| Fractional Hankel Transform is based on Fractional FourierTransform, and there is a close relationship between them. Being akind of independent transform, Fractional Hankel Transform plays animportant role in the application of circular symmetry, and it alsosupplement and complete the Fractional Fourier Transform. Underthe condition of rotational symmetry, consulting the definition ofFractional Fourier Transform given by Lohmann, it gives theexplanation of optical fractional hankel transformation. And it wasapplied to the Fresnel Zone Plate optical system, and mainlydescribes the procession of the light source passes through theZone Plate imaging. If the input function with rotational symmetry,through the discussion and its diffraction integral formula, with thedifferent Fresnel zone plate of fractional hankel transform, thecorresponding output function is also a rotational symmetry. If thefaces of input and output for system is symmetrical, and only in acertain plane can observe the input complex amplitude of FractionalHankel Transform.Being based on the theory of Fourier Transform andFractional Fourier Transform, and under the fully studing of a circularsymmetry, the basic theory of Hankel Transform and Fractional Hankel Transform, mainly includes the definition of their basicproperties, optical implementation, etc, also expounds the conceptand the classification of the zone plate, and applys the Opticalimplementation of different zone plate to the domain of FractionalHankel. By means of Fractional Hankel Transform,it relativelydetailed describes the light field distribution, the spectrum imagingcharacteristics, the composition, and the light intensity after thediffraction of different types of zone plate. It is compared with thoseof the thin lens imaging, provides the further assistance for theapplication of the research zone plate and the conclusion is verifiedby computer simulation. |
