Abstract

The influence of narcissus effect for multilayer diffractive optical elements (MLDOEs) is evaluated from the viewpoint of diffraction efficiency and the narcissus intensity. A modified paraxial evaluation criterion for the reflected narcissus radiation of MLDOEs has been deduced. A practical 812μm IR optical system designed with one two-layer diffractive element has been given to illustrate the distribution of incident narcissus energy among various diffraction orders in the waveband. The narcissus intensities of the two diffractive surfaces have been calculated for those diffraction orders that have the maximum diffraction efficiency. This method can be used in the process of evaluation and control of the narcissus influence in IR optical systems with MLDOEs.

© 2011 Optical Society of America

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References

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  1. J. M. Lloyd, Thermal Imaging Systems (Plenum, 1975), pp. 275–281.
  2. J. B. Cohen, “Narcissus of diffractive optical surfaces,” Proc. SPIE 2426, 380–385 (1995).
    [CrossRef]
  3. T. Liu, Q. Cui, C. Xue, and L. Yang, “Calculation and evaluation of narcissus for diffractive surfaces in infrared systems,” Appl. Opt. 50, 2484–2492 (2011).
    [CrossRef] [PubMed]
  4. Y. Arieli, S. Noach, S. Ozeri, and N. Eisenberg, “Design of diffractive optical elements for multiple wavelengths,” Appl. Opt. 37, 6174–6177 (1998).
    [CrossRef]
  5. C. Xue, Q. Cui, T. Liu, L. Yang, and B. Fei, “Optimal design of a multilayer diffractive optical element for dual wavebands,” Opt. Lett. 35, 4157–4159 (2010).
    [CrossRef] [PubMed]
  6. Zemax Development Corporation, “ZEMAX User Manual,” (2008).

2011 (1)

2010 (1)

1998 (1)

1995 (1)

J. B. Cohen, “Narcissus of diffractive optical surfaces,” Proc. SPIE 2426, 380–385 (1995).
[CrossRef]

Arieli, Y.

Cohen, J. B.

J. B. Cohen, “Narcissus of diffractive optical surfaces,” Proc. SPIE 2426, 380–385 (1995).
[CrossRef]

Cui, Q.

Eisenberg, N.

Fei, B.

Liu, T.

Lloyd, J. M.

J. M. Lloyd, Thermal Imaging Systems (Plenum, 1975), pp. 275–281.

Noach, S.

Ozeri, S.

Xue, C.

Yang, L.

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Figures (4)

Fig. 1
Fig. 1

Structure of a two-layer diffractive lens. H 1 and H 2 are the surface relief heights of the first and second HDEs, respectively. The dashed and solid lines are the reflection by the first and second diffractive surfaces respectively.

Fig. 2
Fig. 2

8 12 μm IR optical system designed with a two-layer diffractive optical element.

Fig. 3
Fig. 3

Maximum comprehensive PIDE versus the first design wavelength when the second design wavelength changed in the 8 12 μm wave bands.

Fig. 4
Fig. 4

Diffraction efficiency of the m th diffracted order versus the 8 12 μm wavelength band for the two-layer diffractive lens: (a) and (b) illustrate the diffraction of the narcissus flux reflected by the first and second diffractive surfaces, respectively.

Tables (8)

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Table 1 First-Order Parameters for the 8 12 μm IR Optical System with MLDOE

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Table 2 Design Wavelengths Pair and Surface Relief Heights of the Two HDEs

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Table 3 Lens Data of the 8 12 μm IR Optical System with MLDOE: Surface Data Summary

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Table 4 Lens Data of the 8 12 μm IR Optical System with MLDOE: Phase Coefficients of Diffractive Surfaces in Zemax

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Table 5 Paraxial Narcissus Values and y, the Paraxial Marginal Ray Height for the First and Second Diffractive Surfaces

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Table 6 Converted Phase Coefficients of Diffractive Surfaces

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Table 7 Modified Narcissus Intensity Evaluation Values for the 32 th   to   22 th Diffraction Orders and the Corresponding Wavelength for the First Diffractive Surface

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Table 8 Modified Narcissus Intensity Evaluation Values for the 43 th   to   29 th Diffraction Orders and the Corresponding Wavelength for the Second Diffractive Surface

Equations (26)

