## Use of spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS)

Optics Express, Vol. 14, Issue 24, pp. 11598-11607 (2006)

http://dx.doi.org/10.1364/OE.14.011598

Acrobat PDF (1779 KB)

### Abstract

Digital speckle pattern interferometry (DSPI) and digital shearography (DS) are well known optical tools for qualitative as well as quantitative measurements of displacement components and its derivatives of engineering structures subjected either static or dynamic load. Spatial phase shifting (SPS) technique is useful for extracting quantitative displacement data from the system with only two frames. Optical configurations for DSPI and DS with a double aperture mask in front of the imaging lens for spatial phase shifting are proposed in this paper for the measurement of out-of-plane displacement and its first order derivative (slope) respectively. An error compensating four-phase step algorithm is used for quantitative fringe analysis.

© 2006 Optical Society of America

## 1. Introduction

5. W. Steinchen and L. Yang, *Digital shearography: Theory and Application of digital speckle pattern shearing interferometry, PM100* (Optical Engineering Press, SPIE, Washington, DC., 2003). [PubMed]

7. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. **24**3053–3058 (1985). [CrossRef] [PubMed]

13. J. Burke, “Application and optimization of the spatial phase shifting technique in digital speckle interferometry,” PhD dissertation, Carl von Ossietzky University, Oldenburg, Germany (2000). http://www.physik.uni-oldenburg.de/holo/443.html

12. R. S. Sirohi, J. Burke, H. Helmers, and K. D. Hinsch, “Spatial phase shifting for pure in-plane displacement and displacement-derivative measurements in electronic speckle pattern interferometry (ESPI),” Appl. Opt. **36**, 5787–5791 (1997). [CrossRef] [PubMed]

^{0}/column of the CCD pixels as it has some additional advantages over 120

^{0}/column [13]. As explained in Sec. 4, this results in a minimum speckle size of 5 pixels. The first arrangement described is for the measurement of out-of-plane displacement. The object and reference waves enter through two separate apertures and are combined coherently at the image plane [14–15

14. J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E: Sci. Instrum. **3**, 214–218 (1970). [CrossRef]

16. R. S. Sirohi and N. Krishna Mohan, “An in-plane insensitive multiaperture speckle shear interferometer for slope measurement,” Opt. Laser Technol. **29**, 415–417 (1997). [CrossRef]

7. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. **24**3053–3058 (1985). [CrossRef] [PubMed]

17. J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller, and N. Streibl, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. **32**, 1883–1885 (1993). [CrossRef]

## 2. Out-of-plane displacement measurement:

_{1}) and the front surfaces coated right angle prism (P). Similarly the reflected smooth wave from the reference mirror is incident on a ground glass plate via mirror (M

_{2}) and the front surfaces coated right angle prism (P). The ground glass is attached to one of the apertures so that the scattered light from it will act as reference wave [15

15. R. K. Mohanty, C. Joenathan, and R. S. Sirohi, “Speckle interferometric methods of measuring small out-ofplane displacements,” Opt. Lett. **9**, 475–477 (1984). [CrossRef] [PubMed]

## 3. Slope measurement:

_{2}. Both the apertures in A, in front of an imaging lens, receive the scattered wave independently via the set of mirrors (M

_{1}-M

_{3}) and (M

_{4}, M

_{5}), and the front surfaces coated right angle prism (P) respectively. Both the waves with identical path length combine coherently at the image plane of the imaging system. One of the mirrors is adjusted for shear (Δ

*x*) along the x-direction.

*x*,

*y*), can be expressed as [4–5, 16

16. R. S. Sirohi and N. Krishna Mohan, “An in-plane insensitive multiaperture speckle shear interferometer for slope measurement,” Opt. Laser Technol. **29**, 415–417 (1997). [CrossRef]

*x*-derivative of the out-of-plane displacement component, i.e. slope only. It may be noticed from the optical geometry that in the absence of the shear between the two object beams, this configuration is insensitive to object deformation, because the scattered beams entering through the apertures undergo identical phase changes and hence the net phase change, Δϕ is zero.

