## Digital holographic interferometer using simultaneously three lasers and a single monochrome sensor for 3D displacement measurements |

Optics Express, Vol. 18, Issue 19, pp. 19867-19875 (2010)

http://dx.doi.org/10.1364/OE.18.019867

Acrobat PDF (980 KB)

### Abstract

The use of digital holographic interferometry for 3D measurements using simultaneously three illumination directions was demonstrated by Saucedo et al. (Optics Express 14(4) 2006). The technique records two consecutive images where each one contains three holograms in it, e.g., one before the deformation and one after the deformation. A short coherence length laser must be used to obtain the simultaneous 3D information from the same laser source. In this manuscript we present an extension of this technique now illuminating simultaneously with three different lasers at 458, 532 and 633 nm, and using only one high resolution monochrome CMOS sensor. This new configuration gives the opportunity to use long coherence length lasers allowing the measurement of large object areas. A series of digital holographic interferograms are recorded and the information corresponding to each laser is isolated in the Fourier spectral domain where the corresponding phase difference is calculated. Experimental results render the orthogonal displacement components *u, v* and *w* during a simple load deformation.

© 2010 OSA

## 1. Introduction

*λ*/30) [1,2]. The surface displacement obtained can be associated with internal changes of the sample due to an external stimulus. The technique could be used in a wide variety of applications like a helpful tool to get detailed mechanical parameters from the sample under study such as micro strains [3

3. T T. Saucedo Anaya, M. De la Torre, and F. Mendoza Santoyo, “Microstrain detection using simultaneous endoscopic pulsed digital holography,” Opt. Eng. **47**(7), 073601 (2008). [CrossRef]

*u, v*and

*w*. At least three no-coplanar sensitivity vectors [4

4. S. Schedin, G. Pedrini, H. J. Tiziani, and F. M. Santoyo, “Simultaneous three-dimensional dynamic deformation measurements with pulsed digital holography,” Appl. Opt. **38**(34), 7056–7062 (1999). [CrossRef]

5. M. De la Torre-Ibarra, F. Mendoza-Santoyo, C. Pérez-López, and S. A. Tonatiuh, “Detection of surface strain by three-dimensional digital holography,” Appl. Opt. **44**(1), 27–31 (2005). [PubMed]

6. Z. Wang, T. Walz, H. R. Schubach, and A. Ettemeyer, “Three dimensional pulsed ESPI:technique of analysis of dynamic problems,” Proc. SPIE **3824**, 58 (1999). [CrossRef]

7. T. Saucedo A, F. M. Santoyo, M. De la Torre Ibarra, G. Pedrini, and W. Osten, “Simultaneous two-dimensional endoscopic pulsed digital holography for evaluation of dynamic displacements,” Appl. Opt. **45**(19), 4534–4539 (2006). [CrossRef] [PubMed]

10. Y. Fu, G. Pedrini, B. M. Hennelly, R. M. Groves, and W. Osten, “Dual-wavelength image-plane digital holography for dynamic measurement,” Opt. Lasers Eng. **47**(5), 552–557 (2009). [CrossRef]

11. I. Yamaguchi, T. Matsumura, and J. Kato, “Phase-shifting color digital holography,” Opt. Lett. **27**(13), 1108–1110 (2002). [CrossRef]

12. P. Picart, D. Mounier, and J. M. Desse, “High-resolution digital two-color holographic metrology,” Opt. Lett. **33**(3), 276–278 (2008). [CrossRef] [PubMed]

13. J.-M. Desse, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express **16**(8), 5471–5480 (2008). [CrossRef] [PubMed]

16. A. Alsam and R. Lenz, “Calibrating color cameras using metameric blacks,” J. Opt. Soc. Am. A **24**(1), 11–17 (2007). [CrossRef]

*u*,

*v*and

*w*. Experimentally and in order to prove our proposed method, a simple load test is performed using a smooth object surface.

## 2. Method

8. A. T. Saucedo, F. Mendoza Santoyo, M. De la Torre-Ibarra, G. Pedrini, and W. Osten, “Endoscopic pulsed digital holography for 3D measurements,” Opt. Express **14**(4), 1468–1475 (2006). [CrossRef] [PubMed]

*I*) registered by the sensor along the

*x*and

*y*directions can be expressed by:where

*λ*represents each of the three different laser wavelengths (

_{m}*m*= 1, 2, 3). The couple

*R*and

_{λm}*O*are the reference and object beam pair corresponding to each laser and illumination position. Once this first image is obtained, a second one (

_{λm}*I’*) with a deformation applied to the object is recorded. Then each image is Fourier transformed to process each laser wavelength independently from the others [17

17. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer based topography and interferometry,” J. Opt. Soc. Am. **72**(1), 156–160 (1982). [CrossRef]

*φ*is the relative phase-difference map for each wavelength (

_{λm}*m*= 1, 2, 3).

