Light Diffraction by Fractals: Comparison of Experimental Data With the Obtained by Numerical Methods Fourier Images of the Object Pictures

Abstract

Abstract. An experimental investigation of diffraction of the collimated light beam (with a wavelength of 0.63 µm) in the zone of Fraunhofer by obtained with computer images of fractals, which are transferred onto a transparent film using an imagesetter with a resolution of 1333 points/cm (3386 dpi) and the spot size of 7.5 µm. Diffraction pattern were visually observed on the screen and recorded using a digital camera and then transferred to the computer for processing. The objects of study were various prefractals of 4th-9th generations: the "classic" (the Sierpinski carpet, a fractal of Vicsek, the Koch snowflake and less known (eg. of L-systems). Observed in experiments diffraction patterns were compared with digitally obtained ones that is, with the Fourier-images of the prefractal pictures, approximated by a mesh function on a uniform square grid at different values of the used in cflculation parameter p, determining the ratio between the ratio of the grid period and the smallest prefractal element size. The relation between the values of the parameters p and the degree of compliance of a digital diffraction patterns to the observed experimentally was determined.

Modified Sierpinsky Carpet

“…The image of the diffraction pattern on the screen in the diffraction plane was recorded using a digital camera. More detailed methods and features of the described experiments are described in [3].…”

“…For the image digitized in this way, the fast Fourier transform was used to determine the values of the quadrate of the Fourier component modules, i.e., the spectral distribution of the intensity of diffracted radiation in the Fraunhofer zone. To display the intensity of diffraction maxima on the plane, circles with a radius proportional to the intensity (or intensity logarithm) were used [3].…”