## 4. Spatial phase shifting (SPS) and phase calculation:

*x*,

*y*) is given by [12

12. R. S. Sirohi, J. Burke, H. Helmers, and K. D. Hinsch, “Spatial phase shifting for pure in-plane displacement and displacement-derivative measurements in electronic speckle pattern interferometry (ESPI),” Appl. Opt. **36**, 5787–5791 (1997). [CrossRef] [PubMed]

*D*is the aperture separation and

*V*is the image distance from the lens. Therefore the image field is modulated by a fringe pattern with a constant spacing of ~λ

*V*/

*D*. Each speckle thus carries the fringe pattern. The average size of the speckle (

*d*) is given by

_{s}*d*=1.22λ

_{s}*V*/

*d*, where

_{a}*d*is the aperture diameter. Since the aperture sizes da can be no larger than the separation of their centers,

_{a}*D*, we have [12

12. R. S. Sirohi, J. Burke, H. Helmers, and K. D. Hinsch, “Spatial phase shifting for pure in-plane displacement and displacement-derivative measurements in electronic speckle pattern interferometry (ESPI),” Appl. Opt. **36**, 5787–5791 (1997). [CrossRef] [PubMed]

13. J. Burke, “Application and optimization of the spatial phase shifting technique in digital speckle interferometry,” PhD dissertation, Carl von Ossietzky University, Oldenburg, Germany (2000). http://www.physik.uni-oldenburg.de/holo/443.html

_{0}is the spatial angular frequency of the carrier fringe (in radians per pixel). Hence, if we adjust ω

_{0}=π/2, the smallest speckle size we can get is

*d*≅5

_{s}*d*, where

_{p}*d*is the pixel size. The fringe width is thus equal to the width of four pixels (4

_{p}*d*) of the CCD sensor for the 900 phase-shift per column. The intensity distribution

_{p}*I*(

_{n}*x*,

_{k}*y*) at a pixel in the

*k*th column of the CCD along the

*x*-direction is given by

*k*<

*M*,

*I*, intensity of the spatially phase shifted frame,

_{n}*I*, bias intensity (due to superposition of two wave-fronts), γ, intensity modulation, ϕ, speckle phase.

_{b}*x*,

_{k}*y*)should be uniform over the speckle dimension, and the same applies to

*I*(

_{b}*x*,

_{k}*y*)and γ(

*x*,

_{k}*y*); that is, spatial fluctuations of these quantities should be as small as possible.

*x*,

_{k}*y*)can be calculated by using error compensating four-phase algorithm given by [17

17. J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller, and N. Streibl, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. **32**, 1883–1885 (1993). [CrossRef]

*N*and

_{s}*D*are the numerator and denominator of the arctangent function and

_{s}*s*represents the state of the object i.e. either before or after object displacement.

_{i}(

*x*,

*y*), changes to ϕ

_{f}(

*x*,

*y*)=ϕ

_{i}(

*x*,

*y*)+Δϕ(

*x*,

*y*), where is Δϕ(

*x*,

*y*) the phase change due to object displacement. This phase change can be calculated either by phase-of-difference method or by difference-of-phases method [4]. The former method involves generation of correlation fringes. One can obtain correlation fringes from SPS interferograms obtained in Eq. (5), according to the relation given by [13

13. J. Burke, “Application and optimization of the spatial phase shifting technique in digital speckle interferometry,” PhD dissertation, Carl von Ossietzky University, Oldenburg, Germany (2000). http://www.physik.uni-oldenburg.de/holo/443.html

*n*∊{-1, 0, 1, 2}.

