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Luneberg apodization problem I.

¹The Charles Stark Draper Laboratory, Inc., Cambridge, Massachusetts 02139, USA.

|August 21, 2009

Summary

To maximize central irradiance in imaging systems, avoid amplitude and phase variations in the pupil function. An unapodized, unaberrated pupil provides the highest central irradiance, with phase aberrations being more detrimental than amplitude variations.

Area of Science:

Optics
Image Science
Optical Engineering

Background:

Apodization techniques aim to optimize the point-spread function (PSF) in incoherent imaging systems.
The Luneberg apodization problem focuses on maximizing the central value of the PSF.
System performance is constrained by fixed total power in the pupil.

Purpose of the Study:

To determine the pupil function that maximizes the central irradiance of the point-spread function.
To analyze the impact of amplitude and phase variations on central irradiance.
To compare the effects of amplitude variations versus phase aberrations.

Main Methods:

Theoretical analysis of the Luneberg apodization problem.
Mathematical modeling of pupil functions with varying amplitude and phase.

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Case studies involving apodization of centrally obscured circular pupils.

Main Results:

Any amplitude variations in the pupil function reduce central irradiance.
Phase variations further decrease central irradiance compared to amplitude variations.
An unapodized and unaberrated pupil yields maximum central irradiance.
Small phase aberrations have a greater detrimental effect on central irradiance than large amplitude variations.

Conclusions:

The optimal pupil function for maximum central irradiance is unapodized and unaberrated.
Minimizing phase aberrations is crucial for maintaining high central irradiance in imaging systems.
Apodization strategies must carefully consider the trade-offs between amplitude and phase modifications.