Abstract

In infrared optical systems, the narcissus effect for diffractive surfaces should be calculated with specific diffraction orders based on the diffraction efficiency. It is shown in this work that the diffraction order of maximum diffraction efficiency varies with the change of the incident angle and wavelength of the backward-traced narcissus flux. Meanwhile, yni, which is the paraxial evaluation criterion of narcissus intensity for a refractive surface, is modified considering diffraction when a ray passes through diffractive surfaces, and a practical example has been given. The analysis can be used to calculate and control the narcissus intensity in infrared optical systems with diffractive surfaces.

© 2011 Optical Society of America

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References

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  1. J. W. Howard and I. R. Abel, “Narcissus: reflections on retroreflections in thermal imaging systems,” Appl. Opt. 21, 3393–3397 (1982).
    [CrossRef] [PubMed]
  2. J. M. Lloyd, Thermal Imaging Systems (Plenum, 1975), pp. 275–281.
  3. K. Lu and S. J. Dobson, “Accurate calculation of narcissus signatures by using finite ray tracing,” Appl. Opt. 36, 6393–6398 (1997).
    [CrossRef]
  4. J. L. Rayces and L. Lebich, “Exact ray tracing computation of narcissus equivalent temperature difference in scanning thermal imagers,” Proc. SPIE 1752, 325–332 (1992).
    [CrossRef]
  5. M. N. Akram, “Simulation and control of narcissus phenomenon using nonsequential ray tracing. I. Staring camera in 3–5 μm waveband,” Appl. Opt. 49, 964–975 (2010).
    [CrossRef] [PubMed]
  6. ZEMAX User Manual, Zemax Development Corporation, 3001 112th Avenue NE, Suite 202, Bellevue, Wash. 98004-8017, USA, 2008.
  7. J. B. Cohen, “Narcissus of diffractive optical surfaces,” Proc. SPIE 2426, 380–385 (1995).
    [CrossRef]
  8. G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multilevel diffractive optical elements,” Tech. Rep. 914, MIT Lincoln Laboratory, 1991.

2010 (1)

2008 (1)

ZEMAX User Manual, Zemax Development Corporation, 3001 112th Avenue NE, Suite 202, Bellevue, Wash. 98004-8017, USA, 2008.

1997 (1)

1995 (1)

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

1992 (1)

J. L. Rayces and L. Lebich, “Exact ray tracing computation of narcissus equivalent temperature difference in scanning thermal imagers,” Proc. SPIE 1752, 325–332 (1992).
[CrossRef]

1991 (1)

G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multilevel diffractive optical elements,” Tech. Rep. 914, MIT Lincoln Laboratory, 1991.

1982 (1)

1975 (1)

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

Abel, I. R.

Akram, M. N.

Cohen, J. B.

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

Dobson, S. J.

Howard, J. W.

Lebich, L.

J. L. Rayces and L. Lebich, “Exact ray tracing computation of narcissus equivalent temperature difference in scanning thermal imagers,” Proc. SPIE 1752, 325–332 (1992).
[CrossRef]

Lloyd, J. M.

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

Lu, K.

Rayces, J. L.

J. L. Rayces and L. Lebich, “Exact ray tracing computation of narcissus equivalent temperature difference in scanning thermal imagers,” Proc. SPIE 1752, 325–332 (1992).
[CrossRef]

Swanson, G. J.

G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multilevel diffractive optical elements,” Tech. Rep. 914, MIT Lincoln Laboratory, 1991.

Appl. Opt. (3)

Proc. SPIE (2)

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

J. L. Rayces and L. Lebich, “Exact ray tracing computation of narcissus equivalent temperature difference in scanning thermal imagers,” Proc. SPIE 1752, 325–332 (1992).
[CrossRef]

Other (3)

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

G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multilevel diffractive optical elements,” Tech. Rep. 914, MIT Lincoln Laboratory, 1991.

ZEMAX User Manual, Zemax Development Corporation, 3001 112th Avenue NE, Suite 202, Bellevue, Wash. 98004-8017, USA, 2008.

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Figures (7)

Fig. 1
Fig. 1

Reflection of backward-traced narcissus radiation for diffractive surfaces: (a) back diffractive surface and (b) front diffractive surface.

Fig. 2
Fig. 2

Rays reflected by two neighboring subperiods of N-level phase profiles: (a) the perpendicular foot point C below the optical surface and (b) the perpendicular foot point C above the optical surface (back diffractive surface).

Fig. 3
Fig. 3

Rays reflected by two neighboring subperiods of N-level phase profiles (front diffractive surface).

Fig. 4
Fig. 4

Narcissus effect for diffractive surfaces.

Fig. 5
Fig. 5

Reflection of diffractive surfaces as N-step blazed gratings.

Fig. 6
Fig. 6

Layout of an 8 12 μm IR system with a cooled detector.

