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Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution

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Imaging by a system with a hexagonal pupil.

José Antonio Díaz¹, Virendra N Mahajan

¹Departamento de Óptica, Universidad de Granada, Granada 18071, Spain.

|July 23, 2013

Summary

We derived an analytical expression for the aberration-free point-spread function (PSF) of hexagonal pupils. This PSF exhibits unique six-fold symmetry, differing significantly from circular pupils, impacting optical system performance.

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.

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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.