## Analysis on enhanced depth of field for integral imaging microscope |

Optics Express, Vol. 20, Issue 21, pp. 23480-23488 (2012)

http://dx.doi.org/10.1364/OE.20.023480

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### Abstract

Depth of field of the integral imaging microscope is studied. In the integral imaging microscope, 3-D information is encoded as a form of elemental images Distance between intermediate plane and object point decides the number of elemental image and depth of field of integral imaging microscope. From the analysis, it is found that depth of field of the reconstructed depth plane image by computational integral imaging reconstruction is longer than depth of field of optical microscope. From analyzed relationship, experiment using integral imaging microscopy and conventional microscopy is also performed to confirm enhanced depth of field of integral imaging microscopy.

© 2012 OSA

## 1. Introduction

1. D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. **13**(1), 191–219 (1984). [CrossRef] [PubMed]

5. C. J. R. Sheppard and X. Q. Mao, “Confocal microscopes with slit apertures,” J. Mod. Opt. **35**(7), 1169–1185 (1988). [CrossRef]

8. J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. **45**(16), 3893–3901 (2006). [CrossRef] [PubMed]

9. Y.-T. Lim, J.-H. Park, N. Kim, and K.-C. Kwon, “Dense light field microscopy,” Proc. SPIE **7237**, 72371Q, 72371Q-12 (2009). [CrossRef]

10. Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express **17**(21), 19253–19263 (2009). [CrossRef] [PubMed]

## 2. Lateral resolution in integral imaging microscope

*f*is the focal length of the micro lens array. To capture more views of the object, third case has to be satisfied.

_{la}## 3. DOF in IIM

*M*

^{2}by the objective and tube lenses. DOF around the object plane is given byFrom Eq. (4) and Eq. (7), both lateral and axial resolutions are determined by

*NA*. Note that extended DOF of the IIM compared to conventional optical microscope means that area of focused depth plane image is extended by micro lens array. The resolution of reconstructed images in the extended DOF has low quality than conventional optical microscope. The IIM still has resolution tradeoff by micro lens array [10

_{la}10. Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express **17**(21), 19253–19263 (2009). [CrossRef] [PubMed]

*NA*= 0.2,

*λ*= 532nm,

*M*= 10,

*f*= 2.4mm,

_{la}*e*= 6

*μ*m, and

*φ*= 125

*μ*m. In Fig. 4(a), DOF of the IIM is longer than DOF of the conventional optical microscope when

*d*= 3.3mm. As mentioned above in section 2,

*NA*<

_{la}*NA*/

*M*, to form an elemental image with multiple view information,

*d*is longer than 3.125mm. In the IIM, the depth information of the object is encoded as a disparity between the elemental images. Hence, the minimum depth deviation which causes a barely detectable change of the disparity between the elemental images can be regarded as a measure of axial resolution. In Fig. 4(b), if

*d*is 3.5mm, then

*g*is 7.6mm. Numerically calculated DOF of the IIM exceed DOF of the conventional optical microscope. In this condition,

*R*is 30.5

_{ele}*μ*m and each object point is imaged to four elemental lens. Four view images can be reconstructed via the OVIR method. However, these images are blurred.

*R*is larger than pixel size of the CCD

_{ele}*e*. Hence, effective range of

*d*has to be set.

## 4. Experiments for generating extended DOF images and comparison with conventional extended depth of field images

*μ*m, the pitch size of the micro lens was 125

*μ*m and

*d*is 10mm.

