## The data processing of the temporarily and spatially mixed modulated polarization interference imaging spectrometer

Optics Express, Vol. 18, Issue 6, pp. 5674-5680 (2010)

http://dx.doi.org/10.1364/OE.18.005674

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### Abstract

Based on the basic imaging theory of the temporally and spatially mixed modulated polarization interference imaging spectrometer (TSMPIIS), a method of interferogram obtaining and processing under polychromatic light is presented. Especially, instead of traditional Fourier transform spectroscopy, according to the unique imaging theory and OPD variation of TSMPIIS, the spectrum is reconstructed respectively by wavelength. In addition, the originally experimental interferogram obtained by TSMPIIS is processed in this new way, the satisfying result of interference data and reconstructed spectrum prove that the method is very precise and feasible, which will great improve the performance of TSMPIIS.

© 2010 OSA

## 1. Introduction

2. M. J. Persky, “A review of spaceborne Fourier transform spectrometer for remote sensing,” Rev. Sci. Instrum. **66**(10), 4763–4793 (1995). [CrossRef]

3. K. D. Möller, “Wave-front-dividing array interferometer without moving parts for real-time spectroscope from the IR to the UV,” Appl. Opt. **34**(9), 1493–1501 (1995). [CrossRef] [PubMed]

6. W. H. Smith and P. D. Hammer, “Digital array scanned interferometer: sensors and results,” Appl. Opt. **35**(16), 2902–2909 (1996). [CrossRef] [PubMed]

7. C. M. Zhang, B. Xiangli, and B. C. Zhao, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. **203**(1-2), 21–26 (2002). [CrossRef]

9. C. M. Zhang, B. C. Zhao, and B. Xiangli, “Wide-field-of-view polarization interference imaging spectrometer,” Appl. Opt. **43**(33), 6090–6094 (2004). [CrossRef] [PubMed]

## 2. TSMPIIS

7. C. M. Zhang, B. Xiangli, and B. C. Zhao, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. **203**(1-2), 21–26 (2002). [CrossRef]

## 3. The interferogram forming principle of the TSMPIIS

## 4. The optical path difference of STMPIIS

12. X. H. Jian and C. M. Zhang, “Wide-spectrum reconstruction method for birefringence interference imaging spectrometer,” Opt. Lett. (to be published). [PubMed]

*a = 1/n*,

_{e}*b = 1/n*,

_{o}*n*and

_{o}*n*are ordinary and extraordinary refractive indices,

_{e}*t*is the thickness of the single Savart plate,

*i*is the incidence angle, and is the angle between the plane of incidence and the principle section of Savart plate.

## 5. Data processing of TSMPIIS

**s**known as the spectrum intensity,

*σ*, states that if the flux versus optical path

*δ*, the Fourier transform of

*σ*. In order to obtain the whole spectrum, it is only need to repeat the calculation of the Fourier transform using Eq. (2) for each wave number in the range of interest. The Fourier Transform theory is perfect without doubt, but in practical applications just as the TSMPIIS, the OPD variety is due to the birefringence effect, which means different wave numbers have different optical path differences, then the theory will be not so accurate. Taking Calcite Crystals as example, and using the OPD Eq. (1), the different maximal OPD of each wave length is obtained as Fig. 4 shows:

12. X. H. Jian and C. M. Zhang, “Wide-spectrum reconstruction method for birefringence interference imaging spectrometer,” Opt. Lett. (to be published). [PubMed]

^{2},and the field of view is

*i≈*3°. Firstly, according to the interferogram forming principle of the TSMPIIS, we need to sample a target’s all interferogram intensity

## 6. Conclusions

- 1. According to the interferogram imaging theory of TSMPIIS, it is known that the TSMPIIS is working under a new model, it can get all detected target plots’ interferogram data at one time, but each plot produces only one interference data in one image. A target’s whole interferogram is the regular combination of interference data from serial sequential images at different time.
- 2. Based on analyzing the basic theory of Fourier Transform Spectroscopy, for avoiding the OPD sample step error caused by birefringence crystals, a new processing method is presented. In this method, each light wave’s interferogram and intensity are calculated and reconstructed respectively. The final target spectrum is the combination of all light waves without Fourier transforms.
- 3. The experimental results prove that the temporally and spatially mixed model theory and the data processing method are very efficient to process the data of TSMPIIS。

## Acknowledgements

## References and links

1. | R. J. Bell, |

2. | M. J. Persky, “A review of spaceborne Fourier transform spectrometer for remote sensing,” Rev. Sci. Instrum. |

3. | K. D. Möller, “Wave-front-dividing array interferometer without moving parts for real-time spectroscope from the IR to the UV,” Appl. Opt. |

