Abstract

The marked chromatic aberration of a Fresnel-zone-plate lens can be used as a variable narrow-band optical filter, and thus a holographic spectrometer. The filtering properties of the zone plate are analyzed, with particular emphasis on the effect of a central stop over the low-order rings. It is shown that the central stop can markedly improve the rejection of frequencies outside the pass band without significant degradation of the spectrometer resolution.

© 1972 Optical Society of America

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References

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  1. W. E. Kock, L. Rosen, and J. Rendeiro, IEEE Proc. 54, 1599 (1966).
    [Crossref]
  2. G. W. Stroke, Phys. Letters 16, 272 (1965).
    [Crossref]
  3. J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967).
  4. S. Lowenthal and A. Aspect, in Proceedings of International Symposium of Holography 1970, edited by J. Ch. Viénot, J. Bulabois, and J. Pasteur (Laboratoire de Physique Générale et Optique, Université de Besançon, Besançon, France, 1970), p. 13.5.
  5. For example, R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).
  6. On general definition of resolving power, see, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964).

1966 (1)

W. E. Kock, L. Rosen, and J. Rendeiro, IEEE Proc. 54, 1599 (1966).
[Crossref]

1965 (1)

G. W. Stroke, Phys. Letters 16, 272 (1965).
[Crossref]

Aspect, A.

S. Lowenthal and A. Aspect, in Proceedings of International Symposium of Holography 1970, edited by J. Ch. Viénot, J. Bulabois, and J. Pasteur (Laboratoire de Physique Générale et Optique, Université de Besançon, Besançon, France, 1970), p. 13.5.

Born, M.

On general definition of resolving power, see, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964).

Burckhardt, C. B.

For example, R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

Collier, R. J.

For example, R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

Kock, W. E.

W. E. Kock, L. Rosen, and J. Rendeiro, IEEE Proc. 54, 1599 (1966).
[Crossref]

Lin, L. H.

For example, R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

Lowenthal, S.

S. Lowenthal and A. Aspect, in Proceedings of International Symposium of Holography 1970, edited by J. Ch. Viénot, J. Bulabois, and J. Pasteur (Laboratoire de Physique Générale et Optique, Université de Besançon, Besançon, France, 1970), p. 13.5.

Rendeiro, J.

W. E. Kock, L. Rosen, and J. Rendeiro, IEEE Proc. 54, 1599 (1966).
[Crossref]

Rosen, L.

W. E. Kock, L. Rosen, and J. Rendeiro, IEEE Proc. 54, 1599 (1966).
[Crossref]

Samson, J. A. R.

J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967).

Stroke, G. W.

G. W. Stroke, Phys. Letters 16, 272 (1965).
[Crossref]

Wolf, E.

On general definition of resolving power, see, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964).

IEEE Proc. (1)

W. E. Kock, L. Rosen, and J. Rendeiro, IEEE Proc. 54, 1599 (1966).
[Crossref]

Phys. Letters (1)

G. W. Stroke, Phys. Letters 16, 272 (1965).
[Crossref]

Other (4)

J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967).

S. Lowenthal and A. Aspect, in Proceedings of International Symposium of Holography 1970, edited by J. Ch. Viénot, J. Bulabois, and J. Pasteur (Laboratoire de Physique Générale et Optique, Université de Besançon, Besançon, France, 1970), p. 13.5.

For example, R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

On general definition of resolving power, see, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964).

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Figures (2)

Fig. 1
Fig. 1

Schematic of spectrometer to analyze chemical compound in polluted air; T, telescope, and EL, electronics.

Fig. 2
Fig. 2

FZP as a spectrometer, (a) without central stop and (b) with central stop.

Equations (28)

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H ( u ) = | 1 + exp ( i k 0 2 R 0 u 2 ) | 2 exp ( - 1 2 ζ 2 u 2 ) ,
f ( x ) = A - d 2 u H ( u ) exp ( i k 2 R ( u - x ) 2 ) .
f ( x ) = 2 π i A R 0 k 0 { A 1 ( k ) + A 2 ( x ; k ) + A 3 ( x ; k ) } ,
A 1 ( k ) = 2 k 0 R k R 0 , A 2 ( x ; k ) = k 0 R k R 0 + k 0 R exp { i 2 k k 0 k R 0 + k 0 R x 2 } ,
A 3 ( x ; k ) = k 0 R k R 0 - k 0 R + i R R 0 / ζ 2 × exp { - i 2 k k 0 k R 0 - k 0 R + i R R 0 / ζ 2 x 2 } .
A 1 = 2 ,             A 2 = 1 2 ,             and             A 3 = i ( k 0 / R 0 ) ζ 2 .
N ( k c ) = [ 2 Re ( A 1 + A 2 ) A 3 * + A 1 A 2 * + A 1 2 + A 2 2 ] k = k c , x = 0 }
S N = A 3 ( 0 ; k c ) 2 / [ 0 S ( k ) N ( k ) d k ] x = 0 .
H ( u ) = H ( u ) [ 1 - G ( u ) ] ,
f ( x ) = A - d 2 u H ( u ) exp { i k 2 R ( u - x ) 2 } .
f ( x ) = 2 π i A R 0 k 0 { A 1 + A 2 + A 3 } ,
A 1 ( k ) 2 k 0 i R 0 r 2 , A 2 ( x ; k ) k 0 2 i R 0 r 2 ( k R 0 k R 0 + k 0 R ) × exp { i 2 k k 0 k R 0 + k 0 R x 2 } ,
A 3 ( x ; k ) k 0 R k R 0 - k 0 R + i R R 0 / ζ 2 × exp { - i 2 k k 0 k R 0 - k 0 R + i R R 0 / ζ 2 x 2 } ,
ρ = 2 i R k r 2 ( = 2 i R 0 k 0 r 2 )
r 2 = 4 π R 0 2 k 0 2 r c 2 .
ρ = 2 r c 2 r 1 2 = 2 N co ,
10 N co N / 10 ,
k Δ k = k 0 ζ 2 R 0 ( 1 - N co / N ) = 4 π N ( 1 - N co )
f ( x ) = exp { i k 2 R x 2 } d 2 x f ( x ) exp { - i k 2 R x 2 } × [ δ 2 ( x - x ) - g ( x - x ) ] ,
G ( u ) = d 2 r g ( r ) exp { i k R u · r }
d 2 r g ( r ) = d 2 r δ ( r ) = 1.
f ( x ) = d 2 x ( f ( x ) - f ( x ) exp { i k 2 R ( x 2 - x 2 ) } ) × g ( x - x ) .
f ( x ) = 2 π i A R 0 k 0 n = 1 3 A n ( x ; k ) d 2 x × ( 1 - exp { 2 π i ( x 2 - x 2 ) l n } ) g ( x - x ) ,
l 2 2 = 4 π R ( k R 0 + k 0 R ) k 2 R 0 , l 3 2 = 4 π R ( k R 0 - k 0 R + i R R 0 / ζ 2 ) k 2 R 0 .
- 2 π i l n 2 A n ( x ; k ) d 2 r r 2 g ( r ) = - 2 π i A n ( x ; k ) r 2 l n 2
A 3 ( x ; k ) d 2 r g ( r ) A 3 ( x ; k ) .
r 2 10 - 2 4 π R 0 k 0 .
r 2 10 4 R 0 2 k 0 2 ζ 2 .