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Reaching Rayleigh Limit, Dawes Limit
I've been researching past posts on Resolution Limits to compile
information for an upcoming article. I keep seeing some of the same misinformation coming up, (mis-stated values for Dawes as one example). The question arises, "What success have user's had reaching Dawes Limit with their scopes?" Generally the user is questioning why a black space cannot be seen between two components of a double with a separation measured at Dawes Limit. The important note here is that neither Rayleigh nor Dawes is intended to represent a separation showing two stars with a black space separating them, although there may be conditions where a black space can be seen at these limits. An understanding of Rayleigh and Dawes Limits is needed to use this information for determining what is the closest stars that can be split. There are some 2-3 year old posts with excellent information on the topic, but the threads can no longer be posted to bring them up front. David Knisely has helped me a great deal to understand resolution. Look up some of the past threads searching on Dawes Limit or Detail in Saturn's Rings. User's should understand the terms and the various limits and clearly understand what these limits impose on their equipment and observations. So I excerpted this brief from what I've written to post here. I believe you will find it useful. http://www.cloudynights.com/ubbthrea...5&o=&fpart= 1 This link provides about 50 targets to illustrate doubles at Rayleigh or Dawes Limits for various scopes and the difficulty associated with various doubles, bright/bright, bright/faint, faint/faint. A full explanation of the affects of these various conditions will be found in the article. edz Rayleigh Limit = 5.45 / D inches (or 138 / Dmm) is a measure of the ability of the scope aperture to split a double star. Likewise, Dawes Limit 4.56 / D inches (or 116 / Dmm) is another measure. Rayleigh Limit states you should be able to tell that a double is two stars if the centers of the diffraction disks of the two stars (commonly referred to as the Airy Disks, but see below) are separated by a dimension equal to the radius of the first diffraction interspace. That's the radius from the center of the Airy disk to the minimum of the space between the disk and the first diffraction ring. (This is important, I will refer to this a little further down). This calculation is directly tied to optics theory and the ability of a lens to resolve detail based on the wave nature of light. The limit of a lens to resolve is determined by the diameter of the lens and the wavelength of light. Take note that this limit, which has the centers of two disks separated by the radius of a disk would not provide for any black space between the two components. Dawes limit was determined by actual field-testing of many and varied double stars. It states the lens should be capable of seeing the double as two components when the centers of the two components are separated by a dimension defined by 116/Dmm. Similar to Rayleigh, that allows you to see a notch, not a complete black space, between the two components. So Dawes limit says you can see doubles closer than Rayleigh limit. Generally, it is held that Dawes should only be applied to equal 6th magnitude doubles. My understanding is that although Dawes performed his testing on many and varied doubles, the stated limit is simply an average of his various results. Although all else here is commonly accepted, this averaging explanation warrants further reading. It is true that you can tell there are two components to a double before you have reached a point where they are completely split with a black space between them. I keep my notes when I use various eyepieces, something like elongated, elongated pointed, notched, barely touching, thin black line, clear black space. Some very good telescopes are capable of exceeding both of these limits. Conversely, some lesser quality scopes will not be able to even reach these limits. But these are good indications of what a good telescope should be able to see. Rayleigh or Dawes limits usually cannot be reached when viewing doubles that are very bright, have widely varying magnitudes or are very faint. These are all more difficult conditions. Pi Aquilae is magnitude 6.1 and 6.9 at a separation of 1.4 arc seconds. This is a good double to test the ability to achieve Dawes limit. It's not exactly equal in magnitude, but it doesn't vary too widely and it is neither too bright nor too faint. I've observed this double recently on two different occasions using my TV85 scope. The TV85 calculates to a Rayleigh and a Dawes limit of: Ray Lim 5.45/3.35=1.63" and Daw Lim 4.56/3.35=1.36". I was not able to completely split this double to a black space, but I was able to identify it as a double at several magnifications. So I did reach Rayleigh and Dawes limits. But is this scope capable of exceeding these limits? I'll explain that in a bit. I was not able to completely split lambda Ophiuchi at 1.5", but I was able to completely split 69 (Tau) Ophiuchi at 1.7" to a thin black line. These are stars that seem to be right at the limit of this 85mm aperture and by all indications they clearly seem to agree with expectations based on the above formulae. Knowing the quality and the aperture of your scope and the limits implied by these formulae will help you solidify your expectations of your scope's performance. Now back to the passage I referred to as important. Let me further explain. First I will repeat what I said earlier. Rayleigh Limit states you should be able to tell that a double is two stars if the centers of the diffraction disks of the two stars is separated by a dimension equal to the radius of the first diffraction interspace. That's the radius from the center of the Airy disk to the minimum of the space between the disk and the first diffraction ring. What if I want to see a double star with at least a thin black space between the components? What are my limits? What should I expect of my scope? Based on the definition above, Rayleigh limit is a measure of a radius. It is the measure from the center of the bright central dot, or the central disk, out to the minimum of the "black space" between the central dot and the first bright diffraction ring that surrounds the Airy disk. If you want to see two stars as completely separated with a thin black space between them it is necessary for the centers of the Airy disks of the two components to be separated so this "black space" overlaps and becomes visible between them. That separation dimension is approximately equal to two radii or the diameter of the Airy disk. Rayleigh Limit for my 85mm scope is 138/85 or 1.6 arcseconds radius. Therefore the Airy disk diameter is 2 x 1.6" or 3.2 arcseconds. The central disk itself is slightly smaller than the Airy disk dimension since the Airy disk is measured out to the minima of the first dark space. It varies with magnitude, but say it's 85% for a bright star and for a faint star it may be less than 50% of the diameter of the Airy disk is occupied by the central bright spot. So the equivalent separation of something less than twice the Rayleigh Limit, we'll use 60% for this example, is needed to have a black space between two stars. If Rayleigh Limit for my 85mm scope is 1.6 arcseconds radius, then any time I can cleanly split doubles of less than 2 x 1.6" or 3.2" x 60% or 1.9 arcseconds, to at least a thin black space between them, then I have exceeded Rayleigh Limit. For brighter stars the central bright spot is larger, therefore I might multiply by 85% rather than 60%. Dawes is not a measure dependant on the wave nature of light. It was empirically determined to represent a point of minimum separation where a double can be noticed as two components. To say that I have exceeded Dawes, I should be able to show that I can notice stars as double when they have a separation of less than 116/Dmm. Do not confuse the definition of the Airy disk as the bright central dot in the diffraction pattern. This is really not correct and this term is very often confused in much of the literature in print. The Airy disk is measured out to the minimum of the first diffraction interspace. The central dot is correctly referred to as the spurious disk. There is no true measurement for the spurious disk itself. The measurement 5.45/D based on the wavelength of light (and specific only to yellow light at 550 nanometers) is out to the first minima. The edges of the central disk usually cannot be seen as the light falls off to zero towards the first minima as we move from the center of the central disk out into the first diffraction interspace where the minima occurs. The dimension of the Airy disk varies with the wavelength of light, being larger for red light and smaller for blue light. Therefore it may be slightly easier to split two blue stars than two yellow stars and both are easier than two red stars would be. edz |
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