First FOM App online
Take a picture with your smart phone and have its Fourier transform calculated, and vice versa. A new App, developed by FOM Institute AMOLF director Albert Polman, PhD student Ernst Jan Vesseur and INFI Inc. is now available online.
The tool is meant for master students and PhD students that are learning about Fourier transform in research areas such as nanophotonics, photovoltaics, and any other field of physics that involves transforms between time and frequency or between space and spatial frequency.
Fourier transform is a well known mathematical concept that is used in many aspects of physics research. For example, a Fourier transform converts a measurement of a sound wave to its frequency spectrum, or it converts an image in real space to a distribution of spatial frequencies that represent the image (reciprocal space).
As humans, we are used to hearing and seeing, hence 'measuring' sound as a function of time and observing space in spatial coordinates. Many physical phenomena, however, are best analyzed or understood in the inverse domain, i.e. terms of temporal or spatial frequencies. Vice versa, many physical measurements, such as e.g. diffraction, create data in reciprocal space, and Fourier transform is then required to create the corresponding image in real space.
The newly developed App carries out elemental Fourier transforms. It is not a research tool, but rather meant to give basic insight in Fourier transform. To operate the App, a smartphone user first takes an image with the phone’s camera. The image is then directly Fourier-transformed and the transform is shown on the phone’s screen. This gives direct insight in the distribution of (two-dimensional) spatial frequencies that together compose the image. As a second feature, using one’s finger tips at the phone’s touch screen either as a pen or an eraser, the Fourier transform can be modified at will, whereupon an inverse transform can be made. In this way additional insight is obtained in what spatial frequencies represent what part of the image.
The App is called 2D-Fourier and is available for free at the Apple App store; it runs on both iPhone and iPad. Versions for additional platforms may become available later.