## Endoscopic pulsed digital holography for 3D measurements

Optics Express, Vol. 14, Issue 4, pp. 1468-1475 (2006)

http://dx.doi.org/10.1364/OE.14.001468

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### Abstract

A rigid endoscope and three different object illumination source positions are used in pulsed digital holography to measure the three orthogonal displacement components from hidden areas of a harmonically vibrating metallic cylinder. In order to obtain simultaneous 3D information from the optical set up, it is necessary to match the optical paths of each of the reference object beam pairs, but to incoherently mismatch the three reference object beam pairs, such that three pulsed digital holograms are incoherently recorded within a single frame of the CCD sensor. The phase difference is obtained using the Fourier method and by subtracting two digital holograms captured for two different object positions.

© 2006 Optical Society of America

## 1. Introduction

## 2. 3-D Evaluation

*ξ*and

*η*are rectangular coordinates at the CCD detector plane.

*f*

_{kξ}and

*f*

_{kη}, represent spatial frequency carriers along directions

*ξ*and

*η*, due to a small inclination of each diverging reference beam with respect to the system optical axis

*z*, see Fig. 1. Upon substitution of Eq. (2) and Eq. (3) into 1,

*f*

_{kξ}and

*f*

_{kη}, and phase modulated by

*φ*

_{k}(

*ξ*,

*η*). As is commonly done in digital holography in order to recover the phase term

*φ*

_{k}(

*ξ*,

*η*) a Fourier transform must be performed on Eq. (4),

*φ*

_{k}(

*ξ*,

*η*) is contained in either of the complex conjugate terms

*C*

_{k}and

*C*

_{k}and

*f*

_{ξ},

*f*

_{η})=0. Only three of these terms are filtered, each belonging to a reference object beam pair, and their inverse Fourier transform calculated in order to obtain the corresponding phase distribution

*ξ*,

*η*), is again extracted from each reference object beam pair obtained on a single CCD frame. Subtraction of the phase distribution obtained from each object position gives,

*n̂*

_{k}y

*n̂*

_{o}are unitary vectors along the direction of object illumination and observation, respectively. For the experiment in hand, it is assumed that the orthogonal coordinate system origin is on the geometrical object center, (see Fig. 3). Eq. (10) allows the combination of the individual phases and sensitivity vectors, all data obtained from the experiment. The only remaining unknown is

*u⃗*, the displacement vector along the

*x*,

*y*and

*z*axes.

## 3. Results and discussion

^{2}, each. The endoscope has the ability to form object images from 3 mm to 12 mm diameter: for this experiment the object area imaged is 12 mm. The separation from the endoscope edge to the object surface may be varied from 5 mm to 25 mm: 25 mm for this experiment. Pulses from a Nd:YAG laser emitting at 532ηm are divided initially into two beams, one that serves as reference and the other as object. Each beam is further divided into three reference and object beams by means of beam splitters.

*z*optical axis. This is the manner in which the unitary vectors of illumination

*n̂*

_{k}are defined. Finally, the three reference beams are sent to the CCD sensor using single mode optical fibers. The diverging beams have a relative inclination with respect to the

*z*optical axis, and therefore to their respective object beam pair, of approximately 1.5°. This is done in order to physically separate the individual reference object beam pair Fourier components.

*φ*

_{k}is obtained by simply subtracting the phase information from one pulse to the other, i.e., the displacement information

*u⃗*may now be calculated from Eq. (10).

*φ*

_{k}for each reference object beam pair, i.e., for every object illumination direction. In order to work with Eq. (10), these phase maps need to be unwrapped so that the 2π discontinuities are taken into consideration. The object image has a diameter of 11mm, and from it only a reduced area (10mm × 9.5mm) is used to unwrap the phase maps. The sensitivity vector is then calculated by measuring the distances, from the origin, to the three object illumination sources and to the CCD sensor center. Once this is done it is possible to calculate

*u⃗*, and indeed to separate independently of each other all three components of the deformation

*x*,

*y*and

*z*. Figure 5 shows the normal, to the surface, displacement component drawn on a computer generated cylinder shape. Figure 6 shows the tangent displacement on the cylinder surface, with the arrows indicating the way in which the cylinder is deforming.

