## Design and fabrication of random phase diffusers for extending the depth of focus

Optics Express, Vol. 15, Issue 3, pp. 910-923 (2007)

http://dx.doi.org/10.1364/OE.15.000910

Acrobat PDF (230 KB)

### Abstract

We present a method for designing non-absorbing optical diffusers that, when illuminated by a converging beam, produce a specified intensity distribution along the optical axis. To evaluate the performance of the diffusers in imaging systems we calculate the three-dimensional distribution of the mean intensity in the neighborhood of focus. We find that the diffusers can be used as depth-of-focus extenders. We also propose and implement a method of fabricating the designed diffusers on photoresist-coated plates and present some experimental results obtained with the fabricated diffusers.

© 2007 Optical Society of America

## 1. Introduction

1. W. T. Welford, “Use of annular apertures to increase focal depth,” J. Opt. Soc. Am. **50**,749–753 (1960). [CrossRef]

2. S. Mezouari and A. A. Harvey, “Phase pupil functions for reduction of defocus and spherical aberrations,” Opt. Lett. **28**,771–773 (2003). [CrossRef] [PubMed]

3. A. Castro and J. Ojeda-Castañeda, “Asymmetric phase masks for extended depth of field,” Appl. Opt. **43**,3474–3479 (2004). [CrossRef] [PubMed]

4. J. Ojeda-Castañeda, J. E. A. Landgrave, and H. M. Escamilla, “Annular phase-only mask for high focal depth,” Opt. Lett. **30**,1647–1649 (2005). [CrossRef] [PubMed]

5. Z. Zalevsky, A. Shemer, A. Zlotnik, E. B. Eliezer, and E. Marom, “All-optical axial super resolving imaging using a low-frequency binary-phase mask,” Opt. Express **14**,2631–2643 (2006). [CrossRef] [PubMed]

6. C. Iemmi, J. Campos, J. C. Escalera, O. López-Coronado, R. Gimeno, and M. J. Yzuel, “Depth of focus increase by multiplexing programmable diffractive lenses,” Opt. Express **14**,10207–10219 (2006). [CrossRef] [PubMed]

7. J. Ojeda-Castañeda, L. R. Berriel-Valdos, and E. Montes, “Spatial filter for increasing the depth of focus,” Opt. Lett. **10**,520–522 (1985). [CrossRef] [PubMed]

8. E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. **34**1859–1866 (1995). [CrossRef] [PubMed]

9. W. Chi, K. Chu, and N. George “Polarization coded aperture,” Opt. Express **14**,6634–6642 (2006). [CrossRef] [PubMed]

10. J. Rosen and A. Yariv, “Synthesis of an arbitrary axial field profile by computer-generated holograms,” Opt. Lett. **19**,843–845 (1994). [CrossRef] [PubMed]

11. R. Piestum, B. Spektor, and J. Shamir, “Unconventional light distributions in three-dimensional domains,” J. Mod. Opt. **43**,1495–1507 (1996). [CrossRef]

12. M. Zamboni-Rached “Stationary optical wave fields with arbitrary longitudinal shape by superposing equal frequency Bessel beams: Frozen Waves,” Opt. Express **12**,4001–4006 (2004). [CrossRef] [PubMed]

13. M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “Theory of frozen waves: modeling the shape of stationary wave fields,” J. Opt. Soc. Am. A **22**,2465–2475 (2005). [CrossRef]

14. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. **44**,592–597 (1954). [CrossRef]

15. Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon - the most important optical element”, Optics and Photonics News **16**,34–39 (2005). [CrossRef]

16. J. Sochacki, A. Kotodziejczyk, Z. Jaroszewicz, and S. Bará, “Nonparaxial design of generalized axicons,” Appl. Opt. **31**,5326–5330 (1992). [CrossRef] [PubMed]

17. L. R. Staroński, J. Sochacki, Z. Jaroszewicz, and A. Kolodziejczyk “Lateral distribution and flow of energy in uniform-intensity axicons,” J. Opt. Soc. Am. A **9**,2091–2094 (1992). [CrossRef]

18. T. A. Leskova, A. A. Maradudin, I. V. Novikov, A. V. Shchegrov, and E. R. Méndez, “Design of one-dimensional band-limited uniform diffusers of light,” Appl. Phys. Lett. **73**,1943–1945 (1998). [CrossRef]

