Abstract
Hyperspectral (HS) imaging retrieves information from data obtained across broadband spectral channels. Information to retrieve is a 3D cube, where two coordinates are spatial and the third one is spectral. This cube is complex-valued with varying amplitude and phase. We consider shearography optical setup, in which two phase-shifted broadband copies of the object projections are interfering at a sensor. Registered observations are intensities summarized over spectral channels. For phase reconstruction, the variational setting of the phase retrieval problem is used to derive the iterative algorithm, which includes the original proximity spectral analysis operator and the sparsity modeling of the complex-valued object 3D cube. We resolve the HS phase retrieval problem without random phase coding of wavefronts typical for the most conventional phase retrieval techniques. We show the performance of the algorithm for object phase and thickness imaging in simulation and experimental tests.
Highlights
Hyperspectral (HS) imaging retrieves information from data collected across hundreds to thousands of spectral channels
Interference between reference and object wavefronts registered as intensity diffraction patterns is used conventionally in spectrally resolved interferometry,[1,2] Fourier transform holography,[3,4] and HS digital holography.[2,5,6]
The high spectral resolution separates the energy obtained by an imaging sensor between many narrow wavebands, which results in small values of signal-to-noise ratio (SNR)
Summary
Hyperspectral (HS) imaging retrieves information from data collected across hundreds to thousands of spectral channels. Two identical but phase-shifted broadband patterns of the object are superimposed on the sensor This scenario, typical for Fourier-transform spectrometry,[9] leads to the phase loss problem, where a complex-valued 3D object should be reconstructed from indirect intensity observations as solutions of the ill-posed inverse problem. One of the key components of the derived iterative algorithm is an original proximal operator enabling both the spectral analysis of intensity observations and their denoising Another important component of the algorithm is the original complex domain filtering of 3D complex-valued object arrays following from the proposed sparsity modeling for complex-valued 3D arrays. It is demonstrated by simulation experiments and processing of experimental data that the HS phase retrieval in the proposed setup can be resolved. We present more stimulation and as well as experimental results with detailed discussion
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