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Φ = Φ 1 + Φ 2 = 2 m π ,
p 1 = H 1 [ n 1 ( λ 2 ) 1 ] λ and p 2 = H 2 [ n 2 ( λ 2 ) 1 ] λ ,
Φ R 1 ( λ ) = 2 λ 2 ( n 1 1 ) λ × 2 p 1 π and Φ R 2 ( λ ) = 2 n 2 λ 2 ( n 2 1 ) λ × 2 p 2 π ,
Φ T 2 ( λ ) = λ 2 λ × 2 p 2 π .
η 1 m = sinc 2 ( ( Φ R 1 ( λ ) + 2 × Φ T 2 ( λ ) ) / 2 π m ) = sinc 2 ( 2 p 1 λ 2 ( n 1 1 ) λ + 2 p 2 λ 2 λ m ) η 2 m = sinc 2 ( Φ R 2 ( λ ) / 2 π m ) = sinc 2 ( 2 n 2 p 2 λ 2 ( n 2 1 ) λ m ) .
y = 4 y n 2 i B f # 2 f # y m max λ max T ,
n 1 i F m λ max T = n 2 i B ,
y = 4 y n 1 i F f # + ( 2 m m max ) 2 f # y λ max T .
Φ = p 1 2 π λ 2 ( a 1 y 2 + a 2 y 4 + a 3 y 6 + ) + p 2 2 π λ 2 ( a 1 y 2 + a 2 y 4 + a 3 y 6 + ) = 2 m π λ 2 ( a 1 y 2 + a 2 y 4 + a 3 y 6 + ) ,
T = [ 1 2 m π d Φ d y ] 1 = [ 1 λ 2 ( 2 a 1 y + 4 a 2 y 3 + 6 a 3 y 5 + ) ] 1 .
y = 4 y n 1 i F f # 4 f # λ max λ 2 ( 2 m m max ) ( a 1 y 2 + 2 a 2 y 4 + 3 a 3 y 6 + ) .
y 4 f # = y n 1 i F + λ max λ 2 ( 2 m m max ) ( a 1 y 2 + 2 a 2 y 4 + 3 a 3 y 6 + ) .
y 4 f # = y n 1 i F + N D ,
N D = λ max λ 2 ( 2 m m max ) ( a 1 y 2 + 2 a 2 y 4 + 3 a 3 y 6 + ) .
H 1 = m λ 1 ( n 2 ( λ 2 ) 1 ) m λ 2 ( n 2 ( λ 1 ) 1 ) ( n 1 ( λ 1 ) 1 ) ( n 2 ( λ 2 ) 1 ) ( n 1 ( λ 2 ) 1 ) ( n 2 ( λ 1 ) 1 ) H 2 = m λ 1 ( n 1 ( λ 2 ) 1 ) m λ 2 ( n 1 ( λ 1 ) 1 ) ( n 1 ( λ 1 ) 1 ) ( n 2 ( λ 2 ) 1 ) ( n 1 ( λ 2 ) 1 ) ( n 2 ( λ 1 ) 1 ) .
φ ( λ ) = 2 π λ ( ( n 1 ( λ ) 1 ) H 1 + ( n 2 ( λ ) 1 ) H 2 ) .
η m int ( λ 1 , λ 2 ) = 1 λ max λ min λ min λ max sinc 2 ( m ϕ ( λ ) 2 π ) d λ ,
p 1 = 9.466 and p 2 = 8.466 .
2 × 11.11 ( 4.0035 1 ) λ max × 9.466 + 2 × 11.11 λ max × ( 8.466 ) m max = 0 ,
2 × 2.1843 × 11.11 ( 2.1843 1 ) λ max × ( 8.466 ) m max = 0 .
m max λ max = 258.1443 ,
m max λ max = 346.9548.
η 1 m max ( λ ) = sinc 2 ( 2 p 1 λ 2 ( n 1 1 ) λ + 2 p 2 λ 2 λ m max ) ,
η 2 m max ( λ ) = sinc 2 ( 2 n 2 p 2 λ 2 ( n 2 1 ) λ m max ) ,
{ a 1 = λ 2 2 π R Norm 2 A 1 a 2 = λ 2 2 π R Norm 4 A 2 a 3 = λ 2 2 π R Norm 6 A 4 .
N D = 2 m λ max λ 2 × ( a 1 y 2 + 2 a 2 y 4 + 3 a 3 y 6 + ) m max λ max λ 2 ( a 1 y 2 + 2 a 2 y 4 + 3 a 3 y 6 + ) .

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