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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 25 — Dec. 6, 2010
  • pp: 25808–25814
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Realization of binary radial diffractive optical elements by two-photon polymerization technique

Vladimir Osipov, Vladimir Pavelyev, Denis Kachalov, Albertas Žukauskas, and Boris Chichkov  »View Author Affiliations


Optics Express, Vol. 18, Issue 25, pp. 25808-25814 (2010)
http://dx.doi.org/10.1364/OE.18.025808


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Abstract

Application of the two-photon polymerization (2PP) technique for the fabrication of submicron-size relief of radial binary diffractive optical elements (DOE’s) is studied. Binary DOE’s for the formation of special longitudinal intensity distribution (axial light segment) are realized. Interferometric investigations of the diffractive relief produced by the 2PP-technique and investigations of optical properties of the formed elements are presented. Results of computer simulations are in good agreement with the experimental observations.

© 2010 OSA

1. Introduction

The two-photon polymerization (2PP) technique has been demonstrated as a powerful tool for the fabrication of high resolution 3D microstructures. By tightly focusing femtosecond laser pulses into the volume of a photosensitive polymer resin, 2PP can be produced in a tiny region of focal spot, where the accumulated energy is higher than the polymerization threshold. As a result, with the 2PP technique it is possible to produce arbitrary 3D structures with subwavelength resolution (see, for example [1

1. S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412(6848), 697–698 (2001). [CrossRef] [PubMed]

5

5. J. Serbin, A. Ovsianikov, and B. Chichkov, “Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties,” Opt. Express 12(21), 5221–5228 (2004). [CrossRef] [PubMed]

], and references herein). It has been reported [6

6. W. Haske, V. W. Chen, J. M. Hales, W. Dong, S. Barlow, S. R. Marder, and J. W. Perry, “65 nm feature sizes using visible wavelength 3-D multiphoton lithography,” Opt. Express 15(6), 3426–3436 (2007). [CrossRef] [PubMed]

] that 2PP technique allows reaching the structuring resolution of up to 65 nm. The high resolution and relatively low costs make it reasonable to use this technique not only for 3D structuring but also for the fabrication of diffractive microrelief. Due to two-photon absorption, higher resolution than it could be possible with the well-known laser direct writing process [7

7. L. L. Doskolovich, D. L. Golovashkin, N. L. Kazanskiy, S. N. Khonina, V. V. Kotlyar, V. S. Pavelyev, R. V. Skidanov, V. A. Soifer, V. S. Solovyev, G. V. Uspleniev, and A. V. Volkov, Methods for Computer Design of Diffractive Optical Elements, Ed. by V. A. Soifer (John Wiley, 2002).

,8

8. V. P. Korolkov, R. K. Nasyrov, and R. V. Shimansky, “Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements,” Appl. Opt. 45(1), 53–62 (2006). [CrossRef] [PubMed]

] can be obtained.

The capability of the 2PP method for the fabrication of high quality diffractive optical elements (DOE’s) with continuous-like diffractive microrelief has been demonstrated in [9

9. B. Jia, J. Serbin, H. Kim, B. Lee, J. Li, and M. Gu, “Use of two-photon polymerization for continuous gray-level encoding of diffractive optical elements,” Appl. Phys. Lett. 90, 1–3 (2007). [CrossRef]

]. Application of the 2PP technique for realization of continuous-like diffractive microrelief on the top of optical fibers has been investigated in [10

10. G. Cojoc, C. Liberale, P. Candeloro, F. Gentile, G. Das, F. De Angelis, and E. Di Fabrizio, “Optical micro-structures fabricated on top of optical fibers by means of two-photon photopolymerization,” Microelectron. Eng. 87, 876–879 (2010). [CrossRef]

]. However, the fabrication of DOE’s with continuous-like diffractive microrelief has been restricted to small DOE aperture sizes (less than 300 microns) due to a relatively long 2PP fabrication time. Possibility of more effective use of laser radiation based on multi-focus 2PP with a special light modulator has been demonstrated in [11

11. K. Obata, J. Koch, U. Hinze, and B. N. Chichkov, “Multi-focus two-photon polymerization technique based on individually controlled phase modulation,” Opt. Express 18(16), 17193–17200 (2010). [CrossRef] [PubMed]

].

