Super-resolution reconstruction of speckle phase in depth-resolved wavelength scanning interference using the total least-squares analysis

Depth-resolved wavelength scanning interferometry (DRWSI) is a tomographic imaging tool that employs phase measurement to visualize micro-displacement inside a sample. It is well known that the depth resolution of DRWSI is restricted by a wavelength scanning range. Recently, a nonlinear least-squares analysis (NLS) algorithm was proposed to overcome the limitation of the wavelength scanning range to achieve super-resolution; however, the NLS failed to measure speckle surfaces owing to the sensibility of initial values. To the best of our knowledge, the improvement of depth resolution on measuring a speckle surface remains an open issue for DRWSI. For this study, we redesigned the signal processing algorithm for DRWSI to refine the depth resolution when considering the case of speckle phase measurement. It is mathematically shown that the DRWSI’s signal is derived as a model of total least-squares analysis (TLSA). Subsequently, a super-resolution of the speckle phase map was obtained using a singular value decomposition. Further, a numerical simulation to measure the micro-displacements for speckle surfaces was performed to validate the TLSA, and the results show that it can precisely reconstruct the displacements of layers whose depth distance is 5 μm. This study thus provides an opportunity to improve the DRWSI’s depth resolution.