## 5. Conclusions

## Acknowledgments

## References and links

1. | D. Hadbawnik,“Holographische endoskopie,” Optik |

2. | H. I. Bjelkhagen, M. D. Friedman, and M. Epstein, “Holographic high resolution endoscopy through optical fiber,” Proc. Laser Inst. Am. |

3. | M. Yonemura, T. Nishisaka, and H. Machida, “Endoscopic hologram interferometry using fiber optics,” Appl. Opt. |

4. | B. Kemper, D. Dirksen, W. Avenhaus, A. Merker, and G. Von Bally, “Endoscopic double pulse electronic speckle pattern interferometer for technical and medical intracavity inspection,” Appl. Opt. |

5. | G. Pedrini, S. Schedin, and H. J. Tiziani, “Use of endoscopes in pulsed digital holographic interferometry,” in Optical Measurement System for Industrial Inspection II: Applications in productions Engineering,
R. Holfling, W. Jupter, and M. Kujawinska, eds. Proc. SPIE |

6. | O. Coquoz, R. Conde, R. Taleblou, and C. Depeursinge, “Performance of endoscopy holography with a multicore optical fiber,” Appl. Opt. |

7. | C. M. Vest, |

8. | Staffan Schedin, G. Pedrini, H. J. Tiziani, and Fernando Mendoza Santoyo, “Simultaneous three-dimensional dynamic deformation measurement with pulsed digital holography,” Appl. Opt. |

9. | G. Pedrini and I, Alexeenko,“Miniaturized optical system based on digital holography,” Sixth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, Procceeding of SPIE, |

10. | Ervin Kolenovic, Wolfgang Osten, Reiner Klattenhoff, Songcan Lai, Chritoph Von Kopylow, and Werner Juptner. “Miniaturized digital holography sensor for distal three-dimensional endoscopy,” Appl. Opt. |

**OCIS Codes**

(090.2880) Holography : Holographic interferometry

(120.4630) Instrumentation, measurement, and metrology : Optical inspection

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(170.2150) Medical optics and biotechnology : Endoscopic imaging

**ToC Category:**

Holography

**History**

Original Manuscript: December 5, 2005

Revised Manuscript: January 30, 2006

Manuscript Accepted: February 1, 2006

Published: February 20, 2006

**Virtual Issues**

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

**Citation**

A. Tonatiuh Saucedo, Fernando Mendoza Santoyo, Manuel De la Torre-Ibarra, Giancarlo Pedrini, and Wolfgang Osten, "Endoscopic pulsed digital holography for 3D measurements," Opt. Express **14**, 1468-1475 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-4-1468

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### References

- D. Hadbawnik,"Holographische endoskopie," Optik 45, 21-38 (1976).
- H. I. Bjelkhagen, M. D. Friedman and M. Epstein, "Holographic high resolution endoscopy through optical fiber," Proc. Laser Inst. Am. 64, 94-103 (1988).
- M. Yonemura, T. Nishisaka, and H. Machida, "Endoscopic hologram interferometry using fiber optics," Appl. Opt. 20, 1664-1667 (1981). [CrossRef] [PubMed]
- B. Kemper, D. Dirksen, W. Avenhaus, A. Merker, and G. Von Bally, " Endoscopic double pulse electronic speckle pattern interferometer for technical and medical intracavity inspection," Appl. Opt. 39, 3899-3905 (1999). [CrossRef]
- G. Pedrini, S. Schedin, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement System for Industrial Inspection II: Applications in productions Engineering, R. Holfling, W. Jupter and M. Kujawinska, eds. Proc. SPIE 4399, 1-8 (2001). [CrossRef]
- O. Coquoz, R. Conde, R. Taleblou, and C. Depeursinge, " Performance of endoscopy holography with a multicore optical fiber," Appl. Opt. 34, 7186-7193 (1995). [CrossRef] [PubMed]
- C. M. Vest, Holography Interferometry, (Wyle, New York, 1979).
- Staffan Schedin, G. Pedrini, H. J. Tiziani, and Fernando Mendoza Santoyo, "Simultaneous three-dimensional dynamic deformation measurement with pulsed digital holography," Appl. Opt. 38, 7056-7062 (1999). [CrossRef]
- G. Pedrini and I , Alexeenko,"Miniaturized optical system based on digital holography," Sixth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, Proc. SPIE, 5503, 423-498 (2004).
- Ervin Kolenovic, Wolfgang Osten, Reiner Klattenhoff, Songcan Lai, Chritoph Von Kopylow, and Werner Juptner. "Miniaturized digital holography sensor for distal three-dimensional endoscopy," Appl. Opt. 42, 5167-5172 (2003). [CrossRef] [PubMed]

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