The present paper is devoted to the realization of binary (two-level) diffractive microrelief of radial DOE’s using the 2PP-technique. These DOE’s can be applied for the generation of any desired longitudinal intensity distributions (coaxial lines, sets of sequential axial focuses, etc.) required for many laser technologies. As important examples the following applications can be mentioned: laser alignment of different units at large distances [12

12. K. Wang, L. Zeng, and Ch. Yin, “Influence of the incident wave-front on intensity distribution of the nondiffracting beam used in large-scale measurement,” Opt. Commun. 216, 99–103 (2003). [CrossRef]

], formation of images from extended or moving objects, which is also required for medicine [13

13. L. Jian-yu and J. F. Greenleaf, “Diffraction-limited beams and their applications for ultrasonic imaging and tissue characterization,” Proc. SPIE 1733, 92–119 (1992). [CrossRef]

,14

14. R. A. Leitgeb, M. Villiger, A. H. Bachmann, L. Steinmann, and T. Lasser, “Extended focus depth for Fourier domain optical coherence microscopy,” Opt. Lett. 31(16), 2450–2452 (2006). [CrossRef] [PubMed]

], nondestructive investigations of materials [15

15. K. S. Lee and J. P. Rolland, “Bessel beam spectral-domain high-resolution optical coherence tomography with micro-optic axicon providing extended focusing range,” Opt. Lett. 33(15), 1696–1698 (2008). [CrossRef] [PubMed]

] and devices [16

16. J. Y. Lu and J. F. Greenleaf, “Producing deep depth of field and depth-independent resolution in NDE with limited diffraction beams,” Ultrason. Imaging 15(2), 134–149 (1993). [CrossRef] [PubMed]

], laser scanning [17

17. J. J. Lunazzi, D. S. F. Magalhães, “Photographing by means of a diffractive axicon,” http://arxiv.org/pdf/physics/0701234.

,18

18. R. Arimoto, C. Saloma, T. Tanaka, and S. Kawata, “Imaging properties of axicon in a scanning optical system,” Appl. Opt. 31(31), 6653–6657 (1992). [CrossRef] [PubMed]

] and interferometry [19

19. M. Fortin, M. Piché, and E. F. Borra, “Optical tests with Bessel beam interferometry,” Opt. Express 12(24), 5887–5895 (2004). [CrossRef] [PubMed]

,20

20. S. Reichelt, H. Tiziani, and H. Zappe, “Self-calibration of wavefront testing interferometers by use of diffractive elements,” Proc. SPIE 6292, 629205.1–629205.10 (2006).

], as well as, the fabrication of intraocular lenses [21

21. A. L. Cohen, “Practical design of a bifocal hologram contact lens or intraocular lens,” Appl. Opt. 31(19), 3750–3754 (1992). [CrossRef] [PubMed]

].

In this paper, application of the 2PP technique for the realization of radial binary diffractive microreliefs (with a 2 mm aperture) is studied. To design the binary relief structures, a special numerical technique developed in [22

22. D. G. Kachalov, V. S. Pavelyev, S. H. Khonina, R. V. Skidanov, and O. Y. Moiseev, “Stochastic optimization of radial DOE forming intensity distribution along an axial focal zone,” Proc. SPIE 7717, 77170E (2010). [CrossRef]

] is applied. Note that the same structures can be produced by ordinary laser and electron beam writer systems. Compared to these systems, 2PP allows the fabrication of much more complex multilayer structures. That is why the DOE fabrication with 2PP technique has much better prospects.

2. Design of binary DOE’s for the forming of special longitudinal intensity distributions

Application of DOE for the transformation of a Gaussian laser beam into a required longitudinal intensity distribution is illustrated in Fig. 1
Fig. 1 Optical scheme for the formation of a longitudinal intensity distribution.
.

Using the Fresnel integral approach [7

7. L. L. Doskolovich, D. L. Golovashkin, N. L. Kazanskiy, S. N. Khonina, V. V. Kotlyar, V. S. Pavelyev, R. V. Skidanov, V. A. Soifer, V. S. Solovyev, G. V. Uspleniev, and A. V. Volkov, Methods for Computer Design of Diffractive Optical Elements, Ed. by V. A. Soifer (John Wiley, 2002).

