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The employment of new mathematical and computer approaches for the fusion of target images from the visible and infrared channels of the sightseeing system (SSS) is one of the ways to increase the efficiency of the SSS of armored vehicles. Modern approaches to improving the efficiency of image fusion are aimed to increase the visibility of the target via improving the quality indices of fused images. This paper proposes a fundamentally new approach to image fusion, namely dynamic image fusion, at which the target is observed in the mode of a video clip composed of a sequence of stationary fused images obtained at different parameters of fusion, in contrast to traditional stationary image fusion, at which the decision is made from one fused image. Unlike stationary image fusion, aimed to increase the visibility of the target, the dynamic image fusion allows one to enhance the conspicuity of the target. The principle of dynamic image fusion proposed in this paper is based on matrix formalism, in which the fused image is constructed in the form of a complex vector function, which by its mathematical form is analogous to the Jones vector of elliptically polarized light wave, which in turn opens the possibility of matrix transformation of the complex vector of the fused image and consequently its parameterization by analogy with the Jones matrix formalism for the light wave. The article presents mathematical principles of matrix formalism, which is the basis for dynamic image fusion, gives examples of stationary and dynamic image fusion by the method of complex vector function and compares with the corresponding images, fused by algorithms of weight addition in the field of real and complex scalars. It is shown that by selecting weight coefficients, the general form of a complex amplitude vector image can be reduced to the algorithms of weight and averaged addition in the field of real scalars, weight amplitude and RMS-image in the field of complex scalar numbers, and geometric-mean image in the field of complex vectors, which, thereby, are partial cases of the general form of the complex amplitude image in the field of complex vectors. The animated images obtained by the method of complex vector function illustrate the increase of conspicuity of the object of observation due to the dynamic change of the fusion parameters.

In spite of significant advances in diagnosis of prostate cancer (PCa), the detection and differential diagnosis of metastatic lymph node involvement remains an important clinical dilemma in a large number of cases. Contrast-enhanced abdominal computed tomography and magnetic resonance imaging (MRI), in part when using T1-weighed images (T1-WI and T2-WI), allow evaluating indirectly the presence of invasion in regional lymph nodes by assessing their diameter and morphology. Nonetheless, these techniques do not appear to be sufficiently sensitive for direct identification of lymph nodes with metastatic lesions.To study the significance of the apparent diffusion coefficient (ADC) of diffusion-weighted MRI in detection of metastatic lymph node involvement in PCa patients.The study involved 35 patients with histologically verified PCa. Based on multiparametric prostatic MRI findings and pathomorphological reports, we have performed ADC measurements for pelvic lymph nodes either with (n = 15, mean size 1.78 ± 0.59 cm) or without metastases (n = 20, mean size: 0.94 ± 0.06 cm) in PCa patients who underwent radical prostatectomy with lymph node dissection.No significant diffe-rences were observed when comparing mean sizes of N+ and N- pelvic lymph nodes. At the same time, when comparing mean ADC values for N+ and N- pelvic lymph nodes, we observed a statistically significant difference: 0.74 ± 0.09 · 10-3 mm2/s in metastatic lymph node vs 1.05 ± 0.23 · 10-3 mm2/s in lymph nodes without metastatic involvement (p 0.001).The use of ADC for diffusion-weighted MRI may provide valuable information for detection of metastatic lymph node involvement in patients with PCa.

We demonstrate that the phase diagram of a Lyotropic Chromonic Liquid Crystal (LCLC) is affected by ultraviolet (UV) light irradiation. UV-irradiation induces a phase transition from the nematic (N) to isotropic (I) state at a fixed temperature. Birefringence measured in-situ decreases under irradiation, until the moment when the isotropic phase starts to nucleate and the initial homogeneous nematic transforms into a biphasic state. On further irradiation the birefringence of the N fraction of the biphasic I-N state increases revealing redistribution of the composition components between the two coexisting phases. The efficiency of the irradiation-induced changes depends on the orientation of the chromonic aggregates w.r.t. the polarization of UV light. Changes of the birefringence are noticeably higher for light polarization perpendicular to the nematic director. The effect can be understood as a photo-induced weakening of the face-to-face molecular attraction within the chromonic aggregates and the resulting shortening of these aggregates.

