Background

In scattering, background refers to the unwanted scattering that arises from sources other than the sample of interest. It thus underlies the signal of interest, decreasing the signal-to-noise ratio, and making analysis more complicated.

Sources

• Detector: Every detector has some background signal. The detector background may also have multiple components: a component that is present in every exposure (e.g. readout noise), as well as a component that scales with the exposure time (e.g. dark current). Detectors may also exhibit signal arises from other sources: e.g. cosmic rays, or even ambient light.

Subtraction

Full background subtraction

In order to remove the effect of the background, the simplest solution is to simply measure it, and subtract it from the experimental data. However, there are a few issues to consider:

• Exposure time: Most of the sources of background scale with exposure time. So a valid subtraction will require using the same exposure time for the background and sample measurements. In principle, one can do a more general background subtraction by rescaling the background and sample measurements by the exposure time; however if the detector has readout noise (which doesn't scale with exposure time), then this procedure is not valid. In such a case, one should get a separate measure of the readout noise, and first subtract this from both images.

$I_{\mathrm {true} }={\frac {(I_{\mathrm {sample} }-I_{\mathrm {readout} })/t_{\mathrm {sample} }}{(I_{\mathrm {background} }-I_{\mathrm {readout} })/t_{\mathrm {background} }}}$

• Flux: In fact, the exposure time is not the metric that matters: the total photon flux (over the course of the exposure) is what matters. I.e.: since a real-world x-ray beam does not have perfectly stable flux, it is better to normalize by the total photon flux during an exposure, rather than the total measurement time. This can be done if the beamline/instrument has a direct-beam monitor. (On some instruments, this is a non-blocking detector upstream of the sample; on others, the beamstop itself may be a photo-diode.)

$I_{\mathrm {true} }={\frac {(I_{\mathrm {sample} }-I_{\mathrm {readout} })/\int \mathrm {flux} _{\mathrm {sample} }\mathrm {d} t}{(I_{\mathrm {background} }-I_{\mathrm {readout} })/\int \mathrm {flux} _{\mathrm {background} }\mathrm {d} t}}$