], the complex amplitude of the laser field F(ρ,z) at the axial distance z and the radial distance ρ can be written as:
F(ρ,z)=ikzeikzexp(ikρ22z)××0Rexp(r2σ2)exp[iφ(r)+ikr22z]J0(krρz)r  d ​r,
(1)
where R is the radius of the DOE, J0(x) is the zero-order Bessel function, φ(r) is the phase of the DOE, σ is the radius of the illuminating Gaussian beam, and k=2π/λ is the wavenumber.

The laser intensity on the optical axis is given by I(0,z)=|F(0,z)|2, where

F(0,z)=ikzexp(ikz)××0Rexp(r2σ2)exp[iφ(r)+ikr22z]r  dr.
(2)

Diffraction efficiency e and root mean square δ (RMS) of intensity were used as criteria for the DOE characterization. Diffraction efficiency is defined as the ratio between the DOE generated intensity and the desired intensity and is expressed by

e=(i=1NI(zi))(i=1NI¯(zi))1.
(5)

RMS is given by

δ=i=1N(I(zi)μCmI¯(zi))2i=1Nμ2Cm2I¯2(zi).
(6)

For the designed DOE the following parameters were realized: diffraction efficiency e = 22%, RMS = 4.3%. The phase of this DOE and the calculated longitudinal intensity distribution are shown in Figs. 2a, b
Fig. 2 a) Phase function of the designed DOE and b) calculated longitudinal intensity distribution on the optical axis.
.

3. Experimental setup and materials

For the fabrication of DOE’s by the two-photon polymerization technique, we apply near-infrared femtosecond laser pulses. When tightly focused into the volume of a photosensitive material (or photoresist), they initiate 2PP process in a highly localized area around the focal spot. This allows the fabrication of any computer-generated 3D structure by direct laser ”recording” into the volume of a photosensitive material. The samples of polymer (mr-NIL 6000 photoresist from Microresist technology GmbH) were prepared by spincoating of glass substrates with the following dimensions 18 × 18 × 0.15 mm3. Thickness of the polymer layer was about 600 nm after deposition and drying at 100°C to increase the mechanical stability. The laser system used for two-photon polymerization, see Fig. 3
Fig. 3 Schematical setup used for 2PP: S – shutter, λ/2 plate, P – polarizer, O1,O2 - objectives; L1–L4 - lenses; DM – dichroic mirror; LED – light-emitting diode, CMOS - camera; PM - power meter; and XYZ stages are used to position the sample.
, is based on the mode-locked Ti:sapphire laser (pulse width <80 fs, λ = 780 nm, maximal power of 20 mW, and repetition rate of 73 MHz). The laser beam is focused by an objective lens (40X, 0.4 NA) to write the desired pattern. Fabrication was performed by translating the sample using a computer controlled 3D positioning stage. The accuracy of the scanner-based writing is ~100 nm, and of the positioning system over the complete travel range it is better than 400 nm.

The processing characteristics and writing laser power were controlled using A3200 AEROTECH software. The designed DOE’s were fabricated with the following parameters: DOE diameter is 2 mm; writing laser power is 3 mW; writing speed is 1 mm/s; number of horizontal slices is 1; photoresist thickness (slice step) is 0.6 µm; laser writing hatch step (inside the binary ring contours) is 0.5 µm; fabrication time of one DOE is 2 hours 20 minutes. After polymerization unexposed monomer was removed during 1 minute in a standard SU-8 developer.

4. Experimental results

The arrays of 2 mm diameter DOE’s were written and the realized diffractive reliefs were investigated by optical and SEM microscopy as well as by white-light interferometry. The results of DOE’s relief characterization are presented in Fig. 4
Fig. 4 Optical (a) and SEM (b) views of the recorded binary DOEs. The scale-bar is 100 µm.
and 5
Fig. 5 a) White-light interferometry image of the DOE central ring, b) X-,Y-profiles of this ring.
.

For investigation of focusing properties of the realized DOEs, the TEM00 mode of cw He-Ne laser with a beam diameter of 1 mm was used as an illuminating source. The laser intensity distributions formed at the different distances from the DOE plane were registered by uEye UI-1450C CCD camera. Intensity distribution in the focusing plane (with a maximum intensity at the optical axis) and longitudinal intensity distribution are presented in Fig. 6a
Fig. 6 Intensity distribution in the focusing plane with a maximum value at the optical axis (a) and longitudinal intensity distribution (b) generated by the 2PP fabricated DOE.
and Fig. 6b, correspondingly. Minimum focal spot diameter is about 30µm. Experimental results are in good agreement with the DOE computer simulations (Fig. 2). The observed differences between the modeling results and experiments can be explained by the presence of higher order laser modes.

