High Resolution Telescopes

[rogerinnh]

There are three t hings that determine the resulution of a telescope: (1) the ratio between the diamter of the primary mirror and the focal length, (2) the absolute measurement of the focal length, and (3) the wavelength of the light (the smaller the wavelength the better the resolution). Typically, when you want to build a high resolution telescope you maximum the overall size of the scope, via items 1 and 2. But how about item 3, the wavelength of light? Suppose you could reduce the wavelength of light? And I don't mean just allowing only short wavelengths of light to enter the teleescope, I mean actually reducing the wavelength of ALL the light entering the telescope.<br /><br />Consider, when light passes into a material of a higher index of refraction it slows down. That slowing down is what causes refraction. But that slowing down also reduces the wavelength of the light, doesn't it? After all, as the waves enter the medium and slow down they kind of "bunch up" together, shortening the wavelength. This is precisely what you see with water waves at the shore. A long wavelength wave approaches the shore and, because of the increasingly shallower water (comparable to increasingly higher index of refraction) as it progresses forward, the wave slows down, bunches up, has shorter wavelength (and eventually topples over on itself, crashing onto the shore). The crashing part isn't significant here, to this discussion. What's important is that the wavelength gets shorter, just as light's wavelength gets shorter as it enters material with a higher index of refraction.<br /><br />Now, generally most materials like glass only have a minor effect on the wavelength because it only slows down the light a relatively small amount. BUT! Recent reports have been published about how under certain special circumstances, passing through a Bose-Einstein Condensate, light can be slowed down an incredible amount, to merely feet per second, as opposed to 180,000 miles per second. Under tho

 

[billslugg]

RogerInNH<br /><br />The ratio of focal length to mirror diameter has nothing to do with resolution. This ratio is called the "focal ratio" or "f-ratio" or "f". It is a measure of the brightness of the image that is formed. The lower the number, the brighter the image.<br /><br />The focal length has nothing to do with resolution. The focal length determines the magnification at the image plane.<br /><br />Resolution is a function of mirror diameter and wavelength. (Assuming a perfect mirror and perfect seeing). There are numerous formulas for calculating it. It depends upon how much contrast is acceptable between the dark and light areas on a test target. Suggest you read up on Rayleigh Criterion, Dawe's Limit, airy disc.<br /><br />As for the proposal to increase resolution by decreasing wavelength, I think it might work. Follow this reasoning:<br /><br />If a star is receding we can only see it in red or infrared or perhaps microwave, with all the associated resolution penalties. If a star is approaching us, we can see it in blue or ultraviolet with the attendant improvement in resolution. What then is the difference between a star approaching us and us approaching a star? In either case the wavelength is shortened and the resolution improved. If we can improve resolution by approachng a star and shortening the wavelength, then what is to prevent us from capturing the wave train, slowing it, shortening the wavelength and improving the resolution? <br /><br /><br /><br /><br /><br /> <div class="Discussion_UserSignature"> <p> </p><p> </p> </div>

 

[rogerinnh]

I agree with you that the limit of resolution of a telescope is dependent upon the mirror diameter and wavelength. I disagree that the focal length is not involved.<br /><br />I have actually done quite a bit of studying over the years on the topic of telescope resolution limits.<br /><br />Consider the Dawes Limit (smallest resolvable angle), given by:<br /><br /> Theta = 115.8/D<br /><br /> where D is the diameter in millimeters and<br /><br /> Theta is the smallest resolvable angle in seconds.<br /><br />Note that the wavelength of light is not included in this definition, which we agree must be included for an accurate calculation. Thus, this Dawes Limit is more of a general guideline or rule-of-thumb rather than a completely accurate calculation of the limit of resolution.<br /><br />Consider, then the Radius Of the Airy Disc. The Airy Disc is formed at the focal plane of a telecope when viewing a far-distant point-source of light. If light had only a particle nature then we would expect that a far-distant point-source of light would result in a point-result of light at the focal plane, or perhaps as small as a photon of light. But light also has a wave nature and as a result we get a "disc" of light (actually a central disc surrounded by increasingly lower intensity rings). The radius of this Airy Disc places a limit on the resolution of the telescope.<br /><br />The equation for calculating the radius of the Airy Disc is given by:<br /><br /> r = 0.043*Lambda*f<br /><br /> where r is the linear radius (one-half the linear diameter) of the Airy disc in mm<br /><br /> Lambda is the wavelength of light in mm (e.g. yellow light is 0.00055)<br /><br /> and<br /><br /> f is the f-number (f/) of the objective<br /><br />Note that the f-number is included in this calculation. The f-number is the ratio of the Focal Length to the Diameter of the primary mirror (objective). The f-number is a dmensionless number. You can have a 2inch diameter telescope and a thousand foot d

