Abstract

Single-layer diffractive optical elements (SLDOEs) have advantages in terms of configuration, fabrication, range of angles and cost; however, the diffraction efficiency decreases sharply with wavelength deviating from the design wavelength, especially for dual-waveband imaging, causing apparent image blur. We propose a point spread function (PSF) model affected by the diffraction efficiency, which is called PSFDOE, and a method of restoring the blurred image to improve imaging performance in dual-waveband infrared systems with an SLDOE. Then, a design example of cooled MWIR and LWIR is presented. Furthermore, imaging simulations with different grades noises and restorations are conducted. Results reveal that the PSFDOE model can significantly improve the image blur caused by the decreased diffraction efficiency.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. G. J. Swanson, “Binary optics technology: the theory and design of multilevel diffractive optical elements,” MIT Lincoln Laboratory Rep. 854 (MIT, Cambridge, Mass, 1989).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  4. D. Elkind, Z. Zalevsky, U. Levy, and D. Mendlovic, “Optical transfer function shaping and depth of focus by using a phase only filter,” Appl. Opt. 42(11), 1925–1931 (2003).
    [Crossref] [PubMed]
  5. D. W. Sweeney and G. E. Sommargren, “Harmonic diffractive lenses,” Appl. Opt. 34(14), 2469–2475 (1995).
    [Crossref] [PubMed]
  6. A. Wood, M.-S. L. Lee, and S. Cassette, “Infrared hybrid optics with high broadband efficiency,” Proc. SPIE 5874, 58740G (2005).
    [Crossref]
  7. 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(24), 4157–4159 (2010).
    [Crossref] [PubMed]
  8. Y. Peng, Q. Fu, H. Amata, S. Su, F. Heide, and W. Heidrich, “Computational imaging using lightweight diffractive-refractive optics,” Opt. Express 23(24), 31393–31407 (2015).
    [Crossref] [PubMed]
  9. Y. Peng, Q. Fu, F. Heide, and W. Heidrich, “The diffractive achromat full spectrum computational imaging with diffractive optics,” ACM Trans. Graph. 35(4), 31 (2016).
    [Crossref]
  10. M. J. Riedl, Optical Design Fundamentals For Infrared Systems (SPIE, 2001).
  11. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Pearson Education, 2008).
  12. D. C. O. Shea, T. J. Suleski, and A. D. Kathman, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).
  13. I. A. Nei, Strathblane, Scotland, “Infrared Objective Lens Systems,” U.S. Patent 4,505,535,(1985).
  14. D. Fish, A. Brinicombe, E. Pike, and J. Walker, “Blind deconvolution by means of the Richardson–Lucy algorithm,” J. Opt. Soc. Am. A 12(1), 58–65 (1995).
    [Crossref]
  15. Y. Zeng, J. Lan, B. Ran, Q. Wang, and J. Gao, “Restoration of motion-blurred image based on border deformation detection: a traffic sign restoration model,” PLoS One 10(4), e0120885 (2015).
    [Crossref] [PubMed]
  16. A. K. Moorthy and A. C. Bovik, “A two-step framework for constructing blind image quality indices,” IEEE Signal Process. Lett. 17(5), 513–516 (2010).
    [Crossref]

2016 (1)

Y. Peng, Q. Fu, F. Heide, and W. Heidrich, “The diffractive achromat full spectrum computational imaging with diffractive optics,” ACM Trans. Graph. 35(4), 31 (2016).
[Crossref]

2015 (2)

Y. Zeng, J. Lan, B. Ran, Q. Wang, and J. Gao, “Restoration of motion-blurred image based on border deformation detection: a traffic sign restoration model,” PLoS One 10(4), e0120885 (2015).
[Crossref] [PubMed]

Y. Peng, Q. Fu, H. Amata, S. Su, F. Heide, and W. Heidrich, “Computational imaging using lightweight diffractive-refractive optics,” Opt. Express 23(24), 31393–31407 (2015).
[Crossref] [PubMed]

2010 (2)

A. K. Moorthy and A. C. Bovik, “A two-step framework for constructing blind image quality indices,” IEEE Signal Process. Lett. 17(5), 513–516 (2010).
[Crossref]

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(24), 4157–4159 (2010).
[Crossref] [PubMed]

2005 (1)

A. Wood, M.-S. L. Lee, and S. Cassette, “Infrared hybrid optics with high broadband efficiency,” Proc. SPIE 5874, 58740G (2005).
[Crossref]

2003 (1)

1996 (1)

1995 (2)

1993 (1)

Amata, H.

Bovik, A. C.

A. K. Moorthy and A. C. Bovik, “A two-step framework for constructing blind image quality indices,” IEEE Signal Process. Lett. 17(5), 513–516 (2010).
[Crossref]

Brinicombe, A.

Cassette, S.

