Enhanced lateral resolution for phase retrieval based on the transport of intensity equation with tilted illumination

Quantitative Phase Imaging based on the Transport of Intensity Equation (TIE) has shown to be a practical tool for retrieving the phase information of biological and technical samples. When recovering the phase information with the TIE, the maximum lateral resolution that can be obtained is limited by the numerical aperture (NA) of the optical system. In order to overcome this limitation, a system that combines structured illumination and TIE-like techniques have been proposed. These methodologies enlarge synthetically the NA of the optical system, and thus, the lateral resolution of the retrieved phase can be improved. However, the employment of structured illumination may bring error amplifications in the retrieved phase due to its sensitiveness to phase discontinuities and shot noise. In this work, we propose a new methodology that improves the lateral resolution of the retrieved phase beyond the diffraction limit avoiding the problems related with the structured illumination. The methodology presented here uses tilted illumination and a TIE solver. We show that when using this configuration, we can extend the set of recovered frequencies by adjusting the angle of the tilted wave-front. Further, our methodology is designed to extend the NA by employing less tilted angles than other similar techniques. Hence, the final retrieved phase will have an enhanced lateral resolution without amplifying the numerical errors and employing a few tilted angles. Moreover, we show that the algorithm presented here can be combined with other TIE algorithms that are used for suppressing the Low Frequency Artifacts (LFAs) usually present when using TIE based techniques.