Hilbert Transform Enhancement of Phase Images Retrieved by Using the Transport of Intensity Equation

• Main Authors: Chen, Chun-Wei, 陳君瑋
• Other Authors: Hsieh, Wen-Feng
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/66j696

碩士 === 國立交通大學 === 光電系統研究所 === 103 === It has been known that the full field can be calculated if the derivative of intensity profile along the propagation is measured by solving the transport of intensity equation (TIE), derived from the free space Helmholtz wave equation under the paraxial wave approximation. Using the TIE, phase recovery by non-interferometric propagation-based techniques has been employed in many experiments to replace the interferometric imaging, in which phase recovery is based on the analysis of experimental interferograms and is technically demanding. Separately using aperiodic dragonfly wings and periodic structure a micro-lens (ML) array, a strong phase plate, as our specimens, we demonstrate recovery of phase images by using conventional TIE (c-TIE), one partial derivative (OPD) and direct Hilbert transform methods. Furthermore, take the advantages of the Hilbert transform for enhancing edges and fine structures of the images, we found in Hilbert treated c-TIE as well as direct Hilbert transform methods display similar and better results. Replacing the process of solving the phase gradient by the Hilbert transform, it is not only simpler but also has smoother phase image than c-TIE and OPD alone. Due to the weak filtering with small parameter of lambda in the other dimension without derivative (says, the y-direction), the OPD images appear many streaks due to integration of noise line-by-line in y-direction.