## An optimal binary amplitude-phase mask for hybrid imaging systems that exhibit high resolution and extended depth of field

Optics Express, Vol. 16, Issue 25, pp. 20540-20561 (2008)

http://dx.doi.org/10.1364/OE.16.020540

Acrobat PDF (582 KB)

### Abstract

The design of a circularly symmetric hybrid imaging system that exhibits high resolution as well as extended depth of field is presented. The design, which assumes spatially incoherent illumination, searches for an optimal “binary amplitude and phase” pupil mask, which for a certain desired depth of field, provides the largest spatial frequency band that assures a certain desired contrast value. The captured images are electronically processed by an off-line Wiener filter, to finally obtain high quality output images. Simulations as well as experimental results are provided.

© 2008 Optical Society of America

## 1. Introduction

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

8. S. Sanyal and A. Ghosh, “High focal depth with quasi-bifocus birefringent lens,” Appl. Opt. **39**, 2321–2325 (2000). [CrossRef]

9. E. Peli and A. Lang, “Appearance of images through a multifocal intraocular lens,” J. Opt. Soc. Am. A **18**, 302–309 (2001). [CrossRef]

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

14. S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “High resolution imaging using integrated optical systems,” Int. J. Imaging Syst. Technol. **14**, 67–74 (2004). [CrossRef]

13. S. Prasad, V. Paul Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended focus, aberration corrected imaging systems,” Proc. SPIE **5559**, 335–345 (2004). [CrossRef]

14. S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “High resolution imaging using integrated optical systems,” Int. J. Imaging Syst. Technol. **14**, 67–74 (2004). [CrossRef]

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

16. N George and W. Chi , “Computational imaging with the logarithmic asphere: theory,” J. Opt. Soc. Am. A **20**, 2260–2273 (2003). [CrossRef]

*et al*[10

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

12. S. S. Sherif, W. T. Cathey, and E. R. Dowski, “Phase plate to extend the depth of field of incoherent hybrid imaging systems,” Appl. Opt. **43**, 2709–2721 (2004). [CrossRef] [PubMed]

17. J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, “Iris recognition with enhanced depth-of-field image acquisition,” Proc. SPIE **5438**, 120–129 (2004). [CrossRef]

18. E. Ben-Eliezer and E. Marom, “Aberration-free superresolution imaging via binary speckle pattern encoding and processing,” J. Opt. Soc. Am. A **24**, 1003–1010 (2007). [CrossRef]

19. E. Ben-Eliezer, N. Konfori, and E. Marom, “Superresolution imaging with noise reduction and aberration elimination via random structured illumination and processing,” Opt. Express **15**, 3849–3863 (2007). [CrossRef] [PubMed]

20. E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-Optical Extended Depth of Field Imaging System,” Pure Appl. Opt. **5**, S164–S169 (2003). [CrossRef]

22. E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “Experimental Realization of an Imaging System with an Extended Depth of Field,” Appl. Opt. **44**, 2792–2798 (2005). [CrossRef] [PubMed]

22. E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “Experimental Realization of an Imaging System with an Extended Depth of Field,” Appl. Opt. **44**, 2792–2798 (2005). [CrossRef] [PubMed]

23. E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, “A Radial Mask for Systems that exhibit High Resolution and Extended Depth of Field,” Appl. Opt. **45**, 2001–2013 (2006). [CrossRef] [PubMed]

23. E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, “A Radial Mask for Systems that exhibit High Resolution and Extended Depth of Field,” Appl. Opt. **45**, 2001–2013 (2006). [CrossRef] [PubMed]

23. E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, “A Radial Mask for Systems that exhibit High Resolution and Extended Depth of Field,” Appl. Opt. **45**, 2001–2013 (2006). [CrossRef] [PubMed]

**45**, 2001–2013 (2006). [CrossRef] [PubMed]

**45**, 2001–2013 (2006). [CrossRef] [PubMed]

*π*” phase rings. We search for optimal designs when considering a mask with a single annular phase ring (providing high contrast and resolution, but reduced DOF range) as well as for a case of two annular phase rings (providing reduced contrast and resolution, but larger DOF range), denoted as “1R” and “2R” respectively.