It should be noted that longitudinal intensity distribution in the formed light segment is practically uniform (Fig. 6b), which is important for applications. Development of fabrication technology for the realization of step-like relief with larger number of quantization levels will allow to increase diffractive efficiency of such elements (see (4), (5)) in the future. The capability of 2PP technique to create complex 3D structures with exceptionally high resolution (less than 100 nm) makes this technology advantageous for the fabrication of 3D microoptical devices. With this technique, one is able to introduce compact and relatively economic DOE’s focusing laser beam to desired areas, which is crucial for the practical applications, especially in metrology, biology and medicine.

The application of multibeam 2PP recording method is perspective for significant reducing of recording time of such DOE’s. In this work we fabricated the designed DOE with diameter 2 mm during 2 hours 20 min., using one-beam writing system. Application of multi-beam [11] system (which is planned to realize in future) can reduce the duration of the recording of such DOE’s in several times.

5. Conclusions

In this work, the ability of two-photon polymerization technique to fabricate high-quality 2 mm-size binary diffractive optical elements has been demonstrated. It has been shown that the fabrication of concentric binary rings with heights about 600 nm from commercially available photoresists is possible. The carried investigations of the optical properties of the fabricated DOE’s have demonstrated that experimental results are in good agreement with the numerical design.

It is particularly important that the 2PP technique may be used for the fabrication of diffractive optical elements forming desired longitudinal laser intensity distributions. Such DOE’s can be applied in metrology and medicine.

Acknowledgements

We would like to gratefully acknowledge EC FP7-Marie Curie-IIF-Program for support of this work (Proposal # 235969).

References and links

1.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412(6848), 697–698 (2001). [CrossRef] [PubMed]

2.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röskel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999). [CrossRef]

3.

S. Maruo, O. Nakamura, and S. Kawata, “Three-dimensional microfabrication with two-photon-absorbed photopolymerization,” Opt. Lett. 22(2), 132–134 (1997). [CrossRef] [PubMed]

4.

J. Serbin, A. Egbert, A. Ostendorf, B. N. Chichkov, R. Houbertz, G. Domann, J. Schulz, C. Cronauer, L. Fröhlich, and M. Popall, “Femtosecond laser-induced two-photon polymerization of inorganic-organic hybrid materials for applications in photonics,” Opt. Lett. 28(5), 301–303 (2003). [CrossRef] [PubMed]

5.

J. Serbin, A. Ovsianikov, and B. Chichkov, “Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties,” Opt. Express 12(21), 5221–5228 (2004). [CrossRef] [PubMed]

6.

W. Haske, V. W. Chen, J. M. Hales, W. Dong, S. Barlow, S. R. Marder, and J. W. Perry, “65 nm feature sizes using visible wavelength 3-D multiphoton lithography,” Opt. Express 15(6), 3426–3436 (2007). [CrossRef] [PubMed]

7.

L. L. Doskolovich, D. L. Golovashkin, N. L. Kazanskiy, S. N. Khonina, V. V. Kotlyar, V. S. Pavelyev, R. V. Skidanov, V. A. Soifer, V. S. Solovyev, G. V. Uspleniev, and A. V. Volkov, Methods for Computer Design of Diffractive Optical Elements, Ed. by V. A. Soifer (John Wiley, 2002).

8.

V. P. Korolkov, R. K. Nasyrov, and R. V. Shimansky, “Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements,” Appl. Opt. 45(1), 53–62 (2006). [CrossRef] [PubMed]

9.

B. Jia, J. Serbin, H. Kim, B. Lee, J. Li, and M. Gu, “Use of two-photon polymerization for continuous gray-level encoding of diffractive optical elements,” Appl. Phys. Lett. 90, 1–3 (2007). [CrossRef]

10.

G. Cojoc, C. Liberale, P. Candeloro, F. Gentile, G. Das, F. De Angelis, and E. Di Fabrizio, “Optical micro-structures fabricated on top of optical fibers by means of two-photon photopolymerization,” Microelectron. Eng. 87, 876–879 (2010). [CrossRef]

11.

