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Equipment Discussions >> Cats & Casses

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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: Alph]
      #5619346 - 01/12/13 04:04 PM Attachment (13 downloads)

Quote:

MTF applies to extended objects only. MTF does NOT describe point sources.

BTW The Dawes limit is off the MTF chart anyway.




Alph, neither statement is correct. Raleigh is 0.82 and Dawes ~ 0.97. The MTF describes diffraction of exactly that: point sources (either singularly or in infinite numbers.)

Here's a rough scale of things, even though both obstructed and unobstructed are normalized to 1. Really, obstructed is compressed horizontally by a factor of (1 - CO^2).

"In effect, an aperture D with central obstruction oD acts as a larger aberrated aperture, D/(1-o2), with its Strehl-like number (in the sense that it indicates both, normalized peak diffraction intensity and relative loss of energy to the ring area) given by (1-o2)2."

http://www.telescope-optics.net/obstruction.htm

Credit for the illustration (I added the Airy disc roughly to scale so the first ring roughly corresponds to the huge drop off. And you can even see how the CO intensity peaks closer to 1, meaning the Airy disc is smaller.) Pretty small scale, really, when working with tight doubles. Now, imagine infinite point sources scattered over Jupiter's surface and you can see the effect of additional light in the first ring, as a minimum.

http://www.handprint.com/ASTRO/ae3.html#centobs

Edited by Asbytec (01/12/13 04:15 PM)


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DesertRat
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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5619397 - 01/12/13 04:34 PM

Norme,
That is one cool looking graph. Thanks! Very clever and well done. Yes you are correct Dawes is clearly on the graph, although barely, as I showed earlier. And thanks for the reference to Vlad's site, his site is a treasure, and I hope he publishes a book someday.

Frank & others,

Optics is a complicated subject filled with approximations, conventions, regions of validity, criteria and a host of special conditions. It has a long and colorful history. Of all the mathematics one has to master as a student of physics it ranks up there in difficulty with some of the more challenging subject areas.

The convention of describing wavefront error referenced to an ideal spherical wavefront is not just found in Suiter but scores of other books. It is also used by those that make optics for telescopes, for example Texereau, Ingalls, and many others. Amateur astronomers, professional astronomers in the field of binaries (like Couteau), reference aberrations observed in terms of what they see as quarter wave spherical, eighth wave coma, etc.

The figure of 1.0 wave you quote is the aberration coefficient of balanced spherical Ai=As(p^4-p^2) for a strehl of 0.8. But the same term is 0.25 for spherical alone Ai=As*p^4. And the wavefront error for both at strehl 0.8 is 0.25. See Mahajan for example pg 85 of "Aberration Theory Made Simple" 2nd edition. I love that title!

Can we at least agree that a scope with no error other than 0.0745wv rms low order spherical (yes I know this is an unlikely case) would yield a strehl of 0.8? If not, then well, I have nothing to add. I choose to use the convention used for many years that amateur astronomers can relate to and that people that make telescopes aim for and see in their tests.

As far as MTF, I never wrote or implied that MTF was "all-encompassing". In fact what I said was that in some contexts it makes no sense as in coherent imaging, significant phase shifts, some fields of microscopy, etc. And obviously when you add an eyepiece or barlow, a detector or the eye, all the MTF's of each component are essentially multiplied.

The real MTF is a measured data set, scanning the PSF for example and taking the transform or simply scanning a test image. This is what the Zeiss firm did for many years. Zeiss also published MTF's with their lenses combined with the best B&W films of the time.

The calculated MTF is for purposes of indicating tendencies, not indicating quantitatively measured results. It does take some investment of time to appreciate what the MTF provides when applicable. Also it should be noted the MTF's I supplied assumed a vertical banded test chart. For spherical aberration or spherical obstructions that's ok. For astigmatism (or any aberration with an angular component like coma) however you have to add orientation data. Hopefully what I posted had some educational value, if not then I failed, not a singular event I must say!

Glenn

Edited by DesertRat (01/12/13 07:34 PM)


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Alph
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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5619769 - 01/12/13 08:25 PM

Quote:

neither statement is correct. Raleigh is 0.82 and Dawes ~ 0.97. The MTF describes diffraction of exactly that: point sources (either singularly or in infinite numbers.)




