vlaiv

One that I managed to find does not quite say 0.004 rad (It might as well as far as I know), but rather this: something, something, something 4, something something 436nm~656nm something 11 something something something It appears that I did not need to look for this - it's been posted on the page 1 of this thread. But we can do this the other way around as well: vs From what I can tell - Japanese text on that image indeed reads the same as google translation of micro radians (I left 0.004 by accident - I typed then number alone first - ignore zeros as text contains 4 and Japanese letters that translate from micro not milli).

Of course. Nothing beats actual use, but I was referring to the specification. Say you want to purchase a new eyepiece. Focal length, eye relief, AFOV and/or field stop diameter (hopefully) will be listed - and these all impact our purchasing decision. Now, wouldn't it be nice if you had the image of what you might expect in terms of sharpness as well? All of the above won't guarantee that you'll enjoy that eyepiece in your scope given your observing style and preferences - but it is important part of decision making process when you want to select eyepiece to try out. In my view - such image would certainly beat any sort of spot diagram or number that you can't really easily relate to the expectation of what the view thru such eyepiece will be like. Think of it this way - you plan a holiday and want to select your accommodation. Sure, you'll get all the info - number of rooms, square footage, view overlooking the bay (if it is a sea resort) facing west, bed size - you name it. Then there are photos of the accommodation and the view - which would you prefer - written specs or images? And certainly - photos can't really entirely show you the feeling of staying in such accommodation - you need to experience that for your self - but they are much better indicator of what to expect then just a list of numbers and facts, right?

I rather like approach that @Louis D has been championing - shoot view thru the eyepiece with camera. If we fix enough parameters and make sure optics and sensor side are uniform enough and don't interfere as much with performance of the eyepiece - we could develop "a standard" for comparing eyepieces. Imagine database of images - with EP manufacturers publishing their own shots on new eyepieces. You can simply take two shots - one of the eyepiece you are familiar with and the new one - and you get instant comparison (at least in part) of their performance. Of course - there are parameters that are going to be individual preference between two eyepieces - but what I'm here saying is that specs don't necessarily need to be in form of numbers and hard to understand graphs - they can be something that we intuitively understand well.

Technical specs are there for a reason. Not everyone can afford to purchase expensive eyepiece just to try it out Not everyone can borrow such eyepiece to try it out Reviews of the eyepiece contain more information if eyepiece is compared to another eyepiece and differences are outlined. Just saying - "it gives excellent views" does not mean much if we don't have reference / baseline. This can pose the same / similar problem as point one above - not everyone had the opportunity to try comparison eyepiece so they won't completely understand performance based on a difference to unknown. We often resort to "hive mind" when choosing an item for our next purchase because of the above. This is why in many fields there is a standard for listing technical specification. People can make informed decision. If an engineer needs a part for a project - they can simply look at the specs with high level of confidence that they will get what they need. I'm afraid that we are not there yet with astronomical equipment.

There is a technique to increase photographic FOV with any telescope without using additional equipment, but it does require some skill and practice and advanced use of software. You can always make mosaic image of the target. Shoot several panes and then stitch them prior to processing the image. However, in order to do that - you need to plan mosaic layout and be able to point the telescope at exact place - which is usually done by plate solving. You also need software that will stitch the image for you. Excessive gradients from light pollution cause problems if not dealt with properly and binning must be used if one does not want to spend large amounts of time on the target.

They show different thing. Upper circle is telescope + eyepiece, lower circle (at least I believe so) is just eyepiece with point source at focal plane - so not airy disk of optics in front of the eyepiece. BTW - 12mm Vixen NLV has 5' star image at the edge of the field (comparable field size and comparable focal length) - it turns out that Vixen NLV performs much better than this eyepiece so why pay more? http://astro-talks.ru/forum/viewtopic.php?f=32&t=1483

That seems too much for premium eyepiece? It is the same as 2mm at arms length (500mm). I'm now looking at ruler at that distance - and I'd be surprised to see a star that size in the eyepiece to be honest.

Agree on diffraction limited near the edge part, but have no idea if they made an error - my first impression was that it is legit, but who knows.

Eyepiece aberration adds to that of telescope. They presented combined spot diagram for Aplanatic optical system + each of their eyepieces to show improvement on axis compared to already existing lines. In lower row - they wanted to show that there is in fact difference between on axis and edge performance of the new eyepiece - but in fact it is so small (both fall in 4 micro radians category) that it is negligible and essentially edge performance is as good as center as far as this eyepiece is concerned. At least that's how I'm reading the diagrams.

Image says 4 micro radians - not milliradians - that is x1000 less.

Very amusing and interesting read.

Not sure what you mean by commonplace things and math being unable to express. They are all well defined within mathematical framework. Sure, they need infinite sums, but we know how to work with those (without actually calculating all the way to infinity and back ).

Yes, but incompleteness means that we can't prove all the theorems. However - we can prove large number of theorems, and if we can prove all the theorems needed to model the universe - I don't see why would incompleteness defined that way pose a problem?

