Abstract

This paper proposes an achromatic annular folded lens (AFL) with a reflective-diffractive optical element (RDOE). We derive novel mathematical models of the diffraction efficiency and polychromatic integral diffraction efficiency (PIDE) of the RDOE and an expression for its microstructure height. An AFL with an RDOE made of an optical plastic substrate material is designed in the visible waveband. To minimize the influence of incident angle on the diffraction efficiency and PIDE, the microstructure height is optimized. The design results indicate that the lateral color of the AFL is corrected, the modulation transfer function considering the diffraction efficiency is larger than 0.25 at 111 cycles/mm for all field of views. The hybrid AFL outperforms the conventional refractive imaging system in terms of the system size, volume, and image quality under the same specifications. It can be used in new-generation miniaturized imaging systems.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

2018 (2)

2017 (1)

2016 (1)

2015 (6)

2011 (2)

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

T. Wang, H. Liu, H. Zhang, H. Zhang, Q. Sun, and Z. Lu, “Effect of incidence angles and manufacturing errors on the imaging performance of hybrid systems,” J. Opt. 13(3), 035711 (2011).
[Crossref]

2010 (1)

R. Morrison, R. Stack, G. Euliss, R. Athale, C. Reese, J. Vizgaitis, J. Stevens, E. Tremblay, and J. Ford, “An alternative approach to infrared optics,” Proc. SPIE 7660, 76601Y (2010).
[Crossref]

2009 (1)

2007 (1)

2003 (1)

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron Devices 50(1), 4–11 (2003).
[Crossref]

2002 (1)

C. Bigwood, “New infrared optical systems using diffractive optics,” Proc. SPIE 4767, 1–12 (2002).
[Crossref]

1992 (1)

Agranov, G.

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron Devices 50(1), 4–11 (2003).
[Crossref]

Amigo, G. A.

Anderson, K.

Arianpour, A.

Athale, R.

R. Morrison, R. Stack, G. Euliss, R. Athale, C. Reese, J. Vizgaitis, J. Stevens, E. Tremblay, and J. Ford, “An alternative approach to infrared optics,” Proc. SPIE 7660, 76601Y (2010).
[Crossref]

Banerji, S.

Bass, M.

M. Bass, G. Li, and E. V. Stryland, Handbook of Optics Volume IV Optical Properties of Materials, Nonlinear Optics, Quantum Optics, Third edition, (McGraw-Hill, 2010).

Bäumer, S.

S. Bäumer, Handbook of Plastic Optics, Second Edition, (Wiley-VCH, 2010).

Berezin, V.

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron Devices 50(1), 4–11 (2003).
[Crossref]

Bigwood, C.

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

C. Bigwood, “New infrared optical systems using diffractive optics,” Proc. SPIE 4767, 1–12 (2002).
[Crossref]

Buralli, D. A.

Campbell, S. D.

Chen, X.

Cheng, D.

Chu, C.

Cui, Q.

M. Piao, Q. Cui, and B. Zhang, “Achromatic negative index lens with diffractive optics,” J. Opt. 17(2), 025608 (2015).
[Crossref]

Deng, H.

Euliss, G.

R. Morrison, R. Stack, G. Euliss, R. Athale, C. Reese, J. Vizgaitis, J. Stevens, E. Tremblay, and J. Ford, “An alternative approach to infrared optics,” Proc. SPIE 7660, 76601Y (2010).
[Crossref]

Fainman, S.

J. Ford, E. Tremblay, and S. Fainman, “Multiple reflective lenses and lens systems,” US Patent, 7898749B2 (2011).

Fischer, R. E.

R. E. Fischer, B. Tadic-Galeb, and P. R. Yoder, Optical System Design, Second Edition (SPIE, 2008).

Ford, J.

R. Morrison, R. Stack, G. Euliss, R. Athale, C. Reese, J. Vizgaitis, J. Stevens, E. Tremblay, and J. Ford, “An alternative approach to infrared optics,” Proc. SPIE 7660, 76601Y (2010).
[Crossref]

J. Ford, E. Tremblay, and S. Fainman, “Multiple reflective lenses and lens systems,” US Patent, 7898749B2 (2011).

Ford, J. E.

