Abstract

A radial Walsh filter is a phase binary diffractive optical element characterized by a set of concentric rings that take the phase values 0 or π, corresponding to the values + 1 or −1 of a given radial Walsh function. Therefore, a Walsh filter can be re-interpreted as an aperiodic multifocal zone plate, capable to produce images of multiple planes simultaneously in a single output plane of an image forming system. In this paper, we experimentally demonstrate for the first time the focusing capabilities of these structures. Additionally, we report the first achievement of images of multiple-plane objects in a single image plane with these aperiodic diffractive lenses.

© 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. X. Wang, Z. Xie, W. Sun, S. Feng, Y. Cui, J. Ye, and Y. Zhang, “Focusing and imaging of a virtual all-optical tunable terahertz Fresnel zone plate,” Opt. Lett. 38(22), 4731–4734 (2013).
    [Crossref] [PubMed]
  2. I. Mohacsi, I. Vartiainen, B. Rösner, M. Guizar-Sicairos, V. A. Guzenko, I. McNulty, R. Winarski, M. V. Holt, and C. David, “Interlaced zone plate optics for hard X-ray imaging in the 10 nm range,” Sci. Rep. 7(1), 43624 (2017).
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    [Crossref]
  6. L. L. Doskolovich, E. A. Bezus, A. A. Morozov, V. Osipov, J. S. Wolffsohn, and B. Chichkov, “Multifocal diffractive lens generating several fixed foci at different design wavelengths,” Opt. Express 26(4), 4698–4709 (2018).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  12. V. Ferrando, F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Bifractal focusing and imaging properties of Thue-Morse Zone Plates,” Opt. Express 23(15), 19846–19853 (2015).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  27. V. Osipov, L. L. Doskolovich, E. A. Bezus, T. Drew, K. Zhou, K. Sawalha, G. Swadener, and J. S. W. Wolffsohn, “Application of nanoimprinting technique for fabrication of trifocal diffractive lens with sine-like radial profile,” J. Biomed. Opt. 20(2), 025008 (2015).
    [Crossref] [PubMed]
  28. U. Hinze, A. El-Tamer, L. L. Doskolovich, E. A. Bezus, S. Reiß, H. Stolz, R. F. Guthoff, O. Stachs, and B. Chichkov, “Additive manufacturing of a trifocal diffractive-refractive lens,” Opt. Commun. 372, 235–240 (2016).
    [Crossref]

2018 (1)

2017 (2)

I. Mohacsi, I. Vartiainen, B. Rösner, M. Guizar-Sicairos, V. A. Guzenko, I. McNulty, R. Winarski, M. V. Holt, and C. David, “Interlaced zone plate optics for hard X-ray imaging in the 10 nm range,” Sci. Rep. 7(1), 43624 (2017).
[Crossref]

L. Ledesma-Carrillo, C. M. Gómez-Sarabia, M. Torres-Cisneros, R. Guzmán-Cabrera, C. Guzmán-Cano, and J. Ojeda-Castañeda, “Hadamard circular masks: high focal depth with high throughput,” Opt. Express 25(15), 17004–17020 (2017).
[Crossref] [PubMed]

2016 (1)

U. Hinze, A. El-Tamer, L. L. Doskolovich, E. A. Bezus, S. Reiß, H. Stolz, R. F. Guthoff, O. Stachs, and B. Chichkov, “Additive manufacturing of a trifocal diffractive-refractive lens,” Opt. Commun. 372, 235–240 (2016).
[Crossref]

2015 (2)

V. Osipov, L. L. Doskolovich, E. A. Bezus, T. Drew, K. Zhou, K. Sawalha, G. Swadener, and J. S. W. Wolffsohn, “Application of nanoimprinting technique for fabrication of trifocal diffractive lens with sine-like radial profile,” J. Biomed. Opt. 20(2), 025008 (2015).
[Crossref] [PubMed]

V. Ferrando, F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Bifractal focusing and imaging properties of Thue-Morse Zone Plates,” Opt. Express 23(15), 19846–19853 (2015).
[Crossref] [PubMed]