*φ*and

_{λm}*φ’*are the phase maps for each wavelength before and after the deformation respectively. Once the three wrapped phase maps are obtained, it is necessary to unwrap them, for instance using the commercially available software (Pv_spua2 by Phase Vision Ltd.). With these unwrapped phase maps and considering the geometry of the optical set up, see Fig. 1 , the displacement components (

_{λm}*u, v, w*) can be associated as follows,from this expression,

*θ*is the angle between the illumination and observation direction with the same value for each laser (see Fig. 1b)

_{.}Using this equation it is possible to obtain the three orthogonal displacement components

*u*,

*v*and

*w*independently using just two digital holographic interferograms.

## 3. Experimental procedure

_{1}= 458 nm and 50mW output power, attenuated to 25 mW by means of a neutral density filter (NDF1). The second one is a diode pumped solid state cw Nd:YAG laser with λ

_{2}= 532 nm with maximum output power of 500mW, attenuated to 25 mW by NDF2. Finally, a He-Ne laser at λ

_{3}= 633 nm with 25mW output power. The intensity adjustment procedure is made in order to match a similar signal within the sensor’s dynamic range, according with its quantum efficiency for each wavelength. Each laser beam is divided into an object and a reference beam using BS1, BS2 and BS3 respectively.

_{1}is directed onto the object using two mirrors (M3 and M4) and a 10X microscope objective to illuminate the object. The reference beam is launched into a single mode fiber (OF1) with the other terminal (OF1’) attached near the beam combiner (BC1). A similar reference and object illumination procedure is followed for λ

_{2}and λ

_{3}. All reference beam terminals (OF1’, OF2’ and OF3′) are placed at the same relative distance to BC1. The angles made by the unit vectors from each observation and illumination directions are the same, i.e., the angle

*θ*is the same for all observation-illumination unit vector pairs. The maximum spatial frequency that can be recorded with the CMOS camera used is given by ƒ

_{max}=

*D*/

*zλ*, where

*D*is the aperture diameter and

*z*is the distance measured from the centre of the lens to the sensor arrangement. The smallest wavelength is used to calculate the aperture which in this case is 3.6mm.

*x*axis leaving the

*y*and

*z*axis free to move. The field of view (FOV) of the system is 25.6 X 20.5 mm using a lens (L) with 25 mm of focal length, which images the object onto the CMOS camera (Pixelink with 1280 X 1024 pixels). Two images are then recorded, one with the object without a load and a second one with the load applied. Once both image interference holograms are processed three wrapped phase maps are obtained. Figures 3a , 3b and 3c show the displacement observed with λ

_{1}, λ

_{2}and λ

_{3}respectively.

*θ*) between the object beam and the observation unit vectors is 23°. Once these three phase maps are unwrapped they give the same displacement for each case.

*u*component whose magnitude is in a good agreement with the mechanical constrains applied to the sample during the load. The

*w*displacement component shows an expected behavior due to the kind of deformation applied as Fig. 4c shows. A similar response is observed in Fig. 4b where the

*v*component is shown. The x and y axes in Fig. 4 represents the FOV while the other one represents the displacement component for each case.

## 4. Discussion

*per se*, something already reported in reference 9

9. C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express **16**(13), 9753–9764 (2008). [CrossRef] [PubMed]

*u*,

*v*and

*w*where a melting is observed in the object’s surface.

## 5. Conclusions

## References

1. | C. M. Vest, |

2. | K. J. Gåsvik, |

3. | T T. Saucedo Anaya, M. De la Torre, and F. Mendoza Santoyo, “Microstrain detection using simultaneous endoscopic pulsed digital holography,” Opt. Eng. |

4. | S. Schedin, G. Pedrini, H. J. Tiziani, and F. M. Santoyo, “Simultaneous three-dimensional dynamic deformation measurements with pulsed digital holography,” Appl. Opt. |

5. | M. De la Torre-Ibarra, F. Mendoza-Santoyo, C. Pérez-López, and S. A. Tonatiuh, “Detection of surface strain by three-dimensional digital holography,” Appl. Opt. |

6. | Z. Wang, T. Walz, H. R. Schubach, and A. Ettemeyer, “Three dimensional pulsed ESPI:technique of analysis of dynamic problems,” Proc. SPIE |

7. | T. Saucedo A, F. M. Santoyo, M. De la Torre Ibarra, G. Pedrini, and W. Osten, “Simultaneous two-dimensional endoscopic pulsed digital holography for evaluation of dynamic displacements,” Appl. Opt. |

8. | A. T. Saucedo, F. Mendoza Santoyo, M. De la Torre-Ibarra, G. Pedrini, and W. Osten, “Endoscopic pulsed digital holography for 3D measurements,” Opt. Express |

9. | C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express |

10. | Y. Fu, G. Pedrini, B. M. Hennelly, R. M. Groves, and W. Osten, “Dual-wavelength image-plane digital holography for dynamic measurement,” Opt. Lasers Eng. |

