Imaging by a system with a hexagonal pupil

Area of Science:

• Optics and Photonics
• Optical Engineering
• Mathematical Physics

Background:

• The point-spread function (PSF) is crucial for characterizing optical system resolution and imaging quality.
• Understanding the impact of pupil shape on optical aberrations is essential for advanced optical design.
• Hexagonal pupils offer potential advantages in certain imaging applications due to their unique symmetry.

Purpose of the Study:

• To derive a closed-form analytical expression for the aberration-free point-spread function (PSF) of a system with a hexagonal pupil.
• To analyze the characteristics of the hexagonal pupil PSF and compare it with that of a circular pupil.
• To investigate the balancing of Seidel aberrations and their effect on the Strehl ratio.

Main Methods:

• Derivation of a closed-form analytical expression for the PSF of a hexagonal pupil.
• Calculation of ensquared power and optical transfer function (OTF) for hexagonal and circular pupils.
• Analysis of Seidel aberrations, their balancing, and their impact on the Strehl ratio.

Main Results:

• The hexagonal pupil PSF displays six-fold symmetry, featuring a central bright spot, dark ring, hexagonal bright/dark rings, and six diffraction arms.
• The PSF structure differs markedly from that of a circular pupil, with distinct diffraction patterns.
• Seidel aberration balancing was illustrated, and their standard deviations were analyzed, showing effects on the Strehl ratio.

Conclusions:

• The study provides a comprehensive analytical description of the hexagonal pupil PSF and its properties.
• Comparison with circular pupils highlights the unique imaging characteristics introduced by hexagonal apertures.
• The findings offer valuable insights for designing optical systems utilizing hexagonal pupils, particularly concerning aberration control and performance optimization.