Abstract

The optimum phase defocus grating for wavefront curvature sensing is proposed. It features an equidistantly quantized, binary-phase-step defocus grating with a phase-step height of π. The diffractive efficiency of the phase defocus grating is theoretically computed. The optical transfer function is obtained. The optimum phase defocus grating is fabricated. The high diffractive efficiencies of the ±1 diffraction orders are verified experimentally, the average values of which are 38.08% and 40.36%, respectively.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  5. S. C. Woods and A. H. Greenaway, "Wave-front sensing by use of a Green's function solution to the intensity transport equation," J. Opt. Soc. Am. A 20, 508-512 (2003).
    [CrossRef]
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    [CrossRef]
  9. D. M. Cuevas, G. R. G. Erry, P. Fournier, P. Harrison, and L. J. Otten, "Distorted grating wavefront sensor and ophthalmic applications," Proc. SPIE 6018, 60180A (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2006 (1)

2005 (1)

D. M. Cuevas, G. R. G. Erry, P. Fournier, P. Harrison, and L. J. Otten, "Distorted grating wavefront sensor and ophthalmic applications," Proc. SPIE 6018, 60180A (2005).
[CrossRef]

2004 (1)

2003 (2)

S. C. Woods and A. H. Greenaway, "Wave-front sensing by use of a Green's function solution to the intensity transport equation," J. Opt. Soc. Am. A 20, 508-512 (2003).
[CrossRef]

G. Erry, P. Harrison, J. Burnett, D. Benton, A. Scott, and S. Woods, "Results of atmospheric compensation using a wavefront curvature based adaptive optics system," Proc. SPIE 4884, 245-249 (2003).
[CrossRef]

2002 (1)

M. Chang and H. N. Gooransarab, "A grating based curvature sensor," Proc. SPIE 4926, 101-106 (2002).
[CrossRef]

2000 (2)

1999 (1)

1991 (1)

F. F. Forbes and N. Roddier, "Adaptive optics using curvature sensing," Proc. SPIE 1542, 140-147 (1991).
[CrossRef]

1989 (1)

G. J. Swanson and W. B. Veldkamp, "Diffractive optical elements for use in infrared systems," Opt. Eng. 28, 605-608 (1989).

1988 (1)

Appl. Opt. (4)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

P. M. Blanchard and A. H. Greenaway, "Broadband simultaneous multiplane imaging," Opt. Commun. 183, 29-36 (2000).
[CrossRef]

Opt. Eng. (1)

G. J. Swanson and W. B. Veldkamp, "Diffractive optical elements for use in infrared systems," Opt. Eng. 28, 605-608 (1989).

Opt. Lett. (1)

Proc. SPIE (4)

G. Erry, P. Harrison, J. Burnett, D. Benton, A. Scott, and S. Woods, "Results of atmospheric compensation using a wavefront curvature based adaptive optics system," Proc. SPIE 4884, 245-249 (2003).
[CrossRef]

D. M. Cuevas, G. R. G. Erry, P. Fournier, P. Harrison, and L. J. Otten, "Distorted grating wavefront sensor and ophthalmic applications," Proc. SPIE 6018, 60180A (2005).
[CrossRef]

F. F. Forbes and N. Roddier, "Adaptive optics using curvature sensing," Proc. SPIE 1542, 140-147 (1991).
[CrossRef]

M. Chang and H. N. Gooransarab, "A grating based curvature sensor," Proc. SPIE 4926, 101-106 (2002).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Distribution diagram of diffractive efficiencies of the multiphase-step Fresnel zone plate.

Fig. 2
Fig. 2

Diagrams of the dependence of the diffractive efficiencies on the phase-step height S and the phase-step width w in the (a) zero order and (b) ± 1 orders.

Fig. 3
Fig. 3

Spots in the zero and ± 1 diffractive orders of the defocus grating.

Fig. 4
Fig. 4

Defocus spot representing the total energy without the phase grating.

Tables (1)

Tables Icon

Table 1 Diffractive Efficiency in Zero, ± 1 Orders

Equations (15)

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t ( ξ ) = e i 2 π ( [ ξ ] + 1 ξ ) = m = + a m e i 2 π m ξ ,
a m = 0 1 t ( ξ ) e i 2 π m ξ d ξ = e i π ( 1 m ) sinc ( 1 + m ) ,
η m = a m 2 = sinc 2 ( 1 + m ) .
t ( ξ ) = e i 2 π Q k .
a m = k = 1 L ( ξ k ξ k 1 ) sinc [ m ( ξ k ξ k 1 ) ] e i π [ 2 Q k + m ( ξ k + ξ k 1 ) ] .
η m = 1 L 2 sinc 2 ( m L ) k = 1 L e i π L [ 2 k ( 1 + m ) ] 2 ,
4 k L = 2 n , n Integer , k = 1 , , L 1 , L .
t ( ξ ) = exp ( i π S ) r e c t ( ξ w ) * n = 0 N 1 δ [ ξ ( n + w 2 ) ] + r e c t ( ξ 1 w ) * n = 0 N 1 δ [ ξ ( n + 1 + w 2 ) ] ,
a 0 = 0 w e i S π d ξ + w 1 d ξ = e i S π w + 1 w .
η 0 = e i S π w + 1 w 2 = cos ( S π ) w + 1 w + i sin ( S π ) 2 .
a m = 0 w e i S π e i 2 π m ξ d ξ + w 1 e i 2 π m ξ d ξ = e i m π ( 1 + w ) { ( 1 w ) sinc [ m ( 1 w ) ] + e i π ( m + S ) w sinc ( m w ) } .
η m = a m 2 = 4 sin 2 [ ( π S ) 2 ] sin 2 ( π m w ) π 2 m 2 .
t ( ξ ) = 2 i m = + e i π m sin ( π m 2 ) sinc ( m 2 ) e i 2 π m ξ .
t ( x , y ) = 2 i m = + e i π m sin ( π m 2 ) sinc ( m 2 ) e 2 π i m ( x 2 + y 2 ) 2 λ f .
t ( x x 0 , y ) = 2 i e π i m x 0 2 λ f m = + e i π m sin ( π m 2 ) sinc ( m 2 ) e 2 π i m ( x 2 + y 2 ) 2 λ f e 2 π i m x x 0 λ f .

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