Related Experiment Video
Updated: Jul 5, 2026

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation
Published on: March 2, 2021
Derivation and validation of a sensitivity formula for slit-slat collimation
R Accorsi1, J R Novak, A S Ayan
1Department of Radiology, The Children's Hospital of Philadelphia and the University of Pennsylvania, Philadelphia, PA 19104, USA. accorsi@email.chop.edu
Abstract:
An analytic formula is derived for the sensitivity of collimators achieving transverse collimation with a slit and axial collimation with a slat assembly whose septa may be parallel or focus on a line. The formula predicts sin(3) phi dependence on the incidence angle and, in the particular case of parallel slats, 1/h dependence on the distance from the slit. More complex expressions for sensitivity that do not diverge at points near the slit or the focal line of the slat assembly are also derived. The predictions of the formulas are checked against simple cases for which solutions are available from direct calculation as well as against Monte Carlo simulation and published experimental data. Agreement is good in all cases analyzed. An approximate penetration model is also introduced: it involves the use of a sensitivity-effective slit width and septal length. Its predictions are compared to simulation results. Agreement was found to be compatible with statistical fluctuation (+/- 0.3%) for geometric sensitivity and better than 3% of total sensitivity in the worst case of septa designed for high-energy (364.5 keV) photons.
More Related Videos
Related Concept Videos
Simpson's Rule II
Derivatives of Inverse Trigonometric Functions
Surface Area Calculations
Deflection of a Beam
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
Beams with Unsymmetric Loadings
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...
Contaminants and Errors
Another key consideration is determining the appropriate number of samples required to...