*x*,

*y*) can be obtained with these phase shifted speckle correlation fringes. But the lateral image shift of course causes lower speckle correlation between

*I*(

_{f}*x*

_{k+n},

*y*) and

*I*(

_{i}*x*,

_{k}*y*) than between

*I*(

_{f}*x*,

_{k}*y*)and

*I*(

_{i}*x*,

_{k}*y*), resulting in non-constant fringe contrast within the set of the

*I*(

_{n,c}*x*,

_{k}*y*), and consequently, unnecessary errors in the phase calculation. Therefore, correlation fringes from SPS are even less suitable for the phase of differences method than are those from temporal phase shifting (TPS) [13

*x*,

*y*) can be obtained by subtracting the evaluated phase maps before and after object displacement and thus the speckle phase noise (ϕ

_{i})will be eliminate [4,7

7. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. **24**3053–3058 (1985). [CrossRef] [PubMed]

18. J. Huntley, “Random phase measurement errors in digital speckle interferometry,” Opt. Lasers Eng. **26**, 131–150 (1997). [CrossRef]

*N*) and the denominator (

*D*) of the arctangent function using 3×3 windowed phase filtering [5

5. W. Steinchen and L. Yang, *Digital shearography: Theory and Application of digital speckle pattern shearing interferometry, PM100* (Optical Engineering Press, SPIE, Washington, DC., 2003). [PubMed]

*x*,

*y*) is the wrapped or modulo- 2π phase map, which range from - π to π. Unwrapping is the procedure, which removes these 2π phase jumps (discontinuities) and the result is converted into desired continuous phase function [19

19. D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and un-weighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A **11**, 107–117 (1994). [CrossRef]

## 5. Results and Discussion

5. W. Steinchen and L. Yang, *Digital shearography: Theory and Application of digital speckle pattern shearing interferometry, PM100* (Optical Engineering Press, SPIE, Washington, DC., 2003). [PubMed]

*x*-direction. Similar processing has been done here in order to get noise improved phase map. Figure 6(a)–(b) show the raw and noise-improved phase maps, respectively, corresponding to the first order displacement derivative or slope. Unwrapped 2D and 3D plots of the phase map after converting to slope are shown in Fig. 6(c) and (d), respectively.

## 6. Conclusion

## Acknowledgements

## References and links

1. | J. N. Butter, R. C. Jones, and C. Wykes, “Electronic speckle pattern interferometry,” in R. K. Erf, ed. |

2. | P. Meinlschmidt, K. D. Hinsch, and R. S. Sirohi eds. |

3. | P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in |

4. | P. K. Rastogi, ed. |

5. | W. Steinchen and L. Yang, |

6. | K. Creath, “Phase measurement interferometry techniques,” in |

7. | K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. |

8. | M. Kujawinska, “Spatial phase measurement methods,” in |

9. | A. J. P. van Haasteren and H.J. Frankena, “Real-time displacement measurement using a multicamera phase-stepping speckle interferometer,” Appl. Opt. |

10. | M. Servin and F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. |

11. | G. Pedrini, Y. L. Zou, and H. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. |

12. | R. S. Sirohi, J. Burke, H. Helmers, and K. D. Hinsch, “Spatial phase shifting for pure in-plane displacement and displacement-derivative measurements in electronic speckle pattern interferometry (ESPI),” Appl. Opt. |

13. | J. Burke, “Application and optimization of the spatial phase shifting technique in digital speckle interferometry,” PhD dissertation, Carl von Ossietzky University, Oldenburg, Germany (2000). http://www.physik.uni-oldenburg.de/holo/443.html |

14. | J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E: Sci. Instrum. |

15. | R. K. Mohanty, C. Joenathan, and R. S. Sirohi, “Speckle interferometric methods of measuring small out-ofplane displacements,” Opt. Lett. |

16. | R. S. Sirohi and N. Krishna Mohan, “An in-plane insensitive multiaperture speckle shear interferometer for slope measurement,” Opt. Laser Technol. |

17. | J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller, and N. Streibl, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. |

18. | J. Huntley, “Random phase measurement errors in digital speckle interferometry,” Opt. Lasers Eng. |

19. | D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and un-weighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A |

