GISAXS measurement time

The time required for a GISAXS measurement of course varies based on numerous factors. The most important factors are the flux of the x-ray source, and the inherent scattering power of the sample in question.

Generally, a single exposure (2D image) takes on the order of 1 s to 60 s at synchrotron beamline. The same measurement on a labscale instrument will of course take considerably longer; typically 10 minutes to a couple hours for a single exposure.

A full measurement on a single sample typically involves aligning the sample (which will take 2-5 minutes), and then exposures at a variety of incident angles. It is usually a good idea to collect data below the critical angle, near the critical angle, and above the critical angle. This multi-angle data makes eventual data interpretation easier: the sub-critical-angle data provides a measure of the structure in the near-surface region. The data above the critical angle is complementary in that it probes the entire depth of the film. Measurements near the critical angle exhibit strong intensity enhancements, which is useful for weak signals; measurements well above the critical angle yield lower scattering intensity, but the data is less complicated by refraction distortion and dynamic scattering (see also GTSAXS).

In total, sample alignment and measurement at 3-8 different incident angles will thus consume approximately 2-10 minutes on a synchrotron instrument. Full characterization of a sample may also involve collecting a reflectivity curve, which will of course increase the measurement time.

Factors affecting exposure time

The amount of time required for a single 2D exposure depends on all the same factors that affect the overall scattering intensity. Of course, it is also affected by the desired signal-to-noise ratio (see below).

• Beam flux: Higher flux will decrease the required exposure time. The effect is linear: so doubling the beam flux will half the measurement time. Undulator beamlines at modern synchrotrons have exceedingly high flux: the required measurement time may only be milliseconds.
• Sample volume: Larger samples of course scatter more. Note that in transmission-mode, if the sample is too thick, it will instead attenuate the scattering (due to absorption or multiple scattering). In grazing-incidence experiments, larger sample sizes increase scattering power and thus decrease measurement time. However, this is only useful up to a point: if the sample is large enough to fully-capture the incident beam (i.e. there is no spill-over from the beam projection), then increasing sample dimensions further will not change anything.
• Ordering: More highly ordered systems scatter more strongly.
• Scattering contrast: The higher the electron-density contrast between the structured materials, the strong the signal.

Signal-to-noise ratio

The signal-to-noise ratio (SNR) is a measure of data quality, wherein one compares the strength of the signal of interest to the complicating background noise. In x-ray scattering measurements, various kinds of background (detector background, substrate scattering, instrument windows, air scattering, etc.) worsen the SNR. However, the largest source of noise is frequently simply shot noise: the inherent counting statistics arising from the small number of photons being detected. For integer counting, the SNR goes as:

${\begin{alignedat}{2}\mathrm {SNR} &={\frac {\mu }{\sigma }}&={\sqrt {N}}\end{alignedat}}$

Where $\mu$ is the (average) signal, and $\sigma$ is the standard deviation of the signal (i.e. the noise), and N is the integer number of counts. Thus, for a pixel that has 10,000 counts, the SNR is 100.

The above equation makes it clear that improving the SNR is in general difficult: to improve the data quality by a factor of 10, one must increase the measurement time by a factor of 10² = 100. In other words, slightly increasing measurements times does not appreciably improve data quality (one must instead increase measurement times by a meaningful factor).

Overcounting

Detector saturation

TBD

Sample damage

TBD

Mitigation

TBD