Abstract

Oblique incidence is the normal working mode for diffractive optical elements (DOEs). The diffraction efficiency is very sensitive to the angle of incidence for multilayer diffractive optical elements (MLDOEs). Therefore, the design and diffraction efficiency analysis of MLDOEs with wide angles of incidence is of universal significance and practice. We propose an integral diffraction efficiency model for MLDOEs with wide angles of incidence in case of polychromatic light and then describe this corresponding optimal design in detail. It is shown that high diffraction efficiency can be realized by the surface micro-structure heights optimization, ensuring high modulation transfer function (MTF) for MLDOEs with wide angles of incidence in hybrid optical systems. On this basis, we present the optimal design process and simulation of an MLDOE working in visible waveband with optical plastic materials combination PMMA and POLYCARB as the two-layer substrates. The result shows that with this optimal design, we can achieve the maximum diffraction efficiency and minimum micro-structure heights, which makes the MLDOE design exactly over the entire waveband and wide angles of incidence especially for zoom hybrid optical system.

© 2019 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, “The theory and design of multi-level diffractive optical elements,” MIT Lincoln Laboratory technical report (1989).
  2. B. Sabushimike, G. Horugavye, and S. Habraken, “Optimization of a multiblaze grating in reflection using a free-form profile,” Appl. Opt. 57(18), 5048–5056 (2018).
    [Crossref] [PubMed]
  3. O. Barlev and M. A. Golub, “Multifunctional binary diffractive optical elements for structured light projectors,” Opt. Express 26(16), 21092–21107 (2018).
    [Crossref] [PubMed]
  4. C. Wu, H. Gu, Z. Zhou, and Q. Tan, “Design of diffractive optical elements for subdiffraction spot arrays with high light efficiency,” Appl. Opt. 56(31), 8816–8821 (2017).
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  5. C. Bigwood and A. Wood, “Two-element lenses for military applications,” Opt. Eng. 50(12), 121705 (2011).
    [Crossref]
  6. D. A. Buralli and G. M. Morris, “Effects of diffraction efficiency on the modulation transfer function of diffractive lenses,” Appl. Opt. 31(22), 4389–4396 (1992).
    [Crossref] [PubMed]
  7. C. Xue and Q. Cui, “Design of multilayer diffractive optical elements with polychromatic integral diffraction efficiency,” Opt. Lett. 35(7), 986–988 (2010).
    [Crossref] [PubMed]
  8. H. Yang, C. Xue, C. Li, J. Wang, and R. Zhang, “Optimal design of multilayer diffractive optical elements with effective area method,” Appl. Opt. 55(25), 7126–7133 (2018).
    [Crossref] [PubMed]
  9. Y. Hu, Q. Cui, L. Zhao, and M. Piao, “PSF model for diffractive optical elements with improved imaging performance in dual-waveband infrared systems,” Opt. Express 26(21), 26845–26857 (2018).
    [Crossref] [PubMed]
  10. Y. H. Zhao, C. J. Fan, C. F. Ying, and S. H. Liu, “The investigation of triple-layer diffraction optical element with wide field of view and high diffraction efficiency,” Opt. Commun. 295, 104–107 (2013).
    [Crossref]
  11. S. Mao, Q. Cui, M. Piao, and L. Zhao, “High diffraction efficiency of three-layer diffractive optics designed for wide temperature range and large incident angle,” Appl. Opt. 55(13), 3549–3554 (2016).
    [Crossref] [PubMed]
  12. C. Fan, “The investigation of large field of view eyepiece with multilayer diffractive optical element,” Proc. SPIE 9272, 92720N (2014).
    [Crossref]
  13. Y. Zhao, C. Fan, C. Ying, and H. Wang, “The investigation of three layers diffraction optical element with wide field of view and high diffraction efficiency,” Optik (Stuttg.) 124(20), 4142–4144 (2013).
    [Crossref]
  14. H. Xie, D. Ren, C. Wang, C. Mao, and L. Yang, “Design of high-efficiency diffractive optical elements towards ultrafast mid-infrared time stretched imaging and spectroscopy,” J. Mod. Opt. 65(3), 255–261 (2018).
    [Crossref]
  15. B. Zhang, Q. Cui, and M. Piao, “Effect of substrate material selection on polychromatic integral diffraction efficiency for multi-layer diffractive optics in oblique incident situation,” Opt. Commun. 415(15), 156–163 (2018).
    [Crossref]
  16. F. Huo, W. Wang, and C. Xue, “Limits of scalar diffraction theory for multilayer diffractive optical elements,” Optik (Stuttg.) 127(14), 5688–5694 (2016).
    [Crossref]
  17. G. I. Greĭsukh, E. G. Ezhov, S. A. Stepanov, V. A. Danilov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of diffraction lenses with a dual-relief and two-layer microstructure,” J. Opt. Technol. 82(5), 308–311 (2015).
    [Crossref]
  18. G. I. Greisukh, V. A. Danilov, E. G. Ezhov, S. A. Stepanov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of relief-phase Diffractive Lenses with Two- and Three-Layer Microstructures,” Opt. Spectrosc. 118(6), 964–970 (2015).
    [Crossref]
  19. G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Spectral and Angular Dependences of the Efficiency of Three-Layer Relief-Phase Diffraction Elements of the IR Range,” Opt. Spectrosc. 125(1), 60–64 (2018).
    [Crossref]
  20. D. C. O. Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics Design, Fabrication, and Test (SPIE, 2004).
  21. G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Minimization of the Total Depth of Internal Saw-Tooth Reliefs of a Two-Layer Relief-Phase Diffraction Microstructure,” Opt. Spectrosc. 124(1), 98–102 (2018).
    [Crossref]
  22. A. P. Wood and P. J. Rogers, “Diffractive optics in modern optical engineering,” Proc. SPIE 5865, 58650B (2005).
    [Crossref]
  23. Y. Arieli, S. Ozeri, N. Eisenberg, and S. Noach, “Design of a diffractive optical element for wide spectral bandwidth,” Opt. Lett. 23(11), 823–824 (1998).
    [Crossref] [PubMed]

