Fast method of computing Fresnel diffraction patterns

We propose a fast algorithm for calculating a Fresnel diffraction pattern. A technique for generating a diffraction pattern will be useful for constructing a holographic digital data storage system without lenses, which make the optical detection unit heavier. However, it usually takes a long time to compute the diffraction pattern from the data that we want to record. Therefore, a fast calculation technique is an important step toward making the system practical. The Fresnel diffraction pattern can be generated using the Fourier transform, because the pattern is produced using a convolution integral of data with the light propagation function. However, if we use the fast Fourier transform, which is a kind of a discrete Fourier transform used in order to reduce the computational complexity, instead of the Fourier transform, many errors will probably occur in the reconstructed data. This is because the diffraction pattern generated using the fast Fourier transform is a huge pattern consisting of many repetitions of a smaller element, but in practical use only one of the small elements is used, so the reconstructed data is different from the source data. In this case, a brightest image, which is not exactly the same as the source data, appears directly below the pattern, and weak reconstructed images appear around it. To solve this problem, the proposed algorithm generates a diffraction pattern in which the image directly below the pattern is made as equal as possible to the source data by using a signal processing technique. In this report, we first describe our algorithm and present simulation results. Then we discuss its effect.