25 replies to this topic

[APO1]

Greetings. For the uninitiated, could someone discuss spot diagrams, how they are made, and what do they indicate about the properties of an optical system, the quality thereof? Does this analytical method apply to both refractors and reflectors? To what extent are eyepieces involved if so? Can I assume that they are a statistical tool?

I'll just sit back and listen, thanx in advance for you'uns (that's how we say it in our neck of the woods) input.

[mikey cee]

Well don't sit back and wait too long. I've yet to really hear or be shown in laymen's terms how any telescope test's are interpreted let alone made. Just a lot of esoteric gobbledygook that a normal person with a modicum of intelligence never is quite able to grasp. I'll bet my bottom dollar this thread will end up the same way.   Mike

[futuneral]

This may give an idea or lead to more specific questions:

 

http://photo.stackex...ns-spot-diagram

[Alan A.]

Hi,

 

For a telescope spot diagrams show well the optics bring rays of light to focus.  An ideal telescope would bring all rays to a point (excluding the phenomenon of diffraction). Spot diagrams are an extremely useful tool for optical designers as well as for any one trying to understand how well a given optical design performs. Spots are useful for refractors, reflectors,catadioptrics, and eyepieces.  I would consider them more of an analysis  tool rather than a statistical one.

 

If you have interest in the topic, while there is some good info on the web, I think the single best introduction to the topic is in a book called Telescopes Eyepieces and Astrographs.
 

http://www.willbell....strographs.html

 

It is beautifully written, has a treasure trove of information on refractors, and actually all types of telescopes and eyepieces, and superb explanations of interpreting spot diagrams.  I must have now over 50 books on optics, this one is by far my favorite.  I know several professionals in the field who have the highest regard for the book.  Regarding eyepieces, I actually had a chance to ask Al Nagler what he thought about the sections covering Televue eyepieces and he thought they were excellent. We are very lucky to have this text available as a resource since it has a ton of pearls on telescope and eyepiece optics that do not appear any where else.

 

best,

 

Alan

 

Edited by Alan A., 23 March 2016 - 11:30 PM.

[turnerjs085]

A spot diagram is a geometric (as in not including diffraction) ray trace of an optical system. Say you plotted a grid of 1000 incoming parallel rays (of the same wavelength) where they enter the objective and followed each one through the system, plotting it's final location at the focal plane. This would give you a pretty good idea of how sharply the optical system would focus light of the wavelength ploted. You can do further ray traces for off axis rays, other colors, expected manufacturing errors, etc.

Basically, a spot diagram is a fairly accurate representation of how a scope of a particular design will work. It is much more of a design tool than a test however.

Jeremy

+1 on the book btw. That plus "telescope optics" and maybe "applied optics and optical design" by Conrady (if you get in deep ) are fantastic books.

Edited by turnerjs085, 25 March 2016 - 09:55 PM.

[jrbarnett]

Greetings. For the uninitiated, could someone discuss spot diagrams, how they are made, and what do they indicate about the properties of an optical system, the quality thereof? Does this analytical method apply to both refractors and reflectors? To what extent are eyepieces involved if so? Can I assume that they are a statistical tool?

I'll just sit back and listen, thanx in advance for you'uns (that's how we say it in our neck of the woods) input.

Usually a spot diagram is a theoretical tool based on a hypothesized perfect implementation of a given optical design.  It tells more about the potential on and off axis performance and color correction of a given model than the actual quality of a specific example of that model.

 

You want bench test results and field reviews of a specific unit to assess its quality.  Quality varies unit to unit to some extent, no matter how expensive the optic.  The hope (sometimes borne out by test results, but not always) is that the more costly optics are more consistently high in quality unit to unit.

 

You can sometimes find spot diagrams for different designs on manufacturer or dealer websites.  For instance, here is a spot diagram for a Takahashi FSQ-85 astrograph from Takahashi Europe:  http://www.takahashi...ptics.spots.htm

 

As for bench test results, they are rare on American sites, as most hobbyists here care little for optical design or science, chalking it up to "gobbledegook", and instead prefer to accept brander marketing hype as gospel.  But the Japanese and Europeans are generally more knowledgeable and selective when it comes to optics.  Here are some examples of European bench tests:

 

http://www.astrosurf...ent/apo140e.htm

 

http://interferometr...140980-tec.html

 

http://r2.astro-fore...sahnestueckchen

 

Here's a good critique of different methods of bench testing.