2018 (8)

B. Sabushimike, G. Horugavye, and S. Habraken, “Optimization of a multiblaze grating in reflection using a free-form profile,” Appl. Opt. 57(18), 5048–5056 (2018).
[Crossref] [PubMed]

O. Barlev and M. A. Golub, “Multifunctional binary diffractive optical elements for structured light projectors,” Opt. Express 26(16), 21092–21107 (2018).
[Crossref] [PubMed]

H. Yang, C. Xue, C. Li, J. Wang, and R. Zhang, “Optimal design of multilayer diffractive optical elements with effective area method,” Appl. Opt. 55(25), 7126–7133 (2018).
[Crossref] [PubMed]

Y. Hu, Q. Cui, L. Zhao, and M. Piao, “PSF model for diffractive optical elements with improved imaging performance in dual-waveband infrared systems,” Opt. Express 26(21), 26845–26857 (2018).
[Crossref] [PubMed]

H. Xie, D. Ren, C. Wang, C. Mao, and L. Yang, “Design of high-efficiency diffractive optical elements towards ultrafast mid-infrared time stretched imaging and spectroscopy,” J. Mod. Opt. 65(3), 255–261 (2018).
[Crossref]

B. Zhang, Q. Cui, and M. Piao, “Effect of substrate material selection on polychromatic integral diffraction efficiency for multi-layer diffractive optics in oblique incident situation,” Opt. Commun. 415(15), 156–163 (2018).
[Crossref]

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Spectral and Angular Dependences of the Efficiency of Three-Layer Relief-Phase Diffraction Elements of the IR Range,” Opt. Spectrosc. 125(1), 60–64 (2018).
[Crossref]