K. Obata, J. Koch, U. Hinze, and B. N. Chichkov, “Multi-focus two-photon polymerization technique based on individually controlled phase modulation,” Opt. Express 18(16), 17193–17200 (2010). [CrossRef] [PubMed]

12.

K. Wang, L. Zeng, and Ch. Yin, “Influence of the incident wave-front on intensity distribution of the nondiffracting beam used in large-scale measurement,” Opt. Commun. 216, 99–103 (2003). [CrossRef]

13.

L. Jian-yu and J. F. Greenleaf, “Diffraction-limited beams and their applications for ultrasonic imaging and tissue characterization,” Proc. SPIE 1733, 92–119 (1992). [CrossRef]

14.

R. A. Leitgeb, M. Villiger, A. H. Bachmann, L. Steinmann, and T. Lasser, “Extended focus depth for Fourier domain optical coherence microscopy,” Opt. Lett. 31(16), 2450–2452 (2006). [CrossRef] [PubMed]

15.

K. S. Lee and J. P. Rolland, “Bessel beam spectral-domain high-resolution optical coherence tomography with micro-optic axicon providing extended focusing range,” Opt. Lett. 33(15), 1696–1698 (2008). [CrossRef] [PubMed]

16.

J. Y. Lu and J. F. Greenleaf, “Producing deep depth of field and depth-independent resolution in NDE with limited diffraction beams,” Ultrason. Imaging 15(2), 134–149 (1993). [CrossRef] [PubMed]

17.

J. J. Lunazzi, D. S. F. Magalhães, “Photographing by means of a diffractive axicon,” http://arxiv.org/pdf/physics/0701234.

18.

R. Arimoto, C. Saloma, T. Tanaka, and S. Kawata, “Imaging properties of axicon in a scanning optical system,” Appl. Opt. 31(31), 6653–6657 (1992). [CrossRef] [PubMed]

19.

M. Fortin, M. Piché, and E. F. Borra, “Optical tests with Bessel beam interferometry,” Opt. Express 12(24), 5887–5895 (2004). [CrossRef] [PubMed]

20.

S. Reichelt, H. Tiziani, and H. Zappe, “Self-calibration of wavefront testing interferometers by use of diffractive elements,” Proc. SPIE 6292, 629205.1–629205.10 (2006).

21.

A. L. Cohen, “Practical design of a bifocal hologram contact lens or intraocular lens,” Appl. Opt. 31(19), 3750–3754 (1992). [CrossRef] [PubMed]

22.

D. G. Kachalov, V. S. Pavelyev, S. H. Khonina, R. V. Skidanov, and O. Y. Moiseev, “Stochastic optimization of radial DOE forming intensity distribution along an axial focal zone,” Proc. SPIE 7717, 77170E (2010). [CrossRef]

23.

M. Meister and R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39–49 (2002). [CrossRef]

OCIS Codes
(050.1380) Diffraction and gratings : Binary optics
(050.1970) Diffraction and gratings : Diffractive optics
(270.4180) Quantum optics : Multiphoton processes

ToC Category:
Diffraction and Gratings

History
Original Manuscript: September 17, 2010
Revised Manuscript: October 20, 2010
Manuscript Accepted: October 21, 2010
Published: November 24, 2010

Citation
Vladimir Osipov, Vladimir Pavelyev, Denis Kachalov, Albertas Žukauskas, and Boris Chichkov, "Realization of binary radial diffractive optical elements by two-photon polymerization technique," Opt. Express 18, 25808-25814 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-25-25808