Groisman, A.

Hu, Y.

Juan, C.

Karp, J. H.

Kathman, A. D.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics Design, Fabrication, and Test (SPIE, 2004).

Laikin, M.

M. Laikin, Lens Design, Fourth Edition (CRC, 2007).

Lan, X.

Legerton, J.

Li, C.

Li, G.

M. Bass, G. Li, and E. V. Stryland, Handbook of Optics Volume IV Optical Properties of Materials, Nonlinear Optics, Quantum Optics, Third edition, (McGraw-Hill, 2010).

Li, L.

Liu, C.

Liu, H.

H. Zhang, H. Liu, A. Lizana, W. Xu, C. Juan, and Z. Lu, “Methods for the performance enhancement and the error characterization of large diameter ground-based diffractive telescopes,” Opt. Express 25(22), 26662–26677 (2017).
[Crossref]

T. Wang, H. Liu, H. Zhang, H. Zhang, Q. Sun, and Z. Lu, “Effect of incidence angles and manufacturing errors on the imaging performance of hybrid systems,” J. Opt. 13(3), 035711 (2011).
[Crossref]

Lizana, A.

Lu, Z.

H. Zhang, H. Liu, A. Lizana, W. Xu, C. Juan, and Z. Lu, “Methods for the performance enhancement and the error characterization of large diameter ground-based diffractive telescopes,” Opt. Express 25(22), 26662–26677 (2017).
[Crossref]

T. Wang, H. Liu, H. Zhang, H. Zhang, Q. Sun, and Z. Lu, “Effect of incidence angles and manufacturing errors on the imaging performance of hybrid systems,” J. Opt. 13(3), 035711 (2011).
[Crossref]

Majumder, A.

Mcleod, R. R.

Meem, M.

Menon, R.

Meyers, W.

Morris, G. M.

Morrison, R.

R. Morrison, R. Stack, G. Euliss, R. Athale, C. Reese, J. Vizgaitis, J. Stevens, E. Tremblay, and J. Ford, “An alternative approach to infrared optics,” Proc. SPIE 7660, 76601Y (2010).
[Crossref]

Morrison, R. L.

Nagar, J.

O’Shea, D. C.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics Design, Fabrication, and Test (SPIE, 2004).

Piao, M.

M. Piao, Q. Cui, and B. Zhang, “Achromatic negative index lens with diffractive optics,” J. Opt. 17(2), 025608 (2015).
[Crossref]

Prather, D. W.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics Design, Fabrication, and Test (SPIE, 2004).

Reese, C.

R. Morrison, R. Stack, G. Euliss, R. Athale, C. Reese, J. Vizgaitis, J. Stevens, E. Tremblay, and J. Ford, “An alternative approach to infrared optics,” Proc. SPIE 7660, 76601Y (2010).
[Crossref]

Ren, H.

Schuster, G. M.

Sensale-Rodriguez, B.

Soskind, Y. G.

Y. G. Soskind, “Diffractive optics technologies in infrared systems,” Proc. SPIE 9451, 94511T (2015).
[Crossref]

Stack, R.

R. Morrison, R. Stack, G. Euliss, R. Athale, C. Reese, J. Vizgaitis, J. Stevens, E. Tremblay, and J. Ford, “An alternative approach to infrared optics,” Proc. SPIE 7660, 76601Y (2010).
[Crossref]

Stack, R. A.

Stamenov, I.

Stevens, J.

R. Morrison, R. Stack, G. Euliss, R. Athale, C. Reese, J. Vizgaitis, J. Stevens, E. Tremblay, and J. Ford, “An alternative approach to infrared optics,” Proc. SPIE 7660, 76601Y (2010).
[Crossref]

Stryland, E. V.

M. Bass, G. Li, and E. V. Stryland, Handbook of Optics Volume IV Optical Properties of Materials, Nonlinear Optics, Quantum Optics, Third edition, (McGraw-Hill, 2010).

Su, V.

Suleski, T. J.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics Design, Fabrication, and Test (SPIE, 2004).