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Minimization of the Total Depth of Internal Saw-Tooth Reliefs of a Two-Layer Relief-Phase Diffraction Microstructure,” Opt. Spectrosc. 124(1), 98–102 (2018).
[Crossref]

2017 (1)

2016 (2)

S. Mao, Q. Cui, M. Piao, and L. Zhao, “High diffraction efficiency of three-layer diffractive optics designed for wide temperature range and large incident angle,” Appl. Opt. 55(13), 3549–3554 (2016).
[Crossref] [PubMed]

F. Huo, W. Wang, and C. Xue, “Limits of scalar diffraction theory for multilayer diffractive optical elements,” Optik (Stuttg.) 127(14), 5688–5694 (2016).
[Crossref]

2015 (2)

G. I. Greĭsukh, E. G. Ezhov, S. A. Stepanov, V. A. Danilov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of diffraction lenses with a dual-relief and two-layer microstructure,” J. Opt. Technol. 82(5), 308–311 (2015).
[Crossref]

G. I. Greisukh, V. A. Danilov, E. G. Ezhov, S. A. Stepanov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of relief-phase Diffractive Lenses with Two- and Three-Layer Microstructures,” Opt. Spectrosc. 118(6), 964–970 (2015).
[Crossref]

2014 (1)

C. Fan, “The investigation of large field of view eyepiece with multilayer diffractive optical element,” Proc. SPIE 9272, 92720N (2014).
[Crossref]

2013 (2)

Y. Zhao, C. Fan, C. Ying, and H. Wang, “The investigation of three layers diffraction optical element with wide field of view and high diffraction efficiency,” Optik (Stuttg.) 124(20), 4142–4144 (2013).
[Crossref]

Y. H. Zhao, C. J. Fan, C. F. Ying, and S. H. Liu, “The investigation of triple-layer diffraction optical element with wide field of view and high diffraction efficiency,” Opt. Commun. 295, 104–107 (2013).
[Crossref]

2011 (1)

C. Bigwood and A. Wood, “Two-element lenses for military applications,” Opt. Eng. 50(12), 121705 (2011).
[Crossref]

2010 (1)

2005 (1)

A. P. Wood and P. J. Rogers, “Diffractive optics in modern optical engineering,” Proc. SPIE 5865, 58650B (2005).
[Crossref]

1998 (1)

1992 (1)

Antonov, A. I.

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Minimization of the Total Depth of Internal Saw-Tooth Reliefs of a Two-Layer Relief-Phase Diffraction Microstructure,” Opt. Spectrosc. 124(1), 98–102 (2018).
[Crossref]

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Spectral and Angular Dependences of the Efficiency of Three-Layer Relief-Phase Diffraction Elements of the IR Range,” Opt. Spectrosc. 125(1), 60–64 (2018).
[Crossref]

Arieli, Y.

Barlev, O.

Bigwood, C.

C. Bigwood and A. Wood, “Two-element lenses for military applications,” Opt. Eng. 50(12), 121705 (2011).
[Crossref]

Buralli, D. A.

Cui, Q.

Danilov, V. A.

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Minimization of the Total Depth of Internal Saw-Tooth Reliefs of a Two-Layer Relief-Phase Diffraction Microstructure,” Opt. Spectrosc. 124(1), 98–102 (2018).
[Crossref]

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Spectral and Angular Dependences of the Efficiency of Three-Layer Relief-Phase Diffraction Elements of the IR Range,” Opt. Spectrosc. 125(1), 60–64 (2018).
[Crossref]

G. I. Greĭsukh, E. G. Ezhov, S. A. Stepanov, V. A. Danilov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of diffraction lenses with a dual-relief and two-layer microstructure,” J. Opt. Technol. 82(5), 308–311 (2015).
[Crossref]

G. I. Greisukh, V. A. Danilov, E. G. Ezhov, S. A. Stepanov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of relief-phase Diffractive Lenses with Two- and Three-Layer Microstructures,” Opt. Spectrosc. 118(6), 964–970 (2015).
[Crossref]

Eisenberg, N.

