Abstract

A lens performs an approximately one-to-one mapping from the object to the image plane. This mapping in the image plane is maintained within a depth of field (or referred to as depth of focus, if the object is at infinity). This necessitates refocusing of the lens when the images are separated by distances larger than the depth of field. Such refocusing mechanisms can increase the cost, complexity, and weight of imaging systems. Here we show that by judicious design of a multi-level diffractive lens (MDL) it is possible to drastically enhance the depth of focus by over 4 orders of magnitude. Using such a lens, we are able to maintain focus for objects that are separated by as large a distance as $\sim {6}\;{\rm m}$ in our experiments. Specifically, when illuminated by collimated light at $\lambda = {0.85}\;{\unicode{x00B5}{\rm m}}$, the MDL produced a beam, which remained in focus from 5 to 1200 mm. The measured full width at half-maximum of the focused beam varied from 6.6 µm (5 mm away from the MDL) to 524 µm (1200 mm away from the MDL). Since the side lobes were well suppressed and the main lobe was close to the diffraction limit, imaging with a horizontal × vertical field of view of ${40}^\circ \times {30}^\circ $ over the entire focal range was possible. This demonstration opens up a new direction for lens design, where by treating the phase in the focal plane as a free parameter, extreme-depth-of-focus imaging becomes possible.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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M. Meem, A. Majumder, and R. Menon, Opt. Express 26, 26866 (2018).
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Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X. C. Yuan, J. Opt. 13, 055301 (2011).
[Crossref]

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Z. Zalevsky, SPIE Rev. 1, 018001 (2010).
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H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
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2005 (1)

Z. Liu, A. Flores, M. R. Wang, and J. J. Yang, Proc. SPIE 5783, 841 (2005).
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2004 (1)

2002 (1)

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1990 (1)

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1984 (1)

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S. Banerji, M. Meem, A. Majumder, F. Vasquez-Guevara, B. Sensale-Rodriguez, and R. Menon, Opt. Lett. 44, 5450 (2019).
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S. Banerji, M. Meem, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Optica 6, 805 (2019).
[Crossref]

M. Meem, S. Banerji, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Proc. Nat. Acad. Sci. 116, 21375 (2019).
[Crossref]

S. Banerji and B. Sensale-Rodriguez, Sci. Rep. 9, 5801 (2019).
[Crossref]

S. Banerji and B. Sensale-Rodriguez, Proc. SPIE 10982, 109822X (2019).
[Crossref]

S. Banerji, M. Meem, A. Majumder, C. Dvonch, B. Sensale-Rodriguez, and R. Menon, OSA Continuum 2, 2968 (2019).
[Crossref]

S. Banerji, M. Meem, A. Majumder, B. Sensale-Rodriguez, and R. Menon, “Imaging over an unlimited bandwidth with a single diffractive surface,” arXiv: 1907.06251 [physics.optics] (2019).

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A. Kolodziejczyk, S. Bara, Z. Jaroszwicz, and M. Zypek, J. Mod. Opt. 37, 1283 (1990).
[Crossref]

Born, M.

M. Born and E. Wolf, Principle of Optics, 7th ed. (Cambridge University, 1999).

Bu, J.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X. C. Yuan, J. Opt. 13, 055301 (2011).
[Crossref]

Cathey, W. T.

Chi, W.

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[Crossref]

Diaz, A.

Dowski, E. R.

Dvonch, C.

Flores, A.

Z. Liu, A. Flores, M. R. Wang, and J. J. Yang, Proc. SPIE 5783, 841 (2005).
[Crossref]

A. Flores, M. R. Wang, and J. J. Yang, Appl. Opt. 43, 5618 (2004).
[Crossref]

Gao, B. Z.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X. C. Yuan, J. Opt. 13, 055301 (2011).
[Crossref]

George, N.

Hans, R.

R. Hans, “Multiple focal length lens,” US patent3,004,470 (17October1961).

Jaroszwicz, Z.

A. Kolodziejczyk, S. Bara, Z. Jaroszwicz, and M. Zypek, J. Mod. Opt. 37, 1283 (1990).
[Crossref]

Kolodziejczyk, A.

