PHASE RETRIEVAL AND 3D TOPOGRAPHY USING TRANSPORT OF INTENSITY

Abstract

Transport of intensity is a non-interferometric technique to obtain the phase of an object by recording optical intensities at different incremental propagation distances around the image plane. The transport of intensity equation (TIE) is also a convenient way to obtain unwrapped phases directly without the need of phase unwrapping techniques. The accuracy of TIE can be improved by incorporating the associated transport of phase equation (TPE). However, TIE (and TPE) suffers from the disadvantage in that image intensities must be recorded at multiple longitudinal distances around the image plane without any transverse misalignment. To avoid this issue, we have proposed a modified TIE with TPE (TIE+TPE) in this research utilizing electrically controllable optical path lengths through bias voltages across liquid crystals (LCs). The most significant advantage of using TIE+TPE with LC is that no physical movement of the detector array is needed to change the optical path lengths around the image plane, as required for the conventional TIE. Additionally, TIE+TPE with LC provides a more accurate evaluation of the phase. Also, this research investigates the combination of digital holography (DH) and TIE+TPE with LC to retrieve the image phase directly without any phase unwrapping. In both cases of phase retrieval, either using conventional imaging or holographic imaging, numericalexamples and simple experimental verifications are provided. In experiments, the 3D topology is recovered from the imaged phase. Finally, we propose a single-shot (single￾ wavelength) alternative to 3D optical imaging that combines DH with TIE and DH with TIE and TPE to conveniently retrieve unwrapped phase and hence the 3D topography of partially bloody fingermarks deposited on substrates and coated with columnar thin films encapsulated by columnar thin films (CTFs).