2014 (2)

P. Mukherjee and L. N. Hazra, “Self-similarity in radial Walsh filters and axial intensity distributions in the far-field diffraction pattern,” J. Opt. Soc. Am. A 31(2), 379–387 (2014).
[Crossref] [PubMed]

P. Mukherjee and L. N. Hazra, “Self-similarity in transverse intensity distributions in farfield diffraction patterns of radial Walsh filters,” Adv. Opt. 2014, 352316 (2014).
[Crossref]

2013 (2)

J. A. Monsoriu, A. Calatayud, L. Remon, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photonics J. 5(3), 3400106 (2013).
[Crossref]

X. Wang, Z. Xie, W. Sun, S. Feng, Y. Cui, J. Ye, and Y. Zhang, “Focusing and imaging of a virtual all-optical tunable terahertz Fresnel zone plate,” Opt. Lett. 38(22), 4731–4734 (2013).
[Crossref] [PubMed]

2010 (1)

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010).
[Crossref]

2008 (1)

2007 (2)

L. N. Hazra, “Walsh filters for tailoring of resolution in microscopic imaging,” Micron 38(2), 129–135 (2007).
[Crossref] [PubMed]

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett. 32(15), 2109–2111 (2007).
[Crossref] [PubMed]

2006 (1)

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69(2), 397–441 (2006).
[Crossref]

2005 (1)

2004 (1)

2003 (1)

1992 (1)

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, and V. A. Soifer, “Computer generated diffractive multi-focal lens,” J. Mod. Opt. 39(6), 1245–1251 (1992).
[Crossref]

1990 (1)

1977 (1)

L. N. Hazra, “A new class of optimum amplitude filters,” Opt. Commun. 21(2), 232–236 (1977).
[Crossref]

1976 (1)

L. N. Hazra and A. Banerjee, “Applications of Walsh functions in generation of optimum apodizers,” J. Opt. 5, 19–26 (1976).

1969 (1)

H. F. Harmuth, “Applications of Walsh functions in communications,” IEEE Spectr. 6(11), 82–91 (1969).
[Crossref]

1964 (1)

1923 (1)

J. L. Walsh, “A closed set of normal orthogonal functions,” Am. J. Math. 45(1), 5–24 (1923).
[Crossref]

Andrés, P.

J. A. Monsoriu, A. Calatayud, L. Remon, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photonics J. 5(3), 3400106 (2013).
[Crossref]

Banerjee, A.

L. N. Hazra and A. Banerjee, “Applications of Walsh functions in generation of optimum apodizers,” J. Opt. 5, 19–26 (1976).

Berriel-Valdos, L. R.

Bezus, E. A.

L. L. Doskolovich, E. A. Bezus, A. A. Morozov, V. Osipov, J. S. Wolffsohn, and B. Chichkov, “Multifocal diffractive lens generating several fixed foci at different design wavelengths,” Opt. Express 26(4), 4698–4709 (2018).
[Crossref] [PubMed]

U. Hinze, A. El-Tamer, L. L. Doskolovich, E. A. Bezus, S. Reiß, H. Stolz, R. F. Guthoff, O. Stachs, and B. Chichkov, “Additive manufacturing of a trifocal diffractive-refractive lens,” Opt. Commun. 372, 235–240 (2016).
[Crossref]

V. Osipov, L. L. Doskolovich, E. A. Bezus, T. Drew, K. Zhou, K. Sawalha, G. Swadener, and J. S. W. Wolffsohn, “Application of nanoimprinting technique for fabrication of trifocal diffractive lens with sine-like radial profile,” J. Biomed. Opt. 20(2), 025008 (2015).
[Crossref] [PubMed]

Cagigal, M.

Calatayud, A.

J. A. Monsoriu, A. Calatayud, L. Remon, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photonics J. 5(3), 3400106 (2013).
[Crossref]

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010).
[Crossref]

Canales, V.

Chen, Q. D.

Chichkov, B.