A. Kolodziejczyk, S. Bara, Z. Jaroszwicz, and M. Zypek, J. Mod. Opt. 37, 1283 (1990).
[Crossref]

Lit, J. W. Y.

Liu, Z.

Z. Liu, A. Flores, M. R. Wang, and J. J. Yang, Proc. SPIE 5783, 841 (2005).
[Crossref]

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[Crossref]

Majumder, A.

S. Banerji, M. Meem, A. Majumder, F. Vasquez-Guevara, B. Sensale-Rodriguez, and R. Menon, Opt. Lett. 44, 5450 (2019).
[Crossref]

S. Banerji, M. Meem, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Optica 6, 805 (2019).
[Crossref]

S. Banerji, M. Meem, A. Majumder, C. Dvonch, B. Sensale-Rodriguez, and R. Menon, OSA Continuum 2, 2968 (2019).
[Crossref]

M. Meem, S. Banerji, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Proc. Nat. Acad. Sci. 116, 21375 (2019).
[Crossref]

M. Meem, A. Majumder, and R. Menon, Opt. Express 26, 26866 (2018).
[Crossref]

S. Banerji, M. Meem, A. Majumder, B. Sensale-Rodriguez, and R. Menon, “Imaging over an unlimited bandwidth with a single diffractive surface,” arXiv: 1907.06251 [physics.optics] (2019).

Mcleod, J. M.

Meem, M.

S. Banerji, M. Meem, A. Majumder, F. Vasquez-Guevara, B. Sensale-Rodriguez, and R. Menon, Opt. Lett. 44, 5450 (2019).
[Crossref]

S. Banerji, M. Meem, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Optica 6, 805 (2019).
[Crossref]

M. Meem, S. Banerji, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Proc. Nat. Acad. Sci. 116, 21375 (2019).
[Crossref]

S. Banerji, M. Meem, A. Majumder, C. Dvonch, B. Sensale-Rodriguez, and R. Menon, OSA Continuum 2, 2968 (2019).
[Crossref]

M. Meem, A. Majumder, and R. Menon, Opt. Express 26, 26866 (2018).
[Crossref]

N. Mohammad, M. Meem, B. Shen, P. Wang, and R. Menon, Sci. Rep. 8, 2799 (2018).
[Crossref]

S. Banerji, M. Meem, A. Majumder, B. Sensale-Rodriguez, and R. Menon, “Imaging over an unlimited bandwidth with a single diffractive surface,” arXiv: 1907.06251 [physics.optics] (2019).

Menon, R.

S. Banerji, M. Meem, A. Majumder, F. Vasquez-Guevara, B. Sensale-Rodriguez, and R. Menon, Opt. Lett. 44, 5450 (2019).
[Crossref]

S. Banerji, M. Meem, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Optica 6, 805 (2019).
[Crossref]

M. Meem, S. Banerji, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Proc. Nat. Acad. Sci. 116, 21375 (2019).
[Crossref]

S. Banerji, M. Meem, A. Majumder, C. Dvonch, B. Sensale-Rodriguez, and R. Menon, OSA Continuum 2, 2968 (2019).
[Crossref]

N. Mohammad, M. Meem, B. Shen, P. Wang, and R. Menon, Sci. Rep. 8, 2799 (2018).
[Crossref]

M. Meem, A. Majumder, and R. Menon, Opt. Express 26, 26866 (2018).
[Crossref]

P. Wang, N. Mohammad, and R. Menon, Sci. Rep. 6, 21545 (2016).
[Crossref]

S. Banerji, M. Meem, A. Majumder, B. Sensale-Rodriguez, and R. Menon, “Imaging over an unlimited bandwidth with a single diffractive surface,” arXiv: 1907.06251 [physics.optics] (2019).

Mohammad, N.

N. Mohammad, M. Meem, B. Shen, P. Wang, and R. Menon, Sci. Rep. 8, 2799 (2018).
[Crossref]

P. Wang, N. Mohammad, and R. Menon, Sci. Rep. 6, 21545 (2016).
[Crossref]

Ojeda-Castañeda, J.