Sun, G.

Sun, Q.

T. Wang, H. Liu, H. Zhang, H. Zhang, Q. Sun, and Z. Lu, “Effect of incidence angles and manufacturing errors on the imaging performance of hybrid systems,” J. Opt. 13(3), 035711 (2011).
[Crossref]

Swanson, G. J.

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

Tadic-Galeb, B.

R. E. Fischer, B. Tadic-Galeb, and P. R. Yoder, Optical System Design, Second Edition (SPIE, 2008).

Tremblay, E.

R. Morrison, R. Stack, G. Euliss, R. Athale, C. Reese, J. Vizgaitis, J. Stevens, E. Tremblay, and J. Ford, “An alternative approach to infrared optics,” Proc. SPIE 7660, 76601Y (2010).
[Crossref]

J. Ford, E. Tremblay, and S. Fainman, “Multiple reflective lenses and lens systems,” US Patent, 7898749B2 (2011).

Tremblay, E. J.

Tsai, D.

Tsai, R. H.

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron Devices 50(1), 4–11 (2003).
[Crossref]

Urness, A. C.

Vasquez, F. G.

Vizgaitis, J.

R. Morrison, R. Stack, G. Euliss, R. Athale, C. Reese, J. Vizgaitis, J. Stevens, E. Tremblay, and J. Ford, “An alternative approach to infrared optics,” Proc. SPIE 7660, 76601Y (2010).
[Crossref]

Wang, D.

Wang, Q.

Wang, T.

T. Wang, H. Liu, H. Zhang, H. Zhang, Q. Sun, and Z. Lu, “Effect of incidence angles and manufacturing errors on the imaging performance of hybrid systems,” J. Opt. 13(3), 035711 (2011).
[Crossref]

Wang, Y.

Werner, D. H.

Wilson, W. L.

Wood, A.

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

Xu, C.

Xu, W.

Xue, C.

Yang, C.

Ye, C.

Yoder, P. R.

R. E. Fischer, B. Tadic-Galeb, and P. R. Yoder, Optical System Design, Second Edition (SPIE, 2008).

Zhang, B.

M. Piao, Q. Cui, and B. Zhang, “Achromatic negative index lens with diffractive optics,” J. Opt. 17(2), 025608 (2015).
[Crossref]

Zhang, H.

H. Zhang, H. Liu, A. Lizana, W. Xu, C. Juan, and Z. Lu, “Methods for the performance enhancement and the error characterization of large diameter ground-based diffractive telescopes,” Opt. Express 25(22), 26662–26677 (2017).
[Crossref]

T. Wang, H. Liu, H. Zhang, H. Zhang, Q. Sun, and Z. Lu, “Effect of incidence angles and manufacturing errors on the imaging performance of hybrid systems,” J. Opt. 13(3), 035711 (2011).
[Crossref]

T. Wang, H. Liu, H. Zhang, H. Zhang, Q. Sun, and Z. Lu, “Effect of incidence angles and manufacturing errors on the imaging performance of hybrid systems,” J. Opt. 13(3), 035711 (2011).
[Crossref]

Appl. Opt. (6)

IEEE Trans. Electron Devices (1)

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron Devices 50(1), 4–11 (2003).
[Crossref]

J. Opt. (2)

T. Wang, H. Liu, H. Zhang, H. Zhang, Q. Sun, and Z. Lu, “Effect of incidence angles and manufacturing errors on the imaging performance of hybrid systems,” J. Opt. 13(3), 035711 (2011).
[Crossref]

M. Piao, Q. Cui, and B. Zhang, “Achromatic negative index lens with diffractive optics,” J. Opt. 17(2), 025608 (2015).
[Crossref]

Opt. Eng. (1)

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

Opt. Express (4)

Opt. Lett. (1)

Optica (2)

Proc. SPIE (3)

Y. G. Soskind, “Diffractive optics technologies in infrared systems,” Proc. SPIE 9451, 94511T (2015).
[Crossref]

R. Morrison, R. Stack, G. Euliss, R. Athale, C. Reese, J. Vizgaitis, J. Stevens, E. Tremblay, and J. Ford, “An alternative approach to infrared optics,” Proc. SPIE 7660, 76601Y (2010).
[Crossref]

C. Bigwood, “New infrared optical systems using diffractive optics,” Proc. SPIE 4767, 1–12 (2002).
[Crossref]

Other (8)

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics Design, Fabrication, and Test (SPIE, 2004).

