Abstract
Microfabricated Lamellar grating interferometers (LGI) require fewer components compared to Michelson interferotemeters and offer compact and broadband Fourier transform spectrometers (FTS) with good spectral resolution, high speed and high efficiency. This study presents the fundamental equations that govern the performance and limitations of LGI based FTS systems. Simulations and experiments were conducted to demonstrate and explain the periodic nature of the interferogram envelope due to Talbot image formation. Simulations reveal that the grating period should be chosen large enough to avoid Talbot phase reversal at the expense of mixing of the diffraction orders at the detector. Optimal LGI grating period selection depends on a number of system parameters and requires compromises in spectral resolution and signal-to-bias ratio (SBR) of the interferogram within the spectral range of interest. New analytical equations are derived for spectral resolution and SBR of LGI based FTS systems.
Highlights
Fourier transform spectrometry (FTS) is an established method that finds use in a variety of applications such as chemical substance detection and analysis, quality control, mining, or bomb detection
This study focuses on the optical design aspects and optimization of the grating period size in order to achieve best efficiency, spectral resolution, and signal-to-bias ratio at the detector
First two limitations are related to the spectral resolution set by the optical path difference in the interferometer arms and the divergence of the source, which are applicable to both Michelson and lamellar grating interferometer (LGI) based FTS
Summary
Fourier transform spectrometry (FTS) is an established method that finds use in a variety of applications such as chemical substance detection and analysis, quality control, mining, or bomb detection. In this configuration, an infrared (IR) source is collimated with a parabolic IR mirror. The two reflected beams interfere and create an interferogram at the detector in response to the changing optical path difference (OPD) between the grating fingers. Besides providing comb-type electrostatic actuation, the aluminum coated comb fingers function as reflectors for the lamellar grating where an optical path difference is created between the movable and fixed fingers. This study focuses on the optical design aspects and optimization of the grating period size in order to achieve best efficiency, spectral resolution, and signal-to-bias ratio at the detector. The relationship between the Talbot image distance and spectral resolution is investigated for the first time and a new fundamental equation for spectral resolution of LGI systems is derived
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