L. L. Doskolovich, E. A. Bezus, A. A. Morozov, V. Osipov, J. S. Wolffsohn, and B. Chichkov, “Multifocal diffractive lens generating several fixed foci at different design wavelengths,” Opt. Express 26(4), 4698–4709 (2018).
[Crossref] [PubMed]

U. Hinze, A. El-Tamer, L. L. Doskolovich, E. A. Bezus, S. Reiß, H. Stolz, R. F. Guthoff, O. Stachs, and B. Chichkov, “Additive manufacturing of a trifocal diffractive-refractive lens,” Opt. Commun. 372, 235–240 (2016).
[Crossref]

Cui, Y.

David, C.

I. Mohacsi, I. Vartiainen, B. Rösner, M. Guizar-Sicairos, V. A. Guzenko, I. McNulty, R. Winarski, M. V. Holt, and C. David, “Interlaced zone plate optics for hard X-ray imaging in the 10 nm range,” Sci. Rep. 7(1), 43624 (2017).
[Crossref]

Doskolovich, L. L.

L. L. Doskolovich, E. A. Bezus, A. A. Morozov, V. Osipov, J. S. Wolffsohn, and B. Chichkov, “Multifocal diffractive lens generating several fixed foci at different design wavelengths,” Opt. Express 26(4), 4698–4709 (2018).
[Crossref] [PubMed]

U. Hinze, A. El-Tamer, L. L. Doskolovich, E. A. Bezus, S. Reiß, H. Stolz, R. F. Guthoff, O. Stachs, and B. Chichkov, “Additive manufacturing of a trifocal diffractive-refractive lens,” Opt. Commun. 372, 235–240 (2016).
[Crossref]

V. Osipov, L. L. Doskolovich, E. A. Bezus, T. Drew, K. Zhou, K. Sawalha, G. Swadener, and J. S. W. Wolffsohn, “Application of nanoimprinting technique for fabrication of trifocal diffractive lens with sine-like radial profile,” J. Biomed. Opt. 20(2), 025008 (2015).
[Crossref] [PubMed]

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, and V. A. Soifer, “Computer generated diffractive multi-focal lens,” J. Mod. Opt. 39(6), 1245–1251 (1992).
[Crossref]

Drew, T.

V. Osipov, L. L. Doskolovich, E. A. Bezus, T. Drew, K. Zhou, K. Sawalha, G. Swadener, and J. S. W. Wolffsohn, “Application of nanoimprinting technique for fabrication of trifocal diffractive lens with sine-like radial profile,” J. Biomed. Opt. 20(2), 025008 (2015).
[Crossref] [PubMed]

El-Tamer, A.

U. Hinze, A. El-Tamer, L. L. Doskolovich, E. A. Bezus, S. Reiß, H. Stolz, R. F. Guthoff, O. Stachs, and B. Chichkov, “Additive manufacturing of a trifocal diffractive-refractive lens,” Opt. Commun. 372, 235–240 (2016).
[Crossref]

Feng, S.

Ferrando, V.

Furlan, W.

Furlan, W. D.

V. Ferrando, F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Bifractal focusing and imaging properties of Thue-Morse Zone Plates,” Opt. Express 23(15), 19846–19853 (2015).
[Crossref] [PubMed]

J. A. Monsoriu, A. Calatayud, L. Remon, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photonics J. 5(3), 3400106 (2013).
[Crossref]

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010).
[Crossref]

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett. 32(15), 2109–2111 (2007).
[Crossref] [PubMed]

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28(12), 971–973 (2003).
[Crossref] [PubMed]

Gimenez, F.

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010).
[Crossref]

Giménez, F.

Golub, M. A.

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, and V. A. Soifer, “Computer generated diffractive multi-focal lens,” J. Mod. Opt. 39(6), 1245–1251 (1992).
[Crossref]

Gómez-Sarabia, C. M.

Guizar-Sicairos, M.

I. Mohacsi, I. Vartiainen, B. Rösner, M. Guizar-Sicairos, V. A. Guzenko, I. McNulty, R. Winarski, M. V. Holt, and C. David, “Interlaced zone plate optics for hard X-ray imaging in the 10 nm range,” Sci. Rep. 7(1), 43624 (2017).
[Crossref]

Guthoff, R. F.