 

http://www.cloudynig...interferometer/

 

Because refractors do not focus each wavelength of light at the same point and the human eye is more sensitive to certain wavelengths than others, Fomalhaut's suggestion in that discussion, that "the Strehl of each measured wavelength should be multiplied with its specific human eyes' visual photopic sensitivity, then all the products be summed up and the result finally be divided by the sum of all the weighting factors used", is a great one.

 

How useful bench test data is in assessing optical quality and field performance really depends on the nature of that data.  Peak Strehl (the highest figure quality reading for a given optic at a single wavelength) is somewhat suggestive of optical quality of that optic.  Better still would be the Strehl for each visible wavelength when perfectly focused on green where the eye is most sensitive.  That would give you an idea of the extent to which visible data captured by your eye falls below the diffraction limit (i.e., the image quality for that wavelength is determined by errors in the optical figure and not errors induced by the atmosphere).  But even that is not perfect as it does not weight the importance of the data at each wavelength relative to how the human eye works at night.

 

Doing a perfect bench test is very hard.  But getting useful information from a bench test isn't hard.  And it's definitely more useful in judging how good an optic is than relying on manufacturer or dealer marketing speak and literature.

 

Lastly, eyepieces are almost irrelevant in determining optical quality - especially on-axis.  Eyepieces primarily magnify whatever data the telescope collects.  If the telescope is poor in quality, it will collect garbage data and the eyepiece will simply magnify that garbage data.  Conversely a well-designed, well-executed optic will collect quality data and the eyepiece won't reduce or increase that quality.

 

With that in mind, are there specific telescopes you're curious about?  There may be some bench test data available for the scopes you're curious about.  Such data is not dispositive on performance, but it is instructive.

 

Regards,

 

Jim

[Jeff B]

I find spot diagrams can be very useful to "see" how well a design may perform relative to the airy disk size (s)  for various wave lengths of light.  They don't give me quantitative information but it's a quick visual to me.  They will not tell you in numbers how much spherical aberration, coma, astigmatism, out of focus...and so forth you have, but you can readily see their aggregate. 

 

And that's just it.  You have to be careful when looking at and drawing conclusions from spot diagrams generated by others than yourself.  The thing is, like anything computer generated, they can be displayed in many different ways and generated with only selected aberrations. For example, there is what I call the single spot display that is just that, a single airy disk with all of the rays stuffed into it.  Then there are those that I like which shows the individual wavelength spots in a row from blue to red with the airy disks for each chosen wavelength.

 

But to be really useful to me, I need to know the assumptions used to generate and display the spots.  I like to see the spots in a row for the usual benchmark wavelengths between 400 and 700.  I like to see those spots generated with the focus in green (were the best correction typically is) and all aberrations included with enough rays to clearly see the overall shape of the spot and what portions are outside the airy disks.  I like to see that type of plot on axis and at .25, .5 and 1.0 degrees off-axis.  

 

You can play games with spot diagrams too.  For example, displaying a single spot but allowing focus to vary in order to show the smallest integrated spot size.   There may be some merit to this type of display as some feel that's how we tend to focus at lower powers and may be of interest to imagers.  

 

And remember, the spots are for a specific design, made perfectly.

 

They can be very useful but be careful and ask questions about how they were generated.

 

Jeff

Edited by Jeff B, 27 March 2016 - 11:05 AM.

[APO1]

Thanx folks. Lots of good information to digest, I'm sure I'll have some questions afterwards.

 

Dan

[Eddgie]

Here is one very important point that is either overlooked or commonly misunderstood,  though one responded mentioned it.

 

The ray trace would suggest that if the plot for one telescope produces a smaller spot than another telescope, then the scope producing the smaller spot will produce a sharper more contrastier image.

 

That is not at all the case.   Almost all spit diagrams show the spots in a circle representing the Airy Disk diameter.  It does not matter if the plot for one scope shows all of the spots in a single point and the other shows them as round ball.  As long as all of the rays fall inside the circle of the Airy Disk in booth cases, both scopes will produce the same sharpness assuming all else is equal.

 

Now this also means that contrast lowering due to obstruction is not reflected but if two scopes with the same obstruction showed one to have tighter spots, as long as the spots for the one with the looser spots had all if the spots within the circle, once. Again, the scopes would perform the same.

