Abstract

The effect of manufacturing errors on diffraction efficiency for multilayer diffractive optical elements (MLDOEs) used in imaging optical systems is discussed in this paper. The relationship of diffraction efficiency and depth-scaling errors are analyzed for two different cases: the two relative depth-scaling errors change in the same sign and in the opposite sign. For the first condition, the corresponding diffraction efficiency decreases more slowly. The effect of periodic width errors on diffraction efficiency is also evaluated. When the two major manufacturing errors coexist, the magnitude of the decrease of diffraction efficiency is analyzed for MLDOEs. The result can be used for analyzing the effects of the manufacturing errors on diffraction efficiency for MLDOEs.

© 2011 Optical Society of America

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G. I. Greisukh, E. A. Bezus, D. A. Bykov, E. G. Ezhov, and S. A. Stepanov, “Suppression of the spectral selectivity of two-layer relief-phase diffraction structures,” Opt. Spectrosc. 106, 621–626 (2009).
[CrossRef]

2007

R. Bittner, “Tolerancing of single point diamond turned diffractive optical elements and optical surfaces,” J. Eur. Opt. Soc. 2, 07028 (2007).
[CrossRef]

2005

A. P. Wood and P. J. Rogers, “Diffractive optics in modern optical engineering,” Proc. SPIE 5865, 83–97 (2005).
[CrossRef]

2003

R. C. Juergens, R. H. Shepard, III, and J. P. Schaefer, “Simulation of single point diamond turning fabrication process errors,” Proc. SPIE 5174, 93–104 (2003).
[CrossRef]

H. Hua, Y. Ha, and J. P. Rolland, “Design of an ultralight and compact projection lens,” Appl. Opt. 42, 97–107 (2003).
[CrossRef] [PubMed]

1998

1997

1995

1994

H. P. Herzig, P. Ehbets, J. M. Teijido, and K. J. Weible, “Diffractive optical elements for space communication terminals,” SPIE Rev. 2210, 104–111 (1994).
[CrossRef]

1992

A. P. Wood, “A hybrid refractive-diffractive lens for manufacture by diamond turning,” SPIE Rev. 1573, 122–128(1992).
[CrossRef]

1982

Arieli, Y.

Bezus, E. A.

G. I. Greisukh, E. A. Bezus, D. A. Bykov, E. G. Ezhov, and S. A. Stepanov, “Suppression of the spectral selectivity of two-layer relief-phase diffraction structures,” Opt. Spectrosc. 106, 621–626 (2009).
[CrossRef]

Bittner, R.

R. Bittner, “Tolerancing of single point diamond turned diffractive optical elements and optical surfaces,” J. Eur. Opt. Soc. 2, 07028 (2007).
[CrossRef]

Blough, C. G.

Bobrov, S. T.

G. I. Greisukh, S. T. Bobrov, and S. A. Stepanov, Optics of Diffractive and Gradient-Index Elements and Systems (SPIE, 1997).

Bykov, D. A.

G. I. Greisukh, E. A. Bezus, D. A. Bykov, E. G. Ezhov, and S. A. Stepanov, “Suppression of the spectral selectivity of two-layer relief-phase diffraction structures,” Opt. Spectrosc. 106, 621–626 (2009).
[CrossRef]

Cox, J. A.

J. A. Cox, “Application of diffractive optics to infrared imagers,” SPIE Rev. 2552, 304–312 (1995).
[CrossRef]

Cui, Q.

Ehbets, P.

H. P. Herzig, P. Ehbets, J. M. Teijido, and K. J. Weible, “Diffractive optical elements for space communication terminals,” SPIE Rev. 2210, 104–111 (1994).
[CrossRef]

Eisenberg, N.

Ezhov, E. G.

G. I. Greisukh, E. A. Bezus, D. A. Bykov, E. G. Ezhov, and S. A. Stepanov, “Suppression of the spectral selectivity of two-layer relief-phase diffraction structures,” Opt. Spectrosc. 106, 621–626 (2009).
[CrossRef]

Fujita, T.

Gale, M. T.

Greisukh, G. I.

