schardin, Ergeb. Exakten Naturwiss. 20, 316 (1942).

Schneider, W. R.

Ugniewski, S.

S. Ugniewski, Comput. Phys. Commun. 14, 155 (1978).
[CrossRef]

S. Ugniewski, in Proceedings Symposium Electron and You Beam Science and Technology, Eighth International Conference, Seattle, 1978 (Electrochemical Society, Princeton, 1978) p. 71–83.

Vasiliev, L. A.

L. A. Vasiliev, Shadow Methods, (Izdat. Nauka, Moscow, 1968), in Russian.

Wolter, H.

H. Wolter, in Handbuch der Physik, S. Fluegge, Ed., Grundlagen der Optik, (Springer, Berlin, 1956) B.24, S. 574.

Ann. Phys. (Leipzig) (1)

W. Frie, Ann. Phys. (Leipzig) 10, 332 (1963).

Appl. Opt. (1)

Comput. Phys. Commun. (1)

S. Ugniewski, Comput. Phys. Commun. 14, 155 (1978).
[CrossRef]

Ergeb. Exakten Naturwiss. (1)

H. Schardin, Ergeb. Exakten Naturwiss. 20, 316 (1942).

SIAM Rev. (1)

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

Other (6)

F. Keilmann, (IPP, IV/4, Garching, W. Germany, 1970).

R. W. Ladenburg, Ed., Physical Measurements in Gas Dynamics and Combustion, (Princeton U. P., Princeton, 1954), Part 1.

H. Wolter, in Handbuch der Physik, S. Fluegge, Ed., Grundlagen der Optik, (Springer, Berlin, 1956) B.24, S. 574.

L. A. Vasiliev, Shadow Methods, (Izdat. Nauka, Moscow, 1968), in Russian.

K. P. Rolff, Dissert. Tech. U. Berlin (1970).

S. Ugniewski, in Proceedings Symposium Electron and You Beam Science and Technology, Eighth International Conference, Seattle, 1978 (Electrochemical Society, Princeton, 1978) p. 71–83.

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Figures (1)

Fig. 1
Fig. 1

Reconstruction of a parabolic refractive-index distribution n(r) = [1 − (1 − r2)]1/2, = 0.01. Continuous line - exact solution; dots - present method using Frie’s AL matrix; triangles - present method using the Nestor & Olsen’s BL matrix.

Equations (12)

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α ( x ) = 2 x n x R d n ( r ) d r d r ( r 2 x 2 ) 1 / 2 , n ( R ) = n ,
n ( r ) n n = 1 π r R α ( x ) d x ( x 2 r 2 ) 1 / 2 .
α ( x ) 1 n d L ( x ) d x , ν ( r ) n ( r ) n ,
L ( x ) = 2 x R ν ( r ) r d r ( r 2 x 2 ) 1 / 2 ,
ν ( r ) = 1 π r R d L ( x ) d x d x ( x 2 r 2 ) 1 / 2 .
U ( r ) 1 r d n ( r ) d r ,
L i = k A i , k L ν k , ν k = k B i , k L L k ,
f sch ( x ) = α ( x ) 2 π x , u sch ( r ) = n ( r ) n n ,
f sch ( x ) = 1 π x R d u sch ( r ) d r d r ( r 2 x 2 ) 1 / 2 ,
u sch ( r ) = 2 r R f sch ( x ) x d x ( x 2 r 2 ) 1 / 2 .
f i sch = k B i , k L u k sch , u i sch = k A i , k L f k sch
d d r ln n ( r ) = 1 n d n ( r ) d r

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