19. E. R. Méndez, E. E. García-Guerrero, H. M. Escamilla, A. A. Maradudin, T. A. Leskova, and A. V. Shchegrov, “Photofabrication of random achromatic optical diffusers for uniform illumination,” Appl. Opt. **40**,1098–1108 (2001). [CrossRef]

20. E. R. Méndez, E. E. García-Guerrero, T. A. Leskova, A. A. Maradudin, J. Muñoz-López, and I. Simonsen, “Design of one-dimensional random surfaces with specified scattering properties,” Appl. Phys. Lett. **81**,798–800 (2002) [CrossRef]

21. E. R. Méndez, T. A. Leskova, A. A. Maradudin, M. Leyva-Lucero, and J. Muñoz-López, “The design of two-dimensional random surfaces with specified scattering properties,” J. Opt. A **7**,S141–S151 (2005). [CrossRef]

## 2. Design of the diffusers

*t*(

*r*), the complex amplitude in the neighborhood of focus can be expressed as [22] (see Fig. 1)

*A*

_{0}is a constant amplitude and

*k*

_{0}= 2

*π*/

*λ*= (

*ω*/

*c*) is the wave number in vacuum where, as usual,

*ω*is the frequency,

*λ*is the wavelength, and

*c*the speed of light in vacuum. The length

*a*is the radius of the circular aperture,

*R*is the distance from the pupil plane to the best focus,

*z*

_{0}is the defocus distance,

*r*

_{0}= (

*x*

^{2}

_{0}+

*y*

^{2}

_{0})

^{(1/2)}is the transverse radial coordinate, J

_{0}(

*z*) is a Bessel function of the first kind and order zero, and

*t*(

*r*) is a complex function of the form

*H*(

*r*) represents the surface profile function of the diffuser. We assume that

*H*(

*r*) is a single-valued function of

*r*that is differentiable, and constitutes a random process, but not necessarily a stationary one. Assuming only small angles of incidence and scattering, we adopt the thin phase screen model and set

*v*

_{3}= 2(

*ω*/

*c*) for a reflection geometry, and

*v*

_{3}= (ω/

*c*)Δ

*n*for a transmission one [23

23. W. T. Welford, “Optical estimation of statistics of surface roughness from light scattering measurements,” Opt. Quantum Electron. **9**,269–387 (1977). [CrossRef]

24. Z. H. Gu, H. M. Escamilla, E. R. Méndez, A. A. Maradudin, J. Q. Lu, T. Michel, and M. Nieto-Vesperinas, “Interaction of two optical beams at a symmetric random surface,” Appl. Opt. **31**,5878–5889 (1992). [CrossRef] [PubMed]

*n*is the difference between the refractive indices of the material from which the diffuser is made and that of the surrounding medium. For definiteness, we consider here a transmission geometry, but the results can be applied equally well to a reflection geometry. We also assume that the phase excursions introduced by the diffuser are much greater than 2

*π*and, thus, that the coherent component of the transmitted field is negligible.

*C*

_{0}= -

*ik*

_{0}(

*A*

_{0}/

*R*

^{2})exp(

*ik*

_{0}

*z*

_{0}) and

*κ*=

*k*

_{0}/2

*R*

^{2}. With the change of variable

26. C. W. McCutchen, “Generalized aperture and the three-dimensional image,” J. Opt. Soc. Am. **54**,240–244 (1964). [CrossRef]

19. E. R. Méndez, E. E. García-Guerrero, H. M. Escamilla, A. A. Maradudin, T. A. Leskova, and A. V. Shchegrov, “Photofabrication of random achromatic optical diffusers for uniform illumination,” Appl. Opt. **40**,1098–1108 (2001). [CrossRef]

18. T. A. Leskova, A. A. Maradudin, I. V. Novikov, A. V. Shchegrov, and E. R. Méndez, “Design of one-dimensional band-limited uniform diffusers of light,” Appl. Phys. Lett. **73**,1943–1945 (1998). [CrossRef]

19. E. R. Méndez, E. E. García-Guerrero, H. M. Escamilla, A. A. Maradudin, T. A. Leskova, and A. V. Shchegrov, “Photofabrication of random achromatic optical diffusers for uniform illumination,” Appl. Opt. **40**,1098–1108 (2001). [CrossRef]

20. E. R. Méndez, E. E. García-Guerrero, T. A. Leskova, A. A. Maradudin, J. Muñoz-López, and I. Simonsen, “Design of one-dimensional random surfaces with specified scattering properties,” Appl. Phys. Lett. **81**,798–800 (2002) [CrossRef]

*H*(

*r*).