Ezhov, E. G.

G. I. Greisukh, V. A. Danilov, E. G. Ezhov, S. A. Stepanov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of relief-phase Diffractive Lenses with Two- and Three-Layer Microstructures,” Opt. Spectrosc. 118(6), 964–970 (2015).
[Crossref]

G. I. Greĭsukh, E. G. Ezhov, S. A. Stepanov, V. A. Danilov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of diffraction lenses with a dual-relief and two-layer microstructure,” J. Opt. Technol. 82(5), 308–311 (2015).
[Crossref]

Fan, C.

C. Fan, “The investigation of large field of view eyepiece with multilayer diffractive optical element,” Proc. SPIE 9272, 92720N (2014).
[Crossref]

Y. Zhao, C. Fan, C. Ying, and H. Wang, “The investigation of three layers diffraction optical element with wide field of view and high diffraction efficiency,” Optik (Stuttg.) 124(20), 4142–4144 (2013).
[Crossref]

Fan, C. J.

Y. H. Zhao, C. J. Fan, C. F. Ying, and S. H. Liu, “The investigation of triple-layer diffraction optical element with wide field of view and high diffraction efficiency,” Opt. Commun. 295, 104–107 (2013).
[Crossref]

Golub, M. A.

Greisukh, G. I.

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Spectral and Angular Dependences of the Efficiency of Three-Layer Relief-Phase Diffraction Elements of the IR Range,” Opt. Spectrosc. 125(1), 60–64 (2018).
[Crossref]

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Minimization of the Total Depth of Internal Saw-Tooth Reliefs of a Two-Layer Relief-Phase Diffraction Microstructure,” Opt. Spectrosc. 124(1), 98–102 (2018).
[Crossref]

G. I. Greisukh, V. A. Danilov, E. G. Ezhov, S. A. Stepanov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of relief-phase Diffractive Lenses with Two- and Three-Layer Microstructures,” Opt. Spectrosc. 118(6), 964–970 (2015).
[Crossref]

G. I. Greĭsukh, E. G. Ezhov, S. A. Stepanov, V. A. Danilov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of diffraction lenses with a dual-relief and two-layer microstructure,” J. Opt. Technol. 82(5), 308–311 (2015).
[Crossref]

Gu, H.

Habraken, S.

Horugavye, G.

Hu, Y.

Huo, F.

F. Huo, W. Wang, and C. Xue, “Limits of scalar diffraction theory for multilayer diffractive optical elements,” Optik (Stuttg.) 127(14), 5688–5694 (2016).
[Crossref]

Li, C.

Liu, S. H.

Y. H. Zhao, C. J. Fan, C. F. Ying, and S. H. Liu, “The investigation of triple-layer diffraction optical element with wide field of view and high diffraction efficiency,” Opt. Commun. 295, 104–107 (2013).
[Crossref]

Mao, C.

H. Xie, D. Ren, C. Wang, C. Mao, and L. Yang, “Design of high-efficiency diffractive optical elements towards ultrafast mid-infrared time stretched imaging and spectroscopy,” J. Mod. Opt. 65(3), 255–261 (2018).
[Crossref]

Mao, S.

Morris, G. M.

Noach, S.

Ozeri, S.

Piao, M.

Ren, D.

H. Xie, D. Ren, C. Wang, C. Mao, and L. Yang, “Design of high-efficiency diffractive optical elements towards ultrafast mid-infrared time stretched imaging and spectroscopy,” J. Mod. Opt. 65(3), 255–261 (2018).
[Crossref]

Rogers, P. J.

A. P. Wood and P. J. Rogers, “Diffractive optics in modern optical engineering,” Proc. SPIE 5865, 58650B (2005).
[Crossref]

Sabushimike, B.

Stepanov, S. A.