4. T. C. Poon and M. Motamedi, “Optical Digital Incoherent Image Processing for Extended Depth of Field,” Appl. Opt. **26**, 4612–4615 (1987). [CrossRef] [PubMed]

## 2. Theory

_{obj}and d

_{img}are the lens focal length, and the distances between the object and the image to the lens respectively. Clearly, for an in-focus position, ψ=0. When defocus occurs, the phase factor, given in Eq. (1), multiplies the pupil of the imaging system, resulting in a generalized pupil, expressed in the following expression:

_{g}(x,y) is the intensity of the image, in a system without diffraction (i.e. geometrical optics considerations), and h(x,y) is the coherent point spread function. Eq. (4) reveals that the phase of the coherent point spread function is irrelevant when considering incoherently illuminated imaging systems.

_{x}and ν

_{y}are the normalized spatial frequencies, Ω defines the integration region and

*P*̄(

*u, v*) is the complex conjugate of

*P*(

*u,v*).

### 2.1 Considerations for choosing the design criterion

**45**, 2001–2013 (2006). [CrossRef] [PubMed]

_{1}…r

_{2N}be the inner and outer radia of N

*π*-phase annular rings. Obviously, each choice of radia, {r

_{1}…r

_{2N}}, results in a certain mask structure that provides a certain DOF range, as well as a PCF value, denoted by ν(r

_{1}…r

_{2N}). This PCF was obtained by examining the corresponding MTF curves obtained for several defocus positions. Then, the radia that provide the highest PCF value were chosen. Mathematically, the direct optimization process is described by the following expression:

_{d}is the desired minimum contrast. We now search for a mask to be ultimately used with incoherently illuminated scenes, such that Eq. (6) is maximized. We expect the image to display high resolution, up to pixel size resolution, for the whole DOF range.

### 2.2 Optimization considerations.

**45**, 2001–2013 (2006). [CrossRef] [PubMed]

_{1}(a,w) and U

_{2}(a,w), which are defined by the following series [2]:

_{m}(w) stands for a Bessel function of the first kind and order m.

**r**

_{1}…

**r**

_{2N}, where smaller index indicates smaller radius value. Therefore, in Eq. (9) the sub-apertures normalized pupil radia are defined as ρ

_{n}=r/r

_{n}. P′(ρ

_{n},a) has been defined in Eq. (7) and ψ is the maximal phase shift at the pupil edge. The reader should note that P′(ρ

_{n}, a)=0 for ρ

_{n}>1. Applying Eq. (8b) to each one of the sub-pupils, one obtains the radial cross-section of the total PSF field distribution. Since we deal with incoherent illumination, we are interested in the square of the absolute value of the PSF radial cross section vectors, to express the intensity impulse response. Thereafter, the OTF radial cross sections are readily calculated by the Bessel-Fourier transform [1–2], of the intensity impulse response:

### 2.3 Optimized binary amplitude-phase circular mask.

4. T. C. Poon and M. Motamedi, “Optical Digital Incoherent Image Processing for Extended Depth of Field,” Appl. Opt. **26**, 4612–4615 (1987). [CrossRef] [PubMed]

_{1}, defines an opaque centered circle, while the rest of the radiuses, r

_{2}…r

_{2N+1}, are the radial positions of the phase transitions. Similar to Eq. (9), the expression for a generalized pupil mask of this family is provided as follows:

## 3. Results

### 3.1 Optimization results

_{max}at the aperture edge, we seek the locations of one or two

*π*-phase rings, with or without an amplitude opaque center that provide the maximal normalized spatial frequency, ν

_{max}, which assures a certain desired minimal contrast, denoted by C

_{d}within the whole DOF range. Since we observed that the contrast has a tendency to fluctuate around the minimal acceptable contrast value, in our calculations we accepted variations of +/-10% from the nominal one. As a result of this, a minimal defined contrast of 10% was essentially allowed to drop as low as 9% and a 5% contrast was allowed to reach 4.5%.

_{d}, of five and nine percents respectively. PCF values in all the tables were normalized assuming that the diffraction-limit cutoff for spatially incoherent illumination is 2.

_{1}is the normalized radius of the opaque circle and the other radia identify the radial locations of the phase transition. Note an additional column that provides the resulting light throughput.

_{max}=10, where for larger DOF ranges, the size of the central opaque circle increases. In order to have high performance in the presence of severe defocus conditions, i.e., large DOF, the optimization was carried out for the case of a binary phase mask with two phase rings, as well as a mask with two phase rings and an opaque central circle. The results are summarized in Tables 5–8 respectively.

