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Is it possible build a telescope on a "field of mirrors" like the image below?
I mean, an energy plant on day time and a telescope in the night
Maybe the mirrors are not enough polished but the reflection surface seems very wide.
I want to know if it's feasible reuse it to build a very big telescope (with an appropriate adapter to focus the image)
Btw, not so much orientable
(Fuentes de Andalucía in Spain)
Regarding the question raised in the title,
Is it possible build a telescope on a field of mirrors?
The answer to this question is a resounding "yes". A number of existing and planned telescopes use arrays of mirrors, depicted below. Noteworthy amongst them include the James Webb Space Telescope, which will use an array of eighteen hexagonal mirrors, and the Thirty Meter Telescope and European Extremely Large Telescope, both of which are absolutely colossal in size.
With regard to the second question,
Is it possible build a telescope on a "field of mirrors" like the image below?
The JWST, TMT, and EELT have one other colossal aspect to them: Their costs. I couldn't even imagine what the costs would be with regard to a telescope of that size.
With regard to the third question,
I mean, an energy plant on day time and a telescope in the night.
Absolutely not. The heat stresses that would inevitably result from daytime and nighttime use would quickly make the field of mirrors useless at night. There's no problem with using a wavy mirror to reflect sunlight towards the collector of a solar power plant. The quality requirements on the mirrors aren't very high. There's a huge problem with using a mirror that is even slightly wavy to reflect starlight towards the central optics of a telescope. The mirror segments in the arrays of mirrors used for those large telescopes need to be nearly perfect. Sunlight never touches them.
You can indeed build a telescope on these principles and indeed thinking about this kind of idea leads to an active branch of astronomy: very large radioastronomy arrays.
At optical frequencies the idea is hard to make practicable on the ground (but see David Hammen's answer for space telescopes): the mirrors would need to be aligned to produce a diffraction limited spot to achieve the full capability of this idea, and the mirrors would thus need to make up a single, focussing surface that would flat to within a tenth of a wavelength or less. This means that any vibration would kill the idea: vibrations of all kinds: seismic, rumblings of cars and truchs and so forth, would impart many wavelengths of aberration on the effective mirror surface. One could try to use "lucky imaging": sampling the image whenever the received power, and thus Strehl ratio, exceeds a threshold. Alternatively, one could gather the image over a larger receiving surface, with very large pixel size so that the aberration would not lead to power loss, but the loss of resolution that goes with this compromise means that you might as well have begun with a smaller mirror in the first place: the achievement of diffraction limited performance with a mirror one hundredth of the diameter would be much easier and cheaper than the achievement of a Strehl ratio of 1/100 with a 100 times loss in resolution with the bigger mirror.
However
Radio waves also bear important astronomical information, not the least because they can peer through dust, e.g. at the galactic center to reveal the paths of stars around the central black hole. Radio waves have wavelengths that are large compared with the deviation from perfection that vibration imposes on the "mirror elements", so your idea is definitely practicable at radio frequencies. However, instead of an array of focussing mirrors imaging onto a surface, though, the elements of the receiver are simple radio receivers, and the operation of the whole array as a phased array and their digital composition means that the whole works as a huge aperture telescope. Moreover, the imposition of phase tilts on the array means that it can be steered.
It is very unlikely that such a system would be viable as an astronomical telescope since it it would be essentially unsteerable. The detection of very faint objects typically requires long exposure times, but I doubt if the solar array would be capable of getting an exposure of more than a few seconds before the target moved out of the field of view.
In addition the fast focal ratio would make optical aberrations extremely bad and so the image quality would be very poor - think of Hubble before it was fixed, but much worse.
