Abstract

A more computationally tractable method to design a multiplexed phase diffractive optical element with optical design software to extend the depth of focus is proposed, through which the intensity distribution of the output beams can also be controlled with great flexibility. The design principle is explained in detail. And the feasibility of this design method is illustrated through a design example followed by computer simulation verification.

©2010 Optical Society of America

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References

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2006 (2)

2004 (3)

2003 (1)

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A, Pure Appl. Opt. 5(5), S164–S169 (2003).
[Crossref]

1994 (1)

1993 (1)

1988 (2)

1984 (1)

Bai, H.

Ben-Eliezer, E.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A, Pure Appl. Opt. 5(5), S164–S169 (2003).
[Crossref]

Campos, J.

Escalera, J. C.

Ezhov, E. G.

Fienup, J.

Flores, A.

George, N.

Gimeno, R.

Greisukh, G. I.

Hegedus, Z. S.

Iemmi, C.

Indebetouw, G.

Konforti, N.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A, Pure Appl. Opt. 5(5), S164–S169 (2003).
[Crossref]

Li, F.

Liu, H.

López-Coronado, O.

Lu, Z.

Marom, E.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A, Pure Appl. Opt. 5(5), S164–S169 (2003).
[Crossref]

Sheppard, C. J. R.

Stepanov, S. A.

Stone, T.

Wang, M. R.

Yang, J. J.

Yatagi, T.

Yoshikawa, N.

Yzuel, M. J.

Zalevsky, Z.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A, Pure Appl. Opt. 5(5), S164–S169 (2003).
[Crossref]

Appl. Opt. (7)

J. Opt. A, Pure Appl. Opt. (1)

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A, Pure Appl. Opt. 5(5), S164–S169 (2003).
[Crossref]

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

Opt. Express (2)

Other (1)

Zemax Optical Design Program User’s Guide Zemax Development Corparation www.zemax.com

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Figures (7)

Fig. 1
Fig. 1 Layout of the optical system
Fig. 2
Fig. 2 Quantified phase of the MPDOE
Fig. 3
Fig. 3 Unwrapped phase of MPDOE
Fig. 4
Fig. 4 the modulus transfer function of optical system using multiplexed phase DOE (a) with −0.15mm defocusing length (b)with 0mm defocusing length (c) with 0.15mm defocusing length
Fig. 5
Fig. 5 the point spread function of optical system using multiplexed phase DOE (a) with −0.15mm defocusing length (b)with 0mm defocusing length (c) with 0.15mm defocusing length
Fig. 6
Fig. 6 the modulus transfer function of optical system without using multiplexed phase DOE (a) with −0.15mm defocusing length (b)with 0mm defocusing length (c) with 0.15mm defocusing length
Fig. 7
Fig. 7 PSF of optical system without MPDOE (a) with −0.15mm defocusing length (b)with 0mm defocusing length (c) with 0.15mm defocusing length

Tables (1)

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Table 1 Parameters of optical system

Equations (17)

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M exp ( i a ) = n = 1 N A n exp ( i ϕ n )
exp ( i a ) = n = 1 N A n M exp ( i ϕ n )
M = [ A 1 2 + A 2 2 + + A N 2 + 2 A 1 A 2 cos ( ϕ 1 ϕ 2 ) + 2 A 1 A 3 cos ( ϕ 1 ϕ 3 ) + + 2 A 1 A N cos ( ( ϕ 1 ϕ N ) + 2 A 2 A 3 cos ( ( ϕ 1 ϕ 3 ) ( ϕ 1 ϕ 2 ) ) + + 2 A 2 A N cos ( ( ϕ 1 ϕ N ) ( ϕ 1 ϕ 2 ) ) + + 2 A N 1 A N cos ( ( ϕ 1 ϕ N ) ( ϕ 1 ϕ N 1 ) ) ] 1 / 2
M ' ( β 1 β 2 β N 1 ) = 1 M = m 1 m N 1 a m 1 m 2 m N 1 exp ( i m 1 β 1 + i m 2 β 2 + + i m N 1 β N 1 )
a = m 1 m 2 m N 1 1 ( 2 π ) N 1 0 2 π 0 2 π 1 M exp ( i m 1 β 1 i m N 1 β N 1 ) d β 1 d β N 1
.. exp ( i a ) = m 1 m N 1 a m 1 m N 1 { A 1 exp [ i ( m 1 + + m N 1 + 1 ) ϕ 1 i m 1 ϕ 2 i m N 1 ϕ N ] + A 2 exp [ i ( m 1 + + m N 1 ) ϕ 1 i ( m 1 1 ) ϕ 2 i m ϕ N 1 N ] + + A N exp [ i ( m 1 + + m N 1 ) ϕ 1 i m 1 ϕ 2 i ( m N 1 - 1 ) ϕ N ] }
N = c e i l ( Δ d 4 λ ( F # ) 2 )
exp ( i a ) = + ( a 00 A 1 + a 10 A 2 + a 01 A 3 ) exp ( i ϕ ) 1 + ( a 00 A 2 + a 10 A 1 + a 11 A 3 ) exp ( i ϕ 2 ) + ( a 00 A 3 + a 0 1 A 1 + a 1 1 A 2 ) exp ( i ϕ 3 ) + = + a 1 exp ( i ϕ 1 ) + a 2 exp ( i ϕ 2 ) + a 3 exp ( i ϕ 3 ) +
A 1 = A 2 = A 3 = 3 3
n 2 sin θ 2 n 1 sin θ 1 = m λ d = m λ T
ϕ c o n ( r ) = m i = 1 n B i r 2 i
Φ D ( r ) = 1 f = λ B 1
V D = λ 0 λ max λ min
ϕ 1 ( r ) = 0.007829 r 2 + 1.021439 × 10 6 r 4 4.263861 × 10 10 r 6
ϕ 2 ( r ) = 0.006565 r 2 + 1.381937 × 10 6 r 4 6.007342 × 10 10 r 6
ϕ 3 ( r ) = 0.008575 r 2 1.249763 × 10 7 r 4 + 5.872878 × 10 12 r 6
exp ( i a ) = 1 M { 3 3 exp ( i ϕ 1 ) + 3 3 exp ( i ϕ 2 ) + 3 3 exp ( i ϕ 3 ) }

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