OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 3, Iss. 1 — Jan. 29, 2008
« Show journal navigation

All-optical axially multi-regional super resolved imaging

Ido Raveh and Zeev Zalevsky  »View Author Affiliations


Optics Express, Vol. 15, Issue 26, pp. 17912-17921 (2007)
http://dx.doi.org/10.1364/OE.15.017912


View Full Text Article

Acrobat PDF (433 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In this paper we present a new approach of all-optical extended depth of focus providing two (or more) discrete ranges of focused imaging for close as well as far ranges. The fact that the extended depth of focus is not continuous allows obtaining improved contrast in the two (or more) axial regions of extended depth of focus. The design is aimed for the cell phone camera applications where dual range extended depth of focus can allow simultaneous reading of business cards at very short distance as well as very high contrasted imaging at far range.

© 2007 Optical Society of America

1. Introduction

Extending the depth of focus for imaging systems was widely explored during the recent years and a large variety of technologies were developed. Some approaches involve digital post processing [1

1. W. T. Cathy and E. R Dowski, “Apparatus and method for extending depth of field in image projection system,” US patent 6069738 (May2000).

5

5. J. van der Gracht, E. Dowski, M. Taylor, and D. Deaver, “Broadband behavior of an optical-digital focus-invariant system,” Opt. Lett. 21, 919–921 (1996). [CrossRef] [PubMed]

], aperture apodization by absorptive mask [6

6. C. M. Hammond, “Apparatus and method for reducing imaging errors in imaging systems having an extended depth of field,” US patent 6097856 (August2000).

10

10. J. O. Castaneda and L. R. Berriel-Valdos, “Zone plate for arbitrary high focal depth,” Appl. Opt. 29, 994–997 (1990). [CrossRef]

] or diffraction optical phase elements such as multi focal lenses or spatially dense distributions that suffer from significant divergence of energy into regions that are not the regions of interest [11

11. E. Ben-Eliezer, Z. Zalevsky, E. Marom, N. Konforti, and D. Mendlovic, “All optical extended depth of field imaging system,” PCT publication WO 03/076984 (September2003).

13

13. E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, “Experimental realization of an imaging system with an extended depth of field,” Appl. Opt. 44, 2792–2798 (2005). [CrossRef] [PubMed]

]. Other interesting approaches included tailoring the modulation transfer functions with high focal depth [14

14. A. Sauceda and J. Ojeda-Castaneda, “High focal depth with fractional-power wavefronts,” Opt. Lett. 29, 560–562 (2004). [CrossRef] [PubMed]

] and usage of logarithmic asphere lenses [15

15. W. Chi and N. George, “Electronic imaging using a logarithmic asphere,” Opt. Lett. 26, 875–877 (2001). [CrossRef]

].

The approach presented in this paper is based on the mathematical as well as logic concepts discussed in Ref. [17

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

] and thus it exhibits all the previously specified advantages. However, the performance of the method that is discussed in this continuation paper is significantly improved. The reason for that stems from new trade-off definitions that can be made in specific applications (such as the cellular cameras market). The payment in the trade-offs significantly improves the contrast and the performance in the close and far range imaging.

Current technology in cell phone cameras provide imaging at ranges starting from a typical minimum object distance of 50cm up to infinity. Yet for the purpose of reading business cards and barcodes, it is required to allow imaging at close ranges of few cm as well. Thus, we will design a dual range system rather than a continuous range extended depth of focus. This is the main difference in comparison to Refs. [16

16. Z. Zalevsky, “Optical method and system for extended depth of focus,” US patent application 10/97494 (August2004).

,17

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

]. The requirement is imaging in close range (e.g. 12.5cm) in order to allow reading of business cards and perfect quality of imaging in far field, while there is no need for focused imaging within all distances in between (30cm–50cm). We will use this apriori information in our mathematical constraints. The mathematical requirement forced in the formulation of the element is such that the axial super resolution has two (dual) ranges. The converged solution is similar to the one that was obtained in Refs. [16

16. Z. Zalevsky, “Optical method and system for extended depth of focus,” US patent application 10/97494 (August2004).

.17

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

]. It is still a phase mask constructed of transparent areas and binary phase lines (e.g. grid) and/or one or more binary phase circles, modulating the entrance pupil of the imaging lens [the Coherent Transfer Function (CTF) plane].

