The display of an Airy function via an optical image processing technique is demonstrated. Using a two-dimensional object with a cubic amplitude transmittance, one can observe a Fourier transformed image of which intensity variation is identical to that of the Airy function. A lens system is used to achieve the Fourier transformation of the object which is a two-dimensional binary filter. A set of computer simulations are performed prior to the optical experiments. Using the same method of optical display, the transient wave propagation in a dispersive medium is optically displayed based on the analogous relationship found between two equations: One is the Fourier form of a transient wave field propagating in a dispersive medium and the other is an equation of the diffraction pattern of an object constructed with two juxtaposed two-dimensional filters. A theoretical analysis is provided along with computer simulations. The use of a Spatial Light Modulator is proposed as the source of the input object in the optical experiment. / Master of Science