A. Wood, M.-S. L. Lee, and S. Cassette, “Infrared hybrid optics with high broadband efficiency,” Proc. SPIE 5874, 58740G (2005).
[Crossref]

Cui, Q.

Davidson, N.

Elkind, D.

Fei, B.

Fish, D.

Friesem, A. A.

Fu, Q.

Y. Peng, Q. Fu, F. Heide, and W. Heidrich, “The diffractive achromat full spectrum computational imaging with diffractive optics,” ACM Trans. Graph. 35(4), 31 (2016).
[Crossref]

Y. Peng, Q. Fu, H. Amata, S. Su, F. Heide, and W. Heidrich, “Computational imaging using lightweight diffractive-refractive optics,” Opt. Express 23(24), 31393–31407 (2015).
[Crossref] [PubMed]

Gao, J.

Y. Zeng, J. Lan, B. Ran, Q. Wang, and J. Gao, “Restoration of motion-blurred image based on border deformation detection: a traffic sign restoration model,” PLoS One 10(4), e0120885 (2015).
[Crossref] [PubMed]

Hasman, E.

Heide, F.

Y. Peng, Q. Fu, F. Heide, and W. Heidrich, “The diffractive achromat full spectrum computational imaging with diffractive optics,” ACM Trans. Graph. 35(4), 31 (2016).
[Crossref]

Y. Peng, Q. Fu, H. Amata, S. Su, F. Heide, and W. Heidrich, “Computational imaging using lightweight diffractive-refractive optics,” Opt. Express 23(24), 31393–31407 (2015).
[Crossref] [PubMed]

Heidrich, W.

Y. Peng, Q. Fu, F. Heide, and W. Heidrich, “The diffractive achromat full spectrum computational imaging with diffractive optics,” ACM Trans. Graph. 35(4), 31 (2016).
[Crossref]

Y. Peng, Q. Fu, H. Amata, S. Su, F. Heide, and W. Heidrich, “Computational imaging using lightweight diffractive-refractive optics,” Opt. Express 23(24), 31393–31407 (2015).
[Crossref] [PubMed]

Lan, J.

Y. Zeng, J. Lan, B. Ran, Q. Wang, and J. Gao, “Restoration of motion-blurred image based on border deformation detection: a traffic sign restoration model,” PLoS One 10(4), e0120885 (2015).
[Crossref] [PubMed]

Lee, M.-S. L.

A. Wood, M.-S. L. Lee, and S. Cassette, “Infrared hybrid optics with high broadband efficiency,” Proc. SPIE 5874, 58740G (2005).
[Crossref]

Levy, U.

Liu, T.

Mendlovic, D.

Moorthy, A. K.

A. K. Moorthy and A. C. Bovik, “A two-step framework for constructing blind image quality indices,” IEEE Signal Process. Lett. 17(5), 513–516 (2010).
[Crossref]

Peng, Y.

Y. Peng, Q. Fu, F. Heide, and W. Heidrich, “The diffractive achromat full spectrum computational imaging with diffractive optics,” ACM Trans. Graph. 35(4), 31 (2016).
[Crossref]

Y. Peng, Q. Fu, H. Amata, S. Su, F. Heide, and W. Heidrich, “Computational imaging using lightweight diffractive-refractive optics,” Opt. Express 23(24), 31393–31407 (2015).
[Crossref] [PubMed]

Pike, E.

Ran, B.

Y. Zeng, J. Lan, B. Ran, Q. Wang, and J. Gao, “Restoration of motion-blurred image based on border deformation detection: a traffic sign restoration model,” PLoS One 10(4), e0120885 (2015).
[Crossref] [PubMed]

Riedl, M. J.

Sommargren, G. E.

Su, S.

Sweeney, D. W.

Walker, J.

Wang, Q.

Y. Zeng, J. Lan, B. Ran, Q. Wang, and J. Gao, “Restoration of motion-blurred image based on border deformation detection: a traffic sign restoration model,” PLoS One 10(4), e0120885 (2015).
[Crossref] [PubMed]

Wood, A.

A. Wood, M.-S. L. Lee, and S. Cassette, “Infrared hybrid optics with high broadband efficiency,” Proc. SPIE 5874, 58740G (2005).
[Crossref]

Xue, C.

Yang, L.

Zalevsky, Z.

Zeng, Y.

