# Quantitative evaluation of statistical errors in small-angle X-ray scattering measurements

## Abstract

A new model is proposed for the measurement errors incurred in typical small-angle X-ray scattering (SAXS) experiments, which takes into account the setup geometry and physics of the measurement process. The model accurately captures the experimentally determined errors from a large range of synchrotron and in-house anode-based measurements. Its most general formulation gives for the variance of the buffer-subtracted SAXS intensity σ ^{2}(q) = [I(q) + const.]/(kq), whereI(q) is the scattering intensity as a function of the momentum transferq;kand const. are fitting parameters that are characteristic of the experimental setup. The model gives a concrete procedure for calculating realistic measurement errors for simulated SAXS profiles. In addition, the results provide guidelines for optimizing SAXS measurements, which are in line with established procedures for SAXS experiments, and enable a quantitative evaluation of measurement errors.

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States). Advanced Photon Source (APS)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1349929

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Applied Crystallography (Online); Journal Volume: 50; Journal Issue: 2

- Country of Publication:
- United States

- Language:
- ENGLISH

- Subject:
- 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY

### Citation Formats

```
Sedlak, Steffen M., Bruetzel, Linda K., and Lipfert, Jan.
```*Quantitative evaluation of statistical errors in small-angle X-ray scattering measurements*. United States: N. p., 2017.
Web. doi:10.1107/S1600576717003077.

```
Sedlak, Steffen M., Bruetzel, Linda K., & Lipfert, Jan.
```*Quantitative evaluation of statistical errors in small-angle X-ray scattering measurements*. United States. doi:10.1107/S1600576717003077.

```
Sedlak, Steffen M., Bruetzel, Linda K., and Lipfert, Jan. Wed .
"Quantitative evaluation of statistical errors in small-angle X-ray scattering measurements". United States.
doi:10.1107/S1600576717003077.
```

```
@article{osti_1349929,
```

title = {Quantitative evaluation of statistical errors in small-angle X-ray scattering measurements},

author = {Sedlak, Steffen M. and Bruetzel, Linda K. and Lipfert, Jan},

abstractNote = {A new model is proposed for the measurement errors incurred in typical small-angle X-ray scattering (SAXS) experiments, which takes into account the setup geometry and physics of the measurement process. The model accurately captures the experimentally determined errors from a large range of synchrotron and in-house anode-based measurements. Its most general formulation gives for the variance of the buffer-subtracted SAXS intensity σ2(q) = [I(q) + const.]/(kq), whereI(q) is the scattering intensity as a function of the momentum transferq;kand const. are fitting parameters that are characteristic of the experimental setup. The model gives a concrete procedure for calculating realistic measurement errors for simulated SAXS profiles. In addition, the results provide guidelines for optimizing SAXS measurements, which are in line with established procedures for SAXS experiments, and enable a quantitative evaluation of measurement errors.},

doi = {10.1107/S1600576717003077},

journal = {Journal of Applied Crystallography (Online)},

number = 2,

volume = 50,

place = {United States},

year = {Wed Mar 29 00:00:00 EDT 2017},

month = {Wed Mar 29 00:00:00 EDT 2017}

}