Ying Ji

Dynamical analysis of periodic bursting in piece-wise linear planar neuron model.

A piece-wise linear planar neuron model, namely, two-dimensional McKean model with periodic drive is investigated in this paper. Periodical bursting phenomenon can be observed in the numerical simulations. By assuming the formal solutions associated with different intervals of this non-autonomous system and introducing the generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the bursting solution induced by the slowly varying periodic drive is presented. It is shown that, the discontinuous Hopf bifurcation occurring at the non-smooth boundaries, i.e., the bifurcation taking place at the thresholds of the stimulation, leads the alternation between the rest state and spiking state. That is, different oscillation modes of this non-autonomous system convert periodically due to the non-smoothness of the vector field and the slow variation of the periodic drive as well.

A novel phase retrieval method from three-wavelength in-line phase-shifting interferograms based on positive negative 2π phase shifts

Abstract A new method to extract quantitative phases for each wavelength from three-wavelength in-line phase-shifting interferograms is proposed. Firstly, seven interferograms with positive negative 2π phase shifts are sequentially captured by using the phase-shifting technique. Secondly, six dc-term suppressed intensities can be achieved by the use of the algebraic algorithm. Finally, the wrapped phases at the three wavelengths can be acquired simultaneously from these six interferograms add-subtracting by employing the trigonometric function method. The surface morphology with increased ambiguity-free range at synthetic beat wavelength can be obtained, while maintaining the low noise precision of the single wavelength measurement, by combining this method with three-wavelength phase unwrapping method. We illustrate the principle of this algorithm, and the simulated experiments of the spherical cap and the HeLa cell are conducted to prove our proposed method, respectively.

Phase-shifting interferometry by a similar matrix 1-norm algorithm

Abstract Phase-shifting interferometry (PSI) is an effective technique in optical measurement. In this paper, a noniterative algorithm for retrieving the unknown phase shifts in three frame generalized PSI is proposed, in which the interference term of each frame is eliminated by the aid of a reference interferogram with the phase shift of π. With this algorithm, the phase shifts can be determined by solving a system of transcendental equations with trigonometric functions, in which this system consists of three different ratios between the similar matrix 1-norms of the intensity difference and the intensity sum. After the determination of phase shifts, a phase can be retrieved easily. The algorithm provides a possible method to solve the limitation of the fringe number existing in some common algorithms. The feasibility and accuracy of this algorithm were demonstrated by the simulation and experimental results.

Statistical estimation method for phase shift in generalized two-step phase-shifting interferometry

Abstract Based on the statistical property of the phase and the spatial frequency relationship between the object and reference waves, a simple estimation method for phase shift extraction is proposed for generalized two-step phase-shifting interferometry. In this method, a phase shift constrained within 0–π is firstly worked out with statistics, and then it is corrected as its principal value within the range (0, 2π) except the singular value of π, according to the sign of tangent form of one half of the relative phase shift. Thus, this method provides a possible method to solve the uncertainty of the phase shift existing in some common algorithms. After the determination of the phase shift, a phase can be retrieved easily. The feasibility and the accuracy of the method were verified by numerical simulations and an optical experiment. In addition, this method is applicable to two or more frames off-axis generalized PSI, including slightly off-axis situation.

The homogeneous and dual-medium cell’s refractive index decoupling method and entropy tomographic imaging

In the paper, a decoupling method for homogeneous and dual-medium cells’ refractive index, and the entropy tomographic phase imaging method are proposed. Based on the decoupling method, the 3D morphology of sample can be obtained by the imaging method, which only needs two phase images of the cell. Thus the information about 3D refractive index distribution is given, and the 3D structure image of the model is reconstructed as well based on the relationship between the refractive index and thickness. In order to verify these methods, we set up the typical models after analysing the characteristic of blood cells, and the related orthogonal phase images are obtained by simulation experiment. Thus the 3D reconstructed structure images of the models are presented in this paper. Finally, the feasibility of this method is verified by simulating on a red blood cell and a monocyte model. The results show that subsurface imaging of samples can be achieved based on this method with a good accuracy.

Quantitative phase imaging using four interferograms with special phase shifts by dual-wavelength in-line phase-shifting interferometry

Abstract A new approach of quantitative phase imaging using four interferograms with special phase shifts in dual-wavelength in-line phase-shifting interferometry is presented. In this method, positive negative 2π phase shifts are employed to easily separate the incoherent addition of two single-wavelength interferograms by combining the phase-shifting technique with the subtraction procedure, then the quantitative phase at one of both wavelengths can be achieved based on two intensities without the corresponding dc terms by the use of the character of the trigonometric function. The quantitative phase of the other wavelength can be retrieved from two dc-term suppressed intensities obtained by employing the two-step phase-shifting technique or the filtering technique in the frequency domain. The proposed method is illustrated with theory, and its effectiveness is demonstrated by simulation experiments of the spherical cap and the HeLa cell, respectively.

A Rapid Detection Method for Morphological Characteristics of Biological Cells Based on Phase Imaging

This paper presents a rapid label-free method for the identification of morphological characteristics of biological cells. Based on quantitative phase microscopy as well as the connotation of phase value, the gradient operator of phase and the associated analytic processing are employed to determine the edge of different parts of the samples. A heterogeneous biological cell model is established by simulation to show the mechanism of this method and a polystyrene bead is selected as a sample to confirm its validity by optical experiment. The result agrees well with the actual situation and this approach is proved to have good antinoise ability. Furthermore, a neutrophil is investigated by this method. Based on the optical experiment and the related analysis, the basic structure characteristics of the cell are obtained. It is indicated that the method presented in this paper could be applied to rapid identification and classification of living cells.

Dynamics Analysis of Neuron Bursting under the Modulation of Periodic Stimulation

A nonsmooth neuron model with periodic excitation which can reproduce spiking and bursting behavior of cortical neurons is investigated in this paper. Based on nonsmooth bifurcation analysis, the mechanism of the bursting behavior induced by slow-changing periodical stimulation as well as the associated evolution with the variation of the stimulation is explored. The modulating character of the external excitation and the effect of the bifurcation occurring at the switching boundary of the vector field are presented.

Mixed-Mode Oscillations in Nonautonomous Modified Chua's Circuit

A nonautonomous system revised from Chua’s circuit with a cubic nonlinearity which could exhibit slow-fast effect is investigated in this paper. Inspired by slow-fast dynamical analysis, the external excitation is considered as a modulation parameter, which changes slowly and periodically. By introducing “transformed phase space,” bifurcation analysis of typical periodic mixed-mode oscillations induced by periodic excitation has been described to reveal the associated dynamical mechanisms.

Characterization Method for 3D Substructure of Nuclear Cell Based on Orthogonal Phase Images

A set of optical models associated with blood cells are introduced in this paper. All of these models are made up of different parts possessing symmetries. The wrapped phase images as well as the unwrapped ones from two orthogonal directions related to some of these models are obtained by simulation technique. Because the phase mutation occurs on the boundary between nucleus and cytoplasm as well as on the boundary between cytoplasm and environment medium, the equation of inflexion curve is introduced to describe the size, morphology, and substructure of the nuclear cell based on the analysis of the phase features of the model. Furthermore, a mononuclear cell model is discussed as an example to verify this method. The simulation result shows that characterization with inflexion curve based on orthogonal phase images could describe the substructure of the cells availably, which may provide a new way to identify the typical biological cells quickly without scanning.