 

I have seen this used in advertising where the tighter spots shown for one scope implied that it would outperform a competitors instrument, but that was just suggestion.  The reality us that as long as the spots all fall into the circle, the scopes are both diffraction limited, and that is where the term diffraction limited comes from.  All else being equal the scopes would perform the same.

 

Since it would be difficult to get more than toy prices for a telescope that was less than diffraction limited, there is no design produced today and sold as a serious telescope today that does not have diffraction limited optics by design, ray traces are really only useful for color correction and off axis performance.

 

Edited by Eddgie, 26 March 2016 - 04:21 PM.

[Alan A.]

Here is one very important point that is either overlooked or commonly misunderstood,  though one responded mentioned it.

 

The ray trace would suggest that if the plot for one telescope produces a smaller spot than another telescope, then the scope producing the smaller spot will produce a sharper more contrastier image.

 

That is not at all the case.   Almost all spit diagrams show the spots in a circle representing the Airy Disk diameter.  It does not matter if the plot for one scope shows all of the spots in a single point and the other shows them as round ball.  As long as all of the rays fall inside the circle of the Airy Disk in booth cases, both scopes will produce the same sharpness assuming all else is equal.

 

 

 

Hi Eddgie, I am glad you highlighted this issue because its very interesting, but I not sure if your statements are correct.  For example, Carl Zambuto makes a point of saying that the best mirrors have close to a 0.5 Relative Transverse Aberration (RTA), indicating that the rays actually all fall in the inner part of the Airy Disk. ( an RTA of 1.0 means that all the rays fall within the Airy disk, and an RTA of 0.5 means that all the rays fall within an area with 1/2 the diameter of the Airy Disk).  If you, or others here, have additional information on this topic it would be of great interest.  Obviously he is talking about mirrors, but the principle would apply to all types of telescopes including refractors.

 

Best,

 

Alan

[MooEy]

Well, spot diagram is just a drawing showing how good the optics converge light based on the design. When it comes to actually execution of the design, many things can happen.

Something good to know, but even if the design shows something awesome, the actual lens may differ slightly.

Another point, for any refractor, it's up to the manufacturer to plot the diagrams. They can simply omitted wavelengths at either end that don't do well, or provide some chart where certain wavelengths are "spread out into thin air". I do not blame these manufacturers, as they are probably at the mercy of their supplier.

Some manufacturers may show you the charts to show off their superior design, others may just want to use the charts to sell more scopes.

Everyone is born with a different luck attribute in their character stats. Whether you get a good scope is partially dependent on that. Good luck and have fun shopping.

~MooEy~

Edited by MooEy, 27 March 2016 - 03:21 AM.

[Eddgie]

 

Here is one very important point that is either overlooked or commonly misunderstood,  though one responded mentioned it.

 

The ray trace would suggest that if the plot for one telescope produces a smaller spot than another telescope, then the scope producing the smaller spot will produce a sharper more contrastier image.

 

That is not at all the case.   Almost all spit diagrams show the spots in a circle representing the Airy Disk diameter.  It does not matter if the plot for one scope shows all of the spots in a single point and the other shows them as round ball.  As long as all of the rays fall inside the circle of the Airy Disk in booth cases, both scopes will produce the same sharpness assuming all else is equal.

 

 

 

Hi Eddgie, I am glad you highlighted this issue because its very interesting, but I not sure if your statements are correct.  For example, Carl Zambuto makes a point of saying that the best mirrors have close to a 0.5 Relative Transverse Aberration (RTA), indicating that the rays actually all fall in the inner part of the Airy Disk. ( an RTA of 1.0 means that all the rays fall within the Airy disk, and an RTA of 0.5 means that all the rays fall within an area with 1/2 the diameter of the Airy Disk).  If you, or others here, have additional information on this topic it would be of great interest.  Obviously he is talking about mirrors, but the principle would apply to all types of telescopes including refractors.

 

Best,

 

Alan

 

 

While there is a grain of truth in this, one has to look at the number of dots used to create the plot.   Typically, 200 dots are used, but what this means is that a relatively small number of dots falling away form the center of the peak intensity can give the appearance of a much larger distribution, but the reality is that most of the rays will still be falling in the central intensity.

 

The difference is contrast will then be so small as to be able to be ignored.

