Dependence of the Michelson Interferometer-Based Membrane-Less Optical Microphone–Photoacoustic Spectroscopy Gas-Sensing Method on the Fundamental Parameters of a Photoacoustic Gas Cell

This article presents a mathematical model of the Michelson interferometer (MI)-based membrane-less optical microphone (MeoM)–photoacoustic spectroscopy (MeoM–PAS) method, which is also referred to as MI-based photoacoustic interferometry (PAI), for gas-sensing applications in complex and adverse environments, as it offers a completely static measurement system and the separation of a photoacoustic (PA) gas cell from the measuring system. It also investigates the dependence of this method on the fundamental parameters of a cubical PA gas cell using axial PA signals. The results indicate that the phase of the method is a sine function of the distance between the two light beams and a power exponent of the cell length, the cell height, and the distance between the excitation source and the nearest light beam, under the condition that the PA gas cell is resonant and that the excitation source is at the position of the peak or valley of the PA signals. It is at its maximum when the distance between the two light beams is approximately half the wavelength of the PA signals under the same conditions. In addition, the dependence of a PA gas cell using non-axial PA signals is described under the conditions that the PA gas cell is resonant, which is consistent with the changing aforementioned parameters for the distance between the two light beams, the cell length and height, and the distance between the excitation source and the nearest light beam. Furthermore, the selection of five common materials (aluminum, brass, glass, quartz, and stainless steel) for the PA gas cell is discussed under the influence of temperature fluctuations outside the PA gas cell, noise inside and outside the PA gas cell, as well as thermal and viscous losses inside the PA gas cell. The results indicate that quartz and stainless steel are promising options. Finally, the parameters related to the sensitivity enhancement of the method are analyzed using mathematical models, where the sensitivity of the method can be theoretically enhanced by reducing the dimensions of the PA gas cell.