• Infrared and Laser Engineering
  • Vol. 50, Issue 2, 20200427 (2021)
Hongming Liu1、3, Yujuan Liu1, Ying Song1, Zhicheng Zhong1, Lingsheng Kong2, and Huaibin Liu2
Author Affiliations
  • 1Key Laboratory of Geophysical Exploration Equipment, Ministry of Education, College of Instrumentation & Electrical Engineering, Jilin University, Changchun 130021, China
  • 2Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130012, China
  • 3Tonghua Normal University, Tonghua 134002, China
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    DOI: 10.3788/IRLA20200427 Cite this Article
    Hongming Liu, Yujuan Liu, Ying Song, Zhicheng Zhong, Lingsheng Kong, Huaibin Liu. Principle and optimum analysis of small near-infrared spectrometers based on digital micromirror device[J]. Infrared and Laser Engineering, 2021, 50(2): 20200427 Copy Citation Text show less

    Abstract

    The DMD small near-infrared spectroscopy instrument is widely used in chemical composition analysis and quality inspection for its advantages of fast detection speed, high sensitivity, no damage detection, and miniaturization of portable instruments. However, as the premise of instrument design, optical optimization design of the whole spectral range is the hard work of the system. In this paper, the theoretical design method of the spectroscopic imaging system based on the small near-infrared spectrometer of DMD was studied. The method was designed by using the double-dispensing anti-aberration lens and combining the geometric aberration theory to optimize the design of a small DMD near-infrared spectrometer to reduce the aberration of the entire system. Then, the optical simulation software was used to align the direct imaging system for optical simulation. And ultimately achieve the design simulation requirements. Simulation results indicate that the whole size of the spectrometer is less than 150 mm×150 mm×150 mm, and the resolution is better than 15 nm in the range of 1000-1700 nm in the working band. Therefore, the proposed method can meet the design requirements and has broad application prospects in practical applications.
    $R = \frac{{\overline {\rm{\lambda }} }}{{\Delta \lambda }} = \frac{{\left( {{\lambda _1} + {\lambda _2}} \right)/2}}{{\left| {{\lambda _1} - {\lambda _2}} \right|}}$(1)

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    ${{R}} = \frac{{{{\overline \lambda }^\prime }}}{{\Delta \lambda '}} = \frac{{({\lambda _1}^\prime + {\lambda _2})/2}}{{{\lambda _2} - {\lambda _1}^\prime }} = \frac{{4\overline \lambda + a/({\rm{d}}l/{\rm{d}}\lambda )}}{{4\Delta \lambda + 2a/({\rm{d}}l/{\rm{d}}\lambda )}}$(2)

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    $\frac{{{\rm{d}}l}}{{{\rm{d}}\lambda }} = \frac{{\rm{{d}}\theta }}{{{\rm{d}}\lambda }}\frac{{{f_2}}}{{\cos \sigma }} = \frac{m}{{{{d}}\cos \theta }}\frac{{{f_2}}}{{\cos \sigma }}$(3)

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    $\frac{{{\rm{d}}l}}{{{\rm{d}}\lambda }} = \frac{L}{{\Delta \lambda }}$(4)

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    ${f_2} = \frac{{{\rm{d}}l}}{{{\rm{d}}\lambda }} \times \frac{{d\cos \theta }}{m} \times \cos \sigma $(5)

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    $f'= - f = - \frac{{{f_1}^\prime {f_2}^\prime }}{\Delta } = \frac{{n{r_1}{r_2}}}{{(n - 1)[n({r_2} - {r_1}) + (n - 1)d]}}$(6)

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    $\begin{array}{l} {\rm{d}}(\sin \theta \pm \sin i) = m\lambda \\ (m = 0, \pm 1, \pm 2,\cdots) \\ \end{array} $(7)

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    $\frac{{{\rm{d}}\theta }}{{{\rm{d}}\lambda }}=\frac{m}{{{\rm{d}}\cos \theta }}$(8)

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    $\frac{{{\rm{d}}l}}{{{\rm{d}}\lambda }}=\frac{m}{{{\rm{d}}\cos \theta }}f'$(9)

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    Hongming Liu, Yujuan Liu, Ying Song, Zhicheng Zhong, Lingsheng Kong, Huaibin Liu. Principle and optimum analysis of small near-infrared spectrometers based on digital micromirror device[J]. Infrared and Laser Engineering, 2021, 50(2): 20200427
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