 

The book Telescope Optics covers this point with respect to the plots for off axis Coma.  They show a 3D distribution showing that while the ray trace can make the comatic fan appear to be very large, for low amounts of coma, most of the intensity is concentrated in the Airy Disc.  Coma though would be of course more damaging than the slight distribution difference inside the Airy Disk on axis.  The specific plot that I am talking about is seen in figure 4.4, on page 25.

 

So, while I agree that there might be a small difference in the intensity peaks, the spots will almost always greatly overstate this difference and the human eye, the view will be the same.

 

I would refer people to page 23 of this book and in particular, this quote.  Emphasis added by me....

 

 

Interpreting spot diagrams is straightforward compared to graphic representations.  However, there is a pitfall the designer should always keep in mind: the relative intensity of parts of the image.   Figure 4.3 and indeed, all such representations, under-represent the intensity in the brightest parts of the image....

 

They then go on to say:

 

 

Anyone using longer dimensions of the comatic blur to assess the effective image size would estimate it 3 times larger than normally records.

 

 

 

in other words, the distribution of the plots almost always over-represents the amount of energy that falls outside of the area of peak intensity and almost always by a very large margin.

 

From a practical standpoint, while Carl Zambuto may be technically correct, the spots do overstate the difference, and since the vast majority of spots are in the area of peak intensity, two diffraction limited telescopes will be, and the name implies, really only be limited by the diffraction of their apertures.  An observer or imager would not be able to discern a difference though if the image were very greatly enlarged, a specialized detector might..

 

For our purposes though, the distribution of spots within the circle that represents the Airy Disk can pretty much be ignored.  As long as all of the dots fall within that circle, the scope is diffraction limited and no observer would be able to see a difference based on the very small difference in peak intensity that would actually be present.

 

This is why it is important to read books like Telescope Optics.   They greatly clarify many of these issues that are often mis-understood or in some cases, used in marketing to highlight differences that are so small as to be meaningless.

Edited by Eddgie, 29 March 2016 - 09:26 AM.

[Eddgie]

With respect to my last post I am reminded of the work done by Dr Bose during the golden age of Stereo "Specsmanship."

 

At the time, the manufactures were engaged in a war where they used various esoteric specifications to show that their equipment would be soniclly superior to the competitors equipment. 

 

Bose was a curious man, and he wanted to understand more about sound reproduction, so he did an enormous amount of study, and the body of work he produced showed that most of the specs that were driving amplifier purchases were so far into overkill as to make them meaningless other than for marketing purposes.

 

In a controversial move, when he designed and produced his Bose 1801 amplifier, rather than actually publish hard specs, what he published was a detail brochure that explained in detail what every spec meant, and more importantly, he published the level of specification that defined the limit of human hearing...     

 

Rather than saying what his actual spec was, he would then say "The Bose 1801 exceeds this spec.."

 

He disengaged form specsmanship and focused his buyer on the fact that there was a "Practical" limit past which the only thing that was being delivered was "Bragging rights".

 

And that is pretty much the case with spot diagrams.  Once the spots are concentrated inside the Airy Disk, there is no meaningful benefit to getting them to fall into a single point because diffraction is now the limit to performance.

 

Quality, obstruction, and chromatic abberation will make many orders of magnitude more difference past this point than halving the size of the bundle in the Airy Disk circle.

 

I invite any skeptics to go to the web page Telescope Optics and look at a bunch of plots for Apos.

 

Here we see that instruments that people rave about having amazing contrast usually have spots that only barely squeeze into the Airy Disk circle:

 

http://telescope-opt...po_examples.htm

 

And yet these scopes are reputed to be the finest instruments per inch of aperture that money can buy..

 

I you looked at the size of the spots in the diagrams though, and took Carl Zambuto's words as indicating that the size of the spots inside the Airy Disk circle was super-important, one would think that most Apos would not be very good scopes yet we know that per inch of aperture thy are quite excellent.     Again, one has to consider that the spot diagram will almost always mis-represent the peak intensity, and in the Apo ray traces, the distribution of the dots is wildly misleading if one only considers the overall diameteter..    That would be true in reflecting systems as well.  

 

As long as the dots all fall within the circle defined by the Airy Disk, all other factors being the same, the instruments will perform pretty much the same because diffraction of the aperture will be the practical limit of performance.

Edited by Eddgie, 29 March 2016 - 10:23 AM.

