Three-dimensional imaging from single-element holographic data

We present a holographic imaging approach for the case in which a single source-detector pair is used to scan a sample. The source-detector pair collects intensity-only data at different frequencies and positions. By using an appropriate illumination strategy, we recover field cross correlations over different frequencies for each scan location. The problem is that these field cross correlations are asynchronized, so they have to be aligned first in order to image coherently. This is the main result of the paper: a simple algorithm to synchronize field cross correlations at different locations. Thus, one can recover full field data up to a global phase that is common to all scan locations. The recovered data are, then, coherent over space and frequency so they can be used to form high-resolution three-dimensional images. Imaging with intensity-only data is therefore as good as coherent imaging with full data. In addition, we use an `-norm minimization algorithm that promotes the low dimensional structure of the images, allowing for deep high-resolution imaging.