G. I. Greisukh, E. A. Bezus, D. A. Bykov, E. G. Ezhov, and S. A. Stepanov, “Suppression of the spectral selectivity of two-layer relief-phase diffraction structures,” Opt. Spectrosc. 106, 621–626 (2009).
[CrossRef]

G. I. Greisukh, S. T. Bobrov, and S. A. Stepanov, Optics of Diffractive and Gradient-Index Elements and Systems (SPIE, 1997).

Ha, Y.

Herzig, H. P.

H. P. Herzig, P. Ehbets, J. M. Teijido, and K. J. Weible, “Diffractive optical elements for space communication terminals,” SPIE Rev. 2210, 104–111 (1994).
[CrossRef]

Hessler, T.

Hua, H.

Juergens, R. C.

R. C. Juergens, R. H. Shepard, III, and J. P. Schaefer, “Simulation of single point diamond turning fabrication process errors,” Proc. SPIE 5174, 93–104 (2003).
[CrossRef]

Kathman, A. D.

C. D. O’ Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics Design, Fabrication, and Test (SPIE, 2004).

Koyama, J.

Kunz, R. E.

Mack, S. K.

Michaels, R. L.

Missig, M. D.

Morris, G. M.

Nishihara, H.

O’ Shea, C. D.

C. D. O’ Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics Design, Fabrication, and Test (SPIE, 2004).

Ozeri, S.

Prather, D. W.

C. D. O’ Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics Design, Fabrication, and Test (SPIE, 2004).

Rogers, P. J.

A. P. Wood and P. J. Rogers, “Diffractive optics in modern optical engineering,” Proc. SPIE 5865, 83–97 (2005).
[CrossRef]

Rolland, J. P.

Rossi, M.

Schaefer, J. P.

R. C. Juergens, R. H. Shepard, III, and J. P. Schaefer, “Simulation of single point diamond turning fabrication process errors,” Proc. SPIE 5174, 93–104 (2003).
[CrossRef]

Shepard, R. H.

R. C. Juergens, R. H. Shepard, III, and J. P. Schaefer, “Simulation of single point diamond turning fabrication process errors,” Proc. SPIE 5174, 93–104 (2003).
[CrossRef]

Sommargren, G. E.

Stepanov, S. A.

G. I. Greisukh, E. A. Bezus, D. A. Bykov, E. G. Ezhov, and S. A. Stepanov, “Suppression of the spectral selectivity of two-layer relief-phase diffraction structures,” Opt. Spectrosc. 106, 621–626 (2009).
[CrossRef]

G. I. Greisukh, S. T. Bobrov, and S. A. Stepanov, Optics of Diffractive and Gradient-Index Elements and Systems (SPIE, 1997).

Suleski, T. J.

C. D. O’ Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics Design, Fabrication, and Test (SPIE, 2004).

Sweeney, D. W.

Teijido, J. M.

H. P. Herzig, P. Ehbets, J. M. Teijido, and K. J. Weible, “Diffractive optical elements for space communication terminals,” SPIE Rev. 2210, 104–111 (1994).
[CrossRef]

Weible, K. J.

H. P. Herzig, P. Ehbets, J. M. Teijido, and K. J. Weible, “Diffractive optical elements for space communication terminals,” SPIE Rev. 2210, 104–111 (1994).
[CrossRef]

Wood, A. P.

A. P. Wood and P. J. Rogers, “Diffractive optics in modern optical engineering,” Proc. SPIE 5865, 83–97 (2005).
[CrossRef]

A. P. Wood, “A hybrid refractive-diffractive lens for manufacture by diamond turning,” SPIE Rev. 1573, 122–128(1992).
[CrossRef]

Xue, C.

Appl. Opt.

J. Eur. Opt. Soc.

R. Bittner, “Tolerancing of single point diamond turned diffractive optical elements and optical surfaces,” J. Eur. Opt. Soc. 2, 07028 (2007).
[CrossRef]

Opt. Lett.

Opt. Spectrosc.

G. I. Greisukh, E. A. Bezus, D. A. Bykov, E. G. Ezhov, and S. A. Stepanov, “Suppression of the spectral selectivity of two-layer relief-phase diffraction structures,” Opt. Spectrosc. 106, 621–626 (2009).
[CrossRef]

Proc. SPIE

A. P. Wood and P. J. Rogers, “Diffractive optics in modern optical engineering,” Proc. SPIE 5865, 83–97 (2005).
[CrossRef]

R. C. Juergens, R. H. Shepard, III, and J. P. Schaefer, “Simulation of single point diamond turning fabrication process errors,” Proc. SPIE 5174, 93–104 (2003).
[CrossRef]

SPIE Rev.

