Method of designing an apodizer.

Side lobes can be suppressed by means of a suitable filter across an aperture. This method is well known in optics as apodization. To obtain the desired field, we approximate it by a Gaussian field. Then it is transformed to the transmittance function of the filter. The field and the transmittance function are Fourier-transform pairs. In general, the Fourier transform of an arbitrary function extends infinitely. This means that we cannot obtain an exact transmittance function of the filter that gives the desired diffraction pattern. We discuss a transmittance function that approximates a specified diffraction pattern. We express the Fraunhofer diffraction pattern as a sum of beam-mode functions and approximate it by the first term. Then, by using the Fourier transform, we can obtain the transmittance function. The diffraction field through the truncated filter is also obtained, and the effect of truncation is discussed.