[Eddgie]

And this... Being the refractor forum, if you study the spots for most refractors, you very quicaly realize that very few refractors are capable of putting all of the energy into the diameter of the Airy Disk.

 

As I mentioned, the problem with Ray Traces is that they under-represent the peak intensity, but for charomatic abberation defocus, they tend to be much more relevant.  

 

The problem though is understanding how much total energy is being lost and how the specific wavelengths contribute to image intensity.

 

For this reason, spot diagrams for refractors are not particularly useful becuase it is hard to integrate the different color plots in a way that tells us about peak intensity.

 

For this, a far more useful way to express design performance would be to use Polychrromatic Strhel.    This method uses mathamatics to combine the energy and express the performance in a way that allows comparing apertures that spots would not easily allow.

 

If you go to this page, you can easily see what I mean.   Figure 149 shows the plots for different colors for a variety of instruments, but by itself, that detail is not all that valuable.

 

If you look at Table 12 on the same page though, the author has "condensed" the data by offering the poly-chromatic Strehl figures for each design.

 

 

http://telescope-opt...po_examples.htm

 

Now we are getting close to being able to compare apertures, but because the apertures are not similar, we need another way to express how the aperture and choromatic errors would affect the performance when the scopes were compared and this is the role of the MTF plot.  Here is just such an example and no surprise, the author has used some of the same instruments and has even provided a table that correlates that performance to obstruction size.

 

http://telescope-opt...romatic_psf.htm

 

This is the problem with spots.   They are superb for comparing off axis performance because here, aberration levels are rarely diffraction limited, and now the plots will tell a great deal about how two different designs will perform.

 

Spots bundle size differences within the Airy Disk are almost meaningless by comparison.

But more than that, for refractive systems, the spots simply can't allow the viewer to easily integrate the system performance the way Poly-chromatic Strehl can, and MTF plots can now be used to compare how different apertures with different polychormatic Strehl ratios would differ in contrast performance.

 

Last but not least, manufacturers are reluctant to publish ray trace diagrams, and I can't blame them.   Reflect on my post regarding stereo specsmanship above. They don't want to get into that kind of battle that often overstates the important of this or that spec (color plot).

 

It is sad that they do not publish poly-chromatic Strehl though, and if one were to really want the most important "Spec" for a refractor, this would be it.  Don't hold your breath on that one though.  I believe Yuri from TEC has given figures int the past and he should be applauded for that. 

Edited by Eddgie, 29 March 2016 - 01:31 PM.

[Alan A.]

"For this reason, spot diagrams for refractors are not particularly useful becuase it is hard to integrate the different color plots in a way that tells us about peak intensity."

 

 

Well, we will just have to agree to disagree on two points.  The first is that unless there is some compelling data to suggest otherwise, it's very unlikely that Carl Zambuto is wrong.  The second is, I completely disagree with the statement from your post that I put in quotes just above.  Professionals  use spot diagrams for all types of telescopes as ONE of their powerful analytic tools to to understand the performance of a particular design.

 

Also, I would rather have a graph of Strehl vs Wavelength than a single polychromatic number, as you get a lot more information from the graph.

 

Best,

 

Alan

[wh48gs]

Well, I don't know what Zambuto actually has said, but saying that RTA of the Foucault test is equivalent of the actual transverse aberration is plain wrong. The reason is the nature of the test, which effectively fragments the total longitudinal aberration, based on the "zero" aberration at the zone chosen as the reference (zero) zone for data reduction. Since the value of the RTA is obtained directly from this fragmented longitudinal aberration, it is inevitably smaller than the actual transverse aberration. The RTA (relative transverse aberration) is doubly relative: first relative to the Airy  disc, which is obvious, and second, relative to the focus of the reference zone, which is not obvious but does make it different (smaller). Moreover, RTA for the same mirror is different for different reference zones: it is the largest if the reference zone is either inner of outer zone, but even then is significantly smaller than the actual aberration, due to the actual longitudinal aberration being trimmed off by averaging inner and outer focus (RTA value will also vary with the number of zones, but to much smaller extent).