_{max}as well as the amount of reduction in the optical light throughput. Tables 9 and 10 show these parameters. The notation 1R means “one ring”. The notation 1RC means “one ring and opaque center”. Similar notations are used for two rings. Table 9 presents the maximal frequency in bold letters in each left sub-column, as well as the light throughput (right sub-column) for an assumed acceptable contrast value of C

_{d}=5%, while Table 10 shows the same, but for a contrast value of C

_{d}=10%.

_{d}=5% and Table 12 for a desired contrast value of 10%.

_{max}value), the size of the opaque center radius

*increases*in case of the annular amplitude ring (Tables 11–12). Therefore, the light throughput is lower for a larger ψ

_{max}. However, in the case of the amplitude

*and phase*masks (1Rc and 2Rc), up to a certain ψ

_{max}value the size of the opaque center

*decreases*with ψ

_{max}, due to the presence of the phase rings. Therefore, the light throughput increases with ψ

_{max}, up to a certain ψ

_{max}value.

_{d}values, the central opaque circle is bigger, and higher resolution is achieved. However, the light throughput for those cases is relatively low. One further notes that up to a certain ψ

_{max }value (ψ

_{max}=10 for one phase ring and ψ

_{max}=16 for two phase rings), the 1RC mask tends to coincide with the 1R mask, and similarly the 2RC mask tends to coincide with the 2R mask. For higher ψ

_{max}values the opaque center size tends to increase since it tries to reduce the aperture size and thus the phase only masks and the amplitude-phase masks do not coincide anymore. This phenomenon is clearer for low C

_{d}values, since if small Cd values are allowed, the resulting OTF tends to resemble an OTF of an amplitude annular ring.

_{d}=5%, is higher than the one achieved for 10%. Moreover, the higher the resolution improvement is, the lower the obtained light throughput.

### 3.2 Performance of the binary phase mask

_{d}) tends to provide higher ACF value (red curve). This is seen in Fig. 4 as well, where the OTF curves of the optimal phase masks with two annular phase rings, which were designed for desired contrast values of 5% (red curve) and 10% (blue curve), for a DOF range of Ψ

_{max}=14 are presented. Defocus conditions of ψ=0, 7 and 14 are shown in Figs. 4 (a)–4(c) respectively.

**45**, 2001–2013 (2006). [CrossRef] [PubMed]

### 3.3 Performance of the binary phase and amplitude mask

_{max}=8 is shown in Fig. 5. The improvement in the PCF values in both cases are clearly seen, when the above results are compared to the OTF of a clear aperture (black curve) that provides the same light throughput, thus having a lateral dimension of about 80% of the lateral dimension of the optimal mask aperture (64% throughput). Note that the frequency range of all the OTF curves shown in Fig. 5 correspond to a full size aperture (100% lateral dimension size). Defocus conditions of ψ=0, 4 and 8 are shown in Figs. 5(a)–5(c) respectively.

## 4. Experimental realizations

### 4.1 Imaging system specifications

^{®}DV5200 camera, equipped with a CMOS detector having a resolution of 1200x1600 pixels (2 mega pixels). The camera lens was composed of five glass elements with effective focal length of 8.5mm, and was considered throughout the experiment as an equivalent achromatic thin lens. Field of view (FOV) of 50 degrees along the sensor diagonal and pixel dimension of 4µm were measured experimentally by counting the number of pixels in an image of an object with known dimensions that was located at a known distance from the camera. The camera lens was positioned in an in-focus condition, where object was located 30 cm from the lens. The required specifications of the imaging system are working distance from 15cm to infinity for wavelength of 532 nm. The required desired contrast value is 5%.

_{max}@λ=532nm) was found to be 20 radians. The optimization results, presented earlier, reveal that the binary amplitude and phase mask with two phase rings provided the highest PCF, and therefore it has been used throughout the experiment.

### 4.2 Mask behavior under polychromatic illumination

### 4.3 Experimental results

^{®}DV 5200 camera. A metal structure that contains the pupil mask was externally mounted on the lens. The experimental apparatus is portable, and can be taken outdoors, or it can be used on an optical table indoor, thus providing the flexibility of checking the behavior for indoor and outdoor illumination with ease. The output images that were acquired with the mask were processed after capture by a digital restoration filter, to achieve improved resolution and contrast. A block diagram of the digital restoration filter that we used is shown in Fig. 9.

