Abstract

We propose a chromatic analysis of multiple annular linear diffractive axicons. Large aperture axicons are optical devices providing achromatic nondiffracting beams, with an extended depth of focus, when illuminated by a white light source, due to chromatic foci superimposition. Annular apertures introduce chromatic foci separation, and because chromatic aberrations result in focal segment axial shifts, polychromatic imaging properties are partially lost. We investigate here various design parameters that can be used to achieve color splitting, filtering, and combining using these properties. In order to improve the low-power efficiency of a single annular axicon, we suggest a spatial multiplexing of concentric annular axicons with different sizes and periods we call multiple annular aperture diffractive axicons (MALDAs). These are chosen to maintain focal depths while enabling color imaging with sufficient diffraction efficiency. Illustrations are given for binary phase diffractive axicons, considering technical aspects such as grating design wavelength and phase dependence due to the grating thickness.

© 2011 Optical Society of America

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2009 (1)

2008 (3)

2007 (2)

2006 (1)

2005 (1)

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

1997 (1)

1996 (1)

1989 (1)

1987 (1)

1986 (1)

1984 (1)

J. E. Harvey and J. L. Forgham, “The spot of Arago: new relevance for an old phenomenon,” Am. J. Phys. 52, 243–247 (1984).
[CrossRef]

1960 (1)

1958 (1)

J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. Lond. A 248, 93–106 (1958).
[CrossRef]

1954 (1)

Bialic, E.

E. Bialic, M. Kessels, I. Hardy, P. Grosso, K. Heggarty, T. Torrès, and P. Pellat-Finet, “Phototraceur UV à micromiroirs pour fonctions optiques intégrées diffractives,” in Proceedings of JNOG, (Journée Nationale d'Optique Guidée, 2008), pp. 128–130.

E. Bialic, M. Piponnier, N. Guérineau, G. Druart, and J. L. de Bougrenet, “Spectro-imaging properties of annular diffractive axicons,” presented at the 5th EOS Topical Meeting on Advanced Imaging Techniques, Engelberg, Switzerland, 29 June–2 July 2010.

Burvall, A.

Dainty, C.

de Bougrenet, J. L.

E. Bialic, M. Piponnier, N. Guérineau, G. Druart, and J. L. de Bougrenet, “Spectro-imaging properties of annular diffractive axicons,” presented at the 5th EOS Topical Meeting on Advanced Imaging Techniques, Engelberg, Switzerland, 29 June–2 July 2010.

Druart, G.

G. Druart, J. Taboury, N. Guérineau, R. Haïdat, H. Sauer, A. Kattnig, and J. Primot, “Demonstration of image-zooming capability for diffractive axicons,” Opt. Lett. 33, 366–368(2008).
[CrossRef] [PubMed]

E. Bialic, M. Piponnier, N. Guérineau, G. Druart, and J. L. de Bougrenet, “Spectro-imaging properties of annular diffractive axicons,” presented at the 5th EOS Topical Meeting on Advanced Imaging Techniques, Engelberg, Switzerland, 29 June–2 July 2010.

Durnin, J.

Dyson, J.

J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. Lond. A 248, 93–106 (1958).
[CrossRef]

Espinosa, J.

Espinosal, J.

Forgham, J. L.

J. E. Harvey and J. L. Forgham, “The spot of Arago: new relevance for an old phenomenon,” Am. J. Phys. 52, 243–247 (1984).
[CrossRef]

Gomez-Reino, C.

Goncharov, A. V.

Grosso, P.

E. Bialic, M. Kessels, I. Hardy, P. Grosso, K. Heggarty, T. Torrès, and P. Pellat-Finet, “Phototraceur UV à micromiroirs pour fonctions optiques intégrées diffractives,” in Proceedings of JNOG, (Journée Nationale d'Optique Guidée, 2008), pp. 128–130.

Guérineau, N.

