The quest of X-ray astronomy is to be able to detect a weak source against a fairly strong background. Principally because of the relative weakness of the sources, integrating detectors (such as film) have not found a place in cosmic X-ray astronomy. Source detection is done on a photon-by-photon basis. A flux of one photon per square centimeter per second (in the 1-10 keV range) observed at Earth constitutes a bright cosmic X-ray source!
X-rays, just like any other kind of light, can be thought of as either electromagnetic waves or as massless particles. Both ways are right -- this is known as duality. The way we use to think about X-rays in a given context is the way that makes the problem the easiest. Thus, when we talk about optics or dispersive spectrometers we will talk about waves, because in these cases we need so see how the waves will interact with surfaces and interfaces, and how they will combine and interfere with each other. When we speak of non-dispersive spectrometers, however, it makes sense to talk about particles of light, called photons.
So how do we measure the energy of an X-ray photon? We need the X-ray to give all its energy to some kind of detector. That energy will change something in the detector and, by measuring that change, we can determine the energy of the incident X-ray. X-rays interact strongly with electrons. You may know that lead is good at blocking X-rays. Well, that's because each lead atom has 82 electrons and lead is a metal, so the atoms are packed together pretty close. Lead stops X-rays because it has a large electron density.
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