Abstract

Large-aperture linear diffractive axicons are optical devices providing achromatic nondiffracting beams with an extended depth of focus when illuminated by white light sources. Annular apertures introduce chromatic foci separation, making chromatic imaging possible despite important radiometric losses. Recently, a new type of diffractive axicon has been introduced, by multiplexing concentric annular axicons with appropriate sizes and periods, called a multiple annular linear diffractive axicon (MALDA). This new family of conical optics combines multiple annular axicons in different ways to optimize color foci recombination, separation, or interleaving. We present different types of MALDA, give an experimental illustration of the use of these devices, and describe the manufacturing issues related to their fabrication to provide color imaging systems with long focal depths and good diffraction efficiency. Application to multispectral image analysis is discussed.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954).
    [CrossRef]
  2. J. Durnin, “Exact solutions for nondiffracting beams, I: The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  3. G. Mikua, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
    [CrossRef]
  4. 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]
  5. I. Golub, “Fresnel axicon,” Opt. Lett. 31, 1890–1892 (2006).
    [CrossRef] [PubMed]
  6. J. Sochacki, Z. Jaroszewicz, L. R. Staronski, and A. Kolodeziejczyk, “Annular aperture logarithmic axicon” J. Opt. Soc. Am. A 10, 1765–1768 (1993).
    [CrossRef]
  7. J. Perez, J. Espinosal, C. Illuecal, C. Vasquez, and I. Moreno, “Real time modulable multifocality through annular optical elements,” Opt. Express 16, 5095–5106 (2008).
    [CrossRef] [PubMed]
  8. L. Niggl, T. Lanzl, and M. Maier, “Properties of Bessel beams generated by periodic grating of circular geometry,” J. Opt. Soc. Am. A 14, 27–33 (1997).
    [CrossRef]
  9. V. Kettunen, J. Simonen, O. Ripoll, M. Kuittinen, 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.
  10. E. Bialic and J. L. de Bougrenet de la Tocnaye, “Multiple annular linear diffractive axicons (MALDA),” J. Opt. Soc. Am. A 28, 523–533 (2011).
    [CrossRef]
  11. C. J. Zapata-Rodriguez and A. Sanchez-Losa, “Three dimensional field distribution in the focal region of low-Fresnel number axicon,” J. Opt. Soc. Am. A 23, 3016–3026(2006).
    [CrossRef]
  12. E. Bialic, M. Piponnier, N. Guérineau, G. Druart, and J. L. de Bougrenet, “Spectro-imaging properties of annular diffractive axicons,” Proc. EOS on Advanced Imaging Systems, (29 June–2 July, 2010).

2011 (1)

2008 (2)

2006 (2)

2005 (1)

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

2002 (1)

V. Kettunen, J. Simonen, O. Ripoll, M. Kuittinen, 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.

1997 (1)

1993 (1)

1987 (1)

1954 (1)

Bialic, E.

E. Bialic and J. L. de Bougrenet de la Tocnaye, “Multiple annular linear diffractive axicons (MALDA),” J. Opt. Soc. Am. A 28, 523–533 (2011).
[CrossRef]

E. Bialic, M. Piponnier, N. Guérineau, G. Druart, and J. L. de Bougrenet, “Spectro-imaging properties of annular diffractive axicons,” Proc. EOS on Advanced Imaging Systems, (29 June–2 July, 2010).

de Bougrenet, J. L.

E. Bialic, M. Piponnier, N. Guérineau, G. Druart, and J. L. de Bougrenet, “Spectro-imaging properties of annular diffractive axicons,” Proc. EOS on Advanced Imaging Systems, (29 June–2 July, 2010).

de Bougrenet de la Tocnaye, J. L.

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,” Proc. EOS on Advanced Imaging Systems, (29 June–2 July, 2010).

Durnin, J.

Espinosal, J.

Golub, I.

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,” Proc. EOS on Advanced Imaging Systems, (29 June–2 July, 2010).

Haïdat, R.

Herzig, H. P.

V. Kettunen, J. Simonen, O. Ripoll, M. Kuittinen, 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.

Illuecal, C.

Jaroszewicz, Z.

Kattnig, A.

Kettunen, V.

V. Kettunen, J. Simonen, O. Ripoll, M. Kuittinen, 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.

Kolodeziejczyk, A.

Kolodziejczyk, A.

G. Mikua, 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, O. Ripoll, M. Kuittinen, 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.

Maier, M.

Makowski, M.

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

McLeod, V. J. H.

Mikua, G.

G. Mikua, 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.

Perez, J.

Piponnier, M.

E. Bialic, M. Piponnier, N. Guérineau, G. Druart, and J. L. de Bougrenet, “Spectro-imaging properties of annular diffractive axicons,” Proc. EOS on Advanced Imaging Systems, (29 June–2 July, 2010).

