Highly Sensitive Photoacoustic NO₂ Measurement System Based on an Optimized Ring-Shaped Resonant Cell

A Photoacoustic-Based Measurement System for Dual Detection of NO2 and CO2 in Combustion Exhaust Gases

“…In more detail, in a resonant PA cell, the acoustic wave can be described in the angular frequency domain through an eigenmode expansion as a function of the position, r, with the following equation [31,32]:…”

“…Moreover, 𝛾 is the specific heat ratio of the gas, I0 is the incident power generated by the optical source, Qn is the quality factor of the n-th eigenmode with angular frequency 𝜔 𝑛 , Fn is the mode shape factor, whereas 𝑠 𝑛 (𝑟) describes its spatial distribution. 𝐿 𝑐𝑒𝑙𝑙 and 𝑉 𝑐𝑒𝑙𝑙 are respectively the length and the volume of the PA cell [31].…”

“…where 𝐹 𝑠 is obtained by spatially integrating the term in eq. ( 1) that describe the spatial distribution of the wave over the microphone receiving lobe [31]. Equation ( 2) clarifies how the acoustical resonance of the cell amplifies the PA signal.…”

“…The developed measurement technique is based on exciting a PA signal in the acoustic resonator (PA cell in Figure 2a), using an optical source (LED in Figure 2a) that among the different compounds present in the exhaust gas, is adsorbed by NO2 only. The ring resonator shown in Figure 2b) [31] is the used PA cell. With this geometry the first eigenmode is characterized by two nodes situated at the endpoints of a diameter, and two antinodes positioned at the endpoints of a diameter perpendicular to the first [31].…”

“…The ring resonator shown in Figure 2b) [31] is the used PA cell. With this geometry the first eigenmode is characterized by two nodes situated at the endpoints of a diameter, and two antinodes positioned at the endpoints of a diameter perpendicular to the first [31]. The LED position determines the illuminated region and thus one antinode position, and the microphone is placed at the other antinode, where the acoustic pressure is maximized, thereby optimizing the signal-to-noise ratio (SNR) of the system.…”