*μ*m. From Eq. (7), calculated

*D*,

*D*, and

_{o}*R*are 180

_{ele}*μ*m, 18

*μ*m, and 12.6

*μ*m, respectively. Figure 7(b) shows the elemental image of Fig. 7(a). The pixel size and number of pixels of the elemental image are 946 × 946 and 11 × 11, respectively. Calculated DOF of the IIM is 18

*μ*m, and then 8 images are required to compare the DOF of a conventional optical microscope shown as Fig. 8 . From Fig. 7(b), depth slice images were generated at a reconstructed distance with z = −3mm to −6mm, and 3mm to 6mm, shown as Fig. 9 . In conventional CIIR method, for a given depth plane, specific depth plane can be generated. CIIR method used in this paper is only effective within integer depth plane . If

*g*is same to focal length of the micro lens array, errors occurs for coding. Each local position of pixels is remapped on certain depth plane. In this case, focal length of the micro lens array is 2.4mm, minimum condition to generate depth plane of center region of the object is 3mm vice versa. In our experiment, 3mm to 6mm and −3mm to −6mm on depth plane of CIIR cover the range of 140

*μ*m.

## 5. Conclusion

## Acknowledgments

## References and links

1. | D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. |

2. | J. G. McNally, C. Preza, J. A. Conchello, and L. J. Thomas Jr., “Artifacts in computational optical-sectioning microscopy,” J. Opt. Soc. Am. A |

3. | S. Liu and H. Hua, “Extended depth-of-field microscopic imaging with a variable focus microscope objective,” Opt. Express |

4. | J. A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods |

5. | C. J. R. Sheppard and X. Q. Mao, “Confocal microscopes with slit apertures,” J. Mod. Opt. |

6. | S. Inoue and R. Oldenbourg, |

7. | Q. Wu, F. A. Merchant, and K. R. Castleman, |

8. | J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. |

9. | Y.-T. Lim, J.-H. Park, N. Kim, and K.-C. Kwon, “Dense light field microscopy,” Proc. SPIE |

10. | Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express |

11. | D.-H. Shin and E.-S. Kim, “Computational integral imaging reconstruction of 3D Object using a depth conversion technique,” J. Opt. Soc. Kor. |

**OCIS Codes**

(100.6890) Image processing : Three-dimensional image processing

(110.0180) Imaging systems : Microscopy

(170.6900) Medical optics and biotechnology : Three-dimensional microscopy

**ToC Category:**

Microscopy

**History**

Original Manuscript: July 6, 2012

Revised Manuscript: September 1, 2012

Manuscript Accepted: September 24, 2012

Published: September 27, 2012

**Citation**

Young-Tae Lim, Jae-Hyeung Park, Ki-Chul Kwon, and Nam Kim, "Analysis on enhanced depth of field for integral imaging microscope," Opt. Express **20**, 23480-23488 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-23480

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### References

- D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng.13(1), 191–219 (1984). [CrossRef] [PubMed]
- J. G. McNally, C. Preza, J. A. Conchello, and L. J. Thomas., “Artifacts in computational optical-sectioning microscopy,” J. Opt. Soc. Am. A11(3), 1056–1067 (1994). [CrossRef] [PubMed]
- S. Liu and H. Hua, “Extended depth-of-field microscopic imaging with a variable focus microscope objective,” Opt. Express19(1), 353–362 (2011). [CrossRef] [PubMed]
- J. A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods2(12), 920–931 (2005). [CrossRef] [PubMed]
- C. J. R. Sheppard and X. Q. Mao, “Confocal microscopes with slit apertures,” J. Mod. Opt.35(7), 1169–1185 (1988). [CrossRef]
- S. Inoue and R. Oldenbourg, Handbook of Optics (McGrawHill, 1995), Chap. 17.
- Q. Wu, F. A. Merchant, and K. R. Castleman, Microscope Image Processing (Academic press, 2008), Chap. 2.
- J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt.45(16), 3893–3901 (2006). [CrossRef] [PubMed]
- Y.-T. Lim, J.-H. Park, N. Kim, and K.-C. Kwon, “Dense light field microscopy,” Proc. SPIE7237, 72371Q, 72371Q-12 (2009). [CrossRef]
- Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express17(21), 19253–19263 (2009). [CrossRef] [PubMed]
- D.-H. Shin and E.-S. Kim, “Computational integral imaging reconstruction of 3D Object using a depth conversion technique,” J. Opt. Soc. Kor.12(3), 131–135 (2008). [CrossRef]

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