Signal Processing for Microscale Optical Spectrometers

Abstract

In this work, we demonstrated that cascaded Fabry-Perot interferometers with low or high mirror reflectivity can be successfully used as a Fourier-domain spectrometer. The integral equation of the response of the cascaded interferometer was solved numerically by an algorithm that expands the source spectrum into trigonometrical series and the Airy functions of the Fabry-Perot interferometers into Fourier series. The algorithm was found to be robust against errors in the mirror reflectivity that can result from the fabrication tolerance and against the noise effect. The resolution was found to be inversely proportional to the scanning range of the interferometer. A theoretical investigation on the capabilities and limitations of the AR algorithm was conducted. The effect of the number of spectral lines and the spacing between these lines were studied, and it was found that the prediction error increases as the interval between the successive lines decreases or as the number of lines increases. The effect of the SNR was investigated, and it was found that the prediction error increases significantly as the SNR decreases. The prediction error also decreases as the required resolution is more relaxed. False peaks may appear in the spectrum as well, if the prediction error is large. Many tests were conducted and it turned out that an error that is larger than -20 dB should be avoided. Moreover, it is showed that the AR model based on singular value decomposition enables the model to decrease the effect of noise by neglecting the small singular values. The AR algorithm was applied on the spectrum of a MEMS FTIR spectrometer to enhance the resolution of standard optical filter with a line width of 1 nm, and multi-lines spectrum of Xenon lamp