*h*(

*t*), and hence

*H*(

*r*), for which the right-hand side of Eq. (6) produces a mean intensity 〈

*I*(

*z*

_{0}, 0)〉 with a prescribed dependence on

*z*

_{0}. As it stands, Eq. (6) is too complicated for us to invert it to obtain

*h*(

*t*) in terms of 〈

*I*(

*z*

_{0},0)〉. We therefore pass to the geometrical optics limit of the expression on the right-hand side of Eq. (6) by expanding

*h*(

*t*) about

*t*=

*t́*,

*h*(

*t*) =

*h*(

*t́*) + (

*t*-

*t́*)

*h́*(

*t́*) + ..., and retaining only terms through the leading nonzero order in (

*t*-

*t́*). The consequences of this approximation will be discussed in the next section. In this way we obtain

*h́*(

*t*) is the derivative of

*h*(

*t*).

*h*(

*t*) that, as we will see, simplifies the design of the diffusers. We first introduce a characteristic length

*b*through the definition

*a*

^{2}=

*Nb*

^{2}, where

*N*is a large integer. We then represent the function

*h*(

*t*) in the form

*α*} in Eq. (8) are assumed to be independent identically distributed random deviates. The probability density function (pdf) of

_{n}*α*,

_{n}*n*. Its definition indicates that

*f*(

*γ*)

*dγ*is the probability that

*α*lies in the interval (

_{n}*γ*,

*γ*+

*dγ*) in the limit as

*dγ*→ 0. In order that the surface be continuous at, say,

*t*= (

*n*+ 1)

*b*

^{2}, the condition

*β*} can be determined from a knowledge of the {

_{n}*α*}, provided that an initial value, e.g.

_{n}*β*, is specified. It is convenient to choose

_{0}*β*= 0, and we will do so in what follows. The solution of Eq. (10) is then

_{0}*h*(

*t*) will become clear below.

*α*} and the fact that they are identically distributed in the last step. Since the integrands in this expression now are independent of

_{n}*n*, the sum on

*n*can be carried out immediately, with the result that the double integral becomes

*h*(

*t*) on

*t*in the interval (

*nb*

^{2}, (

*n*+ 1)

*b*

^{2}), so that its derivative

*h́*(

*t*) is a constant,

*h́*(

*t*) =

*α*, in this interval.

_{n}*x*= sin

*x*/

*x*.

*Nb*≫

*λ*implies that

*a*

^{2}

*v*

_{3}/(2

*b*) ≫ 1, and that in the limit as

*A*→ ∞,

*α*. On inverting Eq. (15) we find that

_{n}*α*} is generated by the rejection method [27], and the surface profile function is constructed on the basis of Eqs. (8), (11), and the fact that

_{n}*t*=

*r*

^{2}. Thus, the surface profile function

*H*(

*r*) can be written as

*z*

_{m}<

*z*

_{0}<

*z*

_{m}, and zero axial intensity for |

*z*

_{0}| >

*z*

_{m}, and evaluate the possibility of employing it to extend the depth of focus of imaging systems. The mean axial intensity we seek the diffuser to produce is therefore

*I*

_{0}is a constant, and θ(

*z*) is the Heaviside unit step function. We obtain from Eqs. (16) and (18) the result

*I*

_{0}is obtained from the normalization of

*f*(

*γ*), with the result that

## 3. Three-dimensional distribution in the neighborhood of focus

*ψ*(

_{n}*z*

_{0},

*r*

_{0};

*α*) represents the diffraction pattern of an annular pupil function with defocus

_{n}*z*

_{0}+

*v*

_{3}

*α*/(

_{n}*bκ*), where

*α*is a random quantity. Diffraction integrals like the one represented by Eq. (25) have been well-studied in the past [1

_{n}1. W. T. Welford, “Use of annular apertures to increase focal depth,” J. Opt. Soc. Am. **50**,749–753 (1960). [CrossRef]

28. J. C. Dainty, “The image of a point for an aberration free lens with a circular pupil,” Opt. Commun. **1**,176–178 (1969). [CrossRef]

*α*} are statistically independent. If we further assume that the coherent component is negligible (i.e. that 〈

_{n}*ψ*(

_{n}*z*

_{0},

*r*

_{0};

*α*)〉 = 0), the expression for the mean intensity simplifies to

_{n}^{4}for all the parameters and values of

*z*

_{0}and

*r*

_{0}assumed in this work. Consequently, in what follows we will use the simpler expression (27) in calculating the mean intensity 〈

*I*(

*z*

_{0},

*r*

_{0})〉.

