## 2 Materials and Methods  
In a typical QEPAS setup a laser beam is focused between the prongs of the tuning fork (and if applicable through an acoustic resonator). The emission wavelength of the laser source is tuned to an absorption line of the target molecule and is additionally modulated with the resonance frequency or half the resonance frequency of the tuning fork depending on the modulation approach, 1f-amplitude modulation or 2f-wavelength modulation, respectively. This is usually done using a separate frequency generator with a precision of at least 0.1 Hz. The tuning fork is connected to a trans-impedance amplifier and the signal is then further amplified by a lock-in amplifier which is referenced by the frequency generator. To determine the correct modulation frequency, the frequency can be scanned in proximity of the expected resonance frequency while recording the signal amplitude of the spectrophone and thus obtaining a resonance curve with a maximum at the spectrophone's resonance frequency. The modulation frequency of the laser has to be realigned frequently if changes in environmental conditions such as pressure, temperature, and gas composition are expected. Even a complete recalibration might be necessary because of changes of the Q-factor if the environmental conditions change perceivably. Many QEPAS systems provide the ability to record resonance curves non-photo-acoustically by directly exciting the tuning fork with the frequency generator as reported by [PERSON] et al. [8]. This feature is typically used for presetting the modulation frequency before optical alignment of the spectrophone and for verifying the modulation frequency after changes in the environmental conditions, but not for the actual measurement. Figure 1 shows the signals for photoacoustic excitation (open red squares), for purely electrical excitation (solid green squares), and for simultaneous electrical and photo-acoustic excitation while the phase between them is altered (filled squares). For this feasibility study pure methane was excited by a cw quantum cascade laser operating at \(\
u=1276.85\) cm\({}^{-1}\) using 2f-modulation. The amplitudes were set to 60 mV for electrical excitation and to 40 mV for photoacoustic excitation by adjusting the amplitude and the modulation width respectively. Figure 1 shows the resulting signal for simultaneous excitation when the phase of the laser modulation is varied from \(\varphi=-210^{\circ}\) to +210\({}^{\circ}\) while the phase of the electrical excitation is fixed. The sinusoidal sum signal varies between R\({}_{\rm{LI}}\) = 20 and 100 mV. The phase difference between two maxima is \(\Delta\varphi=180^{\circ}\). Since the phase was set with respect to the modulation frequency which is half the resonance frequency of the tuning fork because of 2f-modulation the actual phase difference is 360\({}^{\circ}\), as expected. In [9; 10] we already described the ability to incorporate a quartz micro-tuning fork with removed container in an oscillator circuit and to simultaneously focus a laser beam between the tuning fork's prongs to generate acoustic waves upon absorption of the molecule. Since the laser modulation signal is derived from the oscillation circuit that automatically adjusts to the current resonance frequency of the tuning fork, the laser is always modulated with the correct frequency. The measurement signal and the reference which are fed to the lock-in amplifier are also derived from the oscillator circuit. The measurement signal is thus the sum of the electrically generated amplitude and the photo-acoustically induced amplitude, which furthermore depends on the phase between both signals. Until now, the phase was manually adjusted as a temporal delay in the modulation line to obtain a maximum signal amplitude. A scheme of this method is shown in Figure 2a. The phase of a photoacoustic wave is governed by the gas mixture's relaxation dynamics which in turn depends on the collision partner behavior and thus on the gas mixture composition, its pressure and temperature.