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In the beginning of the short YouTube video Arecibo Uncut: Under the Dish with Phil Perillat it is mentioned that while dish antennas are usually a parabola, the problem is that a static parabola would only be useful to see objects for a few minutes as they passed overhead.

But then some guy at DARPA says "Hey why don't you guys make it a sphere?" A sphere has the unique property that from the center of curvature, no matter where you look, it's the same.

That is indeed how the Arecibo dish works; a static primary sphere and a big, funny-looking secondary mirror and associated optics/electronics suspended above on cables that can be moved around in order to "point" in different directions.

Two questions:

  1. While the statement in the block quote about the sphere is correct as far as it goes, was the shape of the correcting optics (secondary, etc) above also independent of where you look? Or ideally would you like a different secondary shape depending on how far off-vertical you look? If so, is this what happens?
  2. Any ideas who "the guy at DARPA" might be?
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  1. While the statement in the block quote about the sphere is correct as far as it goes, was the shape of the correcting optics (secondary, etc) above also independent of where you look? Or ideally would you like a different secondary shape depending on how far off-vertical you look? If so, is this what happens?

I will answer under the assumption this question is asking for the most recent upgraded configuration with the Gregorian dome.

As a spherical reflector, Arecibo was subject to spherical aberration. The antenna was updated with a Gregorian reflector system to correct for the aberration. A description of the design and operation can be found in Multi-feed Systems for the Arecibo Gregorian. This system take rays which would have focused along a line from the spherical reflecting surface and redirects them to come to focus at a point as is desired for reception.

According to Moonbounce from Arecibo Observatory:

Unlike most other radio telescopes and large antennas built for space communication, the Arecibo reflector does not move. However, its beam can be steered by moving the feed antennas. The feed support system is comprised of a circular azimuth track and banana-shaped, 328 foot long azimuth arm, which rotates about a central pivot. Steering in zenith angle is accomplished by moving the feed antennas along a track on the under- side of the azimuth arm.

The interesting thing to note here is that with a circular dish, no matter how we orient the secondary (and tertiary) reflectors we essentially have the same geometry. That means that if we a physically moving the corrector apparatus then if it has the right correction geometry for one steering direction then it is correct for all steering directions. This is of course neglecting illumination issues "vignetting" where we start seeing the edge of the primary reflector and no longer have access to its full aperture.

  1. Any ideas who "the guy at DARPA" might be?

My best guess comes from Genesis of the 1000-Foot Arecibo Dish. Quoting from that article:

Gordon learned at ARPA that the Air Force Cam- bridge Research Laboratories (AFCRL) had been working on spherical reflectors for a decade. ... Gordon credits Ward Low at the Institute for Defense Analyses (IDA) and ARPA for his knowledge and help with spherical dishes, and for connecting him with AFCRL (Butrica, 1996: 89; Gordon, 1979: 26; 1994: 13).

Gordon is William E. Gordon, "father of the Arecibo Observatory". It also sounds like this was before ARPA became DARPA. Either way, it sounds like Ward Low was the one who recommended a spherical primary.

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    $\begingroup$ Wow, thank you for the thorough, insightful and well-sourced answer! It's great when a new takes an old unanswered question and runs with it. Welcome to Astronomy SE! $\endgroup$
    – uhoh
    Oct 11 '21 at 0:02
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    $\begingroup$ Thank you, I've got a soft spot for Arecibo. Unfortunately I never got a chance to visit. $\endgroup$ Oct 11 '21 at 0:04

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