 

For example, taking 300mm f/5 mirror that is 50% corrected (-0.5 conic), the RTA based on the perfectly measured relative longitudinal aberration (which is basically the differential relative to the zero point at the reference zone), the RTAs for a mask with median zonal heights 0.3, 0.5, 0.7 and 0.9, in units of mirror semidiameter, RTA values for the inner zone as the reference are 18.1, 10, 3.6 and zero Airy disc radii, respectively. Taking 0.7 zone as the reference (usually the case), RTA values change to 8, 0, 3.5 and 3.4, in the same order. The actual aberration for this mirror at the best focus (coinciding with the 0.707 zone focus) is 1.07 wave p-v, with the corresponding transverse aberration (geometric blur) 27.9 times the Airy disc diameter. So in this case the RTA (the largest value, 8) is 3.5 times smaller than the actual transverse aberration. If we take this as at least approximate proportion, it implies that the 0.5 RTA criterion corresponds to 1/8 wave of spherical aberration (actual transverse aberration at the best focus 1.6 Airy disc diameters), and RTA of 1 corresponds to 1/4 wave (actual TA 3.26).

 

What level of aberration implies having all rays contained within Airy disc is different subject. The answer will vary greatly with the type of aberration. For instance, the ray spot plot just fitting into Airy disc corresponds to 0.077 wave p-v with primary spherical, 0.27 wave p-v with coma and 0.61 wave with astigmatism (all at the best focus location). In terms of RMS error, it's 0.023, 0.048 and 0.125, in the same order, with the corresponding Strehl values 0.979, 0.909 and 0.54. Obviously, it is a very rough measure.

 

Vla

[Eddgie]

 

 

What level of aberration implies having all rays contained within Airy disc is different subject. The answer will vary greatly with the type of aberration. For instance, the ray spot plot just fitting into Airy disc corresponds to 0.077 wave p-v with primary spherical, 0.27 wave p-v with coma and 0.61 wave with astigmatism (all at the best focus location). In terms of RMS error, it's 0.023, 0.048 and 0.125, in the same order, with the corresponding Strehl values 0.979, 0.909 and 0.54. Obviously, it is a very rough measure.

 

Vla

 

 

I think that you might agree though that these errors (coma, astigmatism. and sphercical aberration) are not common on axis for reflectors (design wise).. They can be seen as a result of fabrication errors of course, but I have never seen anyone publish a spot diagram for a completed system showing fabrication errors when very few even publish ray traces for the designs they make with Celestron EdgeHD and Takahashi being two notable exceptions).

 

In most cases, reflecting systems will have round bundles on axis and in most cases for standard reflecting systems, the ray bundle will fall well inside the Airy Disk diameter.

 

For tilted systems, the case is much different, but even hear, it is unusual for a titled system to have these kinds of aberrations.  

For most reflectors though, the spots will be well within the diameter of the Airy Disk and the apparent difference in size between the bundles will not be particularly meaningful I don't think.

 

Contrast this with a refracting system though, where the plots for all wavelenghts rarely fit into the diameter of the Airy Disk, and it becomes difficult for the spots to be useful because the intensity of the spots cannot easily convey the total encircled energy (or at least it has never been useful to me, and maybe that would be a better thing to say).

While I can see using the spots that these systems are not "perfect", the spots by themselves are not easy to intrepret in terms of how this design would differ from that design (except in a general way).

That is why I believe (and it is just an opinion) that these spots are not as useful to the consumer as other criteria would be.

 

From a design perspective, the polychromatic Strehl of a refracting instrument seems to be a far more useful way to compare apertures.   Knowing the polychromatic Strehl to me is far more valuable than seeing the spots except perhaps in the case of imaging (but even here, people will image even with Achomats, relying on filters to suppress the useless data). 

 

Anyway, this is all just my opinion of of course, and everyone gets one, right or wrong.

 

 

To the OP I would say this though.    Telescope-Optics.net has a lot of information on all of these kinds of tools, and the book Telescope Optics has a very nice section on how spot diagrams work, and how to interpret them.

 

While the spot diagram may be useful to an engineer, it is not always intuitive for the consumer, especiallly for refracting systems, because they simply do not allow us to easily visualize the total error.

 

At least that is my opinion and it is a lay opinion..

 

Perhaps the best thing for you to do is to take some time with these resources and reach your own conclusion and avoid a lot of debate, which won't really make you feel good about anything I suspect.  Your own conclusion will matter far more to you than anything I say for sure.

Edited by Eddgie, 30 March 2016 - 10:46 AM.