The principle of operation is also the same i.e. under spatially incoherent illumination the out of focus effect is expressed as a quadratic phase distortion that is added to the Optical Transfer Function (OTF). The positions of the binary phase transitions in the element are appropriately selected to generate invariance to quadratic phase distortions that contribute to defocusing.

The position of binary phase transitions is computed using an iterative algorithm. During these iterations, various combinations of positioning the phase lines and/or circles are examined. The algorithm converges eventually to those spatial locations that provide maximal contrast of the OTF under a set of chosen out of focus axial regions. The meaning of OTF’s contrast optimization is actually having the out of focused OTF bounded as much as possible away from zero, however this time this constraint is applied in two (or more) separated longitudinal (axial) ranges.

The optical performance of the element is similar to a multi-focal lens but the element itself has no optical power and it contains only low spatial frequencies.

The element presented here was fabricated and tested experimentally. Indeed it provides significant improvement of the closest possible in-focus near field as well as very high image quality in the far field (infinity) imaging.

Section 2 presents the theoretical background and the mathematical derivation. In section 3 one may see the recently obtained experimental results. The paper is concluded in section 4.

2. Theoretical derivation

The mathematical derivation that we present here is based on the presentation we provided in Ref. [17

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

]. In that paper we obtained that the OTF, which is the auto-correlation of the CTF equals to:

H(μ;Zi)=P(x+λZiμ2)n=1Nexp(ianrect(x+λZiμ2nΔxΔx))P*(xλZiμ2)n=1Nexp(ianrect(xλZiμ2nΔxΔx))dxP(x)2dx
(1)

where an are binary coefficients equal either to zero or to a certain phase modulation depth: an=(0, Δϕ) of the phase-only element that we design. Δϕ is the phase depth of modulation. Δx represents the spatial segments of the element. λ is the wavelength and µ is the coordinate of the OTF plane. P is the aperture of the lens having coordinates of x (the plane of the CTF) and Zi is the distance between the imaging lens and the sensor. Since we do not want to create a diffractive optical element, i.e. spatial high frequencies and periodicity (since we wish to have no wavelength dependence) we force Δx≫λ. Figure 1(a) shows an imaging system with a phase-element that is attached to the imaging lens, an object at distance Zo from the lens and a detection array that is positioned at distance Zi from the imaging lens. The OTF function that is given in Eq. (1) can be used to characterize the optical system that is depicted in Fig. 1(a).

Let us start with a general explanation and then show the relevant mathematical formulation. In our formulation, as well as the experimental analysis, we aimed to design a dual range element. However the same formulation can be easily extended to any number of discrete focused axial regions.

Generally speaking the formulation for the optimization criteria should be as follows: compute a phase-only element that will provide maximum for the minimal value of the OTF within the desired spectral (spatial spectrum) region of interest. The OTF that is being computed is composed from two terms. The first term is where the OTF exhibits strong defocusing deformation with large parameter Wm. The second term has a small defocusing deformation (denoted as βWm in Fig. 1(b) where β≪1). The coefficient Wm determines the severity of the defocusing error and is defined as:

Wm=Ψλ2π
(2)

where ψ is a phase factor represents the severity of out of focus:

Ψ=πb2λ(1Zi+1Zo1F)
(3)

Parameter 2b denotes the diameter of the lens, λ is the wavelength, Zo is the distance between the imaging lens and the object, Zi the distance between the imaging lens and the sensor and F is the focal length. When imaging condition is fulfilled, ψ is zeroed, since:

1Zi+1Zo=1F
(4)

Fig. 1. (a). An imaging system with a phase element attached to the aperture (b). schematic configuration of the desired system with two focusing regions. (c). schematic description of the sign inversion for the quadratic phase of defocusing due to the binary EDOF element placed in the aperture of the imaging lens.

Note that the requirement in this newly presented approach is different from the derivation that we performed in Ref. [17

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

] where the two terms of optimization included the defocused as well as the in-focus MTF. Here both terms are of defocused MTF. The fact that here we replaced the second term with slightly defocused MTF is due to the fact that we wish to have focusing in two regions and a defocused image in between those regions.

