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What is the far field pattern of a uniformly illuminated rectangular aperture?

  • A.A sinc function in each principal plane
  • B.A Gaussian function that falls smoothly away with no side lobes at all
  • C.A Bessel function of the first kind divided by its own argument value
  • D.A cosine squared function that reaches zero at ninety degrees from boresight

Answer: A

The transform of a rectangle is a sinc, so each principal plane shows the familiar narrow main lobe with side lobes 13.2 decibels below it. A circular aperture gives the Bessel form instead, which is the Airy pattern of optics with side lobes at minus 17.6 decibels. A Gaussian aperture would give a Gaussian pattern but cannot exist in finite size, and the cosine squared form belongs to a particular taper rather than to uniform illumination. Knowing the two canonical transform pairs covers most aperture problems at the estimating stage.

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