24. R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, “Color image processing pipeline,” IEEE Sig. Proc. Mag. **22**, 34–43 (2005). [CrossRef]

## 5. Conclusions

**45**, 2001–2013 (2006). [CrossRef] [PubMed]

## References and links

1. | J. W. Goodman, |

2. | A. Papoulis, |

3. | M. Mino and Y. Okano, “Improvement in the OTF of a Defocused Optical System Trough the Use of Shaded apertures,” Appl. Opt. |

4. | T. C. Poon and M. Motamedi, “Optical Digital Incoherent Image Processing for Extended Depth of Field,” Appl. Opt. |

5. | J. O. Castaneda, R. Ramos, and A. Noyola-Isgleas, “High focal depth by apodization and digital restoration,” Appl. Opt. |

6. | J. O. Castaneda, E. Tepichin, and A. Diaz, “Arbitrary high focal depth with a quasioptimum real and positive transmittance apodizer,” Appl. Opt. |

7. | J. O. Castaneda and L. R. Berriel-Valdos, “Zone plate for arbitrary high focal depth,” Appl. Opt. |

8. | S. Sanyal and A. Ghosh, “High focal depth with quasi-bifocus birefringent lens,” Appl. Opt. |

9. | E. Peli and A. Lang, “Appearance of images through a multifocal intraocular lens,” J. Opt. Soc. Am. A |

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

11. | J. van der Gracht, E. R. Dowski, M. G. Taylor, and D. M. Deaver, “Broadband behavior of an optical-digital focus-invariant system,” Opt. Lett. |

12. | S. S. Sherif, W. T. Cathey, and E. R. Dowski, “Phase plate to extend the depth of field of incoherent hybrid imaging systems,” Appl. Opt. |

13. | S. Prasad, V. Paul Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended focus, aberration corrected imaging systems,” Proc. SPIE |

14. | S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “High resolution imaging using integrated optical systems,” Int. J. Imaging Syst. Technol. |

15. | W. Chi and N. George, “Electronic imaging using a logarithmic asphere,” Opt. Lett. |

16. | N George and W. Chi , “Computational imaging with the logarithmic asphere: theory,” J. Opt. Soc. Am. A |

17. | J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, “Iris recognition with enhanced depth-of-field image acquisition,” Proc. SPIE |

18. | E. Ben-Eliezer and E. Marom, “Aberration-free superresolution imaging via binary speckle pattern encoding and processing,” J. Opt. Soc. Am. A |

19. | E. Ben-Eliezer, N. Konfori, and E. Marom, “Superresolution imaging with noise reduction and aberration elimination via random structured illumination and processing,” Opt. Express |

20. | E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-Optical Extended Depth of Field Imaging System,” Pure Appl. Opt. |

21. | E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-Optical Extended Depth of Field Imaging System,” Proc. SPIE |

22. | E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “Experimental Realization of an Imaging System with an Extended Depth of Field,” Appl. Opt. |

23. | E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, “A Radial Mask for Systems that exhibit High Resolution and Extended Depth of Field,” Appl. Opt. |

24. | R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, “Color image processing pipeline,” IEEE Sig. Proc. Mag. |

25. | R. C. Gonzalez and R. E. Woods, |

26. | B. R. Hunt and O. Kubler, “Karhunen-Loeve Multispectral Image Restoration, Part I: Theory,” ASSP |

27. | E. Marom, E. Ben-Eliezer, and N. Knoforti, PCT/IL2008/000527 “Optical imaging system with an extended depth-of-field and a method for designing an optical imaging system.” |

**OCIS Codes**

(080.1010) Geometric optics : Aberrations (global)

(080.3620) Geometric optics : Lens system design

(110.0110) Imaging systems : Imaging systems

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: September 23, 2008

Revised Manuscript: October 26, 2008

Manuscript Accepted: October 29, 2008

Published: November 26, 2008

**Citation**

Eyal Ben-Eliezer, Naim Konforti, Benjamin Milgrom, and Emanuel Marom, "An optimal binary amplitude-phase mask for hybrid imaging systems that exhibit high resolution and extended depth of field," Opt. Express **16**, 20540-20561 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20540

