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Basic angles in microelectromechanical system scanning grating spectrometers.

Tino Puegner¹, Jens Knobbe, Hubert Lakner

¹Fraunhofer Institute for Photonic Microsystems (IPMS), Maria-Reiche-Strasse 2, 01109 Dresden, Germany. tino.puegner@s2001.tu‐chemnitz.de

|August 23, 2011

Summary

This study presents a mathematical analysis of miniaturized scanning grating spectrometers (SGSs), focusing on design constraints like symmetrical grating motion. The derived equations help optimize SGS performance and determine spectral range or grating properties.

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Area of Science:

Optics and Photonics
Microelectromechanical Systems (MEMS)

Background:

Miniaturized scanning grating spectrometers (SGSs) often utilize microelectromechanical system (MEMS) devices.
Unlike classical spectrometers, SGSs face unique design constraints, including symmetrical grating motion and limited deflection angles.

Purpose of the Study:

To provide a detailed mathematical analysis of typical SGS configurations under specific design constraints.
To derive equations relating grating properties, angles, and attainable wavelength range for SGS optimization.

Main Methods:

Mathematical analysis of the grating equation applied to SGS configurations.
Derivation of analytical equations considering symmetrical grating motion and limited deflection.
Examination of the solution set for practical application.

Main Results:

Developed equations that link basic angles, grating properties, and the achievable wavelength range of a spectrometer.
Demonstrated that the analytical description enables optimization of SGSs with symmetrically moving gratings.
Established methods to calculate the attainable spectral range for a given grating deflection amplitude or vice versa.

Conclusions:

The presented analytical framework is crucial for optimizing the design of miniaturized scanning grating spectrometers.
The derived equations offer a practical tool for engineers and researchers designing SGS systems.
This work facilitates the precise determination of spectral range or required grating properties for specific applications.