It seems we need bigger telescopes. Bigger telescopes need larger, more perfect mirrors. More perfect mirrors need more accurate geometry for magnification. This has led to spinning mercury mirrors which form a natural parabola but are restricted to remaining perpendicular to gravitational pull,
massive glass mirrors formed in spinning ovens, and segmented multi faceted mirrors on a framework. All of these things have disadvantages and all are limited to the size of the objects we need to manufacture in order to cover all of the various bases.

I was wondering about this today and might have figured out a solution but I'm having a hard time visualizing if it would work or not so I'd like to share it here since I can't tinker with it to find out.

The largest telescope mirrors are something like three meters in diameter. Could a large enough circular pool of still mercury not be made to create a Chladni pattern standing wave node Fresnel reflector of almost any size desired using a central frequency generator?

If so, how large would the pool need to be in order to collect more light than a three meter parabolic mirror ...and would the same concept not also work using a stretched taut sheet of mylar? That would be good because it would be able to be tilted and should function in micro gravity.

You've mis-interpreted that Wikipedia page.
It's about mirrors ABOVE 3m diameter. The largest single-piece mirrors are a bit over 8m diameter, and there are segmented mirrors far larger.

Instead of messing round with big mirrors, wouldn't it be easier just to go to whatever you want to look at, and then use a much simpler, cheaper imaging system from close range ?

You can get in a lot of trouble messing around with big telescopes ... <link>

//The largest single-piece mirrors are a bit over 8m diameter//

Sweet. I did indeed misinterpret that page. Thanks!

//wouldn't it be easier just to go to whatever you want to look at, and then use a much simpler, cheaper imaging system from close range ?//

Maybe... what would that cost? ...and more importantly, what do you think it would cost to make a circular standing wave node Fresnel reflector of enormous size from mercury or mylar?

You should look up the actual cross-section of a Fresnel
lens. I think you will find that you can't generate a
standing wave of that shape. This apples to a Fresnel
reflector, too.

Isn't a standing wave, pretty much by definition, a sine
wave? And aren't focusing mirrors generally parabolic? And
aren't parabolas and sine waves very different shapes?

Just because two things are curvy doesn't mean they are
the same sort of curvy.

It's not a lens I'm going for, but a Fresnel reflector. A series of circular sine waves may not be the ideal shape for focussing 'all' of the incoming light, but some portion of the curve of each wave is at exactly the right angle to converge some of the incoming light onto a single source. By filtering out any of the scattered light not reflected from these optimal zones it should be possible to build as large a mirror as the reflective medium will allow waves to propagate and interfere.

At least that's how I see it working in my minds eye.

The curvature of a sine wave does not have a focal point.
As a result, you're going to get, theoretically, a single line
of photons at a given focal point from each wave, and
that only up until you reach the inflection point on the
wave.

Also, there is no way to "filter out" the unwanted light,
since whatever your receiving optic is will not be able to
distinguish between the desired light from one wave, and
the photons immediately adjacent to it, or the light that
is coming in at a fractionally different angle, but to the
same location, from the next wave.

A Fresnel lens is theoretically piece-wise continuous.
(Each segment is continuous, and the curvature, but not
the location is continuous over the total area of the
lens.) There is no possible way to get that out of this
idea.

As a result, at best, you are far better off with a
segmented mirror.

I don't know what [m-f-t] is... [marked-for-tossing]

//(Each segment is continuous, and the curvature, but not the location is continuous over the total area of the lens.) There is no possible way to get that out of this idea.//

Aha! Thank you. I don't understand these words. That has 'got' to be a good start.

Do you mean that only a very small portion of each circular sine wave will have a reflection which aligns at a given focal point? That, there will be no continuous parabolic mirror, just separated circular slices? rather than a whole image?

If so, I would contend that on any given section of the inner curve of a circular reflective sine wave there is a single cross section of each ripple which will only reflect light at any given focal point, and that the culmination of these differing angles of reflection will result in a coherent image. Any light scattered by circular wave curvature will not approach the focal point.

I want to understand, I really do. I just don't see how taking a different reflected cross section line of each wave wouldn't add up to a total image.