G. Druart, J. Taboury, N. Guérineau, R. Haïdat, H. Sauer, A. Kattnig, and J. Primot, “Demonstration of image-zooming capability for diffractive axicons,” Opt. Lett. 33, 366–368(2008).
[CrossRef] [PubMed]

E. Bialic, M. Piponnier, N. Guérineau, G. Druart, and J. L. de Bougrenet, “Spectro-imaging properties of annular diffractive axicons,” presented at the 5th EOS Topical Meeting on Advanced Imaging Techniques, Engelberg, Switzerland, 29 June–2 July 2010.

Haïdat, R.

Hardy, I.

E. Bialic, M. Kessels, I. Hardy, P. Grosso, K. Heggarty, T. Torrès, and P. Pellat-Finet, “Phototraceur UV à micromiroirs pour fonctions optiques intégrées diffractives,” in Proceedings of JNOG, (Journée Nationale d'Optique Guidée, 2008), pp. 128–130.

Harvey, J. E.

J. E. Harvey and J. L. Forgham, “The spot of Arago: new relevance for an old phenomenon,” Am. J. Phys. 52, 243–247 (1984).
[CrossRef]

Heggarty, K.

E. Bialic, M. Kessels, I. Hardy, P. Grosso, K. Heggarty, T. Torrès, and P. Pellat-Finet, “Phototraceur UV à micromiroirs pour fonctions optiques intégrées diffractives,” in Proceedings of JNOG, (Journée Nationale d'Optique Guidée, 2008), pp. 128–130.

Herzig, H. P.

V. Kettunen, J. Simonen, M. Kuittinen, O. Ripoll, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zero order due to surface depth error,” in Diffractive Optics and Micro-Optics, R.Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), paper DMD3.

Illueca, C.

Illuecal, C.

Indebetouw, G.

Jaroszewicz, Z.

Kattnig, A.

Kessels, M.

E. Bialic, M. Kessels, I. Hardy, P. Grosso, K. Heggarty, T. Torrès, and P. Pellat-Finet, “Phototraceur UV à micromiroirs pour fonctions optiques intégrées diffractives,” in Proceedings of JNOG, (Journée Nationale d'Optique Guidée, 2008), pp. 128–130.

Kettunen, V.

V. Kettunen, J. Simonen, M. Kuittinen, O. Ripoll, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zero order due to surface depth error,” in Diffractive Optics and Micro-Optics, R.Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), paper DMD3.

Kolodziejczyk, A.

M. Makowski, M. Sypek, and A. Kolodziejczyk, “Colorful reconstructions from a thin multi-plane phase hologram,” Opt. Express 16, 11618–11623 (2008).
[CrossRef] [PubMed]

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

Kuittinen, M.

V. Kettunen, J. Simonen, M. Kuittinen, O. Ripoll, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zero order due to surface depth error,” in Diffractive Optics and Micro-Optics, R.Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), paper DMD3.

Lanzl, T.

Mahajan, V. N.

Maier, M.

Makowski, M.

M. Makowski, M. Sypek, and A. Kolodziejczyk, “Colorful reconstructions from a thin multi-plane phase hologram,” Opt. Express 16, 11618–11623 (2008).
[CrossRef] [PubMed]

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

Martinez, J. L.

Martinez-Garcia, A.

Mas, D.

McLeod, J. H.

Mikula, G.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

Moreno, I.

Niggl, L.

Pellat-Finet, P.

E. Bialic, M. Kessels, I. Hardy, P. Grosso, K. Heggarty, T. Torrès, and P. Pellat-Finet, “Phototraceur UV à micromiroirs pour fonctions optiques intégrées diffractives,” in Proceedings of JNOG, (Journée Nationale d'Optique Guidée, 2008), pp. 128–130.

Perez, J.

Piponnier, M.

E. Bialic, M. Piponnier, N. Guérineau, G. Druart, and J. L. de Bougrenet, “Spectro-imaging properties of annular diffractive axicons,” presented at the 5th EOS Topical Meeting on Advanced Imaging Techniques, Engelberg, Switzerland, 29 June–2 July 2010.

