Related Experiment Video
Updated: Jul 19, 2026

Characterization of Recombination Effects in a Liquid Ionization Chamber Used for the Dosimetry of a Radiosurgical Accelerator
Published on: May 9, 2014
Non-diverging analytic expression for the on-axis sensitivity of converging collimators: analytic derivation
1Department of Radiology, The Children's Hospital of Philadelphia, Philadelphia, PA 19104, USA. accorsi@email.chop.edu
A new analytical formula resolves sensitivity divergence issues in converging collimators. This formula offers improved applicability and defines new operational ranges for collimator design.
Area of Science:
- Optics and Photonics
- Instrumentation Science
Background:
- Existing formulas for converging collimator sensitivity exhibit divergence near the focal locus.
- This divergence limits the practical application of current models in precise optical systems.
Purpose of the Study:
- To derive a novel analytical formula for converging collimator sensitivity that avoids divergence.
- To compare the new formula with existing literature expressions.
- To establish guidelines for the appropriate application of the derived formula.
Main Methods:
- Derivation of a non-divergent analytical expression for collimator sensitivity.
- Comparative analysis between the new formula and existing literature formulas.
- Development of approximations to simplify the derived complex formula.
Main Results:
- A new, non-divergent analytical formula for converging collimator sensitivity has been successfully derived.
- The new formula demonstrates improved accuracy and applicability, particularly near the focal locus.
- Simplified approximations of the formula are presented for practical use.
Conclusions:
- The derived analytical formula overcomes the divergence issue present in prior models.
- The new formula and its approximations enhance the understanding and extend the applicability of converging collimator design.
- This work provides a more robust tool for optical engineers working with converging collimators.
More Related Videos
06:49In 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
10:39Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
Published on: October 11, 2016
Related Concept Videos
Derivatives of Inverse Trigonometric Functions
Unsymmetric Bending - Angle of Neutral Axis
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal centroidal axes. The...
Divergence and Curl of Magnetic Field
Polar Equations of Conics
Divergence and Curl of Electric Field
Interval and Radius of Convergence