## Compact static imaging spectrometer combining spectral zooming capability with a birefringent interferometer |

Optics Express, Vol. 21, Issue 8, pp. 10182-10187 (2013)

http://dx.doi.org/10.1364/OE.21.010182

Acrobat PDF (1164 KB)

### Abstract

A compact static birefringent imaging spectrometer (BIS) with spectral zooming capability is presented. It based on two identical Wollaston prisms and has no slit. The most significant advantage of the BIS is that we can conveniently select spectral resolution to adapt to different application requirements and greatly reduce the size of the spectral image data for capturing, saving, transferring, and processing. Also, we show this configuration blend the advantage of a grating spectrometer and a Michelson interferometer: extremely compact, robust, wide free spectral range and very high throughput.

© 2013 OSA

## 1. Introduction

1. D. Bannon, “Hyperspectral imaging: Cubes and slices,” Nat. Photonics **3**(11), 627–629 (2009). [CrossRef]

2. R. Gebbers and V. I. Adamchuk, “Precision agriculture and food security,” Science **327**(5967), 828–831 (2010). [CrossRef] [PubMed]

3. R. G. Sellar and G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. **44**(1), 013602 (2005). [CrossRef]

4. J. Li, J. Zhu, and H. Wu, “Compact static Fourier transform imaging spectropolarimeter based on channeled polarimetry,” Opt. Lett. **35**(22), 3784–3786 (2010). [CrossRef] [PubMed]

5. T. Inoue, K. Itoh, and Y. Ichioka, “Fourier-transform spectral imaging near the image plane,” Opt. Lett. **16**(12), 934–936 (1991). [CrossRef] [PubMed]

6. J. Y. Hardeberg, F. Schmidt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. **41**(10), 2532–2548 (2002). [CrossRef]

7. L. Cheng, T. Chao, M. Dowdy, C. LaBaw, J. Mahoney, G. Reyes, and K. Bergman, “Multispectral imaging systems using acousto-optic tunable filter,” Proc. SPIE **1874**, 224–231 (1993). [CrossRef]

8. B. Chen, M. R. Wang, Z. Liu, and J. J. Yang, “Dynamic spectral imaging with spectral zooming capability,” Opt. Lett. **32**(11), 1518–1520 (2007). [CrossRef] [PubMed]

## 2. Theory

_{1}and WP

_{2}, analyzer A, imaging lens L, focal plane array (FPA). Light from the object is collected and collimated by fore-optics, and then incidents on P. The light emerging from P becomes linearly polarized at 45° to the optic axes of the Wollaston prisms. WP

_{1}and WP

_{2}split the incoming light into two equal amplitude, orthogonally polarized components with a small lateral displacement. After passing through A, the two component rays are resolved into linearly polarized light in the same polarized orientation and launched into the FPA. The interference pattern is thus superimposed on the image. This mode of data acquisition is the so-called “windowing” mode, in which the spectral imaging data cube is derived by the platform scanning the image across the interference pattern.

*i*, and can be described as:where

*f*is the focal length of the imaging lens,

*x*is the longitudinal coordinates showed in the top left part of Fig. 1,

*d*is the lateral displacement introduced by WP

_{1}and WP

_{2}, and can be given by:with where

*t*, θ are the thickness and internal wedge angle of WP

_{1}and WP

_{2}, respectively.

*s*is the spacing between WP

_{1}and WP

_{2}.

*n*

_{o},

*n*

_{e}is the birefringence of the birefringent crystal. Thus the spectral resolution in wavenumber can be written as:The parameters

*t*, θ,

*n*

_{o},

*n*

_{e}are fixed, when the system is built up. According to Eq. (7), the spectral resolution in principle can be selected by changing

*s*, the spacing between the two identical Wollaston prisms.

*N*is the pixel number,

_{min}is the shortest working wavelength of the system.

