Abstract

Partially coherent illumination provided by scanning an object with a laser beam is studied theoretically and experimentally. Two scanning system schemes are considered to produce different forms of spatial coherence functions. It is demonstrated that effective spatial coherence can be controlled by changing the range and width of the scanning beam.

© 1980 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), Chap. 10.
  2. M. V. R. K. Murty, J. Opt. Soc. Am. 54, 1187 (1964).
    [CrossRef]
  3. W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
    [CrossRef]
  4. F. Scudieri, M. Bertolotti, R. Bartolino, Appl. Opt. 13, 181 (1974).
    [CrossRef] [PubMed]
  5. Y. Ohtsuka, Y. Imai, J. Opt. Soc. Am. 69, 684 (1979).
    [CrossRef]
  6. C. E. Thomas, Appl. Opt. 7, 517 (1968).
    [CrossRef] [PubMed]
  7. J. Braat, S. Lowenthal, J. Opt. Soc. Am. 63, 388 (1973).
    [CrossRef]
  8. K. Itoh, Y. Ohtsuka, Opt. Commun. 31, 119 (1979).
    [CrossRef]
  9. D. Kohler, L. Mandel, J. Opt. Soc. Am. 63, 126 (1973).
    [CrossRef]
  10. C. Roddier, F. Roddier, J. Opt. Soc. Am. 63, 661 (1973).
    [CrossRef]
  11. J. C. Dainty, R. J. Scaddan, Mon. Not. R. Astron. Soc. 167, 69 (1974).
  12. K. Itoh, Y. Ohtsuka, in Proceedings, Eleventh ICO International Conference on Optics Today and Tomorrow (Sociedad Espanola de Optica, Madrid, 1978), p. 511.

1979 (2)

K. Itoh, Y. Ohtsuka, Opt. Commun. 31, 119 (1979).
[CrossRef]

Y. Ohtsuka, Y. Imai, J. Opt. Soc. Am. 69, 684 (1979).
[CrossRef]

1974 (2)

J. C. Dainty, R. J. Scaddan, Mon. Not. R. Astron. Soc. 167, 69 (1974).

F. Scudieri, M. Bertolotti, R. Bartolino, Appl. Opt. 13, 181 (1974).
[CrossRef] [PubMed]

1973 (3)

1968 (1)

1964 (2)

M. V. R. K. Murty, J. Opt. Soc. Am. 54, 1187 (1964).
[CrossRef]

W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Bartolino, R.

Bertolotti, M.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), Chap. 10.

Braat, J.

Dainty, J. C.

J. C. Dainty, R. J. Scaddan, Mon. Not. R. Astron. Soc. 167, 69 (1974).

Imai, Y.

Itoh, K.

K. Itoh, Y. Ohtsuka, Opt. Commun. 31, 119 (1979).
[CrossRef]

K. Itoh, Y. Ohtsuka, in Proceedings, Eleventh ICO International Conference on Optics Today and Tomorrow (Sociedad Espanola de Optica, Madrid, 1978), p. 511.

Kohler, D.

Lowenthal, S.

Mandel, L.

Martienssen, W.

W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Murty, M. V. R. K.

Ohtsuka, Y.

Y. Ohtsuka, Y. Imai, J. Opt. Soc. Am. 69, 684 (1979).
[CrossRef]

K. Itoh, Y. Ohtsuka, Opt. Commun. 31, 119 (1979).
[CrossRef]

K. Itoh, Y. Ohtsuka, in Proceedings, Eleventh ICO International Conference on Optics Today and Tomorrow (Sociedad Espanola de Optica, Madrid, 1978), p. 511.

Roddier, C.

Roddier, F.

Scaddan, R. J.

J. C. Dainty, R. J. Scaddan, Mon. Not. R. Astron. Soc. 167, 69 (1974).

Scudieri, F.

Spiller, E.

W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Thomas, C. E.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), Chap. 10.

Am. J. Phys. (1)

W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. (5)

Mon. Not. R. Astron. Soc. (1)

J. C. Dainty, R. J. Scaddan, Mon. Not. R. Astron. Soc. 167, 69 (1974).

Opt. Commun. (1)

K. Itoh, Y. Ohtsuka, Opt. Commun. 31, 119 (1979).
[CrossRef]

Other (2)

K. Itoh, Y. Ohtsuka, in Proceedings, Eleventh ICO International Conference on Optics Today and Tomorrow (Sociedad Espanola de Optica, Madrid, 1978), p. 511.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), Chap. 10.

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Figures (6)

Fig. 1
Fig. 1

Schematic of a moving source system.

Fig. 2
Fig. 2

Optical setup for Case (1). Rotatable mirror Mr realizes a moving focused spot in plane A.

Fig. 3
Fig. 3

Optical setup for Case (2). The rotational motion of Mr is equivalent to lateral translation of the secondary source truncated by slit S.

Fig. 4
Fig. 4

Wave front folding interferometer. The two wave fronts leaving BS1, which are indicated by the solid and broken lines, are recombined at BS2. One of the superposed wave fronts is arranged to have left to right reversal.

Fig. 5
Fig. 5

Fringe patterns obtained by the wave front folding interferometer: (a) Case (1) and (b) Case (2).

Fig. 6
Fig. 6

Degree of effective coherence in the object planes: (a) Case (1) and (b) Case (2). The solid curves indicate the theoretical predictions for the respective cases.

Equations (14)

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I T ( R ) = B B J T ( Q 1 , Q 2 ) F ( Q 1 ) F * ( Q 2 ) K m ( Q 1 , R ) × K m * ( Q 2 , R ) d Q 1 d Q 2 ,
J T ( Q 1 , Q 2 ) = A A U ( P 1 ) U * ( P 2 ) { 1 2 T T T K n [ P 1 + P ( t ) , Q 1 ] × K n * [ P 2 + P ( t ) , Q 2 ] d t } d P 1 d P 2 ,
J T ( Q 1 , Q 2 ) = 1 2 T T T U ( Q 1 , t ) U * ( Q 2 , t ) d t .
μ T ( Q 1 , Q 2 ) = J T ( Q 1 , Q 2 ) J T ( Q 1 , Q 1 ) J T ( Q 2 , Q 2 ) .
x ( t ) = a sin ( π t T ) .
K n ( x , u ) = K 1 exp ( 2 π i x u λ f 4 ) ,
J T ( u 1 , u 2 ) = U ( u 1 ) U * ( u 2 ) J 0 [ 2 π a ( u 1 u 2 ) λ f 4 ] ,
μ T ( u 1 , u 2 ) = exp [ i ψ ( u 1 , u 2 ) ] J 0 [ 2 π a ( u 1 u 2 ) λ f 4 ] ,
J T ( u 1 , u 2 ) = I 0 W L Λ ( x 1 x 2 W ) × K n ( x 1 , u 1 ) K n * ( x 2 , u 2 ) d x 1 d x 2 ,
Λ ( x ) = rect ( x ) rect ( x x ) d x .
J T ( u 1 u 2 ) = I 0 W | K 2 | 2 L M 2 Λ ( u 1 u 2 M W ) .
μ T ( u 1 u 2 ) = Λ ( u 1 u 2 M W ) .
I T ( u ) = 1 2 T T T | U ( u , t ) exp ( i α u ) + U ( u , t ) exp ( i α u ) | 2 d t = I T ( u ) + I T ( u ) + 2 I T ( u ) I T ( u ) | μ T ( 2 u ) | × cos [ arg μ T ( 2 u ) 2 α u ] ,
V ( u ) = | μ T ( 2 u ) | .

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