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Spectral and Angular Dependences of the Efficiency of Three-Layer Relief-Phase Diffraction Elements of the IR Range,” Opt. Spectrosc. 125(1), 60–64 (2018).
[Crossref]

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Minimization of the Total Depth of Internal Saw-Tooth Reliefs of a Two-Layer Relief-Phase Diffraction Microstructure,” Opt. Spectrosc. 124(1), 98–102 (2018).
[Crossref]

G. I. Greisukh, V. A. Danilov, E. G. Ezhov, S. A. Stepanov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of relief-phase Diffractive Lenses with Two- and Three-Layer Microstructures,” Opt. Spectrosc. 118(6), 964–970 (2015).
[Crossref]

G. I. Greĭsukh, E. G. Ezhov, S. A. Stepanov, V. A. Danilov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of diffraction lenses with a dual-relief and two-layer microstructure,” J. Opt. Technol. 82(5), 308–311 (2015).
[Crossref]

Tan, Q.

Usievich, B. A.

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Spectral and Angular Dependences of the Efficiency of Three-Layer Relief-Phase Diffraction Elements of the IR Range,” Opt. Spectrosc. 125(1), 60–64 (2018).
[Crossref]

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Minimization of the Total Depth of Internal Saw-Tooth Reliefs of a Two-Layer Relief-Phase Diffraction Microstructure,” Opt. Spectrosc. 124(1), 98–102 (2018).
[Crossref]

G. I. Greĭsukh, E. G. Ezhov, S. A. Stepanov, V. A. Danilov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of diffraction lenses with a dual-relief and two-layer microstructure,” J. Opt. Technol. 82(5), 308–311 (2015).
[Crossref]

G. I. Greisukh, V. A. Danilov, E. G. Ezhov, S. A. Stepanov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of relief-phase Diffractive Lenses with Two- and Three-Layer Microstructures,” Opt. Spectrosc. 118(6), 964–970 (2015).
[Crossref]

Wang, C.

H. Xie, D. Ren, C. Wang, C. Mao, and L. Yang, “Design of high-efficiency diffractive optical elements towards ultrafast mid-infrared time stretched imaging and spectroscopy,” J. Mod. Opt. 65(3), 255–261 (2018).
[Crossref]

Wang, H.

Y. Zhao, C. Fan, C. Ying, and H. Wang, “The investigation of three layers diffraction optical element with wide field of view and high diffraction efficiency,” Optik (Stuttg.) 124(20), 4142–4144 (2013).
[Crossref]

Wang, J.

Wang, W.

F. Huo, W. Wang, and C. Xue, “Limits of scalar diffraction theory for multilayer diffractive optical elements,” Optik (Stuttg.) 127(14), 5688–5694 (2016).
[Crossref]

Wood, A.

C. Bigwood and A. Wood, “Two-element lenses for military applications,” Opt. Eng. 50(12), 121705 (2011).
[Crossref]

Wood, A. P.

A. P. Wood and P. J. Rogers, “Diffractive optics in modern optical engineering,” Proc. SPIE 5865, 58650B (2005).
[Crossref]

Wu, C.

Xie, H.

H. Xie, D. Ren, C. Wang, C. Mao, and L. Yang, “Design of high-efficiency diffractive optical elements towards ultrafast mid-infrared time stretched imaging and spectroscopy,” J. Mod. Opt. 65(3), 255–261 (2018).
[Crossref]

Xue, C.

Yang, H.

Yang, L.

H. Xie, D. Ren, C. Wang, C. Mao, and L. Yang, “Design of high-efficiency diffractive optical elements towards ultrafast mid-infrared time stretched imaging and spectroscopy,” J. Mod. Opt. 65(3), 255–261 (2018).
[Crossref]

Ying, C.

Y. Zhao, C. Fan, C. Ying, and H. Wang, “The investigation of three layers diffraction optical element with wide field of view and high diffraction efficiency,” Optik (Stuttg.) 124(20), 4142–4144 (2013).
[Crossref]

Ying, C. F.

