Editing Sample Thickness Measurement via Multi-wavelength Laser Interferometry (section)

===Thickness Reconstruction Algorithm Design===

The core task of thickness reconstruction is to identify a unique solution within the solution space defined by:

<math display="block">
L = (m_i + \varepsilon_i)\frac{\lambda_i}{2n_i}
</math>

that satisfies all wavelength constraints simultaneously.

First, the sample thickness is measured multiple times using a vernier caliper. The maximum and minimum measured values are used to define the search interval:

<math display="block">
[L_{min}, L_{max}]
</math>

Within this interval, for each wavelength <math>\lambda_i</math>, the possible range of integer orders <math>m_i</math> is given by:

<math display="block">
m_{i,start} = \left\lceil \frac{2n_i L_{min}}{\lambda_i} - \varepsilon_i \right\rceil,\quad
m_{i,end} = \left\lfloor \frac{2n_i L_{max}}{\lambda_i} - \varepsilon_i \right\rfloor
</math>