I stand by my statements. I should have chosen my words more carefully though.
The MTF in the last 3% of the frequency range (Dawes limit) rapidly approaches zero and is equal to the MTF of an unobstructed aperture. There is no increase or decrease of contrast in that range that could be attributed to aperture obstruction.

A point source becomes a PSF in the image. The PSF is the impulse response of an optical system. OTF (Optical Transfer Function) is Fourier pair of PSF. MTF is the modulus of OTF. However, the MTF is interpreted as the ability of an optical system to transfer spatial modulation (contrast) of an extended object to the image (focal plane). A source point has only one light intensity level.

All, check out this cool MTF and PSF demonstration implemented in webMathematica.


Quote:

Here's a rough scale of things, even though both obstructed and unobstructed are normalized to 1. Really, obstructed is compressed horizontally by a factor of (1 - CO^2).




I was referring to contrast plotted in a logarithmic scale (human eye response). See Fig. 3.6 in Suiter 2nd edition. It's a wash


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DesertRat
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Re: CO vs. All That "Other Stuff"! new [Re: Alph]
      #5619910 - 01/12/13 10:13 PM Attachment (10 downloads)

Alph,

Thanks for the Wyant calculator link, I had seen that before but had not saved it.

At Dawes criterion the MTF does not clearly describe whats happening because it is bunched up over there and frankly was not intended to. I hasten to add the Dawes criteria is normally described for an unobstructed scope and contains the 1.22 factor we all grew up with. For obstructed scopes the distance to the first Airy minimum is somewhat smaller and becomes essentially unity at 50% obstruction.

A blown up MTF shown here indicates some real added contrast at the Rayleigh line for these high spatial frequencies. Actually seeing it and proving the case is another matter. Atmospheric seeing normally prevents demonstrating this effect visually, although I think it could be done with a camera and unbiased processing and analysis. Since the laws of diffraction have been proved countless times on the bench without a seeing problem, I'll leave that experiment to a student!

For a point source it is often better to examine the actual PSF or blink/animate them as I had shown previously in this thread. If one can appreciate the concept that an image is the 'smearing' or convolution of the object with a PSF then it becomes clearer.

Glenn


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5620044 - 01/12/13 11:59 PM

Quote:

The MTF in the last 3% of the frequency range (Dawes limit) rapidly approaches zero and is equal to the MTF of an unobstructed aperture. There is no increase or decrease of contrast in that range that could be attributed to aperture obstruction.




Thanks for clarifying, I don't totally disagree.

Well, yes, that's true. But the contrast at the Dawes level is "off the chart" at a higher spacial frequency than normalized at 1. In the charts shown, both obstructed and unobstructed aperture maximum spacial frequencies are normalized to 1. In reality, an obstructed aperture has a maximum spacial frequency of about D/(1-o^2) at zero contrast. So, the curve for an obstructed aperture actually hits zero contrast a bit beyond the normalized 1.00 max frequency. That would be the improved contrast (higher resolution) attributed to an obstruction. Again, the curves only collapse at 1, seemingly becoming equal at that point, because they are both normalized for max spacial freq. An obstructed scope has a higher max spacial freq.

Excellent comments, Glenn. Thank you for making a few things more clear.
Quote:

Optics is a complicated subject filled with approximations, conventions, regions of validity, criteria and a host of special conditions.

...in some contexts it makes no sense as in coherent imaging, significant phase shifts...

The real MTF is a measured data set...

For astigmatism (or any aberration with an angular component like coma) however you have to add orientation data...

Dawes criteria is normally described for an unobstructed scope and contains the 1.22 factor we all grew up with. For obstructed scopes the distance to the first Airy minimum is somewhat smaller and becomes essentially unity at 50% obstruction.



As I understand it, amateur apertures are, for all intents and purposes, coherent in a range near peak sensitivity. And since phase is responsible for intensity distribution, it is at least somewhat accounted for. One can model asymmetrical aberrations by rotating them to the point of maximum affect, but it would be difficult to capture the aberration fully. The CO is symmetrical, and SA is assumed to be, as I understand it.


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freestar8n
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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5620243 - 01/13/13 07:39 AM

Quote:

The figure of 1.0 wave you quote is the aberration coefficient of balanced spherical Ai=As(p^4-p^2) for a strehl of 0.8. But the same term is 0.25 for spherical alone Ai=As*p^4.