Sensale-Rodriguez, B.

S. Banerji, M. Meem, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Optica 6, 805 (2019).
[Crossref]

S. Banerji, M. Meem, A. Majumder, F. Vasquez-Guevara, B. Sensale-Rodriguez, and R. Menon, Opt. Lett. 44, 5450 (2019).
[Crossref]

S. Banerji, M. Meem, A. Majumder, C. Dvonch, B. Sensale-Rodriguez, and R. Menon, OSA Continuum 2, 2968 (2019).
[Crossref]

M. Meem, S. Banerji, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Proc. Nat. Acad. Sci. 116, 21375 (2019).
[Crossref]

S. Banerji and B. Sensale-Rodriguez, Proc. SPIE 10982, 109822X (2019).
[Crossref]

S. Banerji and B. Sensale-Rodriguez, Sci. Rep. 9, 5801 (2019).
[Crossref]

S. Banerji, M. Meem, A. Majumder, B. Sensale-Rodriguez, and R. Menon, “Imaging over an unlimited bandwidth with a single diffractive surface,” arXiv: 1907.06251 [physics.optics] (2019).

Shen, B.

N. Mohammad, M. Meem, B. Shen, P. Wang, and R. Menon, Sci. Rep. 8, 2799 (2018).
[Crossref]

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[Crossref]

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[Crossref]

Sochacki, J.

Tepichin, E.

Tremblay, R.

Vasquez, F. G.

S. Banerji, M. Meem, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Optica 6, 805 (2019).
[Crossref]

M. Meem, S. Banerji, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Proc. Nat. Acad. Sci. 116, 21375 (2019).
[Crossref]

Vasquez-Guevara, F.

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[Crossref]

Wang, J. G.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X. C. Yuan, J. Opt. 13, 055301 (2011).
[Crossref]

Wang, M. R.

Z. Liu, A. Flores, M. R. Wang, and J. J. Yang, Proc. SPIE 5783, 841 (2005).
[Crossref]

A. Flores, M. R. Wang, and J. J. Yang, Appl. Opt. 43, 5618 (2004).
[Crossref]

Wang, M. W.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X. C. Yuan, J. Opt. 13, 055301 (2011).
[Crossref]

Wang, P.

N. Mohammad, M. Meem, B. Shen, P. Wang, and R. Menon, Sci. Rep. 8, 2799 (2018).
[Crossref]

P. Wang, N. Mohammad, and R. Menon, Sci. Rep. 6, 21545 (2016).
[Crossref]

Wang, R.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X. C. Yuan, J. Opt. 13, 055301 (2011).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principle of Optics, 7th ed. (Cambridge University, 1999).

Yang, J. J.

Z. Liu, A. Flores, M. R. Wang, and J. J. Yang, Proc. SPIE 5783, 841 (2005).
[Crossref]

A. Flores, M. R. Wang, and J. J. Yang, Appl. Opt. 43, 5618 (2004).
[Crossref]

Yuan, X. C.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X. C. Yuan, J. Opt. 13, 055301 (2011).
[Crossref]

Zalevsky, Z.

Z. Zalevsky, SPIE Rev. 1, 018001 (2010).
[Crossref]

Zhang, Q. Q.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X. C. Yuan, J. Opt. 13, 055301 (2011).
[Crossref]

Zhu, S. W.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X. C. Yuan, J. Opt. 13, 055301 (2011).
[Crossref]

Zypek, M.