Y. H. Zhao, C. J. Fan, C. F. Ying, and S. H. Liu, “The investigation of triple-layer diffraction optical element with wide field of view and high diffraction efficiency,” Opt. Commun. 295, 104–107 (2013).
[Crossref]

Zhang, B.

B. Zhang, Q. Cui, and M. Piao, “Effect of substrate material selection on polychromatic integral diffraction efficiency for multi-layer diffractive optics in oblique incident situation,” Opt. Commun. 415(15), 156–163 (2018).
[Crossref]

Zhang, R.

Zhao, L.

Zhao, Y.

Y. Zhao, C. Fan, C. Ying, and H. Wang, “The investigation of three layers diffraction optical element with wide field of view and high diffraction efficiency,” Optik (Stuttg.) 124(20), 4142–4144 (2013).
[Crossref]

Zhao, Y. H.

Y. H. Zhao, C. J. Fan, C. F. Ying, and S. H. Liu, “The investigation of triple-layer diffraction optical element with wide field of view and high diffraction efficiency,” Opt. Commun. 295, 104–107 (2013).
[Crossref]

Zhou, Z.

Appl. Opt. (5)

J. Mod. Opt. (1)

H. Xie, D. Ren, C. Wang, C. Mao, and L. Yang, “Design of high-efficiency diffractive optical elements towards ultrafast mid-infrared time stretched imaging and spectroscopy,” J. Mod. Opt. 65(3), 255–261 (2018).
[Crossref]

J. Opt. Technol. (1)

Opt. Commun. (2)

Y. H. Zhao, C. J. Fan, C. F. Ying, and S. H. Liu, “The investigation of triple-layer diffraction optical element with wide field of view and high diffraction efficiency,” Opt. Commun. 295, 104–107 (2013).
[Crossref]

B. Zhang, Q. Cui, and M. Piao, “Effect of substrate material selection on polychromatic integral diffraction efficiency for multi-layer diffractive optics in oblique incident situation,” Opt. Commun. 415(15), 156–163 (2018).
[Crossref]

Opt. Eng. (1)

C. Bigwood and A. Wood, “Two-element lenses for military applications,” Opt. Eng. 50(12), 121705 (2011).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Opt. Spectrosc. (3)

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Minimization of the Total Depth of Internal Saw-Tooth Reliefs of a Two-Layer Relief-Phase Diffraction Microstructure,” Opt. Spectrosc. 124(1), 98–102 (2018).
[Crossref]

G. I. Greisukh, V. A. Danilov, E. G. Ezhov, S. A. Stepanov, and B. A. Usievich, “Spectral and angular dependences of the efficiency of relief-phase Diffractive Lenses with Two- and Three-Layer Microstructures,” Opt. Spectrosc. 118(6), 964–970 (2015).
[Crossref]

G. I. Greisukh, V. A. Danilov, S. A. Stepanov, A. I. Antonov, and B. A. Usievich, “Spectral and Angular Dependences of the Efficiency of Three-Layer Relief-Phase Diffraction Elements of the IR Range,” Opt. Spectrosc. 125(1), 60–64 (2018).
[Crossref]

Optik (Stuttg.) (2)

F. Huo, W. Wang, and C. Xue, “Limits of scalar diffraction theory for multilayer diffractive optical elements,” Optik (Stuttg.) 127(14), 5688–5694 (2016).
[Crossref]

Y. Zhao, C. Fan, C. Ying, and H. Wang, “The investigation of three layers diffraction optical element with wide field of view and high diffraction efficiency,” Optik (Stuttg.) 124(20), 4142–4144 (2013).
[Crossref]

Proc. SPIE (2)

A. P. Wood and P. J. Rogers, “Diffractive optics in modern optical engineering,” Proc. SPIE 5865, 58650B (2005).
[Crossref]

C. Fan, “The investigation of large field of view eyepiece with multilayer diffractive optical element,” Proc. SPIE 9272, 92720N (2014).
[Crossref]

Other (2)

G. J. Swanson, “The theory and design of multi-level diffractive optical elements,” MIT Lincoln Laboratory technical report (1989).

