A new Integral Transform was introduced in this paper. Fundamental properties of this transform were derived and presented such as the convolution identity, and step Heaviside function. It is proven and tested to solve some basic linear-differential equations and had succesfully solved the Abel's Generalized equation and derived the Volterra Integral Equation of the second kind by means of Initial Value Problem. The Natural Logarithm (e.g log ln e xx ) has been established and defined by means of modifying the Euler Definite Integral based on the Rangaig's fomulation. Hence, this transform may solve some different kind of integral and differential equations and it competes with other known transforms like Laplace, Sumudu and Elzaki Transform.
A method for automated evaluation of fringe localization using focus measure is demonstrated experimentally. Dual-illumination digital holographic interferometry is used to generate phase difference maps (PDMs) of a rough test object. Focus measure values of the PDMs along the axial direction (increment: 10λ=6.33 μm) yield an inverted bell-shaped curve which, in turn, facilitates the characterizations of the plane and region of fringe localization. The method can be applied in the distance measurement of rough objects and in the optimization of fringe visibility.
This paper proposed an automated technique for vibration detection using statistical focus measure to evaluate interferogram contrast. An interferogram sequence from a Mach-Zehnder interferometer setup is recorded (frame rate: 24 fps) and the gray-level variance (GLVA) is plotted versus time. Occurrence of induced vibration in the setup causes a decrease in the interferogram contrast which, in turn, manifests as an evident rapid drop in the variance plot. The technique is demonstrated experimentally using periodic microvibrations (frequency range, ≤6 Hz) and aperiodic disturbances.
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