H. P. Herzig, P. Ehbets, J. M. Teijido, and K. J. Weible, “Diffractive optical elements for space communication terminals,” SPIE Rev. 2210, 104–111 (1994).
[CrossRef]

J. A. Cox, “Application of diffractive optics to infrared imagers,” SPIE Rev. 2552, 304–312 (1995).
[CrossRef]

A. P. Wood, “A hybrid refractive-diffractive lens for manufacture by diamond turning,” SPIE Rev. 1573, 122–128(1992).
[CrossRef]

Other

G. I. Greisukh, S. T. Bobrov, and S. A. Stepanov, Optics of Diffractive and Gradient-Index Elements and Systems (SPIE, 1997).

C. D. O’ Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics Design, Fabrication, and Test (SPIE, 2004).

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Figures (12)

Fig. 1
Fig. 1

Diffraction efficiency of single-layer DOEs versus the depth-scaling error.

Fig. 2
Fig. 2

Profile of single-layer DOEs with the periodic width error.

Fig. 3
Fig. 3

Diffraction efficiency of single-layer DOEs versus the periodic width error.

Fig. 4
Fig. 4

Diffraction efficiency of single-layer DOEs versus depth-scaling error and the periodic width error.

Fig. 5
Fig. 5

Profile of double-layer diffractive optical elements.

Fig. 6
Fig. 6

Diffraction efficiency of double-layer DOEs versus the two equal depth-scaling errors.

Fig. 7
Fig. 7

Diffraction efficiency of double-layer DOEs versus the two opposite depth-scaling errors.

Fig. 8
Fig. 8

Diffraction efficiency of double-layer DOEs versus the two depth-scaling errors.

Fig. 9
Fig. 9

Diffraction efficiency of double-layer DOEs versus the two equal periodic width errors.

Fig. 10
Fig. 10

Profile of double-layer DOEs with manufacturing errors.

Fig. 11
Fig. 11

Diffraction efficiency of double-layer DOEs versus the two same depth-scaling errors and same periodic width errors.

Fig. 12
Fig. 12

Diffraction efficiency of double-layer DOEs versus the two opposite depth-scaling errors and two same periodic width errors.

Tables (3)

Tables Icon

Table 1 Diffraction Efficiency and Some Depth-Scaling Errors

Tables Icon

Table 2 Diffraction Efficiency of Double-Layer DOEs for the First Condition

Tables Icon

Table 3 Diffraction Efficiency of Double-Layer DOEs for the Second Condition

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

η m = s in c 2 { m d 0 λ [ n ( λ ) 1 ] } ,
d = d 0 + Δ d = d 0 ( 1 + ε ) ,
η = η m s in c 2 ( T 1 T 10 T 10 ) = s in c 2 { m d 0 λ [ n ( λ ) 1 ] } · s in c 2 ( T 1 T 10 T 10 ) ,
η m = s in c 2 ( m ( n 1 ( λ ) 1 ) × d 10 + ( n 2 ( λ ) 1 ) × d 20 ) λ ) ,
{ d 1 = d 10 + Δ d 1 = d 10 ( 1 + ε 1 ) d 2 = d 20 + Δ d 2 = d 20 ( 1 + ε 2 ) ,
ε 1 = Δ d 1 / d 10 , ε 2 = Δ d 2 / d 20
{ Δ d 1 = ( Δ d 11 + Δ d 12 + + Δ d 1 N ) / N Δ d 2 = ( Δ d 21 + Δ d 22 + + Δ d 2 N ) / N ,
η = η m s in c 2 ( T 1 T 10 T 10 ) s in c 2 ( T 2 T 20 T 20 ) = s in c 2 ( m ( n 1 ( λ ) 1 ) × d 10 + ( n 2 ( λ ) 1 ) × d 20 ) λ ) s in c 2 ( T 1 T 10 T 10 ) s in c 2 ( T 2 T 20 T 20 ) ,
ξ 1 = T 1 T 10 T 10 , ξ 2 = T 2 T 20 T 20 .

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