Huh? The W040 term is the Seidel term for spherical aberration alone, and it can have a value of 0.96 lambda and still be diffraction limited, with defocus. That's why in the Wyant aberration tool I cited earlier, when you enter 1 for the Spherical aberration and -1 for the defocus, you get an acceptable wavefront. If the spherical aberration is "really" 0.25 - why does he want us to enter 1? This is all aberration theory 101, and I don't find the math hard at all - especially compared to nonlinear and quantum optics.

As an example - how much spherical aberration did the HST have when it was launched? Here is a nice description by Wilson. He draws a simple diagram and demonstrates that the surface error amounts to having the edge flattened by 2.17um, which means the spherical aberration is 4.34 microns. That corresponds to the departure of the wavefront from the Gaussian sphere at the edge, and across that wavefront it will vary as the r^4. Either way, the Seidel wavefront error, or departure from the Gaussian sphere, has both a coefficient of 4.34 um, and a maximum value of 4.34um across the surface. You mentioned earlier that you calculated relative to a Gaussian sphere - albeit a shifted one - but that makes no sense since there is only one Gaussian sphere, and it is the paraxial one - and that is what Wilson uses as the reference.

Separately, Roddier (Appl. Opt. 1993) reported the spherical aberration of the HST with, "The amplitude of the spherical aberration term was estimated to be -0.294-um rms..." The fact that he doesn't just say "-um" but "-um rms" means he is measuring departure from a mean surface and is implicitly including defocus and the meaning is fairly clear, if awkward since it is unusual to place a negative value on an rms. But the context is clear enough, and one can think of it as a net rms error at min rms focus, or as an inherent flaw in the wavefront with r^4 dependence that can be largely cancelled by -r^2 defocus.

The rms value is related to the w040 spherical aberration term by a factor of 1/(6*sqrt(5)).

Unfortunately a lot of optics and aberration theory has different conventions and it isn't always clear which is being used. As Wilson says, "The above figures reveal how
essential it is to define exactly what definition
is being used, otherwise serious
confusion results." In amateur astro there is total confusion over RMS vs. P-V, and even a blanket disregard for aberration theory by including coma as a "field curvature" term. I think it's important, and clarifying, not to confuse the Seidel forms with the Zernike polynomials - particularly when discussing a fixed amount of spherical aberration combined with varying defocus and its impact on MTF.

How bad is an f/9 Newtonian with a spherical mirror? Well, it has almost a full wave of spherical aberration due to the departure of the sphere from a perfect paraboloid, but with defocus the resulting wavefront has lambda/14 rms, yielding a Strehl of 0.8 - even though the wavefront arriving at the image plane is almost a full wave off from the Gaussian sphere.

When I plug such a system into Oslo, I get 0.95 waves for the Seidel w040 spherical aberration term. When I plug that same value into the Wyant tool, where it says "spherical", I get the same result - and a Strehl of 0.8.

Frank


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freestar8n
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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5620274 - 01/13/13 08:14 AM

Quote:

As I understand it, amateur apertures are, for all intents and purposes, coherent in a range near peak sensitivity. And since phase is responsible for intensity distribution, it is at least somewhat accounted for.




Norme - I'm sorry but statements like these really need to be backed by a good reference - either a textbook or journal article. There are many amateur write ups on these topics that make no reference to literature - and I don't know what they use as a basis. On topics such as Fourier optics and its suitability to visual observation in low light near the diffraction limit, at the least you would need to cite a text on Fourier optics - and it is even more challenging since it also folds in optical physics, in terms of coherence, biology, in terms of the eye response, and psychology, in terms of the final perception.

I regularly cite relevant texts and I wish others would also. I have cited these before but I will try again.

Here is Gaskill on MTF:

"The characterization is incomplete... Loss of phase information can be quite significant because the effects of phase distortion are frequently more severe than amplitude distortion."

On coherence and MTF:
"... caution is once again in order for incoherent imaging situations. Light emitted from an incoherent source becomes partially coherent as it propogats, and may invalidate the assumption that each of the intermediate images behaves as an incoherent object for the following system."