Obviously if instead of dual focused range, the aim is to converge into multiple set of focused regions, then the optimization expression should contain larger number of terms (a summation of terms).

The result obtained in Ref. [17

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

] was of an annular-like shape with a phase Δϕ=π/2, which stems from the constraint of a continuous focused region. That element was able to cancel the sign inversions of the quadratic phase that was generated in the aperture plane due to defocusing. Correction was obtained by the addition of proper phase to the spatial frequencies where inversion appeared. Although it seems like in order to cancel sign inversions one has to add a phase of π, the best solution in this case was obtained with a phase of π/2. The reason for a phase of π/2 was due to the requirement for a continuous focused region. In a continuous focused region solution, one has to cancel the inversions of quadratic phase due to defocusing while not creating new sign inversion to the in-focus plane. Thus, a phase of Δϕ=π/2 contributes equally both to the defocused planes as well as the in-focus plane.

When we wish to have dual focusing system, the optimal phase will be close to π, since now we wish to cancel only the sign inversions of the quadratic defocusing phase in the two regions that are located before and after the original in-focus plane. In this approach, the previously in-focus plane will now be distorted. The fact that two non-continuous regions are required, improves the contrast performance in each of the two regions in comparison to the case of Ref. [17

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

] where a continuous requirement was applied. A schematic simplification of the above explanation is brought in Fig. 1(c).

Note that in the case of two focused regions, the phase-only element will have one annular shape, dealing with the sign inversions of certain quadratic phase corresponding to a certain defocusing plane. When multiple, non continuous focused regions are required the phase-only element will have a plurality of annular shapes, corresponding to spectral (spatial spectrum) position of sign inversions (i.e. positions in the coordinates set of the aperture plane) that are due to different quadratic phase factors. Each annular will correct a distinct sign inversion.

Mathematically, the above dual-range and multi-range criteria corresponds to an approach where the goal of the designer is to maximize the minimal value of the MTF within a desired dual- or multi- axial region, for a certain range of spatial frequencies. Maximization is performed by varying parameters of the phase mask and of the imaging system, i.e. varying the number of phase transitions, their modulation depths, shape size and coordinates of phase segments (i.e. varying the phase mask layout), the aperture and the focal distance of the lens and the distance to the photo detection array (PDA). Maximization may only be partial, in accordance with one or more of the above criteria. Such an approach can be formalized for example with the help of an indicator:

infμx<μd,Z0R1R2{H(μx,Z0)}
(5)

In Eq. (5), H(µx,Z0) is the OTF that primarily depends on object’s distance Zo and spatial frequency µx (without a loss of generality, a one dimensional case is considered). In this example, the considered spatial frequencies are those being smaller than maximal spatial frequency of the photo detecting surface µd; the region of interest is dual and constructed of separate axial regions of interest R1 and R2. The OTF is also dependent on the parameters of the optical system and phase mask; varying these parameters allows optimizing the indicator of Eq. (5).

The indicator of Eq. (5) may be generalized, so as to take into account the eventual decline in OTF due to the growth of spatial frequency. The indicator can take a form:

infμx<μd,Z0R1R2{K(μx)H(μx,Z0)}
(6)

where K(µx) is a weight function corresponding to utility of each spatial frequency. Higher spatial frequencies may be assigned lower utility.

Indicators of Eq. (5) may be generalized differently. Considering, for example, an imaging system application, in which a contrast in the near range is tailored for recognition of documents, while a contrast in the far range is tailored for landscape photographing, it may be noted, that targets from regions of R1 and R2 may be decomposed into different spatial frequencies ranges. Then indicator of Eq. (5) may take a form:

infμx<μd,Z0R1R2{K(μx,Z0)H(μx,Z0)}
(7)

where K(µx,Zo) is a utility function dependent both on region of interest and spatial frequency.

