Richardson-Lucy (RL) deconvolution optimizes the likelihood of the object estimate for an incoherent imaging system. It can offer an increase in contrast, but converges poorly, and shows enhancement of noise as the iteration progresses. We have discovered the underlying reason for this problematic convergence behaviour using a Cramér Rao Lower Bound (CRLB) analysis. An analytical expression for the CRLB diverges for spatial frequency components that approach the diffraction limit from below. The resulting mean noise variance per pixel diverges for large images. These results imply that a regular optimum of the likelihood does not exist, and that RL deconvolution is necessarily ill-convergent.

For the focused sensing of targets at different axial depths, the synchronized display of their three-dimensional morphology is challenging. Terahertz waves exhibit selective penetration of some dielectrics and non-polar substances, which produces constructive guidelines for the targets. Here, a high-quality, superior-resolution, and depth-free sensing approach is demonstrated by a terahertz holographic mode. This work proposes and develops a novel stereoscopic-field method of axial multi-depth targets based on terahertz digital holography. The feasibility of the pre-propagating diffraction decomposition strategy is investigated, and the mutual disturbance from the stacking interference patterns is effectively curbed. The optimized holograms are propagated to a pre-screening plane where exclusive mask filters of samples are shaped by using Otsu's method. The signals are reconstructed by classical auto-focusing criteria and the automated merging process can promise the performance of the targets in one stereoscopic-field. Meanwhile, the implementation of extending the field of view method, global and discrete optimization, and the phase retrieval and unwrapping algorithm also contribute to the imaging performance. Furthermore, two representative setups are applied and the positive experimental results indicate the universality and robustness of stereoscopic-field terahertz depth-free holography technology.

Richardson-Lucy deconvolution can offer an increase in contrast, but converges poorly, and is sensitive to noise. We show that the Cramér Rao Lower Bound (CRLB) diverges, which explains the problematic behaviour.