Development Logbook<

Schedule Planning<

Theory<

General Principle<

A common way to measure particles density in aerosols, called liquid water content ("LWC"), is to use light absorbtion and scattering by either measuring how much light is transmitted through the aerosol depending on its LWC or directly how much light is scattered. If one even manage to measure the directions at which the light is scattered, they could obtain informations about particles sizes distribution.

When light interracts with fog, there is a probability that it scatters on a droplet or is absorbed by the latter. By installing a laser going through the fog and a photosensor right in front of the laser, one could measure the light intensity diminution due to the presence of the fog.

Calibration<

Absorbtion<

Let's consider a beam of light entering a fog sample. We define \(z\) as an axis parallel to the direction of the beam. According to Beer-Lambert's law, the output light intensity \(S\) is given by :

\[ \begin{align} S = S_0 e^{- \sigma \int_0^l n(z) dz} \end{align} \]

where \(S_0\) is the emitted light intensity, \(\sigma\) is the cross section, \(n(z)\) is the number density of the droplets in the fog. Therefore if the fog is homogeneous (which we will assume to begin), n is independent of \(z\) and the latter equation reads :

\[ n = \frac{1}{\sigma l}\ln{\frac{S_0}{S}} \]

The liquid water content is defined as :

\[ LWC = \frac{4}{3}\pi r^3 \rho n \]

hence we get :

\[ LWC = \frac{4}{3}\pi r^3 \rho \frac{1}{\sigma l}\ln{\frac{S_0}{S}} \]

however we don't know the cross section of the fog's droplets therefore we will have to calibrate our measurment with a known LWC. The equation we will use is then :

\[ LWC \sim \ln{\frac{S_0}{S}} \]

Phototransistor<

Let's not forget that our device will not directly give \(S\) but instead a voltage. We will use a phototransistor in a circuit with a resistor. The measured tension at the collector \(V_{CE}\) is given by the Ohm's law :

\[ V_{CE} = R\times I \]

and the current \(I\) is given by the phototransistor characteristic equation :

\[ I \sim V_{BE}^2 \sim ? S^2 \]

hence

\[ LWC \sim \ln{\frac{S_0}{S}} \sim ? \frac{1}{2}\ln{\sqrt{\frac{V_{CE}}{V_{CE,0}}}} \sim \frac{1}{2}\ln{\frac{V}{V_0}} \sim \ln{\frac{V}{V_0}} \]

Electronics<

First PCB Design<

First PCB production<

Final PCB<

Phototransistor<

Calibration Setup<

First Prototype with UC2 frames<

Interface<

Arduino Interface<

import pandas as pd
from scipy.signal import savgol_filter
import matplotlib.pyplot as plt

df = pd.read_csv("EXP-2.txt", sep=",",names=["Max", "Min","Data"])

signal = df.Data

window=301

smooth_signal = savgol_filter(signal, window_length=window, polyorder=3, deriv=0)

plt.plot(signal)
plt.plot(smooth_signal)

print(signal.size)