As the use of Digital Micro Mirror Devices (DMDs) becomes more prevalent in optics research, the ability to precisely locate the Fourier “footprint” of an image beam at the Fourier plane becomes a pressing need. In this approach, Bayesian adaptive exploration techniques were employed to characterize the size and position of the beam on a DMD located at the Fourier plane. It couples a Bayesian inference engine with an inquiry engine to implement the search. The inquiry engine explores the DMD by engaging mirrors and recording light intensity values based on the maximization of the expected information gain. Using the data collected from this exploration, the Bayesian inference engine updates the posterior probability describing the beam’s characteristics. The process is iterated until the beam is located to within the desired precision. This methodology not only locates the center and radius of the beam with remarkable precision but accomplishes the task in far less time than a brute force search. The employed approach has applications to system alignment for both Fourier processing and coded aperture design.
A combustion synthesis methodology for the preparation of perovskite Li3xLa1/3‐xTaO3 lithium‐ion conductors with x = 0.033 is presented. Bulk ceramic specimens were sintered under combinations of burial powder and cover crucibles to provide different lithium vapor overpressure conditions. A maximum total lithium ion conductivity of 6 × 10‐6 S cm‐1 at room temperature was found for the pellet covered by a crucible whose lip was sealed using parent powder (moderate overpressure), with agreement to the maximum in the intergranular ion conductivity. Intragranular conductivity was maximized at the low overpressure condition. The trend in ion conductivity was found to correspond to the lithium content in the samples through a combination nuclear reaction analysis and energy dispersive X‐ray spectroscopy phase constitution measurements. The mechanism impacting ion conductivity was determined to be changes in the amount of LaTaO4 secondary phase as driven by the processing conditions during sintering.
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