Sort: Year | Journal | Reset

### References

- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
- A. Papoulis, Systems and Transforms with Applications in Optics (McGraw- Hill, New York, 1968).
- M. Mino and Y. Okano, "Improvement in the OTF of a Defocused Optical System Trough the Use of Shaded apertures," Appl. Opt. 10, 2219-2225 (1971). [CrossRef] [PubMed]
- T. C. Poon and M. Motamedi, "Optical Digital Incoherent Image Processing for Extended Depth of Field," Appl. Opt. 26, 4612-4615 (1987). [CrossRef] [PubMed]
- J. O. Castaneda, R. Ramos, and A. Noyola-Isgleas, "High focal depth by apodization and digital restoration," Appl. Opt. 272583-2586 (1988). [CrossRef]
- J. O. Castaneda, E. Tepichin, and A. Diaz, "Arbitrary high focal depth with a quasioptimum real and positive transmittance apodizer," Appl. Opt. 28, 2666-2669 (1989). [CrossRef]
- J. O. Castaneda and L. R. Berriel-Valdos, "Zone plate for arbitrary high focal depth," Appl. Opt. 29, 994-997 (1990). [CrossRef]
- S. Sanyal and A. Ghosh, "High focal depth with quasi-bifocus birefringent lens," Appl. Opt. 39, 2321-2325 (2000). [CrossRef]
- E. Peli and A. Lang, "Appearance of images through a multifocal intraocular lens," J. Opt. Soc. Am. A 18, 302-309 (2001). [CrossRef]
- E. R Dowski Jr and W. T. Cathey, "Extended depth of field through wave-front coding," Appl. Opt 34, 1859-1866 (1995). [CrossRef] [PubMed]
- J. van der Gracht, E. R. DowskiJr, M. G. Taylor, and D. M. Deaver, "Broadband behavior of an optical-digital focus-invariant system," Opt. Lett. 21, 919-921 (1996). [CrossRef] [PubMed]
- S. S. Sherif, W. T. Cathey, and E. R. Dowski, "Phase plate to extend the depth of field of incoherent hybrid imaging systems," Appl. Opt. 43, 2709-2721 (2004). [CrossRef] [PubMed]
- S. Prasad, V. Paul Pauca, R. J. Plemmons, T. C. Torgersen and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," Proc. SPIE 5559,335-345 (2004). [CrossRef]
- S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004). [CrossRef]
- W. Chi and N. George, "Electronic imaging using a logarithmic asphere," Opt. Lett. 26, 875-877 (2001). [CrossRef]
- N George and W. Chi, "Computational imaging with the logarithmic asphere: theory," J. Opt. Soc. Am. A 20, 2260-2273 (2003). [CrossRef]
- J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004). [CrossRef]
- E. Ben-Eliezer and E. Marom, "Aberration-free superresolution imaging via binary speckle pattern encoding and processing," J. Opt. Soc. Am. A 24, 1003-1010 (2007). [CrossRef]
- E. Ben-Eliezer, N. Konfori, and E. Marom, "Superresolution imaging with noise reduction and aberration elimination via random structured illumination and processing," Opt. Express 15, 3849-3863 (2007). [CrossRef] [PubMed]
- E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-Optical Extended Depth of Field Imaging System," Pure Appl. Opt. 5, S164-S169 (2003). [CrossRef]
- E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-Optical Extended Depth of Field Imaging System," Proc. SPIE 4829, 221-222 (2002).
- E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "Experimental Realization of an Imaging System with an Extended Depth of Field," Appl. Opt. 44, 2792-2798 (2005). [CrossRef] [PubMed]
- E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "A Radial Mask for Systems that exhibit High Resolution and Extended Depth of Field," Appl. Opt. 45, 2001-2013 (2006). [CrossRef] [PubMed]
- R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, "Color image processing pipeline," IEEE Sig. Proc. Mag. 22, 34-43 (2005). [CrossRef]
- R. C. Gonzalez and R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1993).
- B. R. Hunt and O. Kubler, "Karhunen-Loeve Multispectral Image Restoration, Part I: Theory," ASSP 32, 592-600 (1984). [CrossRef]
- E. Marom, E. Ben-Eliezer, and N. Knoforti, PCT/IL2008/000527 "Optical imaging system with an extended depth-of-field and a method for designing an optical imaging system."

## 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.

### Figures

Fig. 1. |
Fig. 2. |
Fig. 3. |

Fig. 4. |
Fig. 5. |
Fig. 6. |

Fig. 7. |
Fig. 8. |
Fig. 9. |

Fig. 10. |
Fig. 11. |
Fig. 12. |

« Previous Article | Next Article »

OSA is a member of CrossRef.