Y. Zeng, J. Lan, B. Ran, Q. Wang, and J. Gao, “Restoration of motion-blurred image based on border deformation detection: a traffic sign restoration model,” PLoS One 10(4), e0120885 (2015).
[Crossref] [PubMed]

ACM Trans. Graph. (1)

Y. Peng, Q. Fu, F. Heide, and W. Heidrich, “The diffractive achromat full spectrum computational imaging with diffractive optics,” ACM Trans. Graph. 35(4), 31 (2016).
[Crossref]

Appl. Opt. (4)

IEEE Signal Process. Lett. (1)

A. K. Moorthy and A. C. Bovik, “A two-step framework for constructing blind image quality indices,” IEEE Signal Process. Lett. 17(5), 513–516 (2010).
[Crossref]

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

Opt. Express (1)

Opt. Lett. (1)

PLoS One (1)

Y. Zeng, J. Lan, B. Ran, Q. Wang, and J. Gao, “Restoration of motion-blurred image based on border deformation detection: a traffic sign restoration model,” PLoS One 10(4), e0120885 (2015).
[Crossref] [PubMed]

Proc. SPIE (1)

A. Wood, M.-S. L. Lee, and S. Cassette, “Infrared hybrid optics with high broadband efficiency,” Proc. SPIE 5874, 58740G (2005).
[Crossref]

Other (5)

M. J. Riedl, Optical Design Fundamentals For Infrared Systems (SPIE, 2001).

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Pearson Education, 2008).

D. C. O. Shea, T. J. Suleski, and A. D. Kathman, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

I. A. Nei, Strathblane, Scotland, “Infrared Objective Lens Systems,” U.S. Patent 4,505,535,(1985).

G. J. Swanson, “Binary optics technology: the theory and design of multilevel diffractive optical elements,” MIT Lincoln Laboratory Rep. 854 (MIT, Cambridge, Mass, 1989).

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Figures (9)

Fig. 1
Fig. 1 Overview of the imaging system. We design a dual-waveband infrared optical system with an SLDOE. The design wavelength of the SLDOE is in the medium waveband. The image of medium waveband is clear and the image of long waveband is blurred on the dual-waveband sensor. The PS F DOE model is estimated to restore the blurred image.
Fig. 2
Fig. 2 A DOE (a) and a refraction diffraction hybrid system (b) diffract light deviating from the design wavelength into multiple orders, resulting in the image blur.
Fig. 3
Fig. 3 Three steps of the PS F DOE model construction. The energy distribution of a specific order of a feature wavelength is initially determined. Subsequently, the energy distribution of all the orders of a feature wavelength is determined. The third step is to select the feature wavelengths and repeat the first and second steps. The results are accumulated and normalized to construct the PS F DOE model.
Fig. 4
Fig. 4 Influence of the stop in different locations. The stop is in the optical system (a) as well as at the back end of the optical system (b).
Fig. 5
Fig. 5 Optical design of the proposed system. The design with an SLDOE integrates MWIR and LWIR that are superimposed on the same sensor.
Fig. 6
Fig. 6 MTFs of MWIR (a) and LWIR (b).
Fig. 7
Fig. 7 The diffraction efficiencies of the proposed system in MWIR (a) and LWIR (b).
Fig. 8
Fig. 8 The PS F DOE model (a) and the partial enlargement of the PS F DOE model (b).
Fig. 9
Fig. 9 Scene 1: (a), (b), (c). Scene 2: (d), (e), (f). Images affected by no noise (a), (d), Gaussian noise with variance of 0.001 (b), (e) and 0.003 (c), (f). Images (a-1), (b-1), (c-1), (d-1), (e-1), (f-1) are the blurred images caused by low diffraction efficiency. Images (a-2), (b-2), (c-2), (d-2), (e-2), (f-2) are the restored images by the PS F DOE model. The areas with red cycles show partial enlargements.

Tables (4)

Tables Icon

Table 1 Basic requirements for the design example.

Tables Icon

Table 2 Parameters of the PS F DOE model.

Tables Icon

Table 3 Quality assessment of the Scene 1.

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Table 4 Quality assessment of the Scene 2.

Equations (17)

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

g(x,y)=f(x,y)h(x,y)+n(x,y).
PSF(λ)= m P(λ,m) .
PS F DOE = λ ω λ PSF(λ) λ m η m (λ) .
η m (λ)= [sinc(m λ 0 λ n λ 1 n λ 0 1 )] 2 ,
φ(r)=2π/λ( A 1 r 2 + A 2 r 4 + A 3 r 6 + A 4 r 8 ),
f DOE = λ 0 2 A 1 mλ .
r(λ,m)= | l l 0 |× R DOE l .
r(λ,m)= | l l 0 |× R stop l l 1 .
R(λ,m)= R stop ×l l l 1 .
ω R = R (λ,m) 2 R DOE 2 .
N= [ r(λ,m) S ] R ,
F(λ,m)= ω R × η m (λ) π N 2 .
P(λ,m)=[ 0 0 F(λ,m) 0 0 0 0 F(λ,m) F(λ,m) F(λ,m) 0 0 0 0 F(λ,m) 0 0 ].
P(λ,1)=[ 0 F(λ,1) 0 ].
N+1= [ r(λ+ λ d ,m) S ] R ,
M(T,λ)= c 1 λ 5 1 e c 2 /λT 1 ,
ω λ = M(T,λ) λ min λ max M(T,λ)dλ .

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