Optimization may be aimed at maximization of a minimum average contrast for various spatial frequencies:

max{infμx<μdZ0R1R2dZ0K(μx,Z0)H(μx,Z0)}
(8)

The latter form can be reduced to a form:

max{infμx<μd{K1H(μx,E1)+K2H(μx;E2)}}
(9)

Here E1 and E2 are boundaries (edges) of the near region and K1 and K2 are weights assigned to these boundaries. The corresponding far region in the first order of approximation is symmetrical to the near region, relatively to the in-focus plane of the lens (the plane with zero defocusing). Here, symmetry is based on defocusing and not the length of the regions. Optimization of Eq. (9) is similar to Eq. (8), but requires less computation. The value maximized in Eq. (9) is composed of two terms with different degrees of defocusing and phase factors.

This approximate symmetry is illustrated in Fig. 1(b). A plane Pi is an in-focus plane of the lens, for the selected PDA distance (i.e. distance between the lensing section and the PDA). From imaged space, the magnitude of geometrical defocusing is the largest either at the left edge of near region or at the right edge of far region. At the right edge of the near region and at the left edge of the far region the geometrical defocusing is the smallest. It should be noted that this smallest defocusing is not zero, as it would be in an EDOF application, but βWm, where β is a number between zero and one. This is due to the effect of the phase mask. The effect of phase mask thus relates to overextending depth of focus.

Note that mathematically, in case that multiple set of N focused axial regions is to be generated the optimization expression takes the form of:

max{infμx<μd{n=1NKnH(μx,En)}}
(10)

In the performed simulations Δx was close to 1/8 of the lens aperture. The numerical optimization of the mathematical condition of Eq. (9) was done using Zemax. The parameter β was chosen such that the obtained focusing ranges will be 12.5cm–25cm and 50cm to infinity for camera with F-number of 3 and focal length of 4.8mm. Numerical simulations of the new design reveal the dual region behavior of the designed element.

Figures 2(a) and 2(b) show the through focus MTF plots where in Fig. 2(a) the object is placed at a distance of 15cm from the camera and in Fig. 2(b) the object is simulated at infinity. The obtained contrast is maximized on the desired working regions (12.5–25cm and 50cm-infinity) whereas there is some contrast degradation in the non constrained axial region of 30–50cm. The new approach allowed us to obtain larger working range in comparison to the previously presented approach of Ref. [17

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

]. The simulation of the through focus MTF was performed for high spatial frequency of 60 cycles/mm.

Fig. 2. Through focus MTF simulations for two discrete focusing regions. (a). object at 15cm, (b). object at infinity.

Additionally, it is possible to use non-equal weighing functions, K1 and K2 of Eq. (9), in order to obtain an unbalanced response. Examples of two different asymmetric systems are shown below. Figure 3(a) shows the through focus MTF of a system having better near field response compared to the far field response. Figure 3(b) shows the through focus MTF of a system having better far field response compared to the near field response. The simulation of the through focus MTF was performed for spatial frequency of 60 cycles/mm.

Fig. 3. Through focus MTF simulations for two discrete focusing regions. (a) emphasis on near objects, (b) emphasis on far objects.

As previously mentioned the same mathematical approach can be used for plurality of discrete focusing regions. In Fig. 4 we show simulations of an optical system with three focal regions around 13cm, 25cm and infinity as presented in the through focus OTF plots. The simulation of the through focus MTF was performed for spatial frequency of 150 cycles/mm.

3. Experimental results

We have fabricated the dual-region element that was designed and simulated in Fig. 2. In the experiment we verified the dual-region EDOF element. The dual-range system was capable of providing simultaneous imaging for far range objects (infinity) with performance that is comparable to a regular lens focused at infinity and at the same time providing a close range imaging around 12.5cm. The overall range of focused images was obtained for objects at 12.5cm–25cm and 50cm to infinity simultaneously. The element had two phase-discontinuities in its cross section and the design as well as the experiment was performed for cell phone camera with focal length of 4.8mm and F-number of 3.

