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.
• Empty cell:

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.)

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

Local background

Although a full (2D image) background subtraction works quite well for transmission-SAXS, it in general does not work for GISAXS or GIWAXS. This is because it is not possible to measure the 'empty cell' in a meaningful way. One might be tempted to do a GISAXS measurement on the bare substrate, and subtract this from the signal coming from the thin film. However, this will not work for a variety of reasons:

1. The size of the bare substrate and the sample of interest are unlikely to be exactly matched (hence the total scattering will not be identical).
2. The scattering from the substrate is modified by the presence of a sample layer on top of it: the reflection geometry modifies the intensity as well as the spatial distribution of scattering (e.g. refraction distortion). E.g. consider an extreme case where one is measuring below the critical angle of the sample film: the scattering of the substrate will be essentially absent.
3. The sample film may also attenuate the substrate scattering due to absorption (the grazing-incidence geometry means that substrate scattering must travel a long path through the film; i.e. even relatively weak absorption will measurably affect the signal).
4. The distinct dynamical scattering features of GISAXS (Yoneda streak, specular rod, reflectivity oscillations, etc.) are all influenced by the complete multi-layer stack (by the film/substrate density profile in the normal direction). Since these features are different in the background and sample measurements, a direct subtraction is not meaningful.
5. The low-q diffuse scattering is influenced by the roughness of interfaces (and scaled by the electron-density contrast across said interfaces). This is another example wherein the scattering of the substrate will be strongly modified by the presence of the sample film on top.

Thus, although one can subtract the detector and direct-beam backgrounds, one cannot hope to subtract the 'empty cell' (substrate) background; this latter background is likely to be dominant. An alternative strategy is to instead subtract a 'local background' when extracting a linecut.