## 3. Experiment and discussion

^{3}with 5° internal wedge angle and made of calcite. A low-cost 1280 × 960 CCD camera with a lens of 50 mm focal length is used to take the interferogram. The total length of the proof system is less than 20 cm. A He-Ne laser is used to generate 632.8 nm monochromatic light being measured. In this way, not only the spectral resolution can be determined by checking the full width at the half maximum (FWHM) of the obtained spectral line, but also the lateral displacement introduced by the Wollaston prisms can be retrieved from the fringe frequency of the acquired interferogram.

*s*. The larger the spacing

*s*, the narrower the fringe width is. The narrower fringe means larger OPD and higher spectral resolution.

_{1}and WP

_{2}at 632.8 nm wavelength. The lateral displacement

*d*changes from 0.13 to 0.75 mm when the spacing

*s*varies from 0 to 20 mm.

*s*. The spectral resolution at 632.8 nm wavelength changes from 985.1 cm

^{−1}to 151.1 cm

^{−1}(35.5 nm to 6.2 nm) when the spacing

*s*varies from 0 to 20 mm. Compared with the theoretical values, the experimental results exhibit favorable accordance and the feasibility of the present idea is validated.

_{1}and WP

_{2}. Although there is no precision tool used to adjust the parallelism of the two Wollaston prisms in the laboratory demonstration, the theoretical and experimental results were shown to yield accuracy better than 5%. This accuracy is quite enough for normal usage and can be highly improved by using a precision adjustment. It also proves that the proposed imaging spectrometer is extremely robust with such a simple, compact configuration. Note that the spectral resolution could be selected either by mechanically changing the spacing of the two Wollaston prisms, or by changing the refractive index of the gap between WP

_{1}and WP

_{2}. The latter would be more stable.

*E*calculation formula

*E*=

*A*Ω , where

*A*is the input aperture,

9. J. Li, J. Zhu, and X. Hou, “Field-compensated birefringent Fourier transform spectrometer,” Opt. Commun. **284**(5), 1127–1131 (2011). [CrossRef]

10. A. R. Harvey and D. W. Fletcher-Holmes, “Birefringent Fourier-transform imaging spectrometer,” Opt. Express **12**(22), 5368–5374 (2004). [CrossRef] [PubMed]

11. P. D. Hammer, L. F. Johnson, A. W. Strawa, S. E. Dunagan, R. G. Higgins, J. A. Brass, R. E. Slye, D. V. Sullivan, W. H. Smith, B. M. Lobitz, and D. L. Peterson, “Surface reflectance mapping using interferometric spectral imagery from a remotely piloted aircraft,” IEEE Trans. Geosci. Rem. Sens. **39**(11), 2499–2506 (2001). [CrossRef]

^{6}[12

12. D. Steers, W. Sibbett, and M. J. Padgett, “Dual-purpose, compact spectrometer and fiber-coupled laser wavemeter based on a Wollaston prism,” Appl. Opt. **37**(24), 5777–5781 (1998). [CrossRef] [PubMed]

## 4. Conclusion

## Acknowledgments

## References and links

1. | D. Bannon, “Hyperspectral imaging: Cubes and slices,” Nat. Photonics |

2. | R. Gebbers and V. I. Adamchuk, “Precision agriculture and food security,” Science |

3. | R. G. Sellar and G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. |

4. | J. Li, J. Zhu, and H. Wu, “Compact static Fourier transform imaging spectropolarimeter based on channeled polarimetry,” Opt. Lett. |

5. | T. Inoue, K. Itoh, and Y. Ichioka, “Fourier-transform spectral imaging near the image plane,” Opt. Lett. |

6. | J. Y. Hardeberg, F. Schmidt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. |

7. | L. Cheng, T. Chao, M. Dowdy, C. LaBaw, J. Mahoney, G. Reyes, and K. Bergman, “Multispectral imaging systems using acousto-optic tunable filter,” Proc. SPIE |

8. | B. Chen, M. R. Wang, Z. Liu, and J. J. Yang, “Dynamic spectral imaging with spectral zooming capability,” Opt. Lett. |

9. | J. Li, J. Zhu, and X. Hou, “Field-compensated birefringent Fourier transform spectrometer,” Opt. Commun. |