This means that the whole basis of Fourier imaging falls apart and you can't think of it as simply the product of individual MTF's. This isn't due to *phase* but to partial *coherence*. It is a separate problem.

People keep talking about how the MTF is "physics" - but it is actually more engineering stripped of the physics that makes it complicated - which involves coherence. General landscape photography doesn't push these issues as much as amateur astro at the diffraction limit, so astro has to be even more careful.

Holst/Lomheim in "CMOS/CCD sensors and camera systems": "An image where the MTF is drastically altered is still recognizable, whereas large [phase] noninearities can destroy recognizability."

More specifically on topic, here is Shannon "Art and Science of Optical Design" on the role of central obstruction and MTF:

"The obscured-aperture OTF shows an apparent increase in contrast for high spatial frequencies as the obscuration is increased. Although this effect certainly does occur, it is a change in contrast, not in total signal level... In cases where obscured apertures must be used, the loss of total signal must be considered in system analysis."

And - I have already cited Rutten on the role of changing brightness on the effective MTF of the eye.

If you have other references either in texts or journal articles I'd be happy to look at them.

Frank


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5620472 - 01/13/13 10:40 AM

"Since, according to Van Cittert-Zernike Theorem, light arriving from stars is coherent in amateur-size telescopes, as long as it is near monochromatic, it is an interesting question how much this coherence factor, combined with the coherence-lowering polychromatic spectrum and OPD differential between two close stars influences their actual resolution limit in the field."

http://www.telescope-optics.net/telescope_resolution.htm
http://home.myfairpoint.net/vzeeg3o2/id4.html

"For photopic eye sensitivity, there is little difference between monochromatic and polychromatic MTF."

"At any given frequency, MTF is a ratio of the output (image) to input (object) modulation amplitude. Mathematically, it is a Fourier transform of the aperture's PSF (more specifically, it is an integrated sum of the PSFs for every point over its intensity distribution profile, i.e. convolution of object's Gaussian image and aperture's PSF)."

http://www.telescope-optics.net/mtf.htm

The statement on phase was inferred from the presence of the diffracted pattern for a perfect optic and an aberrant one. The convention is to rotate the MTF to the angle (on the pupil) of maximum phase.

"Contrast transfer function alone shows the efficiency of contrast transfer from the object to its image for a single orientation in the aberrated image, normally that along the axis of aberration."

"Still, despite the MTF being standardized to a single object form sample and brightness level, it is considered to be a reliable general indicator of the effect of wavefront aberrations - or any other factor affecting wave interference in the focal zone - on image quality."

http://www.telescope-optics.net/mtf.htm

You make great points, Frank. I read the references (links) you post (reading about the Hubble after this.) Most of what I say is studied, processed and regurgitated from credible sources, too, to the best of my ability to understand (as I often cite), interpret, and convey it.

The bottom line is, there is a fall off in contrast with a CO and "all that other stuff." Whether or not anyone can see it depends on so many factors, but it is there. And whether one wishes to use MTF or another model is up to them. I lay my hat on the reference above that states, for our purposes in amateur sized (and quality) scopes, the MTF is a useful tool to discuss aberration and interference.

It is not perfect description of the detector (eyeball or CCD chip) but it describes pretty well what is on the focal plane. I see what I see, others see what they see, and a chips see what they see. The entire subject can become so complex, for example discussing infinite emitters on the wavefront and the resulting phase, that no discussion can occur on any level.

Anyway, it's a great discussion. I know what I need to know, at the moment, and am exploring, "...OPD differential between two close <unequal> stars influences their actual resolution limit in the field." <Insert is mine.> So far, it seems pretty consistent with the MTF/PSF (visual observation in excellent seeing.) I'll leave it to others to decide what they need or want to know.

Some easy reading here...
http://www.handprint.com/ASTRO/ae1.html


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freestar8n
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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5620681 - 01/13/13 12:25 PM

Hi Norme-

For an in-depth topic like this I encourage references to textbooks and journal articles as I have provided. If you are interested in these topics, and you appear to be, I recommend Linear Systems, Fourier Transforms, and Optics by Gaskill. Since people were citing Mahajan, I think Gaskill was Mahajan's thesis advisor - and I believe Goodman was Gaskill's. Anyway, it's a standard text on Fourier optics and is often cited. For coherence stuff, there is Born and Wolf.