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

M. Laikin, Lens Design, Fourth Edition (CRC, 2007).

R. E. Fischer, B. Tadic-Galeb, and P. R. Yoder, Optical System Design, Second Edition (SPIE, 2008).

M. Bass, G. Li, and E. V. Stryland, Handbook of Optics Volume IV Optical Properties of Materials, Nonlinear Optics, Quantum Optics, Third edition, (McGraw-Hill, 2010).

Zemax Development Corporation, “OpticStudio User Manual,” (2016).

S. Bäumer, Handbook of Plastic Optics, Second Edition, (Wiley-VCH, 2010).

J. Ford, E. Tremblay, and S. Fainman, “Multiple reflective lenses and lens systems,” US Patent, 7898749B2 (2011).

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Figures (10)

Fig. 1.
Fig. 1. Light rays passing through two neighboring subperiods of the RDOE
Fig. 2.
Fig. 2. Profile of the RDOE
Fig. 3.
Fig. 3. Petzval-type lens. (a) Optical system layout. (b) MTF.
Fig. 4.
Fig. 4. Image quality evaluation of the initial AFL. (a) Lateral color curve. (b) Spot diagram.
Fig. 5.
Fig. 5. System layout of the final designed AFL. (a) Optical system layout. (b) Solid model.
Fig. 6.
Fig. 6. Image quality evaluation of the final designed AFL. (a) Lateral color curve. (b) Spot diagram.
Fig. 7.
Fig. 7. Flow diagram of the optimization process.
Fig. 8.
Fig. 8. Diffraction efficiency and PIDE for the RDOE. (a) Diffraction efficiency. (b) PIDE.
Fig. 9.
Fig. 9. MTF with considering the diffraction efficiency for the AFL.
Fig. 10.
Fig. 10. Phase plot and the line frequency versus aperture for the RDOE.

Tables (5)

Tables Icon

Table 1. Design Specifications

Tables Icon

Table 2. Lens Data of Hybrid AFL with RDOE

Tables Icon

Table 3. Detail Data for Even Asphere

Tables Icon

Table 4. Minimum Diffraction Efficiency and PIDE versus Incident Angle for RDOE

Tables Icon

Table 5. MTF values with considering the diffraction efficiency at different field of views

Equations (20)

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

η m = E R m E R 0 ,
η m = sin c 2 ( m ϕ ) .
η m N = { sin [ π ( m ϕ ) ] sin [ π ( m ϕ ) N ] sin ( m π N ) π m } 2 .
ϕ = N φ ,
φ = n λ ( y 2 y 1 ) ,
y 1 = k sin θ + t cos θ y 2 = k sin θ t cos θ .
φ = 2 n λ t cos θ .
ϕ = N φ = 2 n H λ cos θ ,
ϕ 0 = 2 H n 0 λ 0 cos θ 0 = 1.
H = λ 0 2 n 0 cos θ 0 ,
ϕ = n λ 0 cos θ n 0 λ cos θ 0 .
η m N = { sin [ π ( m n λ 0 cos θ n 0 λ cos θ 0 ) ] sin [ π N ( m n λ 0 cos θ n 0 λ cos θ 0 ) ] sin ( m π N ) π m } 2 .
η m = sin c 2 ( m + 2 n H λ cos θ ) .
O T F a ( f x , f y ) = η ¯ m O T F T ( f x , f y ) ,
η ¯ m = 1 λ max λ min λ min λ max sin c 2 ( m + 2 n H λ cos θ ) d λ ,
L = f n R ,
D e f f = D 1 α o b s 2 ,
z = c r 2 1 + 1 ( 1 + p ) c 2 r 2 + i = 1 8 α i r 2 i ,
Φ b 2 = m i = 1 s A i ρ 2 i ,
ρ = r r n o r m ,

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