Abstract: Fraunhofer diffraction transforms in a simple way under a linear deformation of the shape of thetwo-dimensional aperture.Based on simple linear transformation，we derive general analytic expressions for the diffraction amplitude in the case of triangular and rhomboidal apertures of arbitrary shape at any given position in a coordinate system.Without performing integration，we solve the Fraunhofer diffraction by any polygon aperture of any shape，through purely algebraic operations.As an example，we apply the present method to find the diffraction intensity distribution for a regular hexagon aperture，and simulate it on a computer based on our analytical results.

Key words: Fraunhofer diffraction, linear transformation, triangle aperture, parallelogram aperture, regular hexagon aperture