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References

  1. S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412(6848), 697–698 (2001). [CrossRef] [PubMed]
  2. B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röskel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999). [CrossRef]
  3. S. Maruo, O. Nakamura, and S. Kawata, “Three-dimensional microfabrication with two-photon-absorbed photopolymerization,” Opt. Lett. 22(2), 132–134 (1997). [CrossRef] [PubMed]
  4. J. Serbin, A. Egbert, A. Ostendorf, B. N. Chichkov, R. Houbertz, G. Domann, J. Schulz, C. Cronauer, L. Fröhlich, and M. Popall, “Femtosecond laser-induced two-photon polymerization of inorganic-organic hybrid materials for applications in photonics,” Opt. Lett. 28(5), 301–303 (2003). [CrossRef] [PubMed]
  5. J. Serbin, A. Ovsianikov, and B. Chichkov, “Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties,” Opt. Express 12(21), 5221–5228 (2004). [CrossRef] [PubMed]
  6. W. Haske, V. W. Chen, J. M. Hales, W. Dong, S. Barlow, S. R. Marder, and J. W. Perry, “65 nm feature sizes using visible wavelength 3-D multiphoton lithography,” Opt. Express 15(6), 3426–3436 (2007). [CrossRef] [PubMed]
  7. L. L. Doskolovich, D. L. Golovashkin, N. L. Kazanskiy, S. N. Khonina, V. V. Kotlyar, V. S. Pavelyev, R. V. Skidanov, V. A. Soifer, V. S. Solovyev, G. V. Uspleniev, and A. V. Volkov, Methods for Computer Design of Diffractive Optical Elements, Ed. by V. A. Soifer (John Wiley, 2002).
  8. V. P. Korolkov, R. K. Nasyrov, and R. V. Shimansky, “Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements,” Appl. Opt. 45(1), 53–62 (2006). [CrossRef] [PubMed]
  9. B. Jia, J. Serbin, H. Kim, B. Lee, J. Li, and M. Gu, “Use of two-photon polymerization for continuous gray-level encoding of diffractive optical elements,” Appl. Phys. Lett. 90, 1–3 (2007). [CrossRef]
  10. G. Cojoc, C. Liberale, P. Candeloro, F. Gentile, G. Das, F. De Angelis, and E. Di Fabrizio, “Optical micro-structures fabricated on top of optical fibers by means of two-photon photopolymerization,” Microelectron. Eng. 87, 876–879 (2010). [CrossRef]
  11. K. Obata, J. Koch, U. Hinze, and B. N. Chichkov, “Multi-focus two-photon polymerization technique based on individually controlled phase modulation,” Opt. Express 18(16), 17193–17200 (2010). [CrossRef] [PubMed]
  12. K. Wang, L. Zeng, and Ch. Yin, “Influence of the incident wave-front on intensity distribution of the nondiffracting beam used in large-scale measurement,” Opt. Commun. 216, 99–103 (2003). [CrossRef]
  13. L. Jian-yu and J. F. Greenleaf, “Diffraction-limited beams and their applications for ultrasonic imaging and tissue characterization,” Proc. SPIE 1733, 92–119 (1992). [CrossRef]
  14. R. A. Leitgeb, M. Villiger, A. H. Bachmann, L. Steinmann, and T. Lasser, “Extended focus depth for Fourier domain optical coherence microscopy,” Opt. Lett. 31(16), 2450–2452 (2006). [CrossRef] [PubMed]
  15. K. S. Lee and J. P. Rolland, “Bessel beam spectral-domain high-resolution optical coherence tomography with micro-optic axicon providing extended focusing range,” Opt. Lett. 33(15), 1696–1698 (2008). [CrossRef] [PubMed]
  16. J. Y. Lu and J. F. Greenleaf, “Producing deep depth of field and depth-independent resolution in NDE with limited diffraction beams,” Ultrason. Imaging 15(2), 134–149 (1993). [CrossRef] [PubMed]
  17. J. J. Lunazzi, D. S. F. Magalhães, “Photographing by means of a diffractive axicon,” http://arxiv.org/pdf/physics/0701234 .
  18. R. Arimoto, C. Saloma, T. Tanaka, and S. Kawata, “Imaging properties of axicon in a scanning optical system,” Appl. Opt. 31(31), 6653–6657 (1992). [CrossRef] [PubMed]
  19. M. Fortin, M. Piché, and E. F. Borra, “Optical tests with Bessel beam interferometry,” Opt. Express 12(24), 5887–5895 (2004). [CrossRef] [PubMed]
  20. S. Reichelt, H. Tiziani, and H. Zappe, “Self-calibration of wavefront testing interferometers by use of diffractive elements,” Proc. SPIE 6292, 629205.1–629205.10 (2006).
  21. A. L. Cohen, “Practical design of a bifocal hologram contact lens or intraocular lens,” Appl. Opt. 31(19), 3750–3754 (1992). [CrossRef] [PubMed]
  22. D. G. Kachalov, V. S. Pavelyev, S. H. Khonina, R. V. Skidanov, and O. Y. Moiseev, “Stochastic optimization of radial DOE forming intensity distribution along an axial focal zone,” Proc. SPIE 7717, 77170E (2010). [CrossRef]
  23. M. Meister and R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39–49 (2002). [CrossRef]

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