[Doc Willie]

 

If you have interest in the topic, while there is some good info on the web, I think the single best introduction to the topic is in a book called Telescopes Eyepieces and Astrographs.
 

http://www.willbell....strographs.html

 

 

****. Something else I have to buy at NEAF.

[Alan A.]

 

 

What level of aberration implies having all rays contained within Airy disc is different subject. The answer will vary greatly with the type of aberration. For instance, the ray spot plot just fitting into Airy disc corresponds to 0.077 wave p-v with primary spherical, 0.27 wave p-v with coma and 0.61 wave with astigmatism (all at the best focus location). In terms of RMS error, it's 0.023, 0.048 and 0.125, in the same order, with the corresponding Strehl values 0.979, 0.909 and 0.54. Obviously, it is a very rough measure.

 

Vla

 

Hi Vla,

 

Thanks for adding this information about the way the Rays fall into the airy disk. Very  illuminating  information.

 

Best,

 

Alan

[SandyHouTex]

Here is one very important point that is either overlooked or commonly misunderstood,  though one responded mentioned it.

 

The ray trace would suggest that if the plot for one telescope produces a smaller spot than another telescope, then the scope producing the smaller spot will produce a sharper more contrastier image.

 

That is not at all the case.   Almost all spit diagrams show the spots in a circle representing the Airy Disk diameter.  It does not matter if the plot for one scope shows all of the spots in a single point and the other shows them as round ball.  As long as all of the rays fall inside the circle of the Airy Disk in booth cases, both scopes will produce the same sharpness assuming all else is equal.

 

Now this also means that contrast lowering due to obstruction is not reflected but if two scopes with the same obstruction showed one to have tighter spots, as long as the spots for the one with the looser spots had all if the spots within the circle, once. Again, the scopes would perform the same.

 

I have seen this used in advertising where the tighter spots shown for one scope implied that it would outperform a competitors instrument, but that was just suggestion.  The reality us that as long as the spots all fall into the circle, the scopes are both diffraction limited, and that is where the term diffraction limited comes from.  All else being equal the scopes would perform the same.

 

Since it would be difficult to get more than toy prices for a telescope that was less than diffraction limited, there is no design produced today and sold as a serious telescope today that does not have diffraction limited optics by design, ray traces are really only useful for color correction and off axis performance.

You make a good point, but most of the spot diagrams I've looked at show that off-axis almost every optical system, does not focus all of the rays into the Airy disk.

 

"Telescope Optics" by Rutten and Van Verooj is a great source to learn more.

Edited by SandyHouTex, 31 March 2016 - 08:53 AM.

[wh48gs]

 

 

 

What level of aberration implies having all rays contained within Airy disc is different subject. The answer will vary greatly with the type of aberration. For instance, the ray spot plot just fitting into Airy disc corresponds to 0.077 wave p-v with primary spherical, 0.27 wave p-v with coma and 0.61 wave with astigmatism (all at the best focus location). In terms of RMS error, it's 0.023, 0.048 and 0.125, in the same order, with the corresponding Strehl values 0.979, 0.909 and 0.54. Obviously, it is a very rough measure.

 

Vla

 

 

I think that you might agree though that these errors (coma, astigmatism. and sphercical aberration) are not common on axis for reflectors (design wise).. They can be seen as a result of fabrication errors of course, but I have never seen anyone publish a spot diagram for a completed system showing fabrication errors when very few even publish ray traces for the designs they make with Celestron EdgeHD and Takahashi being two notable exceptions).

 

Can't agree to that, Eddgie. Spherical aberration is quite common on axis, and it is not a rarity that astigmatism is present as well. Fabrication errors of some kind are omnipresent, n fact, we could say that there is no such thing as a perfect optical surface, let alone a system. Most of published designs will show axial spot smaller than the Airy disc, but the actual instruments are different story. Even if being 1/8 wave p-v of primary spherical on axis, which is about as good as anyone could hope for, the actual blur at the best focus is 1.64 times the Airy disc diameter (if the smallest blur is shown, which is often done to make the spots look better, the blur reduces in half, but the p-v/RMS error for that focus point is larger by a factor of 2.16).

 

Also, going by this rule will mislead toward underrating size of diffraction limited field with coma, and overrating it with astigmatism.

