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We study the thermal light correlated interference using a He-Ne laser beam with intensities modulated by mathematical functions. Three mathematical functions are adopted: a power function f [I(x)] = I n(x); an exponential function f [I(x)] = exp[ pI(x)]; and an inverse trigonometric function f [I(x)] = tan-1[qI(x)]. Our results show that these correlation methods influence the contrast of correlated interference fringes, but not the periods of the fringes, which just depend on the relation of correlated spatial coordinates. [ABSTRACT FROM AUTHOR]

We report a theoretical study about length measurement with polychromatic vortex beam in Mach-Zehnder (MZ) interferometer. The interference results show gear shapes as orbital angular momentum interference. According to the gear shape, we can predict the length difference explicitly. Our results suggest implicit measurement can be achieved with this method. [ABSTRACT FROM AUTHOR]

We report a theoretical study about length measurement with polychromatic vortex beam in Mach-Zehnder (MZ) interferometer. The interference results show gear shapes as orbital angular momentum interference. According to the gear shape, we can predict the length difference explicitly. Our results suggest implicit measurement can be achieved with this method. [ABSTRACT FROM AUTHOR]