A. Kolodziejczyk, S. Bara, Z. Jaroszwicz, and M. Zypek, J. Mod. Opt. 37, 1283 (1990).
[Crossref]

Appl. Opt. (5)

J. Mod. Opt. (1)

A. Kolodziejczyk, S. Bara, Z. Jaroszwicz, and M. Zypek, J. Mod. Opt. 37, 1283 (1990).
[Crossref]

J. Opt. (1)

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X. C. Yuan, J. Opt. 13, 055301 (2011).
[Crossref]

J. Opt. Soc. Am. (2)

Nat. Photonics (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Optica (1)

OSA Continuum (1)

Proc. Nat. Acad. Sci. (1)

M. Meem, S. Banerji, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, Proc. Nat. Acad. Sci. 116, 21375 (2019).
[Crossref]

Proc. SPIE (2)

S. Banerji and B. Sensale-Rodriguez, Proc. SPIE 10982, 109822X (2019).
[Crossref]

Z. Liu, A. Flores, M. R. Wang, and J. J. Yang, Proc. SPIE 5783, 841 (2005).
[Crossref]

Sci. Rep. (3)

P. Wang, N. Mohammad, and R. Menon, Sci. Rep. 6, 21545 (2016).
[Crossref]

N. Mohammad, M. Meem, B. Shen, P. Wang, and R. Menon, Sci. Rep. 8, 2799 (2018).
[Crossref]

S. Banerji and B. Sensale-Rodriguez, Sci. Rep. 9, 5801 (2019).
[Crossref]

SPIE Rev. (1)

Z. Zalevsky, SPIE Rev. 1, 018001 (2010).
[Crossref]

Other (3)

R. Hans, “Multiple focal length lens,” US patent3,004,470 (17October1961).

M. Born and E. Wolf, Principle of Optics, 7th ed. (Cambridge University, 1999).

S. Banerji, M. Meem, A. Majumder, B. Sensale-Rodriguez, and R. Menon, “Imaging over an unlimited bandwidth with a single diffractive surface,” arXiv: 1907.06251 [physics.optics] (2019).

Supplementary Material (3)

NameDescription
» Supplement 1       Supplementary Information
» Visualization 1       Video of EDOF imaging
» Visualization 2       Video of EDOF imaging

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic of a multi-level diffractive lens (MDL) that exhibits extreme-depth-of-focus (ExDOF) imaging. (b) Geometry of the MDL with focal ${\rm range} = {5}$ to 1200 mm, ${\rm aperture} = {1.8}\;{\rm mm}$. The (c) simulated and (d) measured intensity distributions in the $y - z$ plane for the MDL with ${\rm focal}\;{\rm lengths} = {5}$ to 1200 mm. The operating wavelength is 850 nm.
Fig. 2.
Fig. 2. (a) Optical micrograph of the fabricated MDL, with the inset showing a magnified view of the center of the lens. (b) Measured, simulated, and diffraction-limited full-width at half-maximum (FWHM) as a function of $ z $. (c–i) Simulated and (j–p) measured point-spread functions (light intensity distributions in the $x - y$ planes) as a function of $ z $, the distance from the MDL.
Fig. 3.
Fig. 3. Imaging different object distances without refocusing. (a) Focused images of objects at different distances $ u $ from the MDL are formed at the same image distance $ v $. (b) Images of the Air Force resolution chart for fixed $ v $ and varying $ u $. The value of $ v $ is fixed for each row, and the value of $ u $ is noted in parentheses in each image. (c) Magnification as a function of $ u $ for various values of $ v $ extracted from the recorded images. Imaging at different image distances without refocusing.
Fig. 4.
Fig. 4. (a) Focused images of objects at fixed distance $ u $ are formed at a large range of image distances $ v $. (b) Images of the Air Force resolution chart for fixed $ u $ and varying $ v $. The value of $ u $ is fixed for each row, and the value of $ v $ is noted in parentheses in each image. (c) Magnification as a function of $ v $ for various values of $ u $ extracted from the recorded images.
Fig. 5.
Fig. 5. Imaging a scene with large depth of field. Objects with distances from 200 mm to $\sim{6}\;{\rm m}$ are in focus. The distance of each object from the MDL ($ u $) is noted in the figure. Video recordings of similar scenes are included as Visualization 1 and Visualization 2. A visible image of this scene is also included in Fig. S5, Supplement 1.

Equations (3)

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

D O F 4 W 2 λ = λ N A 2 ,
N A = sin ( tan 1 ( R z ) ) ,
e D O F = f max f min λ max ( N A ) 2 ,