 

[rogerinnh]

I'm glad to hear that you think my idea for increasing telescope resolution by slowing down light to descrease its wavelength "might work".<br /><br />I, too, considered the issues regarding relative velocities between the telescope and the observed objects. Since accelerating a telescope towards the viewed object up to velocities suitable for increasing the resolution seemed a bit beyond reason, I looked for other means to accomplish the same thing. That's when I realized that the slowing down of light as it enters areas of higher index of refraction must also cause a shortening of the wavelength of the light. And since scientists have succeeded in slowing light down to "a crawl" using some pretty sophisticated techniques, I figured the idea might be extended to optical devices in order to produce extremely high resolution devices.<br /><br />Now, filling up the Keck Telescope (I live in Hawaii) with sufficient Bose-Einstein Condensate might not be feasible (at this point in time, anyway) perhaps it could be tried with a much smaller deivce, at least to explore the valididty of the concept. Or, maybe there's some other means of slowing down light that's more straighforward.<br /><br />Perhaps someone in this forum could offer some suggestions.<br /><br />Roger Garrett<br />

 

[rogerinnh]

Hmmm, I'm wondering if maybe it needn't be necessary to fill the entire optics of a telescope with Bose-Einstein Condensate (or similar medium) to reduce the wavelength of light (via the aforementioned slowing down of the speed of light) in order to obtain extremely high telescope resolution previously described in this thread. Maybe it might be sufficient to fill just a small distance up to the focal plane of the telescope. In other words, create the short wavelengths just before impinging on the image capture surface at the focal plane.<br /><br />Some more food for thought.<br />

 

[billslugg]

I can't quite pick apart your logic but I can tell a few things:<br /><br />- In the formula Θ = 115.8/D the wavelength of light is included in the 115.8<br /><br />- The formula for the radius of the airy disc is probably calculated for a single focal ratio, then expressed as a function of focal length. I can assure you that if resolving power were a function of focal length and not mirror diameter, there woud be a raft of advertisements in the back of Sky and Telescope for 2" diameter x 5000 foot focal length scopes allowing one to "See the Rovers on Mars!"<br /><br /><br /> <div class="Discussion_UserSignature"> <p> </p><p> </p> </div>

 

[rogerinnh]

bill,<br /><br />You write:<br /><br />------------------<br />In the formula Θ = 115.8/D the wavelength of light is included in the 115.8 <br />------------------<br /><br />I agree. An average, mid-visual range wavelength of light is indeed included in the 115.8 constant that is used in the equation. Which just further supports my contention that the Dawes Limit is merely a general rule-of-thumb for the limiting power of optical devices based on their diameter. It provides a quick-and-easy calculation, but not a precisely accurate calculation.<br /><br />You further write:<br /><br />------------------<br />The formula for the radius of the airy disc is probably calculated for a single focal ratio, then expressed as a function of focal length.<br />------------------<br /><br />No, the Airy Disc calculation explicitly includes the f-number of whatever optical device you are doing the calculation for.<br /><br /><br />You further write:<br /><br />------------------<br />I can assure you that if resolving power were a function of focal length and not mirror diameter, there woud be a raft of advertisements in the back of Sky and Telescope for 2" diameter x 5000 foot focal length scopes allowing one to "See the Rovers on Mars!" <br />------------------<br /><br />Resolving power, as I have shown, is a function of wavelength, f-number (Focal Length divided by Diameter), and Focal Length. A 2" diameter x 5000 foot focal length telescope would have extremely LOW resolution because its f-number would be so incredibly HIGH. The long focal length would not offset the high f-number.<br /><br />You get high resolution when the f-number (ratio of Focal Length to Diameter) is LOW, meaning a rather squat set of optics, but the overal telescope is rather large, meaning a long focal length.<br /><br />Companies emphasize the primary mirror diameter for two reasons. 1) The general-purpose Dawes Limit calulation provides a rule-of-thumb better value for large diameter scopes than for small diamter scopes (ev

 

[rogerinnh]

