Nonreciprocal broken ray transforms with applications to fluorescence imaging.

Area of Science:

• Optics and photonics
• Medical imaging
• Computational physics

Background:

• Broken ray transforms (BRTs) are typically reciprocal, assuming constant photon energy along a ray.
• Loss of reciprocity occurs when photon energy changes at the ray vertex, relevant in fluorescence and Compton scattering.
• Non-reciprocal BRTs have applications in optical fluorescence imaging and X-ray imaging with single Compton scattering.

Purpose of the Study:

• To investigate the application of non-reciprocal BRTs in tomographic optical fluorescence imaging.
• To demonstrate simultaneous and independent reconstruction of all optical properties of a medium.
• To extend the methodology to problems involving single Compton scattering.

Main Methods:

• Utilizing the non-reciprocity inherent in the data function by reversing photon paths.
• Applying tomographic reconstruction techniques to optical fluorescence data.
• Developing algorithms for inverting non-reciprocal BRTs.

Main Results:

• Simultaneous and independent reconstruction of intrinsic attenuation coefficients (excitation and fluorescence frequencies) and contrast agent concentration.
• Successful application of the method to tomographic optical fluorescence imaging.
• Validation of the approach for inverting BRTs arising from single Compton scattering.

Conclusions:

• Non-reciprocal BRTs offer a powerful approach for comprehensive optical property reconstruction in fluorescence imaging.
• The developed method enhances the capabilities of tomographic imaging by enabling simultaneous parameter retrieval.
• This work provides a unified framework applicable to both optical fluorescence and X-ray scattering imaging problems.