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There are many applications for orbital space mirrors in astronomy (better telescopes) and space propulsion (solar power for deep space probes), but this is limited by the minimum beam divergence achievable with current technology

So, i'm trying to understand what physical and technological limits exists in our capacity to build mirrors that can keep as small beam divergence as possible. For instance, a sail probe to Saturn would require that the beam doesn't significantly diverge above 300m-600m (the biggest sail we can conceive of building in the inmediate future) at distances as big as 5-6 AU ($10^{11} - 10^{13}$ meters)

What is the best beam focusing divergence we can achieve for solar light with mirrors right now, and what limits the improvement of this? technological limits? fundamental physical limits?

Edit let's assume the concrete case of a wavelength of $10^{-6}$ meters, and a distance of $10^{12}$ meters (Neptune orbit). Can't i, for instance, build a focusing element with a focal length of $10^{12}$ meters that would push the far field beam divergence at farther distances from the focal point? Is this a manufacturing limitation of focusing element engineering (not enough precision to build lens made of atoms with the required focal length), or something more instrinsic, say, a focal point cannot be farther than some finite distance that depends on the wavelength?

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This is not a technological limitation. Beam divergenceis llimited by diffraction. The minimum divergenceis dictated by wwavelength and beam diameter. –  Colin K Feb 4 '13 at 19:18
    
what is 'beam diameter'? you mean that a bigger mirror will have smaller divergence? is there a formula for that? –  lurscher Feb 4 '13 at 19:34
    
A number of random comments here. First, you claim a particular limit on the size of the sail---well, I can conceive of a lot---I assume you've based this on something like the areal density and the current single payload lift limits. It might help us to know what you think causes the limit. Second, ideally you'd like a spot size comparable to the sail size, but there is nothing to stop you using it even when the spot is "too big", you just get lower thrust. –  dmckee Feb 4 '13 at 19:59
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Third, Forward suggested a big Fresnel lens rather than a mirror in his Rocheworld books, which might be easier in-so-far as the focusing element is under less thrust and half of it can be empty space which should nearly double it's area for a given mass. –  dmckee Feb 4 '13 at 19:59
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Lurscher, yes, the optimum is when the source beam width is the square root of the distance to the target, when all distances/sizes are measured in wavelengths. –  Jim Graber Feb 5 '13 at 23:45
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