Limitations of the paraxial Debye approximation

Area of Science:

• Optical physics
• Microscopy imaging

Background:

• The paraxial Debye integral approximation for focusing neglects higher-order defocus terms.
• This simplification can introduce significant errors in aberration analysis, particularly for systems with low numerical aperture.

Purpose of the Study:

• To present an alternative integration variable for the Debye integral to avoid errors from ignored higher-order defocus terms.
• To analyze and quantify aberrations introduced by optical elements like glass slabs (e.g., coverslips).

Main Methods:

• Reformulating the Debye integral with a novel integration variable.
• Expanding aberrations of a glass slab in terms of the new variable.
• Expressing these aberrations using Zernike polynomials for aberration balancing.

Main Results:

• The proposed method accurately accounts for higher-order defocus terms, eliminating errors inherent in the paraxial approximation.
• Aberrations from glass slabs are systematically analyzed and represented.
• The use of Zernike polynomials facilitates effective aberration balancing in optical systems.

Conclusions:

• A modified Debye integral approach provides a more accurate treatment of aberrations in optical focusing systems.
• This method enhances the analysis and correction of aberrations caused by elements like coverslips, crucial for high-resolution imaging.