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

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Figures (9)

Fig. 1
Fig. 1 Micro-structure and light transmission of the double-separated MLDOE. (a) Micro-structure; (b) diagram of light transmission.
Fig. 2
Fig. 2 Distribution of the incident angle on the surface of MLDOE. (a) For a large aperture system; (b) for a large field of view system.
Fig. 3
Fig. 3 Flow chart of MLDOEs optimization design.
Fig. 4
Fig. 4 Micro-structure heights versus design wavelength pairs. (a) First layer; (b) second layer.
Fig. 5
Fig. 5 Relationship between design wavelength pairs and integral diffraction efficiency with the angle of incidence.
Fig. 6
Fig. 6 Design wavelength versus integral diffraction efficiency with an angle of incidence.
Fig. 7
Fig. 7 Diffraction efficiencies versus angle of incidence for different design wavelength pairs.
Fig. 8
Fig. 8 Diffraction efficiency versus wavelength for different wavelength pairs with angle of incidence of 15°.
Fig. 9
Fig. 9 Diffraction efficiency versus waveband and incident angle for different wavelengths. (a) λ1 = 450 nm, λ2 = 550 nm; (b) λ1 = 435 nm, λ2 = 598 nm; (c) λ1 = 486 nm, λ2 = 656 nm.

Tables (3)

Tables Icon

Table 1 Micro-structure heights and corresponding integral diffraction efficiencies for different wavelengths of MLDOE

Tables Icon

Table 2 Micro-structure heights and corresponding integral diffraction efficiencies for different wavelength pairs of MLDOE

Tables Icon

Table 3 Micro-structure heights and its corresponding integral diffraction efficiency for different wavelength pairs and angle of incidence for MLDOE (θ = 0°~15°, λ = 400 nm~700 nm)

Equations (7)

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{ j=1 N H j ( n ji ( λ 1 )cos θ ji n jt ( λ 1 )cos θ jt ) =m λ 1 j=1 N H j ( n ji ( λ k )cos θ ji n jt ( λ k )cos θ jt ) =m λ k j=1 N H j ( n ji ( λ N )cos θ ji n jt ( λ N )cos θ jt ) =m λ N m=1
η m ( λ,θ )= { sinc[ m ϕ( λ,θ ) 2π ] } 2 ,
ϕ( λ,θ )=2π{ H 1 λ [ 1 n 1 2 ( λ ) sin 2 θ n 1 2 ( λ )cosθ ]+ H 2 λ [ n 2 2 ( λ ) n 1 2 ( λ ) sin 2 θ 1 n 1 2 ( λ ) sin 2 θ ] },
{ H 1 = m λ 2 A( λ 1 )m λ 1 A( λ 2 ) B( λ 2 )A( λ 1 )B( λ 1 )A( λ 2 ) H 2 = m λ 1 A( λ 1 )m λ 2 A( λ 1 ) B( λ 2 )A( λ 1 )B( λ 1 )A( λ 2 ) ,
A( λ )= n 2 2 ( λ ) n 1 2 ( λ )si n 2 θ 1 n 1 2 ( λ )si n 2 θ ,and B( λ )= n 1 ( λ )cosθ 1 n 1 2 ( λ )si n 2 θ .
η m ( λ,θ )=sin c 2 { m H 1 λ [ 1 n 1 2 ( λ ) sin 2 θ n 1 2 ( λ )cosθ ]- H 2 λ [ n 2 2 ( λ ) n 1 2 ( λ ) sin 2 θ 1 n 1 2 ( λ ) sin 2 θ ] }
η ¯ m (θ,λ)= 1 λ max λ min θ min θ max λ min λ max η m dλdθ, = 1 λ max λ min θ min θ max λ min λ max sinc 2 [ m ϕ(λ,θ) 2π ] dλdθ

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