The underpinning concept behind coherent diffractive imaging (CDI) is that diffraction is predictable. Brilliant physicists with names that begin with F, such as Fraunhofer, Fresnel, and Fourier have given us incredibly detailed equations to describe how light behaves after interacting with objects.[1] Specifically, we know that far-field diffraction patterns are Fourier transforms of the objects that cause them. If you know the object, you can calculate diffraction pattern, and vice versa.
Each point in the object and the diffraction pattern has an amplitude and a phase. In the diffraction pattern, this is pretty straightforward—the photons are hitting the detector with a certain amplitude and phase. In the object, however, this can be a bit confusing. How can a physical object have an amplitude and phase? But think about the light immediately after it passes through the object, before it’s had a chance to form any kind of diffraction pattern. That cross section of light is known as the ''exit wave'', and it definitely has an amplitude and phase. The amplitude is whatever wasn’t absorbed by the object, and the phase is whatever delay the light incurred as it passed through the object. In other words, the amplitude and phase of the exit wave are the absorptivity and refractivity of the object—exactly the information we’re hoping to image.
Coherent diffractive imaging is the process of reconstructing the exit wave (object) based on the diffraction pattern. This would be pretty simple if we had the amplitude and phase of the diffraction pattern, but unfortunately light is really quick[citation needed], and even the best detectors simply can't take data fast enough to measure differences in phase. This leaves us with just the amplitude, which isn't enough to reconstruct the object without some kind of phase retrieval process.