11. | I. Yamaguchi, T. Matsumura, and J. Kato, “Phase-shifting color digital holography,” Opt. Lett. |

12. | P. Picart, D. Mounier, and J. M. Desse, “High-resolution digital two-color holographic metrology,” Opt. Lett. |

13. | J.-M. Desse, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express |

14. | M. S. Millán, E. Valencia, and M. Corbalán, “3CCD camera’s capability for measuring color differences: experiment in the nearly neutral region,” Appl. Opt. |

15. | C. van Trigt, “Visual system-response functions and estimating reflectance,” J. Opt. Soc. Am. A |

16. | A. Alsam and R. Lenz, “Calibrating color cameras using metameric blacks,” J. Opt. Soc. Am. A |

17. | M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer based topography and interferometry,” J. Opt. Soc. Am. |

18. | T. Kreis, |

**OCIS Codes**

(090.2880) Holography : Holographic interferometry

(120.3940) Instrumentation, measurement, and metrology : Metrology

(120.4290) Instrumentation, measurement, and metrology : Nondestructive testing

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

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: May 11, 2010

Revised Manuscript: August 6, 2010

Manuscript Accepted: August 12, 2010

Published: September 3, 2010

**Citation**

Tonatiuh Saucedo-A., M. H. De la Torre-Ibarra, F. Mendoza Santoyo, and Ivan Moreno, "Digital holographic interferometer using simultaneously three lasers and a single monochrome sensor for 3D displacement measurements," Opt. Express **18**, 19867-19875 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-19867

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### References

- C. M. Vest, Holography Interferometry, (Wyle, New York, 1979).
- K. J. Gåsvik, Optical Metrology, (John Wiley & Sons Ltd., Chichester, 2002).
- T T. Saucedo Anaya, M. De la Torre, and F. Mendoza Santoyo, “Microstrain detection using simultaneous endoscopic pulsed digital holography,” Opt. Eng. 47(7), 073601 (2008). [CrossRef]
- S. Schedin, G. Pedrini, H. J. Tiziani, and F. M. Santoyo, “Simultaneous three-dimensional dynamic deformation measurements with pulsed digital holography,” Appl. Opt. 38(34), 7056–7062 (1999). [CrossRef]
- M. De la Torre-Ibarra, F. Mendoza-Santoyo, C. Pérez-López, and S. A. Tonatiuh, “Detection of surface strain by three-dimensional digital holography,” Appl. Opt. 44(1), 27–31 (2005). [PubMed]
- Z. Wang, T. Walz, H. R. Schubach, and A. Ettemeyer, “Three dimensional pulsed ESPI:technique of analysis of dynamic problems,” Proc. SPIE 3824, 58 (1999). [CrossRef]
- T. Saucedo A, F. M. Santoyo, M. De la Torre Ibarra, G. Pedrini, and W. Osten, “Simultaneous two-dimensional endoscopic pulsed digital holography for evaluation of dynamic displacements,” Appl. Opt. 45(19), 4534–4539 (2006). [CrossRef] [PubMed]
- A. T. Saucedo, F. Mendoza Santoyo, M. De la Torre-Ibarra, G. Pedrini, and W. Osten, “Endoscopic pulsed digital holography for 3D measurements,” Opt. Express 14(4), 1468–1475 (2006). [CrossRef] [PubMed]
- C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express 16(13), 9753–9764 (2008). [CrossRef] [PubMed]
- Y. Fu, G. Pedrini, B. M. Hennelly, R. M. Groves, and W. Osten, “Dual-wavelength image-plane digital holography for dynamic measurement,” Opt. Lasers Eng. 47(5), 552–557 (2009). [CrossRef]
- I. Yamaguchi, T. Matsumura, and J. Kato, “Phase-shifting color digital holography,” Opt. Lett. 27(13), 1108–1110 (2002). [CrossRef]
- P. Picart, D. Mounier, and J. M. Desse, “High-resolution digital two-color holographic metrology,” Opt. Lett. 33(3), 276–278 (2008). [CrossRef] [PubMed]
- J.-M. Desse, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express 16(8), 5471–5480 (2008). [CrossRef] [PubMed]
- M. S. Millán, E. Valencia, and M. Corbalán, “3CCD camera’s capability for measuring color differences: experiment in the nearly neutral region,” Appl. Opt. 43(36), 6523–6535 (2004). [CrossRef]
- C. van Trigt, “Visual system-response functions and estimating reflectance,” J. Opt. Soc. Am. A 14(4), 741–755 (1997). [CrossRef]
- A. Alsam and R. Lenz, “Calibrating color cameras using metameric blacks,” J. Opt. Soc. Am. A 24(1), 11–17 (2007). [CrossRef]
- M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982). [CrossRef]
- T. Kreis, Hand book of holographic Interferometry, (Wiley-VCH, 2005).

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