A schematic sketch of the experimental setup is given in Fig. 5(a). The binary phase element was placed in the entrance plane of the imaging lens. Figure 5(b) presents the image captured when an object was placed at 15cm and yet there is scenery at far field about 7km away. One may see that the near object is in high contrast and the label of “made in France” can be read easily although the letters are very small (font size of 1mm). The far field objects are imaged with good contrast as well. Figure 5(c) shows an experiment where a business card is placed at range of 20cm from the camera. Once again the image contains both close and far range objects. The left image is the result obtained with the dual-region phase mask and the right image is from a reference camera with no element attached. One may see that the image from the dual-range system displays simultaneously the business card as well as the far field objects with good contrast whereas the regular system is capable of providing a good contrast only for the far field objects.

Fig. 4. Through focus MTF simulations for three discrete focusing regions, (a). object at 13cm (b). object at 25cm (c). object at infinity.

Figure 5(d) shows the contrast behavior along the Z-axis (obtained with the EDOF element). The image contains targets of line-widths of 0.5,1,2,4 and 8pt that are positioned at distances of 10,20,40,80 and 160cm respectively. The line-widths are adjusted according to the varying optical magnification so that they are imaged with equal size on the sensor. One can see that although the lines are imaged on sensor with same width, their contrast is not equal. The line positioned at 20cm exhibits high contrast whereas the line at 40cm has some contrast degradation, which is increased again when moving along the Z-axis towards infinity. This dual region contrast behavior is with full agreement to the through focus plots given in Figs 2(a) and 2(b). The experiment of Fig. 5(d) verified the theoretical prediction for the dual-region design.

4. Conclusions

In this paper we have demonstrated a novel approach that is based upon the technique of Refs. [16

16. Z. Zalevsky, “Optical method and system for extended depth of focus,” US patent application 10/97494 (August2004).

,17

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

], that optimizes the extended depth of focus performance in two (or more) ranges.

Figure 5. Experimental results with dual-region EDOF element. (a). the schematic sketch of the setup. (b). experiment with near objects at 15cm and far objects at more than 7km. (c). experiment with near-field business card at 20cm and far objects; left image - results obtained with the EDOF element; right image- a reference camera without the element. (d). varying line-width objects at distances of 10,20,40,80 and 160cm corresponding to the optical magnification and showing the resulted contrast behavior along the Z-axis.

Numerically as well as experimentally we have demonstrated improved performance in two ranges of 12.5cm–25cm and 50cm to infinity. The fact that in the optimization process we allowed contrast degradation in the range of 30cm–50cm, resulted with significant enhancement of the performance at close and far ranges. The extended depths of focus images are obtained in an all-optical manner. The phase-element is binary and contains only low spatial frequencies and thus it is simple to fabricate, it does not exhibit chromatic aberrations and its energetic efficiency is high.

References and links

1.

W. T. Cathy and E. R Dowski, “Apparatus and method for extending depth of field in image projection system,” US patent 6069738 (May2000).

2.

W. T. Cathy and E. R Dowski, “Extended depth of field optical systems,” PCT publication WO 99/57599 (November1999).

3.

W. T. Cathy, “Extended depth field optics for human vision,” PCT publication WO 03/052492 (June2003).

4.

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

5.

J. van der Gracht, E. Dowski, M. Taylor, and D. Deaver, “Broadband behavior of an optical-digital focus-invariant system,” Opt. Lett. 21, 919–921 (1996). [CrossRef] [PubMed]

6.

C. M. Hammond, “Apparatus and method for reducing imaging errors in imaging systems having an extended depth of field,” US patent 6097856 (August2000).

7.

D. Miller and E. Blanko, “System and method for increasing the depth of focus of the human eye,” US patent 6554424 (April2003).

8.

N. Atebara and D. Miller, “Masked intraocular lens and method for treating a patient with cataracts,” US patent 4955904 (September1990).

9.

J. O. Castaneda, E. Tepichin, and A. Diaz, “Arbitrary high focal depth with a quasi optimum real and positive transmittance apodizer,” Appl. Opt. 28, 2666–2669 (1989). [CrossRef]

10.

J. O. Castaneda and L. R. Berriel-Valdos, “Zone plate for arbitrary high focal depth,” Appl. Opt. 29, 994–997 (1990). [CrossRef]

11.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, N. Konforti, and D. Mendlovic, “All optical extended depth of field imaging system,” PCT publication WO 03/076984 (September2003).

