ABSTRACT
In this work, we present a new approach to retrieve the optical phase map of an object which is projected by a single differentiated two-beam interference pattern. This approach is based on the differentiation of the intensity equation of the two-beam interference with respect to the carrier's phase angle. Therefore, two interference patterns which are shifted by a very small phase angle can be obtained. Then, these two patterns are projected on the object. By exploiting the definition of the mathematical differentiation, the optical phase object's variations are retrieved from the recorded intensity distributions of both projected patterns. According to this method, the extracted optical phase angles are raised as an inverse "sin" function. This means that the unwrapping process of this function limits the recovered phase angles between - π/2 and π/2. So, the unwrapping process of these unusual wrapped phase angles is explained. The proposed method is applied on (a) two objects which are simulated by combinations of multiple Gaussian functions and (b) a 3D real object. It is found that the inclination of the projected interference pattern on the object redistributes the intensity distribution due to the Lamber's "cos" aw of illumination. This effect is considered in the retrieving process of the object's phase map. The limitations of the presented method are discussed and the obtained results are found promising.
ABSTRACT
We have investigated the morphologies of Langmuir layers of charged, polymeric hard-core/interlayer/soft-shell nanoparticles spread at the air-water interface. Depending on various mutual interactions, which are correlated to the areal densities of the deposited nanoparticles, we observed ordered patterns of nondense and closed-packed arrangements of core/interlayer/shell (CIS) nanoparticle ordering. At low areal densities, we found an almost regular distribution of the charged CIS nanoparticles on the water surface, which resulted from long-range repulsive electrostatic interactions between them. At higher areal densities, domains of more closely packed and ordered nanoparticles were formed, coexisting with regions of randomly and sparsely distributed nanoparticles. We relate these domains to the interplay of electrostatic repulsion and capillary attraction caused by the dipolar character of like-charged particles at the interface, allowing for a characteristic separation distance between nanoparticles of about 3-4 times the nanoparticle diameter. At relatively high areal densities, attractive van der Waals forces were finally capable of making nanoparticles to come in contact with each other, leading to densely packed patches of hexagonally ordered nanoparticles coexisting with regions of rather well-ordered nanoparticles separated by about 1 µm and regions of randomly and sparsely distributed nanoparticles. Intriguingly, upon re-expansion of the area available per nanoparticle, these densely packed patches disappeared, indicating that steric repulsion due to the presence of soft shells as well as long-range electrostatic repulsive forces were strong enough to assure reversibility of the morphological behavior.
