Luneberg apodization problem I.
The Luneberg apodization problem on the determination of pupil function giving maximum central value of the point-spread function of an incoherent imaging system is considered subject to the condition that the total power in the pupil is fixed. It is shown that, irrespective of the shape of the pupil, any amplitude variations reduce the central irradiance and any phase variations further reduce it, thus showing that an unapodized-unaberrated pupil gives maximum central irradiance. Through consideration of several examples of apodization of centrally obscured circular pupils, it is shown that the effects of large amplitude variations on the central irradiance are small compared with the effects of small phase aberrations.
Mahajan
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The Charles Stark Draper Laboratory, Inc., Cambridge, Massachusetts 02139, USA.