**OCIS Codes**

(120.2650) Instrumentation, measurement, and metrology : Fringe analysis

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

(120.6150) Instrumentation, measurement, and metrology : Speckle imaging

(120.6160) Instrumentation, measurement, and metrology : Speckle interferometry

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: July 5, 2006

Revised Manuscript: November 16, 2006

Manuscript Accepted: November 16, 2006

Published: November 27, 2006

**Citation**

Basanta Bhaduri, N. K. Mohan, M. P. Kothiyal, and R. S. Sirohi, "Use of spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS)," Opt. Express **14**, 11598-11607 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-24-11598

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### References

- J. N. Butter, R. C. Jones and C. Wykes, "Electronic speckle pattern interferometry," in R. K. Erf, ed. Speckle Metrology (Academic Press, New York 1978).
- P. Meinlschmidt, K. D. Hinsch and R. S. Sirohi eds. Selected papers on electronic speckle pattern interferometry: Principles and Practice, MS132 (Optical Engineering Press, SPIE, Washington, DC., 1996).
- P. K. Rastogi, "Techniques of displacement and deformation measurements in speckle metrology," in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), Chap.2.
- P. K. Rastogi, ed. Digital speckle pattern interferometry and related techniques (John Wiley, England, 2001).
- W. Steinchen, and L. Yang, Digital shearography: Theory and Application of digital speckle pattern shearing interferometry, PM100 (Optical Engineering Press, SPIE, Washington, DC., 2003). [PubMed]
- K. Creath, "Phase measurement interferometry techniques," in Progress in optics, vol. xxvi, E. Wolf, ed. (Amsterdam, North-Holland, 1998).
- K. Creath, "Phase-shifting speckle interferometry," Appl. Opt. 243053-3058 (1985). [CrossRef] [PubMed]
- M. Kujawinska, "Spatial phase measurement methods," in Interferogram Analysis -Digital Fringe Pattern Measurement Techniques, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Bristol, U.K, 1993) Chap.5.
- A. J. P. van Haasteren and H.J. Frankena, "Real-time displacement measurement using a multicamera phase-stepping speckle interferometer," Appl. Opt. 33, 4137-4142 (1994). [CrossRef]
- M. Servin and F. J. Cuevas, "A novel technique for spatial phase-shifting interferometry," J. Mod. Opt. 42, 1853-1862 (1995). [CrossRef]
- G. Pedrini, Y. L. Zou, and H. Tiziani, "Quantitative evaluation of digital shearing interferogram using the spatial carrier method," Pure Appl. Opt. 5, 313-321 (1996). [CrossRef]
- R. S. Sirohi, J. Burke, H. Helmers and K. D. Hinsch, "Spatial phase shifting for pure in-plane displacement and displacement-derivative measurements in electronic speckle pattern interferometry (ESPI)," Appl. Opt. 36, 5787- 5791 (1997). [CrossRef] [PubMed]
- J. Burke, "Application and optimization of the spatial phase shifting technique in digital speckle interferometry," PhD dissertation, Carl von Ossietzky University, Oldenburg, Germany (2000), http://www.physik.uni-oldenburg.de/holo/443.html.
- J. A. Leendertz, "Interferometric displacement measurement on scattering surfaces utilizing speckle effect," J. Phys. E: Sci. Instrum. 3, 214-218 (1970). [CrossRef]
- R. K. Mohanty, C. Joenathan and R. S. Sirohi, "Speckle interferometric methods of measuring small out-of-plane displacements," Opt. Lett. 9, 475-477 (1984). [CrossRef] [PubMed]
- R. S. Sirohi and N. Krishna Mohan, "An in-plane insensitive multiaperture speckle shear interferometer for slope measurement," Opt. Laser Technol. 29, 415-417 (1997). [CrossRef]
- J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller and N. Streibl, "New compensating four-phase algorithm for phase-shift interferometry," Opt. Eng. 32, 1883-1885 (1993). [CrossRef]
- J. Huntley, "Random phase measurement errors in digital speckle interferometry," Opt. Lasers Eng. 26, 131-150 (1997). [CrossRef]
- D. C. Ghiglia, and L. A. Romero, "Robust two-dimensional weighted and un-weighted phase unwrapping that uses fast transforms and iterative methods," J. Opt. Soc. Am. A 11, 107-117 (1994). [CrossRef]

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