*n*-th ring is given by

*a*

^{2}=

*Nb*

^{2}and the fact that the width of the diffraction structure obtained in Eq. (29) does not depend on the order of the ring. We note that the first term in the argument of the sinc function is a deterministic defocus term, while the second one contains the random numbers

*α*. Apart from this random term, the result agrees with the well-known expression for the axial intensity produced by an annular aperture [1

_{n}1. W. T. Welford, “Use of annular apertures to increase focal depth,” J. Opt. Soc. Am. **50**,749–753 (1960). [CrossRef]

29. E. H. Linfoot and E. Wolf, “Diffraction images in systems with annular apertures,” Proc. Phys. Soc. London Sect. B **66**,145149 (1953). [CrossRef]

*ψ*(

_{n}*z*

_{0},0;

*α*)|

_{n}^{2}produced by different zones of the diffuser. To help in the visualization of this result, in Fig. 2 we show two of these contributions for the particular case

*α*= 0. The optical system has

_{n}*a*= 2cm,

*R*= 15cm, and

*λ*= 0.633

*μ*m. The circular aperture was divided into

*N*= 100 annular apertures, resulting in a value of

*n*= 0, and is just the diffraction pattern produced by a circular aperture of radius

*b*. Figure 2(b) corresponds to the annular pupil with

*n*= 25. The figures represent meridional sections of the rotationally symmetric three-dimensional diffraction patterns. These figures confirm our earlier remark that the distribution of the axial intensity is independent of the order of the ring. In this case, the first axial zeroes occur around

*z*

_{0}= ±0.71cm. On the other hand, the transverse distribution decreases in size with the order of the ring.

*z*

_{0}≤ 2cm of the optical axis. The pdf of

*α*for this case is given by Eq. (22), so that from Eq. (27) we have

_{n}*a*= 2cm,

*R*= 15cm,

*λ*= 0.633

*μ*m, and

*N*= 100. The parameter Δ

*n*= 0.6.

*I*(

*z*

_{0},

*r*

_{0})〉 is illustrated in Fig. 3. From this meridional intensity map we see that the intensity is fairly constant in the design region of the optical axis, and that it decreases rapidly outside it and for off-axis points. These same data were used to generate Fig. 4, where we show the mean intensity distribution along the optical axis (a) and the mean intensity in the transverse direction for the plane

*z*

_{0}= 0 (b). From Eq. (30), we observe that the mean axial intensity can be expressed as the convolution of a sinc

^{2}function with the desired distribution. Consequently, the axial intensity distribution is not perfectly rectangular, but smoothed by diffraction effects whose extent depend on the parameter 2

*λ*(

*R*/

*b*)

^{2}. For reference, we mention that the first zeroes of the axial response of the system without diffuser occur at

*z*

_{0}= ±71

*μ*m. Also, in Fig. 4(b), we show the Airy pattern that corresponds to the transverse response of the system with a clear pupil function. We see that the width of the central core is similar in the two cases and that the main difference is the relatively slow decay of the tails in the response of the system with the diffuser. Summarizing, the mean PSF consists of a bright central core with a broad halo, and its structure is fairly invariant within the design region. A predictable consequence of the halo is that the high frequency components will be transferedto the image with low contrast. Despite this, the sharpness of the central core indicates that the diffusers can be useful in imaging applications.

*z*

_{0}. As an example, we show in Fig. 6 (a) and (b) the calculated transverse intensity images at

*z*

_{0}= -1 and

*z*

_{0}= 1cm.

*z*

_{0}= -1cm and

*z*

_{0}= 1cm by averaging over 400 different wavelengths in the visible region of the spectrum. One can see that the ring structure has practically disappeared and that the shape of the PSFs approaches that of the ensemble-averaged PSF. This resemblance improves with the number of independent patterns employed and with the number of rings

*N*.

