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Suppose a parabolic mirror of a telescope is large enough (or equivalently that the camera exposure time is short enough) that you need to take into account the transit time of the light signal from hitting the mirror to reaching the focal point.

What shape should the mirror be to have the same effect as a parabolic mirror that doesn't take into account light transit time ?

Added after comments:

Suppose you want to view surface details on an exoplanet with an array of space mirrors spanning millions or even billions of km, also redirecting photons towards a detector at a focal point. The property to preserve is photons from an event on the exoplanet arriving at the focal point at the same time.

If the transit time from hitting the mirror to reaching the focus is long enough then given that objects aren't ideal or at infinity, then any discrepancy at all in arrival times is magnified by the huge transit-time so if the object being viewed changes fast it can change significantly during the discrepancy.

In talking about shutter speed I was thinking about viewing an object whose properties change very quickly (say clouds moving on a giant exoplanet). If there is a discrepancy in the time it takes for photons leaving the object to reach the focal point and the object changes during that time then the image would be blurred (temporally aberrated).

As Ross Millikan points out distances to the focus point should be the same, so I was misunderstanding things, however looking at Wikipedia exact focus only exists for point sources otherwise there is coma aberration. The article also says there is something called bestform or aplantic lenses to minimise this, but you can't apply a lense to an array of mirrors spanning billions of km, so the original question stands but with a changed understanding.

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    @Wade: That's what I originally thought, but actually it's about photons that leave the object at the same time, arrive at the focus at the same time.2010-12-01

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As Willie Wong points out, this is not an issue for a parabolic mirror. In fact, another way to think about optical focus is that it makes constructive interference at the image point. This means that all light rays coming from the subject take the same travel time to reach the focus or else the interference wouldn't be constructive.

Note that shutter speed doesn't matter unless you are thinking about exposing different parts of the sensor at different times (like the old 35mm curtain cameras) and the subject is moving. Focus is focus for any shutter speed.

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    Actually aberrations occur for point sources, too, if they are off axis. They are worse for fast optical systems as the angle of light rays can be farther from axis. There is a developed theory of representing various aberrations in terms of linear and angular distance from axis. But this still doesn't depend upon how far the light has traveled.2010-12-01