10. | A. R. Harvey and D. W. Fletcher-Holmes, “Birefringent Fourier-transform imaging spectrometer,” Opt. Express |

11. | P. D. Hammer, L. F. Johnson, A. W. Strawa, S. E. Dunagan, R. G. Higgins, J. A. Brass, R. E. Slye, D. V. Sullivan, W. H. Smith, B. M. Lobitz, and D. L. Peterson, “Surface reflectance mapping using interferometric spectral imagery from a remotely piloted aircraft,” IEEE Trans. Geosci. Rem. Sens. |

12. | D. Steers, W. Sibbett, and M. J. Padgett, “Dual-purpose, compact spectrometer and fiber-coupled laser wavemeter based on a Wollaston prism,” Appl. Opt. |

**OCIS Codes**

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

(300.6300) Spectroscopy : Spectroscopy, Fourier transforms

(110.4234) Imaging systems : Multispectral and hyperspectral imaging

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: February 21, 2013

Revised Manuscript: April 3, 2013

Manuscript Accepted: April 5, 2013

Published: April 16, 2013

**Citation**

Jie Li, Jingping Zhu, Chun Qi, Chuanlin Zheng, Bo Gao, Yunyao Zhang, and Xun Hou, "Compact static imaging spectrometer combining spectral zooming capability with a birefringent interferometer," Opt. Express **21**, 10182-10187 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-10182

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### References

- D. Bannon, “Hyperspectral imaging: Cubes and slices,” Nat. Photonics3(11), 627–629 (2009). [CrossRef]
- R. Gebbers and V. I. Adamchuk, “Precision agriculture and food security,” Science327(5967), 828–831 (2010). [CrossRef] [PubMed]
- R. G. Sellar and G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng.44(1), 013602 (2005). [CrossRef]
- J. Li, J. Zhu, and H. Wu, “Compact static Fourier transform imaging spectropolarimeter based on channeled polarimetry,” Opt. Lett.35(22), 3784–3786 (2010). [CrossRef] [PubMed]
- T. Inoue, K. Itoh, and Y. Ichioka, “Fourier-transform spectral imaging near the image plane,” Opt. Lett.16(12), 934–936 (1991). [CrossRef] [PubMed]
- J. Y. Hardeberg, F. Schmidt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng.41(10), 2532–2548 (2002). [CrossRef]
- L. Cheng, T. Chao, M. Dowdy, C. LaBaw, J. Mahoney, G. Reyes, and K. Bergman, “Multispectral imaging systems using acousto-optic tunable filter,” Proc. SPIE1874, 224–231 (1993). [CrossRef]
- B. Chen, M. R. Wang, Z. Liu, and J. J. Yang, “Dynamic spectral imaging with spectral zooming capability,” Opt. Lett.32(11), 1518–1520 (2007). [CrossRef] [PubMed]
- J. Li, J. Zhu, and X. Hou, “Field-compensated birefringent Fourier transform spectrometer,” Opt. Commun.284(5), 1127–1131 (2011). [CrossRef]
- A. R. Harvey and D. W. Fletcher-Holmes, “Birefringent Fourier-transform imaging spectrometer,” Opt. Express12(22), 5368–5374 (2004). [CrossRef] [PubMed]
- P. D. Hammer, L. F. Johnson, A. W. Strawa, S. E. Dunagan, R. G. Higgins, J. A. Brass, R. E. Slye, D. V. Sullivan, W. H. Smith, B. M. Lobitz, and D. L. Peterson, “Surface reflectance mapping using interferometric spectral imagery from a remotely piloted aircraft,” IEEE Trans. Geosci. Rem. Sens.39(11), 2499–2506 (2001). [CrossRef]
- D. Steers, W. Sibbett, and M. J. Padgett, “Dual-purpose, compact spectrometer and fiber-coupled laser wavemeter based on a Wollaston prism,” Appl. Opt.37(24), 5777–5781 (1998). [CrossRef] [PubMed]

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