## 4. Experimental techniques and results

*λ*= 442nm) from a He-Cd laser transmitted through a rotating ground glass (to reduce its coherence). A schematic diagram of the experimental setup employed in the fabrication is shown in Fig. 7. An incoherent image of a disk-shaped mask is formed on the rotating photoresist-coated plate by a well-corrected imaging system with magnification

*m*. The plate is exposed during a time

*T*, during which it executes a large number of revolutions. As explained below, the arrangement is such that the total exposure of the plate is a scaled version of the profile function employed in the generation of the mask.

_{e}*H*(

*r*) generated according to Eqs. (17), (22), and (11) in both, the vertical and horizontal directions. That is, we are interested on the mean intensity produced by a diffuser with a surface profile function

*AH*(

*mr*), where

*A*and

*m*are dimension-less constants, with reference to the mean intensity obtained with the original function

*H*(

*r*). From Eq. (17) we see that the transformation is equivalent to chosing new random deviates

*Am*

^{2}

*α*. In consequence, the parameter that defines the new region of constant intensity is

_{n}*ź*=

_{m}*Am*

^{2}

*z*. In other words, by scaling the function

_{m}*H*(

*r*) in the vertical or horizontal direction one changes the length of the region of constant intensity. These transformation are almost inevitable in our fabrication scheme and are defined by the exposure of the plate and by the magnification of the optical system (see Fig. 7).

*H*(

*r*). An example is shown in Fig. 8(a). Then, we define the function Δ

_{H}(

*r*) =

*KH*(

*r*) that, with an appropriate choice of the units of the constant

*K*, can be interpreted as an angle. For a given radius, the angles θ that fall in the transparent section of the mask are defined by the condition Δ

_{H}(

*r*) >

*θ*> Δ

_{0}, where Δ

_{0}is a constant smaller than the minimum value of Δ

_{H}(

*r*) [see Fig. 8(b)].

## 5. Summary and concluding remarks

## Acknowledgments

## References and links

1. | W. T. Welford, “Use of annular apertures to increase focal depth,” J. Opt. Soc. Am. |

2. | S. Mezouari and A. A. Harvey, “Phase pupil functions for reduction of defocus and spherical aberrations,” Opt. Lett. |

3. | A. Castro and J. Ojeda-Castañeda, “Asymmetric phase masks for extended depth of field,” Appl. Opt. |

4. | J. Ojeda-Castañeda, J. E. A. Landgrave, and H. M. Escamilla, “Annular phase-only mask for high focal depth,” Opt. Lett. |

5. | Z. Zalevsky, A. Shemer, A. Zlotnik, E. B. Eliezer, and E. Marom, “All-optical axial super resolving imaging using a low-frequency binary-phase mask,” Opt. Express |

6. | C. Iemmi, J. Campos, J. C. Escalera, O. López-Coronado, R. Gimeno, and M. J. Yzuel, “Depth of focus increase by multiplexing programmable diffractive lenses,” Opt. Express |

7. | J. Ojeda-Castañeda, L. R. Berriel-Valdos, and E. Montes, “Spatial filter for increasing the depth of focus,” Opt. Lett. |

8. | E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. |

9. | W. Chi, K. Chu, and N. George “Polarization coded aperture,” Opt. Express |

10. | J. Rosen and A. Yariv, “Synthesis of an arbitrary axial field profile by computer-generated holograms,” Opt. Lett. |

11. | R. Piestum, B. Spektor, and J. Shamir, “Unconventional light distributions in three-dimensional domains,” J. Mod. Opt. |

12. | M. Zamboni-Rached “Stationary optical wave fields with arbitrary longitudinal shape by superposing equal frequency Bessel beams: Frozen Waves,” Opt. Express |

13. | M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “Theory of frozen waves: modeling the shape of stationary wave fields,” J. Opt. Soc. Am. A |

14. | J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. |

15. | Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon - the most important optical element”, Optics and Photonics News |

16. | J. Sochacki, A. Kotodziejczyk, Z. Jaroszewicz, and S. Bará, “Nonparaxial design of generalized axicons,” Appl. Opt. |

17. | L. R. Staroński, J. Sochacki, Z. Jaroszewicz, and A. Kolodziejczyk “Lateral distribution and flow of energy in uniform-intensity axicons,” J. Opt. Soc. Am. A |

18. | T. A. Leskova, A. A. Maradudin, I. V. Novikov, A. V. Shchegrov, and E. R. Méndez, “Design of one-dimensional band-limited uniform diffusers of light,” Appl. Phys. Lett. |

