Effect of light-collection geometry on reconstruction errors in Abel inversions

Area of Science:

• Combustion diagnostics
• Optical physics
• Tomographic reconstruction

Background:

• The Abel inversion reconstructs axisymmetric radial profiles from line-of-sight intensity data.
• It is widely applied in spatially resolved combustion measurements.
• Practical optical systems often collect light over a nonzero solid angle, deviating from the parallel ray assumption.

Purpose of the Study:

• To investigate the impact of optical collection geometry on Abel inversion accuracy.
• To understand how non-parallel rays affect measured intensity signals and reconstructed emissivity profiles.
• To validate simulation findings with experimental emission tomography data.

Main Methods:

• Ray-tracing simulations were conducted to model light collection through various optical systems.
• Simulated intensity signals were analyzed to assess the influence of collection geometry.
• Reconstructed emissivity profiles from simulations were compared to experimental measurements.
• Emission tomography was performed on an axisymmetric laminar diffusion flame.

Main Results:

• Optical collection geometry significantly affects measured intensity signals.
• Non-parallel rays lead to distortions in reconstructed emissivity profiles.
• Ray-tracing simulations accurately predicted experimental observations.
• Deviations from the parallel ray assumption introduce errors in Abel inversion.

Conclusions:

• The standard Abel deconvolution is insufficient for optical systems with significant collection angles.
• Ray-tracing simulations are valuable tools for understanding and correcting optical geometry effects.
• Accurate spatially resolved combustion measurements require accounting for optical collection geometry.