Fig. 7
Fig. 7

Phase plot and the line frequency versus aperture for (a) the back diffractive surface and (b) the front diffractive surface.

Tables (8)

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Table 1 Efficiencies η m for Different Diffraction Orders at Various Incident Angles for a First-Order DOE on Ge

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Table 2 First-Order Parameters for the 8 12 μm IR Optical System

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

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Table 4 Lens Data of the 8 12 μm IR Optical System: Even Asphere Coefficients

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Table 5 Lens Data of the 8 12 μm IR Optical System: Phase Coefficients of Diffractive Surfaces in ZEMAX

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Table 6 Converted Phase Coefficients of Diffractive Surfaces

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Table 7 Diffraction Efficiencies η m for Different Diffraction Orders at the Back and Front Diffractive Surfaces of the Two ZnSe Lenses

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Table 8 Paraxial Narcissus Values and Modified Narcissus Values of the IR Optical System

Equations (44)

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ϕ s = 1 λ 0 ( n l 1 n l 2 ) ,
A C = A B sin A B C = A B sin i chief ,
A F l 1 = ( δ y + A E ) sin i chief ,
A F = E F cos A F E = δ z cos i chief ,
A E = E F tan A F E = δ z tan i chief ,
l 1 = δ z cos i chief sin i chief ( δ y + δ z tan i chief ) .
D G = F G sin D F G = F G sin ( i chief ) .
l 2 B G = ( δ y G H ) sin ( i chief ) .
B G = δ z cos G B H = δ z cos ( i chief ) = δ z cos i chief ,
G H = δ z tan G B H = δ z tan ( i chief ) .
l 2 = δ z cos i chief sin i chief ( δ y + δ z tan i chief ) .
ϕ s = 2 n δ z cos i chief λ 0 .
ϕ 0 = N ϕ s = 2 N n δ z cos i chief λ 0 ,
ϕ 0 = 2 n cos i chief n 0 1 m ,
ϕ 0 = 2 n 0 cos i chief n 0 1 m .
ϕ 0 = { 2 cos i chief n 0 1 m for back diffractive surfaces 2 n 0 cos i chief n 0 1 m for front diffractive surfaces ,
m max = { 2 n 0 1 m for back diffractive surfaces 2 n 0 n 0 1 m for front diffractive surfaces .
η m = sinc 2 [ m ϕ 0 ] .
ϕ λ = N ϕ s ( λ ) = 2 N n λ δ z cos i chief λ ,
ϕ λ = 2 λ 0 cos i chief ( n 0 1 ) λ m .
ϕ λ = 2 n λ λ 0 cos i chief ( n 0 1 ) λ m ,
m ϕ λ = { 2 λ 0 cos i chief ( n 0 1 ) λ m for back diffractive surfaces 2 n λ λ 0 cos i chief ( n 0 1 ) λ m for front diffractive surfaces .
m ϕ 0 = { 2 n 0 1 m for back diffractive surfaces 2 n 0 n 0 1 m for front diffractive surfaces .
sin θ = m max λ 0 n B T sin i B ,
I = y d n B u B y n B u d ,
I = y n B [ i B θ ] ,
θ = m max λ 0 n B T i B .
I = 2 y n B i B + y m max λ 0 T .
I = y n u = y 2 f # ,
y = 4 y n B i B f # 2 f # y m max λ 0 T .
n F sin i F = n B sin i B ,
n F sin i F m λ 0 T = n B sin i B ,
n F i F m λ 0 T = n B i B .
y = 4 y n F i F f # + 2 f # y λ 0 T ( 2 m m max ) .
Φ = 2 π λ 0 ( a 1 y 2 + a 2 y 4 + a 3 y 6 + ) ,
T = ( 1 2 m π d Φ d y ) 1 = [ 1 m λ 0 ( 2 a 1 y + 4 a 2 y 3 + 6 a 3 y 5 + ) ] 1 .
y = 4 y n F i F f # 4 f # ( 2 m max m ) ( a 1 y 2 + 2 a 2 y 4 + 3 a 3 y 6 + ) .
y 4 f # = y n F i F + ( 2 m max m ) ( a 1 y 2 + 2 a 2 y 4 + 3 a 3 y 6 + ) .
y 4 f # = y n F i F + N D ,
N D = ( 2 m max m ) ( a 1 y 2 + 2 a 2 y 4 + 3 a 3 y 6 + ) .
z = c y 2 1 + 1 ( 1 + k ) c 2 y 2 + α 1 y 2 + α 2 y 4 + α 3 y 6 + ,
Φ = A 1 ρ 2 + A 2 ρ 4 + A 3 ρ 6 + ,
ρ = y R Norm ,
{ a 1 = λ 0 2 π R Norm 2 A 1 a 2 = λ 0 2 π R Norm 4 A 2 a 3 = λ 0 2 π R Norm 6 A 4 .

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