Abstract

A vector angular-spectrum iterative algorithm for the design of diffractive optical elements to produce uniform illumination is described. In the algorithm, the beam polarization is related to a unit wave vector and a random mixture of intensity is used for super-Gaussian beam shaping. The simulated results show that 95.3% of the incident energy has converged into the desired region. The greatest profile error and the mean-square error of intensity fitted to the corresponding parameters of the 100th-power super-Gaussian function are approximately 8×10-4 and 3.5×10-3, respectively.

© 2004 Optical Society of America

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Corrections

Yiqiong Zhao, Yong-Ping Li, and Qiu-Gui Zhou, "Vector iterative algorithm for the design of diffractive optical elements applied to uniform illumination: erratum," Opt. Lett. 29, 2085-2085 (2004)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-29-17-2085

References

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2002 (2)

Y. Q. Zhao, D. W. Chen, and Y. P. Li, Proc. SPIE 4914, 201 (2002).
[CrossRef]

J. S. Liu and M. R. Taghizadeh, Opt. Lett. 27, 1463 (2002).
[CrossRef]

2001 (1)

1996 (2)

1994 (2)

J. R. Leger, D. Chen, and Z. Wang, Opt. Lett. 19, 108 (1994).
[CrossRef]

M. P. Chang and O. K. Erosy, Optik (Stuttgart) 95, 155 (1994).

1991 (1)

1989 (1)

1988 (1)

Y. P. Li, D. Hui, and Y. Kun, Opt. Commun. 66, 122 (1988).
[CrossRef]

1986 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

1980 (1)

J. R. Fienup, Opt. Eng. 19, 297 (1980).
[CrossRef]

1974 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

Bernhardt, M.

Bryngdahl, O.

Chang, M. P.

M. P. Chang and O. K. Erosy, Optik (Stuttgart) 95, 155 (1994).

Chen, D.

Chen, D. W.

Y. Q. Zhao, D. W. Chen, and Y. P. Li, Proc. SPIE 4914, 201 (2002).
[CrossRef]

Deng, X. G.

Erosy, O. K.

M. P. Chang and O. K. Erosy, Optik (Stuttgart) 95, 155 (1994).

Fan, D. Y.

Fienup, J. R.

J. R. Fienup, Opt. Eng. 19, 297 (1980).
[CrossRef]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

Gregory, N. P.

Hui, D.

Y. P. Li, D. Hui, and Y. Kun, Opt. Commun. 66, 122 (1988).
[CrossRef]

Kessler, T. J.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Kun, Y.

Y. P. Li, D. Hui, and Y. Kun, Opt. Commun. 66, 122 (1988).
[CrossRef]

Lawrence, G. N.

Leger, J. R.

Li, Y. P.

Y. Q. Zhao, D. W. Chen, and Y. P. Li, Proc. SPIE 4914, 201 (2002).
[CrossRef]

X. G. Deng, Y. P. Li, D. Y. Fan, and Y. Qiu, Opt. Lett. 21, 1963 (1996).
[CrossRef] [PubMed]

Y. P. Li, D. Hui, and Y. Kun, Opt. Commun. 66, 122 (1988).
[CrossRef]

Lin, Y.

Liu, J. S.

Mansuripur, M.

Qiu, Y.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

Stephen, M. D.

Taghizadeh, M. R.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Wang, Z.

Wyrowski, F.

Zhao, Y. Q.

Y. Q. Zhao, D. W. Chen, and Y. P. Li, Proc. SPIE 4914, 201 (2002).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

Y. P. Li, D. Hui, and Y. Kun, Opt. Commun. 66, 122 (1988).
[CrossRef]

Opt. Eng. (1)

J. R. Fienup, Opt. Eng. 19, 297 (1980).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Optik (Stuttgart) (2)

M. P. Chang and O. K. Erosy, Optik (Stuttgart) 95, 155 (1994).

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

Proc. SPIE (1)

Y. Q. Zhao, D. W. Chen, and Y. P. Li, Proc. SPIE 4914, 201 (2002).
[CrossRef]

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the uniform-illumination system. The DOE is placed at z=0, and z=Z is the image plane upon which a super-Gaussian profile is formed.

Fig. 2
Fig. 2

(a) Two-dimensional projected isogram and (b) three-dimensional representation of the simulated intensity on the desired plane. The incident beam is 95.3% homogeneous in the 1000 µm×1000 µm region and decreases abruptly to zero at the rim of a target region such as a square distribution.

Fig. 3
Fig. 3

Fractional energy and MSE of the intensity versus the bucket dimension from the origin of a coordinate. Fractional energy of the simulated and of the ideal 100th super-Gaussian (SG) distributions is shown. The simulated result fits the corresponding parameters of the 100th super-Gaussian beam with a TPE of 8×10-4 and a MSE of the intensity of 3.509×10-3.

Tables (1)

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Table 1 Components of the Polarization Vector of a Linearly Polarized Plane Wave Propagating along Unit Vector σˆ =α,β,γ

Equations (12)

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

Il=exp-xlrl2Nl-ylrl2Nl,  l=input,output.
Aaαλ,βλ0=-Uax,y;0Tx,y×exp-i2πλxα+yβdxdya=x,y,
Ubx,y;Z=-ψabAaαλ,βλ;0×expj2πλ1-α2-β21/2Z×expj2παλx+βλydαλdβλb=x,y,z.
Ux,y;Z=Uxx,y;Zxˆ+Uyx,y;Zyˆ+Uzx,y;Zzˆ,
Ix,y;Z=Uxx,y;Z2+Uyx,y;Z2+Uzx,y;Z2,
Ukx,y;Z=SUa,kx,y;0=SIinputx,y;01/2×expiϕUa,k-1x,y;0,
Ukx,y;Z=1+ζIoutputx,y;Z1/2-ζI1/2x,y;ZexpiϕUa,kx,y;Z,
Ua,kx,y;0=S-1Ukx,y;Z,
Ua,k+1x,y;0=Iinputx,y;01/2 expiϕUa,kx,y;0,
MSEamp=x,yIx,y;Z-Ioutput2x,yIoutput,
MSEint=x,yIx,y;Z-Ioutput2x,yIoutput2.
TPE=x,ytopIx,y;Z-Ioutput2x,yIoutput,x,yDoutput,

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