Primot, J.

Prokopowicz, C.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

Ripoll, O.

V. Kettunen, J. Simonen, M. Kuittinen, O. Ripoll, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zero order due to surface depth error,” in Diffractive Optics and Micro-Optics, R.Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), paper DMD3.

Roman Dopazo, J. F.

Sanchez-Losa, A.

Sauer, H.

Simonen, J.

V. Kettunen, J. Simonen, M. Kuittinen, O. Ripoll, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zero order due to surface depth error,” in Diffractive Optics and Micro-Optics, R.Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), paper DMD3.

Sypek, M.

M. Makowski, M. Sypek, and A. Kolodziejczyk, “Colorful reconstructions from a thin multi-plane phase hologram,” Opt. Express 16, 11618–11623 (2008).
[CrossRef] [PubMed]

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

Taboury, J.

Torrès, T.

E. Bialic, M. Kessels, I. Hardy, P. Grosso, K. Heggarty, T. Torrès, and P. Pellat-Finet, “Phototraceur UV à micromiroirs pour fonctions optiques intégrées diffractives,” in Proceedings of JNOG, (Journée Nationale d'Optique Guidée, 2008), pp. 128–130.

Vasquez, C.

Wilford, W. T.

Zapata-Rodriguez, C. J.

Am. J. Phys. (1)

J. E. Harvey and J. L. Forgham, “The spot of Arago: new relevance for an old phenomenon,” Am. J. Phys. 52, 243–247 (1984).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

Opt. Eng. (1)

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. R. Soc. Lond. A (1)

J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. Lond. A 248, 93–106 (1958).
[CrossRef]

Other (3)

V. Kettunen, J. Simonen, M. Kuittinen, O. Ripoll, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zero order due to surface depth error,” in Diffractive Optics and Micro-Optics, R.Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), paper DMD3.

E. Bialic, M. Kessels, I. Hardy, P. Grosso, K. Heggarty, T. Torrès, and P. Pellat-Finet, “Phototraceur UV à micromiroirs pour fonctions optiques intégrées diffractives,” in Proceedings of JNOG, (Journée Nationale d'Optique Guidée, 2008), pp. 128–130.

E. Bialic, M. Piponnier, N. Guérineau, G. Druart, and J. L. de Bougrenet, “Spectro-imaging properties of annular diffractive axicons,” presented at the 5th EOS Topical Meeting on Advanced Imaging Techniques, Engelberg, Switzerland, 29 June–2 July 2010.

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Figures (13)

Fig. 1
Fig. 1

First-order diffraction efficiency as a function of the reading wavelength for thickness e = 565 nm , a design wavelength of 723 nm , and λ B = 460 nm , λ G = 520 nm , λ R = 640 nm .

Fig. 2
Fig. 2

Binary phase grating (a) view and (b) cross section observed at the interferometric microscope, with a depth resolution of 20 nm and a spatial resolution of 500 nm (using a Sony CCD ICX039).

Fig. 3
Fig. 3

Foci and cross section of an annular aperture diffractive axicon illuminated by a polychromatic source. Only orders 0, 1 , and + 1 are represented.

Fig. 4
Fig. 4

First and third orders on axis longitudinal fields for an RGB source, d = 60 μm , R min = 3 mm , and R max = 7 mm , for (a) binary phase ( e = 565 nm ) gratings, and (b) the corresponding amplitude gratings. Arbitrary units in ordinate; propagation distance in abscissa.

Fig. 5
Fig. 5

Nondiffracting field in the far-field regime of a thin annular aperture observed in the focal plane of a converging lens, corresponding to an asymptotic case of annular axicon.