Frank


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5620907 - 01/13/13 02:21 PM

Yes, thanks, Frank. Living abroad, often good reference material is difficult to come by - shipping can be expensive, no references to peruse living in the sticks. So, I rely heavily on what resources are readily available. I have some books on order to pick up when returning to the US next month. I will look over those you reference. As you know, what sparked my interest 2 years ago and since was star testing my scope, then later that monster effective aperture thread.

But, in closing, I do have to say that observations in better than average seeing are pretty much consistent with what MTF suggests, if imperfectly. Namely, reduced diffraction effects improving my CO ratio from 37% to ~28% at full aperture (yea, I did the unthinkable...:)), and splitting stars /reported/ at below Dawes with noticeable contrast between the peaks. No immediately apparent improvement in planetary contrast, however, there may have been some. All of this is pretty much consistent. I am not an MTF crusader, but I do understand what it's telling us.

You are correct. You can have 1 wave PV at paraxial focus and, with defocus, correct to 1/4 PV at best focus. But we do not focus at paraxial, we add defocus aberration when observing. That is where the curve above was drawn.

By the way, reading the Hubble link above, it's apparent to me Nelson was at smallest blur to get his 100% "geometric" light figure within 1.5" arc. I am sure the previous 70% measurements were at best focus with the correspondingly larger blur radius. And he seems to imply half wave of error in red light, which is probably closer to the reported error at 5500 angstroms. There must be a typo, he gives longitudinal error at 40mm. He must mean microns, and without doing the math that may explain Suiter's report of 1.7 PV at Gaussian focus.


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freestar8n
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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5620923 - 01/13/13 02:29 PM

Quote:

But, in closing, I do have to say that observations in better than average seeing are pretty much consistent with what MTF suggests, if imperfectly. Namely, reduced diffraction effects improving my CO ratio from 37% to ~28% at full aperture (yea, I did the unthinkable...:)), and splitting stars /reported/ at below Dawes with noticeable contrast between the peaks. No immediately apparent improvement in planetary contrast, however, there may have been some. All of this is pretty much consistent. I am not an MTF crusader, but I do understand what it's telling us.




Hi Norm-

Thanks - I really value reports at the eyepiece coupled with interpretations. I am not anti-theory at all - but when a system is as complicated as I think this topic is - I like to go by observations first, backed by theory - rather than just go by theory.

Thanks,
Frank


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5620974 - 01/13/13 02:49 PM

Cheers, Frank. You made me brush up on LSA.

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DesertRat
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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5621371 - 01/13/13 06:12 PM

Frank,

Mahajan shows images of PSF's for balanced spherical aberration As(p^4-p^2) in his book noted earlier. They match pretty closely to what Suiter shows for 0.25wvPTV given As = 1wv. Mahajan shows (As=1) == (Wp-v=0.25) for balanced spherical aberration in table 8-2 pg 85 in book referenced.

I think it clear you are speaking of a coefficient. I should have realized this by noting you don't say 0.95wv PTV but just 1 or 0.95 wave. My code aberrates the wavefront with components given in waves rms or they can be alternately set to PTV values. I prefer this method as it corresponds to what the wider community of amateurs and telescope makers are familiar with.

The reference sphere I referred to above probably was not made clear, a drawing could help but my skills there are limited. I reference the diagram fig 1.2 in Suiter as an alternative.

My references to the quarter wave criteria go back to Rayleigh. He wrote that performance begins to degrade when the total wavefront error exceeded 1/4 wv of yellow-green light. For this description I can cite the following, they are not Phys Rev but for the community here of amateur astronomers useful:

Ceravolo et. al. "Optical Quality in Telescopes" , Sky & Telescope March 1992 pg253
Texereau "How to Make a Telescope" 1951 , republished 1984 Willmann-Bell Inc.

I understand you might not like their treatment, or Rayleigh, or Suiter's, but I would argue they are more valuable for our purposes here than Goodman (from which I used to code angular spectrum methods for microscopy applications), Gaskill etc. I think it important to note that Suiter is an experimental physicist, not inclined to mislead the community. The scrutiny his work has received far exceeds that which a lot of professional journals provide.

It would be useful to focus (!) on 2 questions:

1) Does a Strehl ratio of 0.8 result from an aberration of approx sigma = lambda/14 ?