U. Hinze, A. El-Tamer, L. L. Doskolovich, E. A. Bezus, S. Reiß, H. Stolz, R. F. Guthoff, O. Stachs, and B. Chichkov, “Additive manufacturing of a trifocal diffractive-refractive lens,” Opt. Commun. 372, 235–240 (2016).
[Crossref]

Guzenko, V. A.

I. Mohacsi, I. Vartiainen, B. Rösner, M. Guizar-Sicairos, V. A. Guzenko, I. McNulty, R. Winarski, M. V. Holt, and C. David, “Interlaced zone plate optics for hard X-ray imaging in the 10 nm range,” Sci. Rep. 7(1), 43624 (2017).
[Crossref]

Guzmán-Cabrera, R.

Guzmán-Cano, C.

Harmuth, H. F.

H. F. Harmuth, “Applications of Walsh functions in communications,” IEEE Spectr. 6(11), 82–91 (1969).
[Crossref]

Hazra, L. N.

P. Mukherjee and L. N. Hazra, “Self-similarity in radial Walsh filters and axial intensity distributions in the far-field diffraction pattern,” J. Opt. Soc. Am. A 31(2), 379–387 (2014).
[Crossref] [PubMed]

P. Mukherjee and L. N. Hazra, “Self-similarity in transverse intensity distributions in farfield diffraction patterns of radial Walsh filters,” Adv. Opt. 2014, 352316 (2014).
[Crossref]

L. N. Hazra, “Walsh filters for tailoring of resolution in microscopic imaging,” Micron 38(2), 129–135 (2007).
[Crossref] [PubMed]

L. N. Hazra, “A new class of optimum amplitude filters,” Opt. Commun. 21(2), 232–236 (1977).
[Crossref]

L. N. Hazra and A. Banerjee, “Applications of Walsh functions in generation of optimum apodizers,” J. Opt. 5, 19–26 (1976).

Hinze, U.

U. Hinze, A. El-Tamer, L. L. Doskolovich, E. A. Bezus, S. Reiß, H. Stolz, R. F. Guthoff, O. Stachs, and B. Chichkov, “Additive manufacturing of a trifocal diffractive-refractive lens,” Opt. Commun. 372, 235–240 (2016).
[Crossref]

Holt, M. V.

I. Mohacsi, I. Vartiainen, B. Rösner, M. Guizar-Sicairos, V. A. Guzenko, I. McNulty, R. Winarski, M. V. Holt, and C. David, “Interlaced zone plate optics for hard X-ray imaging in the 10 nm range,” Sci. Rep. 7(1), 43624 (2017).
[Crossref]

Kazanskiy, N. L.

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, and V. A. Soifer, “Computer generated diffractive multi-focal lens,” J. Mod. Opt. 39(6), 1245–1251 (1992).
[Crossref]

Kharitonov, S. I.

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, and V. A. Soifer, “Computer generated diffractive multi-focal lens,” J. Mod. Opt. 39(6), 1245–1251 (1992).
[Crossref]

Ledesma-Carrillo, L.

Maciá, E.

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69(2), 397–441 (2006).
[Crossref]

McCutchen, C. W.

McNulty, I.

I. Mohacsi, I. Vartiainen, B. Rösner, M. Guizar-Sicairos, V. A. Guzenko, I. McNulty, R. Winarski, M. V. Holt, and C. David, “Interlaced zone plate optics for hard X-ray imaging in the 10 nm range,” Sci. Rep. 7(1), 43624 (2017).
[Crossref]

Mohacsi, I.

I. Mohacsi, I. Vartiainen, B. Rösner, M. Guizar-Sicairos, V. A. Guzenko, I. McNulty, R. Winarski, M. V. Holt, and C. David, “Interlaced zone plate optics for hard X-ray imaging in the 10 nm range,” Sci. Rep. 7(1), 43624 (2017).
[Crossref]

Monsoriu, J.

