+Finally, the whole summarizes in an algorithm (called LSQ in the following) in two parts, one before and one during the acquisition loop :
+\begin{algorithm}[h]
+\caption{LSQ algorithm - before acquisition loop.}
+\label{alg:lsq-before}
+
+ $M \leftarrow $ number of pixels of the profile\\
+ I[] $\leftarrow $ intensities of pixels\\
+ $f \leftarrow $ frequency of the profile\\
+ $s4i \leftarrow \sum_{i=0}^{M-1} sin(4\pi f.i)$\\
+ $c4i \leftarrow \sum_{i=0}^{M-1} cos(4\pi f.i)$\\
+ $nb_s \leftarrow $ number of discretization steps of $[-\pi,\pi]$\\
+
+ \For{$i=0$ to $nb_s $}{
+ $\theta \leftarrow -\pi + 2\pi\times \frac{i}{nb_s}$\\
+ lut\_sin[$i$] $\leftarrow sin \theta$\\
+ lut\_cos[$i$] $\leftarrow cos \theta$\\
+ lut\_A[$i$] $\leftarrow cos 2 \theta \times s4i + sin 2 \theta \times c4i$\\
+ lut\_sinfi[$i$] $\leftarrow sin (2\pi f.i)$\\
+ lut\_cosfi[$i$] $\leftarrow cos (2\pi f.i)$\\
+ }
+\end{algorithm}
+
+\begin{algorithm}[h]
+\caption{LSQ algorithm - during acquisition loop.}
+\label{alg:lsq-during}
+
+ $\bar{x} \leftarrow \frac{M-1}{2}$\\
+ $\bar{y} \leftarrow 0$, $x_{var} \leftarrow 0$, $xy_{covar} \leftarrow 0$\\
+ \For{$i=0$ to $M-1$}{
+ $\bar{y} \leftarrow \bar{y} + $ I[$i$]\\
+ $x_{var} \leftarrow x_{var} + (i-\bar{x})^2$\\
+ }
+ $\bar{y} \leftarrow \frac{\bar{y}}{M}$\\
+ \For{$i=0$ to $M-1$}{
+ $xy_{covar} \leftarrow xy_{covar} + (i-\bar{x}) \times (I[i]-\bar{y})$\\
+ }
+ $slope \leftarrow \frac{xy_{covar}}{x_{var}}$\\
+ $start \leftarrow y_{moy} - slope\times \bar{x}$\\
+ \For{$i=0$ to $M-1$}{
+ $I[i] \leftarrow I[i] - start - slope\times i$\tcc*[f]{slope removal}\\
+ }
+
+ $I_{max} \leftarrow max_i(I[i])$, $I_{min} \leftarrow min_i(I[i])$\\
+ $amp \leftarrow \frac{I_{max}-I_{min}}{2}$\\
+
+ $Is \leftarrow 0$, $Ic \leftarrow 0$\\
+ \For{$i=0$ to $M-1$}{
+ $Is \leftarrow Is + I[i]\times $ lut\_sinfi[$i$]\\
+ $Ic \leftarrow Ic + I[i]\times $ lut\_cosfi[$i$]\\
+ }
+
+ $\theta \leftarrow -\pi$\\
+ $val_1 \leftarrow 2\times \left[ Is.\cos(\theta) + Ic.\sin(\theta) \right] - amp\times \left[ c4i.\sin(2\theta) + s4i.\cos(2\theta) \right]$\\
+ \For{$i=1-n_s$ to $n_s$}{
+ $\theta \leftarrow \frac{i.\pi}{n_s}$\\
+ $val_2 \leftarrow 2\times \left[ Is.\cos(\theta) + Ic.\sin(\theta) \right] - amp\times \left[ c4i.\sin(2\theta) + s4i.\cos(2\theta) \right]$\\
+
+ \lIf{$val_1 < 0$ et $val_2 >= 0$}{
+ $\theta_s \leftarrow \theta - \left[ \frac{val_2}{val_2-val_1}\times \frac{\pi}{n_s} \right]$\\
+ }
+ $val_1 \leftarrow val_2$\\
+ }
+
+\end{algorithm}
