Closed-form solution for thin lens image irradiance under arbitrary solid angle.

Area of Science:

• Computer Vision
• Optical Imaging Systems
• Radiometry

Background:

• Optical imaging systems are crucial for inferring 3D environmental properties from 2D images.
• Existing models, like Horn's irradiance equation, rely on approximations that can limit accuracy.

Purpose of the Study:

• To propose a novel relationship between object radiance and image irradiance.
• To generalize and improve upon existing irradiance equations for optical imaging.

Main Methods:

• Developed a new equation based on power conservation and a thin lens model.
• Utilized ray tracing simulations and real-world image intensity comparisons.
• Provided closed-form and numerical solutions for focused and unfocused points.

Main Results:

• The proposed equation demonstrates superior accuracy compared to Horn's equation.
• Improvements are most significant for systems with large lenses and near-focused images.
• The model validates Horn's approximation in regimes where the pinhole model is applicable.

Conclusions:

• The new irradiance equation offers a more accurate and theoretically grounded approach for optical imaging.
• This advancement is particularly beneficial for computer vision applications requiring precise radiometric information.
• The findings provide a more robust foundation for understanding the relationship between 3D scenes and 2D image formation.