Monsoriu, J. A.

V. Ferrando, F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Bifractal focusing and imaging properties of Thue-Morse Zone Plates,” Opt. Express 23(15), 19846–19853 (2015).
[Crossref] [PubMed]

J. A. Monsoriu, A. Calatayud, L. Remon, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photonics J. 5(3), 3400106 (2013).
[Crossref]

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010).
[Crossref]

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett. 32(15), 2109–2111 (2007).
[Crossref] [PubMed]

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28(12), 971–973 (2003).
[Crossref] [PubMed]

Morozov, A. A.

Mukherjee, P.

P. Mukherjee and L. N. Hazra, “Self-similarity in radial Walsh filters and axial intensity distributions in the far-field diffraction pattern,” J. Opt. Soc. Am. A 31(2), 379–387 (2014).
[Crossref] [PubMed]

P. Mukherjee and L. N. Hazra, “Self-similarity in transverse intensity distributions in farfield diffraction patterns of radial Walsh filters,” Adv. Opt. 2014, 352316 (2014).
[Crossref]

Niu, L. G.

Ojeda-Castañeda, J.

Osipov, V.

L. L. Doskolovich, E. A. Bezus, A. A. Morozov, V. Osipov, J. S. Wolffsohn, and B. Chichkov, “Multifocal diffractive lens generating several fixed foci at different design wavelengths,” Opt. Express 26(4), 4698–4709 (2018).
[Crossref] [PubMed]

V. Osipov, L. L. Doskolovich, E. A. Bezus, T. Drew, K. Zhou, K. Sawalha, G. Swadener, and J. S. W. Wolffsohn, “Application of nanoimprinting technique for fabrication of trifocal diffractive lens with sine-like radial profile,” J. Biomed. Opt. 20(2), 025008 (2015).
[Crossref] [PubMed]

Oti, J.

Reiß, S.

U. Hinze, A. El-Tamer, L. L. Doskolovich, E. A. Bezus, S. Reiß, H. Stolz, R. F. Guthoff, O. Stachs, and B. Chichkov, “Additive manufacturing of a trifocal diffractive-refractive lens,” Opt. Commun. 372, 235–240 (2016).
[Crossref]

Remon, L.

J. A. Monsoriu, A. Calatayud, L. Remon, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photonics J. 5(3), 3400106 (2013).
[Crossref]

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010).
[Crossref]

Rösner, B.

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[Crossref]

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Sawalha, K.

V. Osipov, L. L. Doskolovich, E. A. Bezus, T. Drew, K. Zhou, K. Sawalha, G. Swadener, and J. S. W. Wolffsohn, “Application of nanoimprinting technique for fabrication of trifocal diffractive lens with sine-like radial profile,” J. Biomed. Opt. 20(2), 025008 (2015).
[Crossref] [PubMed]

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M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, and V. A. Soifer, “Computer generated diffractive multi-focal lens,” J. Mod. Opt. 39(6), 1245–1251 (1992).
[Crossref]

Stachs, O.

U. Hinze, A. El-Tamer, L. L. Doskolovich, E. A. Bezus, S. Reiß, H. Stolz, R. F. Guthoff, O. Stachs, and B. Chichkov, “Additive manufacturing of a trifocal diffractive-refractive lens,” Opt. Commun. 372, 235–240 (2016).
[Crossref]

Stolz, H.

U. Hinze, A. El-Tamer, L. L. Doskolovich, E. A. Bezus, S. Reiß, H. Stolz, R. F. Guthoff, O. Stachs, and B. Chichkov, “Additive manufacturing of a trifocal diffractive-refractive lens,” Opt. Commun. 372, 235–240 (2016).
[Crossref]

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V. Osipov, L. L. Doskolovich, E. A. Bezus, T. Drew, K. Zhou, K. Sawalha, G. Swadener, and J. S. W. Wolffsohn, “Application of nanoimprinting technique for fabrication of trifocal diffractive lens with sine-like radial profile,” J. Biomed. Opt. 20(2), 025008 (2015).
[Crossref] [PubMed]