 

In fact, no conic aberration obeys this "rule". Here's spot plots for some common aberrations, for 0.80 Strehl level. The differences are tremendous. For defocus, the blur at this aberration level is 0.8 times the Airy disc diameter, which means that with the two equal the actual error is 0.325 wave p-v, i.e. 0.093 RMS, for 0.71 Strehl. And the rays are still all within the Airy disc. The problem is, energy doesn't go where the rays go. I'd like it too if it was as simple as this rule, but it isn't. On the other hand, it is not really complicated. The ray spot plot criterion can never be as accurate as the RMS or Strehl, but  just knowing what is shown here will make using it it much more reliable. 

 

 

Vla

[Alan A.]

Hi Vla,

 

i was under the impression that the energy distribution would follow the density distribution of spots.  Is that not so?  In other words in OSLO, for example, it appears the PSF follows the density distribution of the spot diagram.

 

best,

 

Alan

[DesertRat]

Vlad,
Your RTA discussion above is quite illuminating.  It could help settle some ATM arguments on the matter where Foucault readings are assembled in various spreadsheets and applications which often do not agree.  This assumes any argument can actually be settled in a CN forum!

 

Spot diagrams are generally a design tool, and not the best predictor of actual performance.  Simply stated a ray spot diagram assumes that the effective wavelength of light is zero.  In actual truth each ray has an associated phase, and its the superposition of a nearly infinite number of rays of varying phase which result in the true image.

 

The ray spot plots for various aberrations at the so-called "diffraction limited" mark are also interesting.  Although they all are at Strehl 0.80  their impact on actual image quality is quite different.  The worst by far in degrading an extended image, by reason of its asymmetry, is 0.42λ of coma. What it does to an otherwise good optic can only be described as ugly.  In imaging it fairly easy to recover contrast lost due to small amounts of spherical error or central obstructions.   Coma does not respond well to conventional sharpening which uses mostly spherically symmetric processing.  Since coma normally changes across a field it is even more of a challenge.

 

For resolution of point sources like binaries, coma matters hardly at all as long as the secondary is not in the tail of the comatic image.  For extended images however its impact is awful.  Now balanced spherical is entirely different.  Most would find the focus at minimum rms the best choice, assuming the aberration is at least "diffraction limited".  The original HST had a level much higher, and best focus was a compromise closer to smallest blur as it turned out it was easier to process.

 

Glenn

[wh48gs]

Hi Alan,

 

It does work well with spherical and coma but, obviously, not with astigmatism and radially symmetrical aberrations with a compact round spot (defocus, spherical at the circle of least confusion). They are still spilling significant amount of energy out even when the spot is significantly smaller than Airy disc. There is no universal rule here, but knowing some basic characteristics of the most common aberration forms in this respect - which is rather easy to memorize - is all that's needed to be able to properly interpret the magnitude of aberration in most cases. Btw. in my experience OSLO often deviates from the theoretical ray spot plot size (sometimes from the p-v/RMS ratio as well), but the deviations are generally small.

 

Hi Vla,

 

i was under the impression that the energy distribution would follow the density distribution of spots.  Is that not so?  In other words in OSLO, for example, it appears the PSF follows the density distribution of the spot diagram.

 

best,

 

Alan

 

Vla

[wh48gs]

Glenn,

 

The ray spot plots for various aberrations at the so-called "diffraction limited" mark are also interesting.  Although they all are at Strehl 0.80  their impact on actual image quality is quite different.  The worst by far in degrading an extended image, by reason of its asymmetry, is 0.42λ of coma. What it does to an otherwise good optic can only be described as ugly.  In imaging it fairly easy to recover contrast lost due to small amounts of spherical error or central obstructions.   Coma does not respond well to conventional sharpening which uses mostly spherically symmetric processing.  Since coma normally changes across a field it is even more of a challenge.

 

Coma is considered the worst (conic) aberration, and what you are saying illustrates why. But its effect depends on the detail orientation, going from worse than for radially symmetrical aberration of the same magnitude, to better. For instance, a square detail on some kind of background will, in the case of vertically oriented blur, lose more of its image contrast than with a symmetrical aberration on the top and bottom (with the loss also likely being somewhat different for the two), but less on the sides. So when talking coma (also with astigmatism, but to a smaller extent) we are only talking the average, which is reflected in the relative energy loss from Airy disc (interestingly, it is also implied by the ray spot shape with coma, but not with astigmatism).

 

Vla