## 5 Discussion  
Experiments of RH variations have been carried out on softwoods that are representative materials used for panel paintings between the 15 th and 16 th centuries, inside an environmental chamber simulating real variations found inside specific museums. The homemade airtight climate chamber helps to stimulate the correlation between the RH fluctuations with the surface deformation of the object of interest. The RH fluctuations followed in the climate chamber are based on RH variations found in a museum's rooms. Two mock-ups made of spruce, a wood of interest, are tested with different thicknesses of 19 mm and 50 mm with equal other dimensions. The surface is monitored by a well-known system designed by FORTH, DHSPI for around 3 days. Figure 12: Deformation maps between the beginning of the experiment and five minutes later of experiment on mock-up n°51 (**a**) 2D of the unwrapped phase of interferogram with CPUISI algorithm applied on denoised interferogram with \(\text{ite}_{\text{Max}}\)300e0.001, the phase–known point at the point nearer to zero in the denoised interferogram (**b**) 3D of the same unwrapped phase (**c**) FORTH processing. Deformation maps between five minutes after the beginning of the experiment and five minutes later on mock-up n°44 (**d**) 2D of the unwrapped phase of with CPUISI algorithm applied on denoised interferogram with \(\text{ite}_{\text{Max}}\)300e0.001, the phase–known point at the point nearer to zero in the denoised interferogram (**c**) 3D of the same unwrapped phase (**f**) FORTH software. The interferograms are reconstructed in the pre-processing step and the obtained images are named the wrapped phase. This step is followed by the processing including the denoising of the wrapped phase images and the unwrapping of these images. The denoising includes a median filter followed by a Sine-Cosine Average with Stationary Wavelet Transform (SCA-SWT) algorithm. The unwrapped phase is realised with the Calibrated Phase Unwrapping based on Least-Square and Iterations (CPULSI) algorithm with its MatLab function. The next step, called post-processing is the calculation and display of the deformation map. All these steps can be executed for all the acquired data of one surface mock-up in one row. From the acquired data, a raw interferogram, also called the wrapped phase, can be reconstructed. In the studied case, a set of images is taken every five minutes and a first pattern could be identified for these five minutes after reconstruction. This raw wrapped phase is denoised by a 2D median filter with symmetric padding and a square window size that have to be at least 3 \(\times\) 3 to denoise enough and not more than 4 \(\times\) 4 to keep all the details. The time of computing is slightly increasing with the increase of the size of the window. A second algorithm, called SCA-SWT, is applied to the already denoised images to have a better signal-to-noise ratio. This method uses a stationary wavelet transform on the sine and cosine denoised interferograms with a five-level decomposition and a db2 or sym2 analysing wavelets that are chosen for their sharp form and fast processing time. This transform is followed by the application of a Birge-Massart threshold with a default sigma and an alpha equal to 6.25. The inverse transform of the sine and the cosine are calculated before the denoised wrapped phase reconstruction. Some drawbacks due to the image extension can appear on the border of the image. The wrapping process can be performed by two different algorithms depending on what one is looking for. The PUSLI method can give us rapidly the absolute variation or displacement of one image useful for giving an alert. The CPULSI with a longer calculation time will give the real value and orientation of the displacement. Both of them are based on the least-squares method that needs a suitable limit of iteration chosen at 300 and an error to reach that is given at 0.001.