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I. Mohacsi, I. Vartiainen, B. Rösner, M. Guizar-Sicairos, V. A. Guzenko, I. McNulty, R. Winarski, M. V. Holt, and C. David, “Interlaced zone plate optics for hard X-ray imaging in the 10 nm range,” Sci. Rep. 7(1), 43624 (2017).
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I. Mohacsi, I. Vartiainen, B. Rösner, M. Guizar-Sicairos, V. A. Guzenko, I. McNulty, R. Winarski, M. V. Holt, and C. David, “Interlaced zone plate optics for hard X-ray imaging in the 10 nm range,” Sci. Rep. 7(1), 43624 (2017).
[Crossref]

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V. Osipov, L. L. Doskolovich, E. A. Bezus, T. Drew, K. Zhou, K. Sawalha, G. Swadener, and J. S. W. Wolffsohn, “Application of nanoimprinting technique for fabrication of trifocal diffractive lens with sine-like radial profile,” J. Biomed. Opt. 20(2), 025008 (2015).
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[Crossref]

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M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, and V. A. Soifer, “Computer generated diffractive multi-focal lens,” J. Mod. Opt. 39(6), 1245–1251 (1992).
[Crossref]

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[Crossref]

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Supplementary Material (1)

NameDescription
» Visualization 1       Images obtained with a Walsh Zone Plate and with the equivalent periodic zone plate of the same resolution.

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Figures (7)

Fig. 1
Fig. 1 Graphical representation of the Walsh functions up to order k = 64. The yellow bars correspond to the value + 1 while the red bars correspond to the value ‒1. The blue arrow indicates the order k = 22, which has been used to design the WZP shown in Fig. 2.
Fig. 2
Fig. 2 (a) WZP generated from the 1-D function q22(ς) shown in Fig. 1 and a FZP with the same number of Fresnel zones. Yellow and red rings correspond to a phase 0 ( + 1 transmittance value) and π (‒1 transmittance value), respectively. (b) Numerically computed axial irradiance produced by both lenses shown against the reduced axial coordinate u.
Fig. 3
Fig. 3 The grey-code bars represent the normalized axial irradiances, I, for WZPs of different orders k, being I = 1 in the white regions and I = 0 in the black regions. The reduced axial coordinate has been normalized to = u/N, where N is the number of zones. The red, green and blue boxes show the same structure at different scales.
Fig. 4
Fig. 4 Experimental setup for the assessment of (a) the multi-focusing properties of WZPs and (b) the multi-imaging capabilities by replacing the laser light source by a monochromatic LED illuminating a binary object (a smiley face).
Fig. 5
Fig. 5 (a) Experimental transverse intensity distribution produced by a WZP of order k = 22. (b) Profile of Fig. 5(a) (blue line) showing the axial irradiance distribution. The theoretical values of the irradiance are shown in green line for comparison. In both cases, the values are normalized to the peak intensity.
Fig. 6
Fig. 6 (6.15 Mb) Images obtained with the WZP of order k = 22 and with the equivalent periodic zone plate of the same resolution (see Visualization 1). Five different location, z, were considered corresponding to the four image planes of the quadrifocal WZP (first, second, fourth and fifth rows) and the image plane of the monofocal FZP (third row).
Fig. 7
Fig. 7 (a) Experimental setup used to obtain images of different axially displaced objects at the same image plane. (b) Experimental results obtained with an amplitude WZP of order k = 22. The position of the object is given in diopters.

Tables (1)

Tables Icon

Table 1 Ratios of the full width at half-maximum (FWHM) of the axial irradiance peaks provided by the WZP and the corresponding FZP with the same number of zones. A, B, C, and D correspond to the peaks shown in Fig. 5.

Equations (4)

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k= i=0 m1 k i 2 i ,
q k ( ς )= i=0 m1 sgn[ cos( π 2 i k i ς ) ] .
sgn[ x ]={ +1, x>0 0, x=0 1, x<0 .
I(u)=4 π 2 u 2 | 0 1 q(ζ)exp( i2πuζ )dζ | 2 ,

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