Spectrum reconstruction from dose measurements as a linear inverse problem.

Area of Science:

• Medical Physics
• Radiation Oncology
• Photon Beam Dosimetry

Background:

• Determining the energy spectrum of clinical photon beams is crucial for accurate radiation therapy.
• Existing methods include direct measurement, source modeling, and reconstruction.
• Reconstruction offers an independent verification of source models and utilizes readily available equipment.

Purpose of the Study:

• To present a novel method for reconstructing clinical photon beam spectra.
• To avoid spectrum discretization or parametrization, unlike previous methods.
• To provide a rigorous error analysis for spectral component measurement confidence.

Main Methods:

• Utilizing ion-chamber measurements of dose after beam attenuation.
• Employing attenuators of varying compositions (water, lead) and thicknesses.
• Applying singular value decomposition (SVD) to characterize the forward problem and analyze measurement capabilities.

Main Results:

• The singular value decomposition (SVD) effectively characterizes the linear operator relating spectra to dose measurements.
• The right singular vectors form a basis for the spectrum, with measurable components linked to singular values above a threshold.
• Simulations and a practical example with water and lead attenuators illustrate the reconstruction theory and error analysis.

Conclusions:

• Spectrum reconstruction from ion-chamber measurements is a viable and independent method for characterizing clinical photon beams.
• The SVD-based approach provides a framework for understanding the limits and confidence in spectral component measurements.
• This method enhances the understanding and verification of radiation beam properties in clinical settings.