In this paper we present a polarization based technique for optical sectioning and imaging of multi-layer cell patterns separated by a weakly diffused media. Multi-layer cell pattern is important to study because this type of structure is often used for heterogeneous three dimensional cell culture and bio-chips applications, where information at different depths would be crucial. Functioning of this type of bi-layer or multilayer cell patterns can easily be monitored using polarization based imaging techniques. For polarization based imaging, samples are excited by white light source with different set of band-pass filter and linear polarizer, and images are collected through corresponding long-pass filters and analyzer by CCD camera. Preliminary experiments are carried out using absorption inhomogeneity separated by a weakly diffused thin polymer layers. Polarized images at various angles are collected at a set of excitation wavelength. Such measurements can identify 3x3 sub-matrix elements out of the full 4x4 sixteen elements of Mueller matrix. In order to enhance the image contrast, the 3x3 Mueller components are further decomposed into diattenuation and depolarization power images. Superficial layer image information is found to be more prominent in the depolarization power images, and diattenuation images provide sub layer information. By comparing the decomposition images at various wavelengths, we can observe sub-layer structures at different depths.
The frequency responses of eight apodized systems with circular aperture have been investigated . The apodization has been done by dividing the aperture into two and three rings of different areas either by using a 7r-phase distribution or by amplitude transmittance variations in the different rings . It is found that the response of the system can be improved in any desired range of frequencies by selecting its special form, its obstruction ratios and transmittances in the different rings, as the case may be . IntroductionThe diffraction pattern produced by an optical system consists of a central part and a number of side maxima . The central part determines the principal performance of the system, particularly its ability to resolve two equally bright object points. In general, the relative intensities of the side maxima are such as to decrease the resolution in the case of observation of very high contrast details . In spectroscopy and microscopy applications, the side maxima are not desirable. So, the process known as apodization has been investigated by several authors [1,2] . Apodization involves the suppression of the side maxima of the diffraction pattern . This process has a side effect of enlarging the central part of the pattern, i .e . decreasing the resolution of the system for point objects of equal brightness. Thus this process of apodization does not improve simultaneously all the imaging properties of an optical system . Jacquinot and Roizen-Dossier [2] have considered in detail the general properties of the pupil with non-uniform transmission . They have paid little attention to filters having various phase changes in the different parts . However, compared with the usual filters having non-uniform transmission, the filter with a 7r-phase change does not cause any loss of light and has a high capability of changing the diffraction pattern . In addition, the preparation of phase filters is made relatively easy by the use of the vacuum evaporation technique . Tsujiuchi [1] investigated the use of phase filters with the retardation of 7r-phase for the compensation of aberrations and for the improvement of the image . Thompson [3] proposed the use of a semi-transparent and a-phase annular filter for improving the resolving power (for two point objects of equal brightness) and focal depth of optical instruments .The calculation of the optical transfer function (OTF) is now used extensively [4, 5] as a means of assessing and predicting the image quality of optical systems . In this paper we have studied the OTF of aberration-free apodized systems, viz .(1) 7r-phase systems, (2) ring-shaped 7r-phase systems, (3) semi-transparent systems and (4) ring-shaped semi-transparent systems . The shape of the apertures are considered to be circular in all cases .
The far field diffraction by generalized annular apertures of light waves rendered partially coherent due to atmospheric turbulence has been examined theoretically. The phase structure function generated by the atmospheric turbulence has been assumed to obey the square law which leads to Gaussian type correlation function. The expressions are worked out for the field irradiance and central irradiance distributions. The two point resolution according to Sparrow-criterion has been also worked out. The field irradiance and the central irradiance distributions, and the two point resolution have been presented and discussed as functions of transmittance and phase variations in the two parts of the aperture, size of the central part of the aperture and degree of coherence etc.
Supersymmetric vacua are stable. It is interesting to ask: how long-lived are vacua which are nearly supersymmetric? This question is relevant if our universe is approximately supersymmetric. It is also of importance for a number of issues of the physics of the landscape and eternal inflation. In this note, we distinguish a variety of cases. In all of them the decay is slow. For a flat space theory decaying to a deep AdS vacuum, the leading behavior of the decay amplitude, if a thin wall approximation is valid, is A = γe −2π 2 /(Re m 3/2 ) 2 (where the phase of m 3/2 is defined in the text) for Re m 3/2 > 0, and zero otherwise. Metastable supersymmetry breaking generally yields parametrically more rapid decays. For nearly supersymmetric decays, we will see that it is necessary to compute subleading terms in the exponential to extraordinarily high accuracy before one can meaningfully discuss the prefactor.
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