### IMPORT¶

The data is read from ISF files, using the isfreader library. It is installed bellow automatically if not already installed.

### Spectral analysis of signals¶

The mixer signals is a base sine wave (the envelope of the mixing) at a frequency close to 500 kHz. The reference saw-tooth frequency sweeping wave has the same base frequency, but with a trail of harmonics forming the sharp saw-tooth shape.

### Base band signal analysis¶

The difference between the phase of the reference and mixer signal is proportional to the line-integrated electron density. Therefore, it is necessary to obtain the "phase" of both signals.

The instantaneous phase and amplitude of the base signal can be inferred only for the base band, i.e. by removing higher and lower frequencies (i.e. extracting the base sine wave from the reference saw-tooth signal)

cut 0.1 ms from the beginning and from the end

### Estimation of the electron density¶

The ordinary wave (O-mode) with a carrier frequency $\omega$ traveling through a collisionless plasma with the plasma frequency $\omega_{p} = \sqrt{\frac{n_e e^2}{\epsilon_0 m_e}}$ has a refractive index $$N_O=\sqrt{1-\frac{\omega_p^2}{\omega^2}}$$ Under the assumption that the carrier wave frequency is much larger than the plasma frequency $\omega>>\omega_p$ this formula can be expanded into a Taylor series as $$N_O\approx 1-\frac{\omega_p^2}{2\omega^2}$$ A wave traveling through a medium with a refractive index $N(l)$ accumulates a total phase shift $\varphi = \frac{\omega}{c} \int N(l) \mathrm{d}l$. Therefore, in comparison to a wave traveling in vacuum (or clear air) with $N\approx 1$, the wave traveling through the plasma over a chord with length $L$ accumulates a relative phase shift of $$\Delta \varphi = \frac{e^2}{2\omega c\epsilon_0 m_e}\int\limits_L n_e(l) \mathrm{d}l$$ Therefore, it is possible to estimate the line-averaged density $\bar n_e = \frac{1}{L} \int\limits_L n_e(l) \mathrm{d}l$ from the detected phase shift between the reference and mixer signals.