Primot, J.

Prokopowicz, C.

G. Mikua, 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, O. Ripoll, M. Kuittinen, 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.

Sanchez-Losa, A.

Sauer, H.

Simonen, J.

V. Kettunen, J. Simonen, O. Ripoll, M. Kuittinen, 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.

Sochacki, J.

Staronski, L. R.

Sypek, M.

G. Mikua, 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.

Vasquez, C.

Zapata-Rodriguez, C. J.

J. Opt. Soc. Am. (1)

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

Opt. Eng. (1)

G. Mikua, 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 (1)

Opt. Lett. (2)

Other (2)

V. Kettunen, J. Simonen, O. Ripoll, M. Kuittinen, 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. Piponnier, N. Guérineau, G. Druart, and J. L. de Bougrenet, “Spectro-imaging properties of annular diffractive axicons,” Proc. EOS on Advanced Imaging Systems, (29 June–2 July, 2010).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

On axis diffracted fields for various apertures, for an RGB LED source, d = 60 μm , (a)  R min = 3 mm , R max = 10 mm , (b)  R min = 3 mm , R max = 6 mm , (c)  R min = 5.5 mm R max = 6 mm .

Fig. 3
Fig. 3

4-MALDA grating profiles (quarter of the pupil only displayed), R max = 1.5 mm , R min = 0.4 mm . (b) Principle of the color foci superimposition with a three ring MALDA.

Fig. 4
Fig. 4

3-iMALDA: (a) Grating profile, R max = 2 mm , R max = 1.73 mm , R max = 1.61 mm , R min = 1.5 mm , with d = 20 μm , 16 μm , and 17 μm . (b) Principle of the color foci interleaving.

Fig. 5
Fig. 5

iMALDA example of color foci interleaving, with the blue and red foci superimposing here between 26 and 30 cm .

Fig. 6
Fig. 6

Part of a MALDA cross section at the interferometric microscope.

Fig. 7
Fig. 7

Imaging of a white object by a single axicon observed at: (a)  z = 20 cm with τ = 18 ms , (b)  z = 28 cm with τ = 26 ms , (c)  z = 47 cm with τ = 60 ms , (d)  z = 72 cm with τ = 133 ms , compared to an equivalent MALDA observed at the same locations with, respectively, (e)  τ = 6 , (f) 7, (g) 15, and (h)  38 ms .

Fig. 8
Fig. 8

Magnification factor as a function of the focal distance corresponding to Fig. 6.

Fig. 9
Fig. 9

Chromatic foci of triple MALDA; vertical lines indicate the locations of the CCD.

Fig. 10
Fig. 10

Visualization of the higher orders + 5 and + 3 when imaging the “EOS” picture: (a)  + 5 order with z = 8 cm , (b), (c), and (d)  + 3 order, with, respectively, z = 9 cm , z = 11 cm , and z = 13 cm , compared to the + 1 order in (e), (f), (g), and (h) with z = 27 cm , z = 34 cm , z = 35 cm , and z = 49 cm , respectively.

Fig. 11
Fig. 11

Multispectral imaging of the Aculed (a) by a single axicon observed at: (b)  z = 11.5 cm with τ = 54 ms and (c)  z = 17.5 cm with τ = 82 ms , compared to the MALDA observed at locations displayed in Fig. 7, (d)  z = 11.5 cm with τ = 16 ms , (e)  z = 13.5 cm with τ = 16 ms , (f)  z = 15.5 cm with τ = 22 ms , (g)  z = 17.5 cm with τ = 28 ms , and (h)  z = 26 cm with τ = 44 ms .

Fig. 12
Fig. 12

Multispectral imaging of the Aculed by the iMALDA at (a)  z = 33 cm and (b)  z = 47 cm . (c) Imaging the letter “y” with a composite color obtained by color superimposition at z = 12 cm .

Equations (8)

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

T bin ( r ) = m = c m ( λ ) exp ( i k sin ( θ m ) r ) with sin θ m = m λ / d ,
PSF m ( r , z ) = π 2 λ z θ m 2 λ 2 J 0 2 ( 2 π θ m λ r )
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 ) .
R max ( 1 ) ( λ M ) = [ 1 Δ λ λ M ] R max ( 0 ) with R max ( 1 ) ( λ M ) = R min ( 0 ) ( λ M ) .
| Δ R ( n ) | = | R ( n 1 ) R ( n ) | = Δ λ λ M [ 1 Δ λ λ M ] ( n 1 ) ϕ 2 .
S = 1 [ 1 Δ λ λ min ] ,
R max = λ B min λ C max R min with z C max = d R max λ C min and z C min = d R min λ C max .
d = z C max λ C min R min and R min = z C min λ C max d .

Metrics