4. | J. B. Rafert, R. G. Sellar, and J. H. Blatt, “Monolithic Fourier transform imaging spectrometer,” Appl. Opt. |

5. | P. D. Matthew and A. K. Mohammad, “Solid-block stationary Fourier-transform spectrometer,” Appl. Opt. |

6. | W. H. Smith and P. D. Hammer, “Digital array scanned interferometer: sensors and results,” Appl. Opt. |

7. | C. M. Zhang, B. Xiangli, and B. C. Zhao, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. |

8. | C. M. Zhang, B. Xiangli, and B. C. Zhao, “Analysis of the modulation depth affected by the polarization orientation in polarization interference imaging spectrometers,” Opt. Commun. |

9. | C. M. Zhang, B. C. Zhao, and B. Xiangli, “Wide-field-of-view polarization interference imaging spectrometer,” Appl. Opt. |

10. | C. M. Zhang, B. Xiangli, and B. C. Zhao, “Permissible deviations of the polarization orientation in the polarization imaging spectrometer,” J. Opt. A. |

11. | C. M. Zhang, X. G. Yan, and B. C. Zhao, “A novel model for obtaining interferogram and spectrum based on the temporarily and spatially mixed modulated polarization interference imaging spectrometer,” Opt. Commun. |

12. | X. H. Jian and C. M. Zhang, “Wide-spectrum reconstruction method for birefringence interference imaging spectrometer,” Opt. Lett. (to be published). [PubMed] |

13. | L. Wu, C. M. Zhang, and B. C. Zhao, “Analysis of the lateral displacement and optical path difference in wide-field-of-view polarization interference imaging spectrometer,” Opt. Commun. |

**OCIS Codes**

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation

(300.6300) Spectroscopy : Spectroscopy, Fourier transforms

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: September 24, 2009

Revised Manuscript: January 13, 2010

Manuscript Accepted: January 13, 2010

Published: March 5, 2010

**Citation**

Xiaohua Jian, Chunmin Zhang, Lin Zhang, and Baochang Zhao, "The data processing of the temporarily and spatially mixed modulated polarization interference imaging spectrometer," Opt. Express **18**, 5674-5680 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5674

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### References

- R. J. Bell, Introductory to Fourier Transform Spectroscopy (Academic, 1972)
- M. J. Persky, “A review of spaceborne Fourier transform spectrometer for remote sensing,” Rev. Sci. Instrum. 66(10), 4763–4793 (1995). [CrossRef]
- K. D. Möller, “Wave-front-dividing array interferometer without moving parts for real-time spectroscope from the IR to the UV,” Appl. Opt. 34(9), 1493–1501 (1995). [CrossRef] [PubMed]
- J. B. Rafert, R. G. Sellar, and J. H. Blatt, “Monolithic Fourier transform imaging spectrometer,” Appl. Opt. 34(31), 7228–7230 (1995). [CrossRef] [PubMed]
- P. D. Matthew and A. K. Mohammad, “Solid-block stationary Fourier-transform spectrometer,” Appl. Opt. 31, 6096–6101 (1992).
- W. H. Smith and P. D. Hammer, “Digital array scanned interferometer: sensors and results,” Appl. Opt. 35(16), 2902–2909 (1996). [CrossRef] [PubMed]
- C. M. Zhang, B. Xiangli, and B. C. Zhao, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1-2), 21–26 (2002). [CrossRef]
- C. M. Zhang, B. Xiangli, and B. C. Zhao, “Analysis of the modulation depth affected by the polarization orientation in polarization interference imaging spectrometers,” Opt. Commun. 227(4-6), 221–225 (2003). [CrossRef]
- C. M. Zhang, B. C. Zhao, and B. Xiangli, “Wide-field-of-view polarization interference imaging spectrometer,” Appl. Opt. 43(33), 6090–6094 (2004). [CrossRef] [PubMed]
- C. M. Zhang, B. Xiangli, and B. C. Zhao, “Permissible deviations of the polarization orientation in the polarization imaging spectrometer,” J. Opt. A. 6, 815–817 (2004).
- C. M. Zhang, X. G. Yan, and B. C. Zhao, “A novel model for obtaining interferogram and spectrum based on the temporarily and spatially mixed modulated polarization interference imaging spectrometer,” Opt. Commun. 281, 2050–2056 (2008).
- X. H. Jian and C. M. Zhang, “Wide-spectrum reconstruction method for birefringence interference imaging spectrometer,” Opt. Lett. (to be published). [PubMed]
- L. Wu, C. M. Zhang, and B. C. Zhao, “Analysis of the lateral displacement and optical path difference in wide-field-of-view polarization interference imaging spectrometer,” Opt. Commun. 273(1), 67–73 (2007). [CrossRef]

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