12.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A: Pure Appl. Opt. 5, S164–S169 (2003). [CrossRef]

13.

E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, “Experimental realization of an imaging system with an extended depth of field,” Appl. Opt. 44, 2792–2798 (2005). [CrossRef] [PubMed]

14.

A. Sauceda and J. Ojeda-Castaneda, “High focal depth with fractional-power wavefronts,” Opt. Lett. 29, 560–562 (2004). [CrossRef] [PubMed]

15.

W. Chi and N. George, “Electronic imaging using a logarithmic asphere,” Opt. Lett. 26, 875–877 (2001). [CrossRef]

16.

Z. Zalevsky, “Optical method and system for extended depth of focus,” US patent application 10/97494 (August2004).

17.

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

OCIS Codes
(110.4850) Imaging systems : Optical transfer functions
(170.1630) Medical optics and biotechnology : Coded aperture imaging

ToC Category:
Imaging Systems

History
Original Manuscript: October 11, 2007
Revised Manuscript: December 10, 2007
Manuscript Accepted: December 13, 2007
Published: December 17, 2007

Virtual Issues
Vol. 3, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Ido Raveh and Zeev Zalevsky, "All-optical axially multi-regional super resolved imaging," Opt. Express 15, 17912-17921 (2007)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-15-26-17912


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. W. T. Cathy and E. R Dowski, "Apparatus and method for extending depth of field in image projection system," US patent 6069738 (May 2000).
  2. W. T. Cathy and E. R Dowski, "Extended depth of field optical systems," PCT publication WO 99/57599 (November 1999).
  3. W. T. Cathy, "Extended depth field optics for human vision," PCT publication WO 03/052492 (June 2003).
  4. E. R Dowski and W. T. Cathey, "Extended depth of field through wave-front coding," Appl. Opt. 34, 1859-1866 (1995). [CrossRef] [PubMed]
  5. J. van der Gracht, E. Dowski, M. Taylor and D. Deaver, "Broadband behavior of an optical-digital focus-invariant system," Opt. Lett. 21, 919-921 (1996). [CrossRef] [PubMed]
  6. C. M. Hammond, "Apparatus and method for reducing imaging errors in imaging systems having an extended depth of field," US patent 6097856 (August 2000).
  7. D. Miller and E. Blanko, "System and method for increasing the depth of focus of the human eye," US patent 6554424 (April 2003).
  8. N. Atebara and D. Miller, "Masked intraocular lens and method for treating a patient with cataracts," US patent 4955904 (September 1990).
  9. J. O. Castaneda, E. Tepichin and A. Diaz, "Arbitrary high focal depth with a quasi optimum real and positive transmittance apodizer," Appl. Opt. 28, 2666-2669 (1989). [CrossRef]
  10. J. O. Castaneda and L. R. Berriel-Valdos, "Zone plate for arbitrary high focal depth," Appl. Opt. 29, 994-997 (1990). [CrossRef]
  11. E. Ben-Eliezer, Z. Zalevsky, E. Marom, N. Konforti and D. Mendlovic, "All optical extended depth of field imaging system," PCT publication WO 03/076984 (September 2003).
  12. E. Ben-Eliezer, Z. Zalevsky, E. Marom and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A: Pure Appl. Opt. 5, S164-S169 (2003). [CrossRef]
  13. E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "Experimental realization of an imaging system with an extended depth of field," Appl. Opt. 44, 2792-2798 (2005). [CrossRef] [PubMed]
  14. A. Sauceda and J. Ojeda-Castaneda, "High focal depth with fractional-power wavefronts," Opt. Lett. 29, 560-562 (2004). [CrossRef] [PubMed]
  15. W. Chi and N. George, "Electronic imaging using a logarithmic asphere," Opt. Lett. 26, 875-877 (2001). [CrossRef]
  16. Z. Zalevsky, "Optical method and system for extended depth of focus," US patent application 10/97494 (August 2004).
  17. Z. Zalevsky, A. Shemer, A. Zlotnik, E. Ben-Eliezer and E. Marom, "All-optical axial super resolving imaging using low-frequency binary-phase mask," Opt. Express 14, 2631-2643 (2006). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited