Applications Of Vortex Filtering To Edge Enhancement

The spatial filtering operations can be used for optical field imaging transformation and processing. The Hilbert transform widely used in signal processing also has been developed into the spatial filtering system for imaging processing to achieve for one-dimensional edge enhancement of objects. In recent years, the radial Hilbert transform (RHT) of objects can be implemented by introducing an optical vortex on the spatial frequency spectrum of input field, which permits two-dimensional isotropic edge enhancement of arbitrarily shaped objects. Therefore, this vortex filtering operation has been widely employed in image processing, phase contrast microscopy and astronomy, and other fields.From the viewpoint of the spatial distribution of polarization, light beams can be classified into scalar or vector beams:the scalar beams have a spatially homogeneous states of polarization, while the vector beams own a spatially variant states of polarization. In general, the optical vortex means a special optical field has a helical-shaped wavefront with a phase singularity, which isn’t associated with the polarization distribution of the optical field, so it is called scalar optical vortex; In recent years, The study of an optical field with spiral Pancharatnam geometric phase reveals it is also a kind of optical vortex, but the geometric phase is associated with the polarization spatially inhomogeneous distribution of the optical field, so it is called vectorial optical vortex. Both the two optical vortices are the solutions of the wave equation under the paraxial approximation, in this paper, we introduced some typical optical systems and optical components to generate them and analyzed the advantages and disadvantages of each method.Base on the special structure of optical vortex, we studied the scalar and vectorial vortex filtering in the application of edge enhancement under some conditions. We started from the point spread function (PSF) of the spatial filtering system, and analyzed the physical process that the vortex filtering with integer topological charge(TC) could inhibit the non-edge information of input field and obtain edge enhanced image, then we conducted several computer numerical simulations and laboratory experiments to verify the performance of vortex filtering in different situations:For scalar vortex filtering, the PSF of the system is essentially an interference between a vortex beam with integer TC and a non-vortex beam. While the more concentrated energy of the vortex term and the smaller intensity of the non-vortex term, we could obtain a better isotropic edge enhancement of the input field. Therefore, vortex singularity on-axis filtering with TC=1 is usually used to implement isotropic edge enhancement imaging processing, and the TC=2 vortex filtering forms an eclipses-like effect can be applied to suppress strong background light; we can also modulate the non-vortex term by changing the vortex filter’s position and orientation or using fractional TC vortex filter to obtain an anisotropic selective edge enhancement.For vectorial vortex filtering, it has a similar physical process with scalar vortex filtering, we also using the vortex singularity on-axis filtering with TC=1 to implement isotropic edge enhancement imaging processing. And it is different from scalar vortex filtering that we can get part information of the output field as a selective edge enhancement by exerting a polarization analyzer before the output plane. Since the non-vortex term of the PSF of vectorial vortex filtering caused by the filter’s position deviation or the non-monochromatic incident light is linear polarized, and its polarization direction is determined by the polarization direction of the incident field and the position of filter. So we can filter out the linear polarized non-vortex term by the analyzer and get a selective edge enhancement of the input field which results from the vectorial vortex term with integer TC. We can use this property to correct the position of the filter, also we can achieve an isotropic non-monochromatic edge enhancement by combining two selective edge enhancement results from different polarized incident field. Thus, the vectorial vortex filtering has a good application prospect in the selective edge enhancement and achromatic edge enhancement.