19. | E. R. Méndez, E. E. García-Guerrero, H. M. Escamilla, A. A. Maradudin, T. A. Leskova, and A. V. Shchegrov, “Photofabrication of random achromatic optical diffusers for uniform illumination,” Appl. Opt. |

20. | E. R. Méndez, E. E. García-Guerrero, T. A. Leskova, A. A. Maradudin, J. Muñoz-López, and I. Simonsen, “Design of one-dimensional random surfaces with specified scattering properties,” Appl. Phys. Lett. |

21. | E. R. Méndez, T. A. Leskova, A. A. Maradudin, M. Leyva-Lucero, and J. Muñoz-López, “The design of two-dimensional random surfaces with specified scattering properties,” J. Opt. A |

22. | M. Born and E. Wolf, |

23. | W. T. Welford, “Optical estimation of statistics of surface roughness from light scattering measurements,” Opt. Quantum Electron. |

24. | Z. H. Gu, H. M. Escamilla, E. R. Méndez, A. A. Maradudin, J. Q. Lu, T. Michel, and M. Nieto-Vesperinas, “Interaction of two optical beams at a symmetric random surface,” Appl. Opt. |

25. | E. R. Méndez and D. Macías, “Inverse problems in optical scattering,” in |

26. | C. W. McCutchen, “Generalized aperture and the three-dimensional image,” J. Opt. Soc. Am. |

27. | W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, |

28. | J. C. Dainty, “The image of a point for an aberration free lens with a circular pupil,” Opt. Commun. |

29. | E. H. Linfoot and E. Wolf, “Diffraction images in systems with annular apertures,” Proc. Phys. Soc. London Sect. B |

**OCIS Codes**

(110.2990) Imaging systems : Image formation theory

(290.5880) Scattering : Scattering, rough surfaces

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: September 18, 2006

Revised Manuscript: November 3, 2006

Manuscript Accepted: January 11, 2007

Published: February 5, 2007

**Citation**

E. E. García-Guerrero, Eugenio R. Méndez, Héctor M. Escamilla, Tamara A. Leskova, and Alexei A. Maradudin, "Design and fabrication of random phase diffusers for extending the depth of focus," Opt. Express **15**, 910-923 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-3-910

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### References

- W. T. Welford, "Use of annular apertures to increase focal depth," J. Opt. Soc. Am. 50, 749-753 (1960). [CrossRef]
- S. Mezouari and A. A. Harvey, "Phase pupil functions for reduction of defocus and spherical aberrations," Opt. Lett. 28, 771-773 (2003). [CrossRef] [PubMed]
- A. Castro and J. Ojeda-Castaneda, "Asymmetric phase masks for extended depth of field," Appl. Opt. 43, 3474- 3479 (2004). [CrossRef] [PubMed]
- J. Ojeda-Casta˜neda, J. E. A. Landgrave, and H. M. Escamilla, "Annular phase-only mask for high focal depth," Opt. Lett. 30, 1647-1649 (2005). [CrossRef] [PubMed]
- Z. Zalevsky, A. Shemer, A. Zlotnik, E. B. Eliezer, and E. Marom, "All-optical axial super resolving imaging using a low-frequency binary-phase mask," Opt. Express 14, 2631-2643 (2006). [CrossRef] [PubMed]
- C. Iemmi, J. Campos, J. C. Escalera, O. Lopez-Coronado, R. Gimeno, and M. J. Yzuel, "Depth of focus increase by multiplexing programmable diffractive lenses," Opt. Express 14, 10207-10219 (2006). [CrossRef] [PubMed]
- J. Ojeda-Castaneda, L. R. Berriel-Valdos, and E. Montes, "Spatial filter for increasing the depth of focus," Opt. Lett. 10, 520-522 (1985). [CrossRef] [PubMed]
- E. R. Dowski and W. T. Cathey, "Extended depth of field through wave-front coding," Appl. Opt. 341859-1866 (1995). [CrossRef] [PubMed]
- W. Chi, K. Chu, and N. George "Polarization coded aperture," Opt. Express 14, 6634-6642 (2006). [CrossRef] [PubMed]
- J. Rosen and A. Yariv, "Synthesis of an arbitrary axial field profile by computer-generated holograms," Opt. Lett. 19, 843-845 (1994). [CrossRef] [PubMed]
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