We propose a double image encryption by using random binary encoding and gyrator transform. Two secret images are first regarded as the real part and imaginary part of complex function. Chaotic map is used for obtaining random binary matrix. The real part and imaginary part of complex function are exchanged under the control of random binary data. An iterative structure composed of the random binary encoding method is designed and employed for enhancing the security of encryption algorithm. The parameters in chaotic map and gyrator transform serve as the keys of this encryption scheme. Some numerical simulations have been made, to demonstrate the performance this algorithm.

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Jatropha-oil based polyurethane is one of the initiative for replacing conventional petroleum based polyurethane. The vegetable oil-based polyurethane is more cost-effective and synthesize from renewable resources. Polyurethane was synthesized through prepolymerization method between jatropha oil-based polyol and diphenylmethane 4, 4'diisocyanate, (MDI) in inert condition. Then, lithium perchloride ion (LiClO 4) was added to the polyurethane system to form electrolyte film via solution casting technique. The polymer electrolytes were prepared by varying the amount of LiClO 4 ion 10 wt.% to 30 wt. %. The highest conductivity is achieved at 25 wt.% of LiClO 4 salt content, which is 1.29 × 10 −4 S/cm at room temperature 30 °C. The FTIR results showed the shifting of carbonyl group (C O) (1750 cm −1-1730 cm −1), ether and ester group (C-O-C) (1300 cm −1-1000 cm −1) and amine functional groups (N-H) (1650 cm −1-1500 cm −1) in polyurethane electrolytes from the blank polyurethane shows that oxygen and nitrogen atom acts as electron donor in the electrolytes system. It also confirmed that the intermolecular reaction had occurred in the electrolytes system. While, the XRD analysis showed the semi-crystalline properties of polyurethane have been reduced to amorphous phase upon the increasing addition of lithium ion. SEM results revealed the morphology analysis of the polyurethane electrolytes. There is homogenous and smooth surface in polyurethane and the dissociation of salt was observed after the addition of salt indicates there was interaction between salt and the polymer host.

We demonstrate that hollow Gaussian beams can be obtained from Fourier transform of the differentials of a Gaussian beam, and thus they can be generated by spatial filtering in the Fourier domain with spatial filters that consist of binomial combinations of even-order Hermite polynomials. A typical 4f optical system and a Michelson interferometer type system are proposed to implement the proposed scheme. Numerical results have proved the validity and effectiveness of this method. Furthermore, other polynomial Gaussian beams can also be generated by using this scheme. This approach is simple and may find significant applications in generating the dark hollow beams for nanophotonic technology.

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