Swimming pool in the sunshine (phase->intensity)
Our TIE logo
Fast Discrete Cosine Transform (DCT)-based TIE solver
Demodulation of digital hologram using the TIE
Micro-lens array characterization using the TIE
TIE phase imaging using spatially modulated illuminations
Generalized TIE in phase-space
Optimal frequency selection (OFS)
Phase discrepancy compensation
Phase = Fringe?
Transport of intensity equation (TIE)
![]() We are dedicated to discover the key theories and explore related new methods associated with noninterferometric phase retrieval and quantitative phase contrast microscopy imaging by using the transport of intensity equation (TIE). With only intensity measurements at several distances along its propagation direction, the phase can be quantitatively retrieved by solving the TIE deterministically, without resorting to interferometry or separated reference wave. Our new technology endows the conventional microscope with the ability of three-dimensional (3D) quantitative phase imaging, enabling us to obtain 3D morphology and optical properties of phase specimens with nanometer-scale and millisecond temporal resolution. ![]() Introduction ![]() Although phase objects cannot be observed directly, they incessantly, and implicitly manifest their existence: the twinkling of stars in the night, the distorted scene outside the window in the rain, the network of bright lines at the bottom of a swimming pool in the sunshine. These are all manifestations of phase, implying the inextricably ties between phase and intensity of light wave. In 1983, Teague first establish the quantitative relationship between the longitudinal intensity variation and phase of transporting light with use of a second-order elliptic partial differential equation, so called transport of intensity equation (TIE). With only intensity measurements at several distances along its propagation direction, the phase can be quantitatively retrieved by solving the equation deterministically, without resorting to interferometry or separated reference wave. ![]() The TIE outlines the relation between object-plane phase and the first order derivative of intensity with respect to the optical axis in the near Fresnel region. With appropriate boundary conditions, the solution to TIE is known to exist and be unique. That is, the phase can be uniquely determined by solving TIE with determined intensity and longitudinal intensity derivative (by simply capturing a minimum of two intensity images at different z planes and using them to estimate dI/dz). Though everything looks quite easy and straightforward, there are several important technical issues needs to be solved in order to put this promising technique into practical use: ![]() A deep and systematic research has been conducted by our group to discover the key theories and related new methods associated with noninterferometric phase retrieval and quantitative phase contrast microscopy imaging by using the TIE. It is expected to address several key issues in both the theoretic aspects as well of the practical application of the TIE, so that developing the TIE from a theortical equation into a powerful metrology tool. Our new technology endows the conventional microscope with the ability of three-dimensional (3D) quantitative phase imaging, enabling us to obtain 3D morphology and optical properties of phase specimens with nanometer-scale and millisecond temporal resolution. This technology provides the following unique advantages:
Overview of Our Work
Solution to the TIE ![]() Fast Discrete Cosine Transform (DCT)-based TIE solver ![]() Phase discrepancy analysis and compensation Axial intensity derivative estimation ![]() Optimum derivative estimation using Savitzky-Golay differentiation filter Extension of the TIE to partially coherent fields ![]() Generalized TIE in phase-space for partially coherent fields
Dynamic TIE phase microscopic systems and applications ![]() Electrically tunable lens based TIE (TL-TIE)
![]() Noninterferometric single-shot quantitative phase microscopy (SQPM)
![]() TIE phase retrieval using spatially modulated illumination Applications to micro-optics characterization ![]() Micro-optics characterization using the TIE
Comparsion and combination between DH and TIE ![]() Comparsion and combination between DH and TIE
|