STABILITY AND ERROR OF THE NEW NUMERICAL SOLUTION OF FRACTIONAL RIESZ SPACE TELEGRAPH EQUATION WITH TIME DELAY

In this paper, we propose a numerical method for Riesz space fractional telegraph equation with time delay. The Riesz fractional telegraph equation is approximated with the interpolating polynomial P2. First a system of fractional differential equations are obtained from the telegraph equation with respect to the time variable. Then our numerical algorithm is proposed. The convergence order and stability of the fractional order algorithms are proved. Finally, some numerical examples are constructed to describe the usefulness and profitability of the numerical method. Numerical results show that the accuracy of order O(t3)

Encoding multiple holograms for speckle-noise reduction in optical display.

In digital holography (DH) a mixture of speckle and incoherent additive noise, which appears in numerical as well as in optical reconstruction, typically degrades the information of the object wavefront. Several methods have been proposed in order to suppress the noise contributions during recording or even during the reconstruction steps. Many of them are based on the incoherent combination of multiple holographic reconstructions achieving remarkable improvement, but only in the numerical reconstruction i.e. visualization on a pc monitor. So far, it has not been shown the direct synthesis of a digital hologram which provides the denoised optical reconstruction. Here, we propose a new effective method for encoding in a single complex wavefront the contribution of multiple incoherent reconstructions, thus allowing to obtain a single synthetic digital hologram that show significant speckle-reduction when optically projected by a Spatial Light Modulator (SLM)

Single-shot color digital holography based on the fractional Talbot effect

We present a method for recording on-axis color digital holograms in a single shot. Our system performs parallel phase-shifting interferometry by using the fractional Talbot effect for every chromatic channel simultaneously. A two-dimensional binary amplitude grating is used to generate Talbot periodic phase distributions in the reference beam. The interference patterns corresponding to the three chromatic channels are captured at once at different axial distances. In this scheme, one-shot recording and digital reconstruction allow for real-time measurement. Computer simulations and experimental results confirm the validity of our method

Single-shot digital holography by use of the fractional Talbot effect

We present a method for recording in-line single-shot digital holograms based on the fractional Talbot effect. In our system, an image sensor records the interference between the light field scattered by the object and a properly codified parallel reference beam. A simple binary two-dimensional periodic grating is used to codify the reference beam generating a periodic three-step phase distribution over the sensor plane by fractional Talbot effect. This provides a method to perform single-shot phase-shifting interferometry at frame rates only limited by the sensor capabilities. Our technique is well adapted for dynamic wavefront sensing applications. Images of the object are digitally reconstructed from the digital hologram. Both computer simulations and experimental results are presente

Detection of Calcium-induced morphological changes on RBCs by digital holographic microscopy and blinking optical tweezers

Ca+2 level in the circulating red blood cells (RBCs) takes part not only in controlling biophysical properties, but also affects the membrane composition, and its morphological and rheological properties. Excessive accumulation of Ca2+ within the cells is associated with a number of important pathological diseases. In this paper, by the use of digital holographic microscopy (DHM), we quantitatively analyzed the volumetric behavior of RBC membrane under influence of excess Calcium ions. DHM in a transmission mode is an effective tool for quantitative visualization of phase objects. By deriving the associated phase changes 3D information on the morphology variation of the cells at arbitrary time scales is obtained. Individual cells are immobilized by the use of optical tweezers and are monitored live with DHM system, while the concentration of Ca2+ ions in the buffer is changed simultaneously. We utilized blinking optical tweezers, by inserting an optical chopper to modulate intensity of the trapping laser beam. Blinking optical tweezers, while keeping the cell trapped during the experiments, ensures of minimizing the photo-damage of trapping laser beam on the cell. Our experimental results are in agreement with previous biological studies and predictions, and experimental observations of living RBCs under Ca2+ influence. © 2016 IEEE

Microsphere-assisted super-resolved Mirau digital holographic microscopy for cell identification

In this paper, we use a glass microsphere incorporated into a digital holographic microscope to increase the effective resolution of the system, aiming at precise cell identification. A Mirau interferometric objective is employed in the experiments, which can be used for a common-path digital holographic microscopy (DHMicroscopy) arrangement. High-magnification Mirau objectives are expensive and suffer from low working distances, yet the commonly used low-magnification Mirau objectives do not have high lateral resolutions. We show that by placing a glass microsphere within the working distance of a low-magnification Mirau objective, its effective numerical aperture can be increased, leading to super-resolved three-dimensional images. The improvement in the lateral resolution depends on the size and vertical position of microsphere, and by varying these parameters, the lateral resolution and magnification may be adjusted. We used the information from the super-resolution DHMicroscopy to identify thalassemia minor red blood cells (tRBCs). Identification is done by comparing the volumetric measurements with those of healthy RBCs. Our results show that microsphere-assisted super-resolved Mirau DHMicroscopy, being common path and off-axis in nature, has the potential to serve as a benchtop device for cell identification and biomedical measurements. © 2017 Optical Society of America