Fig. 6
Fig. 6

Annular linear diffractive axicon focal planes (first and third orders) for various Δ R / d : (a) ALDA3, Δ R / d = 116 , R min = 3 mm , R max = 10 mm ; (b) ALDA2, Δ R / d = 50 , R min = 3 mm , R max = 6 mm ; (c) ALDA1, Δ R / d = 8 , R min = 5.5 mm , R max = 6 mm ; (d) pinhole case, Δ R / d = 1 , R min = 3 mm , R max = 3.1 mm . Arbitrary units in ordinate, propagation distance in abscissa.

Fig. 7
Fig. 7

Parts of ALDA radial distribution: (a) ALDA1, R max = 10 mm , Δ R = 0.5 mm ; ALDA2 R max = 2.5 mm , Δ R = 1 mm , on the same substrate d = 40 μm , z = 33 cm ; (b) ALDA3 alone, R max = 2.5 mm , Δ R = 2 mm , d = 40 μm , z = 36 cm . Thickness, e = 565 nm .

Fig. 8
Fig. 8

Color splitting and filtering by a dark spot in the annular axicon focal plane.

Fig. 9
Fig. 9

Color filtering from an annular axicon illuminated by a collimated white LED: (a) LED spectrum; (b) radial plane observation without the filter; (c) observation with the filter at z f = 35 cm , for R f = 0.5 mm ; (d) for R f = 0.25 mm .

Fig. 10
Fig. 10

Cross section of a double annular aperture diffractive axicon illuminated by a polychromatic source. Each annular axicon having different periods d and d . Only orders 0, 1 , and + 1 are represented.

Fig. 11
Fig. 11

Cross section (a) of a double ALDA observed at the interferometric microscope; (b) first-order focus intensity profile measured along z, when illuminated by a white LED filtered in the red.

Fig. 12
Fig. 12

Double aperture axicon first- and third-order foci (a) outer ring contribution, R = 5 mm , Δ R = 0.5 mm , d = 60 μm ; (b) inner ring, R = 3.75 mm , Δ R = 0.4 mm , d = 80 μm ; (c) superimposition of outer and inner rings; (d) interleaving of outer and inner rings, for R = 6 mm , Δ R = 0.5 mm , d = 60 μm , R = 3.75 mm , Δ R = 0.4 mm , d = 80 μm . Arbitrary units in ordinate, propagation distance in abscissa.

Fig. 13
Fig. 13

Grating profile of a four-multiplexed MALDA (pupil quarter), R max = 1.5 mm , R min = 0.4 mm .

Equations (15)

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T bin ( r ) = m = c m exp ( i k sin ( θ m ) r ) , with   sin θ m = m λ / d ,
I ( r , z ) = π 2 λ z m | c m | 2 θ m 2 λ 2 J 0 2 ( 2 π θ m λ r ) .
η m ( ϕ ) = 1 4 | 1 + e i ϕ e i m π | 2 ( sin ( m π / 2 ) m π / 2 ) 2 .
R min = min λ ( z min λ / d ) , R max = z max λ max / d .
N F = α θ / λ , with the maximum focus value   L = α / θ ,
R min R min z red z = R min + Δ R z blue z ( R min + Δ R ) ,
z = 2 R min + Δ R R min + Δ R z blue + R min z red .
z f = 2 R + min Δ R λ B + λ R d ,
R f = R max λ R 2 R + min Δ R λ B + λ R .
d R max 1 λ = d R max 2 λ ,
Δ R d = Δ R d .
R max ( 1 ) ( λ ) = [ 1 Δ λ λ ] R max ( 0 ) , with   R max ( 1 ) ( λ ) = R min ( 0 ) ( λ ) .
R min ( n ) ( λ ) = [ 1 Δ λ λ ] R min ( n 1 ) ( λ ) , and   R min ( n ) ( λ ) = [ 1 Δ λ λ ] n ϕ 2 ,
| Δ R ( n ) | = | R ( n 1 ) R ( n ) | = Δ λ λ [ 1 Δ λ λ ] ( n 1 ) ϕ 2 .
n = ln ( 2 β λ 2 / ϕ Δ λ ) ln ( 1 Δ λ / λ ) 1 ,

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