I might also point out that I've done an awful lot of thinking and studying up on this topic of the limits of resolution over the years. Long ago it occurred to me that, although it is quite clear why a larger diameter mirror collects more light than a small diameter mirror, it was not at all clear why the large diamter mirror should also have a higher resolution, i.e better resolving power. I read through a hell of a lot of books and articles and textbooks and web sites and finally just had to start with the very basics of the wave nature of light and how it produces an Airy Disc at the focal plane and work back from there to finally figure out, for myself, how it all worked. And it makes sense to me now.<br /><br />I've discussed this with a number of "people-in-the know" and they acknowledge that my descriptions are accurate.<br /><br />If you do find a fault in the logic that I presented then please let me know. <br /><br />Of course, we've gotten a bit off of the original topic, which was my suggestion for higher resolution optics by slowing down light. Any other people care to weigh in on that concept?

 

[billslugg]

RogerInNH<br /><br />Let me take another stab at this:<br /><br />Refer to Fred Hoyle's Astronomy and Cosmology 1975 p. 181:<br />Airy disc radius = 1.22 * lambda * Focal length / Diameter<br /><br />The angle resolved is then determined by dividing this radius by the focal length. <br />Theta = 1.22 * lambda / diameter<br /><br />In determining the resolution angle, we first multiplied by the focal length to calculate a disc radius, and then we divided by the focal length to determine an angle. <br /><br />Yes, the focal length "was involved in" the calculation of the resolution angle. We multiplied by it and then we divided by it. In doing two complementary mathematical operations, the focal length "fell out". <br /><br />The Airy disc diameter is directly a function of the wavelength and the focal length and inversely a function of the objective diameter. <br /><br />The telescope resolution angle is directly a function of the wavelength, inversely a function of the diameter and not a function of focal length.<br /><br /><br /> <div class="Discussion_UserSignature"> <p> </p><p> </p> </div>

 

[philscopes71]

The angular radius of the Airy disc is Lambda*focal length/diameter of objective. *1.22<br />At least that's the way I understand it. The actual physical diameter is 2.44*Lambda* focal ratio. I'm no real expert, so please put me right if this is not so.<br />I would like to add that greater focal length can appear to improve resolution, but this is due to the probable increase in power, as this appears to darken the sky background, making it easier to see the image, and hence improve resolution. Please remember I'm no expert, just a lifelong user with personal experience.

 

[billslugg]

philscopes71<br />Welcome to SDC sir, it is good to have a new member, and someone to scour the old posts!<br /><br />The formula you cite <font color="yellow">Lambda*focal length/diameter of objective. *1.22</font>gives the diameter of the Airy disc in in units of length as measured at the focal plane. In order to determine the angular radius, you must then divide by the focal length.<br /><br />I don't know about your statement relative to background darkening, I've never looked through a long focal length instrument.<br /><br /> <div class="Discussion_UserSignature"> <p> </p><p> </p> </div>

 

[philscopes71]

Thanks, Billslugg. I have used long and short focal lengths. The darkening of the sky background with increase in power can be useful, especially when splitting a close double star. Anything above 30X per inch of aperture permits the diffraction rings to begin interfering with resolution.<br />Phil

 

[philscopes71]

I have read this several times, and I have a problem with it. Perhaps you would be kind enough to put me right. The Airy disc, Ignoring the diffraction rings, is itself not a point source. It is a definite disc, made up of the various wavelengths of light that leaves the objective lens. It is, from centre to edge, coloured with each wavelength. This is determined by diffraction. As I see it, the only way to improve resolution is to somehow (?) permit the shortest accessible wavelength to arrive at the focal plane. A filter, maybe a diffraction grating, would supply the monochromatic light for this.<br />This appears to me as a possible phyiscal solution, and does not lead us into the realms of impossible dreams of Bose-Einstein condensates. Now I know I am wrong, so please tell me where?

 

[billslugg]

philscopes71<br />The Airy disc is made of the first few diffraction rings. Those rings are not made of the different wavelengths of light, but are made of constructive/destructive interference of any given wavelength. The shorter wavelengths show a smaller set of rings, thus a smaller Airy disc. <br /><br />Yes, you are correct, if you filter in the shortest wavelength from a scene, you will get better resolution. Does your part of the world have "Blu-Blocker" sunglasses? They claim to make your view in higher resolution by blocking out the "blu" rays. It is a great idea, but they have it wrong. They should be blocking out the red end of the spectrum. Of course, I doubt that very many people have vision corrected to the point where they are diffraction limited.<br /><br /> <div class="Discussion_UserSignature"> <p> </p><p> </p> </div>