## Role of the filter phase in phase sampling interferometry |

Optics Express, Vol. 19, Issue 21, pp. 19987-19992 (2011)

http://dx.doi.org/10.1364/OE.19.019987

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### Abstract

Any linear phase sampling algorithm can be described as a linear filter characterized by its frequency response. In traditional phase sampling interferometry the phase of the frequency response has been ignored because the impulse responses can be made real selecting the correct sample offset. However least squares methods and recursive filters can have a complex frequency response. In this paper, we derive the quadrature equations for a general phase sampling algorithm and describe the role of the filter phase.

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## 1 Quadrature phase detection

*b*is the background or DC term,

*m*the modulation or AC term, and

*g*

2. M. Servin, J. C. Estrada, and J. A. Quiroga, “The general theory of phase shifting algorithms,” Opt. Express **17**(24), 21867–21881 (2009). [CrossRef] [PubMed]

3. J. L. Marroquin, J. E. Figueroa, and M. Servin, “Robust quadrature filters,” J. Opt. Soc. Am. A **14**(4), 779–791 (1997). [CrossRef]

4. J. A. Quiroga, J. C. Estrada, M. Servín, and J. Vargas, “Regularized least squares phase sampling interferometry,” Opt. Express **19**(6), 5002–5013 (2011). [CrossRef] [PubMed]

2. M. Servin, J. C. Estrada, and J. A. Quiroga, “The general theory of phase shifting algorithms,” Opt. Express **17**(24), 21867–21881 (2009). [CrossRef] [PubMed]

## 2 The role of the filter phase in quadrature phase detection: the group delay

*FT*we obtain

## 3 Two illustrative examples

6. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. **26**(13), 2504–2506 (1987). [CrossRef] [PubMed]

*K*and the first sample start in

2. M. Servin, J. C. Estrada, and J. A. Quiroga, “The general theory of phase shifting algorithms,” Opt. Express **17**(24), 21867–21881 (2009). [CrossRef] [PubMed]

*g*. The spectral response of this filter is [2

**17**(24), 21867–21881 (2009). [CrossRef] [PubMed]

## 4 Conclusions

## References

1. | D. Malacara, M. Servín, and Z. Malacara Interferogram Analysis For Optical Testing, Second ed. CRC Press 2005. |

2. | M. Servin, J. C. Estrada, and J. A. Quiroga, “The general theory of phase shifting algorithms,” Opt. Express |

3. | J. L. Marroquin, J. E. Figueroa, and M. Servin, “Robust quadrature filters,” J. Opt. Soc. Am. A |

4. | J. A. Quiroga, J. C. Estrada, M. Servín, and J. Vargas, “Regularized least squares phase sampling interferometry,” Opt. Express |

5. | A. V. Oppenheim, and R. W. Schafer, Discrete-Time Signal processing, Pearson (2010) |

6. | P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. |

7. | http:\\goo.gl/BGjJ9 |

**OCIS Codes**

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.3940) Instrumentation, measurement, and metrology : Metrology

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

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: March 7, 2011

Revised Manuscript: April 6, 2011

Manuscript Accepted: April 21, 2011

Published: September 28, 2011

**Citation**

Juan Antonio Quiroga, Manuel Servín, Julio Cesar Estrada, Javier Vargas, and Francisco Javier Torre-Belizon, "Role of the filter phase in phase sampling interferometry," Opt. Express **19**, 19987-19992 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-19987

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### References

- D. Malacara, M. Servín, and Z. Malacara Interferogram Analysis For Optical Testing, Second ed. CRC Press 2005.
- M. Servin, J. C. Estrada, and J. A. Quiroga, “The general theory of phase shifting algorithms,” Opt. Express17(24), 21867–21881 (2009). [CrossRef] [PubMed]
- J. L. Marroquin, J. E. Figueroa, and M. Servin, “Robust quadrature filters,” J. Opt. Soc. Am. A14(4), 779–791 (1997). [CrossRef]
- J. A. Quiroga, J. C. Estrada, M. Servín, and J. Vargas, “Regularized least squares phase sampling interferometry,” Opt. Express19(6), 5002–5013 (2011). [CrossRef] [PubMed]
- A. V. Oppenheim, and R. W. Schafer, Discrete-Time Signal processing, Pearson (2010)
- P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt.26(13), 2504–2506 (1987). [CrossRef] [PubMed]
- http:\\goo.gl/BGjJ9

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