2) Given a sigma of 0.0745wv rms what is the corresponding PTV error for low order spherical ? Assume any approximations or qualifications as you see fit.

I'd like to focus on those 2 questions, and maybe we can clear this all up. Later we can discuss coherence as it applies to standard backyard astronomy!


Norme,
Thanks for the link to Vlad's work on coherence as it relates to telescope resolution. I'll have to review that!


General audience (are you still here? )

On MTF
A calculated MTF does a decent job of describing obstruction, effects of smaller amounts of low order spherical and astigmatism (if careful to include orientation data). However for coma it is not that useful, since the OTF has a significant imaginary part in that case. Also for very large amounts of defocus it does not apply well. In both those instances contrast reversal is possible, the phase portion is too large to ignore.

Glenn


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freestar8n
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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5622085 - 01/14/13 04:03 AM

I am referring to third order spherical the same way Oslo, Wyant, Wilson - etc., refer to it - as the wavefront discrepency from the Gaussian sphere. It is both a coefficient and an actual distance you can see. For the Hubble telescope, it is about 4.3 um, or 8 waves at 0.5um lambda. In Wilson's write up - he is not referring simply to an abstract coefficient - he is measuring something in a figure. I can only conclude you think he is wrong to say the HST has 4.3um spherical aberration.

If someone says they have a telescope with an overall wavefront rms of lambda/14 I would deduce they are referring to the rms measured relative to diffraction focus, and I would conclude that if the only aberration is spherical, then they could have up to 0.96 waves of spherical.

If they said they had about a full wave of spherical based on an interferometry report, I would tell them it could still have a Strehl of 0.8 since defocus would compensate for most of the aberration.

If they said it had lambda/14 rms, again I would assume they mean at diffraction focus, and if the only aberration was spherical, I would conclude they have about 1 wave of spherical, and the P-V error would be 1 wave at paraxial focus, but about 1/4 wave at diffraction focus. If the lambda/14 is measured at paraxial focus, I would say they had very good optics since an adjustment of focus would take it down further.

Regarding "what Rayleigh said" - I spent some time on this a while ago actually reading his papers and realized that, in his own words, he regarded 1/4 wave as a limit early in his publications, but later he did empirical measurements and concluded the true limit is 1/2 wave. This is an example of why I think it's important to refer to primary sources - particularly when referring to what someone was thinking in the past. There is no question people refer to the Rayleigh 1/4 wave rule, and he did allude to that in his papers - but later he measured how much error was allowed before it was noticed in an image, and concluded it was 1/2 wave.

In Rayleigh's experiment, he used defocus as an aberration and measured how much he could tolerate before he noticed the loss of image quality. That is exactly in line with the way I regard defocus - as a separate aberration term that can be varied independent of an intrinsic amount of third order aberration. I disagree with his conclusion that it's about 1/2 wave though - and would put it more at 1/4 wave, P-V.

I did not cite phys. rev. letters - I cited optics textbooks and journal articles by people well known in the optics community. Since the discrepancy here involves convention - it's important to cite people in optics rather than physics, particularly when they are self taught.

Frank


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5622290 - 01/14/13 09:03 AM

I get the feeling you are both correct in the context from which you argue the point.

"...gives the aberration function for paraxial focus, or so-called classical aberrations. Advance in calculation methods revealed that Gaussian image point is not the best focus location...requires shift from the Gaussian image point to their respective best focus location, where the central intensity of diffraction pattern is at its maximum (thus, best focus location is also called diffraction focus). Primary aberrations evaluated at best focus location are called orthogonal or balanced primary aberrations."

"For spherical aberration, the amount of defocus from paraxial focus needed for the shift to diffraction focus location is given by P=-S, with P and S being the peak aberration coefficients for defocus and spherical aberration, respectively..."

http://www.telescope-optics.net/lower_order_spherical.htm


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Peter Natscher
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Re: CO vs. All That "Other Stuff"! new [Re: pstarr]
      #5622358 - 01/14/13 09:57 AM

HST

Quote:

Quote:

My other scopes have been dobs 6,8and 10 inch. From my expereance optical quality is number one, much more than telescope type.




