Abstract

We establish that, in six different cases, binary phase gratings can be applied to implement Talbot array illuminators. Three of the six cases are reported for what is to our knowledge the first time.

© 1993 Optical Society of America

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References

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  1. A. W. Lohmann, Optik (Stuttgart) 79, 41 (1988).
  2. A. W. Lohmann, J. A. Thomas, Appl. Opt. 29, 4337 (1990).
    [CrossRef] [PubMed]
  3. X.-Y. Da, Appl. Opt. 31, 2983 (1992).
    [CrossRef] [PubMed]
  4. R. F. Edgar, Opt. Acta 16, 281 (1969).
    [CrossRef]

1992 (1)

1990 (1)

1988 (1)

A. W. Lohmann, Optik (Stuttgart) 79, 41 (1988).

1969 (1)

R. F. Edgar, Opt. Acta 16, 281 (1969).
[CrossRef]

Appl. Opt. (2)

Opt. Acta (1)

R. F. Edgar, Opt. Acta 16, 281 (1969).
[CrossRef]

Optik (1)

A. W. Lohmann, Optik (Stuttgart) 79, 41 (1988).

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Figures (2)

Fig. 1
Fig. 1

Schematic representation of the optical setup.

Fig. 2
Fig. 2

Binary functions for (a) the phase grating, (b) the complex amplitude u(x, z), and (c) the laterally shifted amplitude u(x + d/2, z).

Tables (1)

Tables Icon

Table 1 Binary Phase Grating Parameters for Obtaining Binary Amplitude Patterns

Equations (16)

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t ( x ) = 1 + [ exp ( i ϕ ) 1 ] m = a m exp ( i 2 π m x / d ) ,
a m = ( w / d ) sinc ( m w / d ) .
w / d = P / Q ,
u ( x , z ) = 1 + [ exp ( i ϕ ) 1 ] m = a m × exp [ i 2 π m 2 ( z / Z t ) ] exp ( i 2 π m x / d ) ,
u ( x + d / 2 , z ) = u ( x , z + Z t / 2 ) .
u ( x , z ) = h m = c m exp ( i 2 π m x / d ) ,
c m = ( w / d ) sinc ( m w / d ) .
I 0 = | h | 2 c 0 .
1 + [ exp ( i ϕ ) 1 ] a 0 = h c 0 ,
[ exp ( i ϕ ) 1 ] a m exp [ i 2 π m 2 ( z / Z t ) ] = h c m .
w / d = P / Q ,
| h | = 1 / c 0 .
cos ( ϕ ) = 1 + ( c 0 1 ) / [ 2 a 0 ( 1 a 0 ) ] .
F ( m ) = exp ( i 2 π m 2 z / Z t ) = K ( ϕ , a 0 , c 0 ) ( c m / a m ) ,
K ( ϕ , a 0 , c 0 ) = { 1 + [ exp ( i ϕ ) 1 ] a 0 } / { [ exp ( i ϕ ) 1 ] c 0 } = [ exp ( i ϕ ) 1 ] + [ 2 2 cos ( ϕ ) ] a 0 [ 2 2 cos ( ϕ ) ] c 0 .
F ( m ) = exp ( i π / 2 ) .

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