Why? There is no indication that model of universe needs to be of infinite complexity. Maybe we can prove that subset of math that is needed to model the universe is in fact complete?

That is not quite what I've said (nor was it claimed by Tak). I'll need a bit of an introduction that you and anyone else reading this explanation may already know - then consider this as a reminder and setting the context for what will be said. Telescope is a projection device - it projects angles onto a focal plane. Eyepiece is "inverse" of above - it takes image from focal plane and turns it into output rays at certain angles. When we combine the two we get system that magnifies the image - or increases incident rays by some factor. To understand what I meant by factor of x287 over airy disk of F/10 scope we need to think of eyepiece as magnification lens - much like regular magnifying lens. Whatever is placed at focal plane of eyepiece - we will be able to see it magnified. Now, back to original TAK diagram and their claim They claim that single spot at focal plane produces above image. Not star image thru a telescope - but single spot. Think of it as single atom of light emitting phosphorus or something like that in focal plane. That single point will produce object that is up to 4 micro radians to our eyes or 0.825 arc seconds. Now in perfect system - single dot, no matter how magnified will still be single dot - but this eyepiece "blurs" that perfect dot into something that has angular size like say one of the moons of Jupiter - viewed by the naked eye. Now, let's for the moment say we have perfect eyepiece - one that introduces no aberrations. 4" F/10 telescope will produce airy disk 2.77 arc seconds. Such telescope has 1000mm focal length and if we pair it with perfect 12.5mm eyepiece - image will be magnified by 1000/12.5 = x80 To our eye - star, or rather its airy disk will look like it is 2.77" * x80 = 221.6 arc seconds large So perfect spot in focal plane with Tak eyepiece will be presented to us like 0.825" large circle (in worst case at edge of the field) while 4" F/10 scope with perfect eyepiece (in fact both can be perfect optical system) - will present star image to our eyes that is 221.6 arc seconds large. Difference between these two images is 221.6 / 0.825 = x268 (I obviously made a typo or copy error in initial calculation - as result is 268 not 287). The way one needs to interpret that would be - perfect eyepiece in 4" F/10 scope will produce around 221.6" airy disk size to our eyes, but with Tak eyepiece that size will be increased by roughly 1/268th of that to 222.4" - at the edge of the field. Or in simple words - blur that eyepiece adds to perfect airy disk (for 4" F/10 scope) is about 1/268 of the size of that airy disk - of we could say insignificant. Hope this makes sense now.

Well, I think we do need to be careful with our use of the term comprehensible. I will give you an example of distinction between two things that might give you clue of different meanings of the word. One is for example - reading the future from chicken intestine. Here we have: a) pattern b) someone who recognizes the pattern c) does interpretation of the pattern (right or wrong) We do need sentience for that On the other hand - here is another example: All powers of 2 written in binary form have same structure - 1 followed by some number of zeros. Here we have a) pattern b) no need for recognition or interpretation - pattern just exists and there are relationships behind it that can be comprehended by someone if that someone exists - or not Now, we must be careful with how we use word pattern again. Throw bunch of lego bricks on the floor and you'll be able to spot so many patterns. Here pattern is formed because we assign it some "meaning" - but it is not necessarily "universal" pattern that would exist without us assigning it a meaning. Strange thing about universe is that it is ordered in such way that universal patterns exist (regardless of the fact if anyone is there to recognize them as patterns or not). In vast configuration space of possible universes - there is much more those that are chaotic without any rules (the same reason why we have second law of thermodynamics - there are more disordered states of the system then ordered ones).

I'm sure they had sightings - but did not have Nokia 3310 to make a recording of it

Well, it this is nicely summed up in famous quote: The least comprehensible thing about universe is that it is comprehensible. As far as I can tell (and been able to find on google), it was Einstein who said that, and I completely agree. This goes in line with your assertion Olly - yes, math is language of comprehensible and given the nature is comprehensible - it is no wonder it can be expressed in language of math. However - that really does not explain why it's comprehensible in the first place and the fact that comprehensible universes are rather low in probability in space of all possible universes

Yes

It's 1mm

Does star exterminator work on color data or per channel? This is in red channel only.

Can you explain why, for my benefit. Try to explain it in simple terms so I can understand.

I think that cosmological principle plays a part here. Scale factor is the same for every point with same proper time from the big bang. Proper times are also "synchronized" so to say as general curvature of space time is the same in every point due to cosmological principle and expansion of space does not imply that points are moving away from each other in local sense / special relativity sense. In simple terms - time evolved in the same way in origin of the photon, our location and every point along the trajectory. Also - all of these points of interest do not move in relativistic sense - they are all on the same "now" slice with respect to us (or close enough so we can assert that scale factor is the same). if we have non linear time - we can simply introduce a parameter that is linear and instead of having a(t(p)) - which is a * t(p) we can simply replace that with a'(p) in linear parameter. There is no reason why integral in our proper time would not work for scale factor along the whole trajectory.

You are quite right. Even at F/4 (this is for binocular lens telescope) - it is still to fine adjustment. It could have easily worked with x3-x4 coarser focusing mechanism.