Traditionally, optical spatial dispersion (OSD) is defined as the dependence $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\varepsilon}}(\stackrel{P\vec}{k})$ of the dielectric permittivity tensor $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\varepsilon}}$ on the light wave vector $\stackrel{P\vec}{k}$, similarly to the frequency ($\ensuremath{\omega}$) dispersion of the dielectric tensor $\ensuremath{\varepsilon}(\ensuremath{\omega})$. We have developed an approach for the description of the OSD phenomena in the framework of Jones calculus. In Jones calculus the differential Jones matrix (DJM) $N$ is the generalization of the light wave-vector $\stackrel{P\vec}{k}$ in the same sense that $\stackrel{P\vec}{k}$ is the generalization of the light wave number $k$. The latter inspires us to expect that there must exist a way to describe the OSD phenomena in terms of the DJM. We show that such a relation between the OSD phenomena and Jones calculus indeed exists. To prove the latter we derive a general relation between the DJM and components of the dielectric permittivity tensor $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\varepsilon}}$. We establish the relation of the DJM approach, proposed in this paper, to the traditional OSD approach of the gyration pseudotensor as well as to that developed by Mauguin for light propagation in cholesteric liquid crystals [M. C. Mauguin, Bull. Soc. Fr. Mineral. Crystallogr. N3, 71 (1911)]. We demonstrate that both the gyration pseudotensor and Mauguin's approach can be derived as particular cases of the proposed DJM approach. In our approach the integral Jones matrix (IJM) of the medium taking into account OSD is the product of the IJM without taking into account OSD by the correction IJM, which accounts for the OSD effects. In a general case, when all components of the OSD DJM ${N}^{D}$ are nonzero, the secular equation for the refractive indices of the eigenwaves is a quartic equation. The coefficient ${a}_{3}$ at the cubic term in the secular equation is nonzero only for nonzero OSD corrections to the average refractive index. For transparent crystals at nonzero OSD correction to the average refractive index and zero to all other correction parameters in ${N}^{D}$, the secular equation has two distinct real and two complex-conjugate roots. We assign the complex-conjugate roots to the forward and backward light scattering. Therefore, taking into account the OSD effect on the refractive index, the Jones calculus becomes capable of describing light scattering. The proposed Jones calculus approach is a general tool for taking into account OSD in optically inhomogeneous media, in which several or all OSD correction parameters are simultaneously nonzero, for example, in liquid-crystal cells with a spatially nonuniform director field, including those containing defects.

A complex function is proposed as a template for the fusion of visual and infrared images such that one of the partial images is chosen as the real part and the other one as the imaginary part of the complex function. The amplitude and the phase of the complex function are two generic algorithms for the synthesis of the amplitude and phase images. Several no–reference quality indices are measured for fused amplitude and phase images and compared to those obtained for the partial images and the images fused with the average fusion, Laplace pyramid transform, and modified discrete wavelet transform methods for four observation scenes.

Optically pumped light emissions in imperfectly aligned dye-doped cholesteric cells with glance and frosted glass substrates of three different cell gap thicknesses are experimentally studied. Alignment imperfections show up in emission spectra by a broadening of the photonic bandgap (PhBG) lasing (allowed) lines at short- and long-wavelength PhBG edges and by an additional (forbidden) emission line inside the PhBG. Forbidden and allowed lines differ distinctively by their stability in the course of pumping. The origin of the forbidden line is discussed.

The 2×2 ray tracing matrix (RTM) method is employed for the description of optical aberrations caused by the refractive index mismatch (RIM) in fluorescent confocal polarization microscopy. We predict and experimentally confirm that due to the RIM a liquid crystal layer with highly non-uniform director distribution appears to be imaged as a layer with non-uniform thickness, which shows up in the roughness of the rear surface. For the off-axial focusing of the probing beam in a droplet dispersed in an immiscible liquid, we have developed an extended method still keeping the 2×2 dimensionality of the RTM.

We describe a compact point laser source based on dye-doped cholesteric encapsulated in a flexible polymer film. Optically pumped emission spectra...