Image Subtraction in Fourier Space

Image subtraction is essential for transient detection in time domain astronomy. The point spread function (PSF) of images from ground-based optical telescopes generally varies across the image field due to atmospheric seeing and instrumental optical distortion, and image subtraction needs to match the PSF and sensitivity variations across the entire imaging field. An algorithm that can be fully parallelized is also highly desirable for future surveys. Here we show the Saccadic Fast Fourier Transform (SFFT) algorithm for image differencing. The algorithm has been tested extensively in real astronomical data taken by a variety of telescopes. Unlike other popular methods, the proposed method does not rely on isolated stars for PSF matching, instead, SFFT can make use of all statistically valid pixels in the image for the construction of the image matching. It can also be used to co-add images by matching the PSFs and flux scales of a time sequence of images to that of a reference image, thus provide robust differential photometric measurements for time-domain surveys which are crucial for microlensing and pixel lensing observations.