A SCT with perfect optics and a 30% central obstruction can never give better that 1/4 wave performance. Not that 1/4 wave performance is bad. That said, you will never find a SCT, or any other design with perfect optics.




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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: Peter Natscher]
      #5622522 - 01/14/13 11:40 AM

Quote:

Quote:

My other scopes have been dobs 6,8and 10 inch. From my expereance optical quality is number one, much more than telescope type.




A SCT with perfect optics and a 30% central obstruction can never give better that 1/4 wave performance. Not that 1/4 wave performance is bad. That said, you will never find a SCT, or any other design with perfect optics.




That's likely true in general while observing, the difference is probably too hard to tell at any distance from max spacial frequency. Still, it is somewhat misleading. I only mention it because it's interesting and it leads to the very reason obstructed scope perform differently. Contrast transfer can be comparable to 1/4 PV SA in terms of performance, but only over a very small range. The effect on the Airy disc is different for an obstruction than LSA, and this gives rise to a perfect obstructed scope's advantage.

With perfect obstructed optics, the Strehl-like peak intensity can be about 89% with co = 0.32D. This is due to the added diffraction effects with cause the Airy disc radius to become smaller and a bit brighter than it normally would be (if it remained at 1.22 Lambda/D.) It's not, it's at 1.11 Lambda/D for 0.3D. Actually, the contrast transfer equivalent of a perfect obstructed system can be approximated (co </= 0.4) using w ~ .21co ~ (.21 * .3) ~ 0.063 RMS of LSA, a bit better than 0.074 RMS for 1/4 PV SA.

Toss in some aberration, say a very good S = 0.95 Strehl, and Strehl-like intensity falls to Sn ~ S * I, with I = (1 - co^2)^2, ~ 0.95 * 0.83 ~ 79%. That figure is normalized to 1, just as an unobstructed scope's peak intensity is equal to it's Strehl (0.838 * S, also normalized to 1.) This gives a peak intensity of ~98% vs ~79% for the obstructed scope (with accompanying ring brightness.) This is the advantage refractors share along with very good Strehl on the high end.

There is a reason perfect obstructed performance exceeds perfect unobstructed performance at higher frequencies. You can begin to see how the (1 - co) rule of thumb for mid range frequency resolution came about. Truth is, an obstructed scope might perform close to (1 - co) in the mid range but exceeds performance at high frequencies by D/(1 - co^2.) This is the advantage obstructed scopes share, provided reasonably good Strehl.

It turns out, obstructed approximation for equivalent aperture over mid ranges is about 0.67D (for co = 0.33D) and for 1/4 PV SA is more like 0.58D over the same range. If the CO is less than 0.33D, then the equivalent performance increases to > 0.67D (until, of course, the CO becomes zero with 1.0D equivalent aperture as expected.) Add some aberration in both samples, and things change. So, Yes, optical performance means a lot.

In effect, an obstructed scope has the mid range performance of a smaller aperture and the high end resolution of a (~8%) larger /aberrant/ aperture. And this is due to the diffraction effects that differ from 1/4 PV LSA over most of the MTF, especially the right hand side.

http://www.telescope-optics.net/obstruction.htm

So, while it might be true performance across some of the spacial frequencies approximates 1/4 PV SA, it's not true entirely. The difference can be important depending on how critical one observes, the type of observing, and the conditions one observes in. But 'quick look' observing or 7/10 seeing might not distinguish between the two and the difference can be considered roughly the same, I'd say.


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orion61

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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5622584 - 01/14/13 12:19 PM

Nice points But..BRAIN HURTS NOW.

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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: orion61]
      #5622639 - 01/14/13 01:00 PM

It quits hurting once numbness sets in, like mine.

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DesertRat
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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5622727 - 01/14/13 01:51 PM Attachment (9 downloads)

Looks like we are in agreement now, hopefully its clear now to others the different ways to view aberrations.

From the standpoint of an amateur astronomer viewing a star inside and outside of focus he can get some idea of the wavefront error with all the qualifications Suiter describes. Rayleigh was primarilly investigating the appearance of a star in focus, and that would indeed be difficult but not impossible to determine 1/4wv vs 1/2wv LSA PTV.

Add some defocus on an obstructed scope the situation is quite different. See attached view of only 2 waves for LSA 0.10wv PTV.

Glenn


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