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What did Lord Rayleigh say.

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#1 Dick Parker

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Posted 20 August 2012 - 07:59 PM

It seems that there have been a few threads lately that have some reliance on the definition of the Rayleigh criteria. Whether the Rayleigh ¼ wave criterion is “correct” or “the best”, or whether you agree with it, is not the point of this post. The point here is to bring forward what Lord Rayleigh did or did not say. Hint – he did NOT say that “..1/4 wave was sensibly perfect..” I think you may find it interesting that his ¼ wave limit was an important but incidental point of much broader discussion. The material below is a combination of two posts I made on another forum a few years ago. Perhaps it will help.

Lord Rayleigh discusses optics in a series of philosophical discourses that were published in the Philosophical Magazine over the period from October 1879 to January 1880. I made it a point to go to the Library of Congress and get copies of all his articles relative to optics, specifically because I wanted to know exactly what it was that Lord Rayleigh published. I believe I mentioned that in my Mirror Quality part II video. I even have a picture of myself in front of the Library.

The short answer is yes the quote “aberration begins to become decidedly prejudicial when the wave-surface deviates from its proper place by about a quarter of a wavelength” is in Lord Rayleigh’s writings. In “The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science”, “fifth series” November 1879 , Number XLVI, Sect 4” page 409.

That is the second time a phrase similar to that appears in this article.

Let me embellish just a bit. The small tidbit that we use that contains the “Rayleigh limit” is part of a series of four installments that were published in the Philosophical Magazine over the period from Oct 1879 – Jan 1880. The title of the article is “Investigation in Optics with Special Reference to the Spectroscope”.

In the first installment, containing 3 sections (Oct 1789), he initially discusses the resolving power of the telescope, but then turns his attention to rectangular sections. Much of his mathematical treatment considers light through a slit, the advancing beam being cylindrical, and diffraction producing a slit of light with side bands. This is very convenient because the mathematics he uses for the point spread function (he knows of Airy’s work) become simplified by being two dimensional and what he seems primarily interested in is the resolution of spectral lines in a spectroscope. For a telescope he assumes symmetry about an axis and the arguments hold. (see footnote at end)

The second installment (Nov 1879), is a continuation of the article started in October and starts with sect 4. It is in this discussion where he holds aperture constant and mathematically calculates the effect of increasing aberration on the point spread function. After doing this, he makes the statement for the first time, on page 407, “…It appears that aberration begins to be distinctly mischievous when the wave-surface deviates at each end by a quarter wave-length from the true plane…”

On Page 408 he then considers symmetry about an axis by opening a paragraph with “…In most optical instruments other than spectroscopes the section of the beam is circular, and there is symmetry about an axis. The calculation of the intensity-curves as affected by aberration could be performed by quadratures from tables of Bessel’s functions….” He then proceeds with a page of algebra /(calculus?) equations and concludes by saying “…Hence in this case, as in the preceding, we may consider that aberration begins to be decidedly prejudicial when the wave surface deviates from its proper place by about a quarter of a wave-length….” This is the quote you spoke of.

One of the initial questions I had which took me to the library of Congress was the question: upon what did Lord Rayleigh base his judgment that ¼ wave was a limit? He never actually says in direct terms, but let me introduce few additional points of interest. Going back to his two dimensional treatment, on page 408 he compares the central peak intensity with aberrations and without by normalizing the ‘without aberration” case to unity and has mathematics to conclude that 1/8th wave intensity is .9576 and ¼ wave is .84109. Notice this is the Strehl ratio. Lord Rayleigh had this already figured out!!! Keep in mind his analysis is assuming the surfaces are otherwise smooth, and is not considering local errors or roughness.

Another hint is in the third installment (Dec 1879), which opens by continuing his prior title, starting with sect. 5 “On the Accuracy required in Optical Surfaces.” He opens with “…Foucault, in the memoir already referred to, was, I believe, the first to show that the errors of optical surfaces (edit notice the change to surface rather than wave-front) should not exceed a moderate fraction of the wave-length of light…” Apparently here, he acknowledges that it was already known that the admissible error was a few fractions of a wave length light, Lord Rayleigh was apparently working to refine this into some quantifiable number that could be practically useful and show that rule of thumb could be backed up by mathematics.

Also in section 5, page 477 Lord Rayleigh translates the wave front limit which he presented in Sect 4 (previously discussed) to optical surfaces, Here he recognizes that “…In the case of perpendicular reflection from mirrors, the results of sect 4 lead to the conclusion that no considerable area of the surface should deviate from truth by more than one eighth of the wave-length…” then goes on to say about lenses “…for a glass surface refracting at nearly perpendicular incidence the admissible error is about four times as great…” but also Notice “..no considerable area…”?? Is this where the idea of local irregularities come from??? It is a departure from all his discussion

It took me a while to answer your note, because I wanted to re read the material several times. NOWHERE in Lord Rayleigh’s writings (that I could find) is a statement even close to “…at a quarter wave the performance is sensibly perfect..”. I did check my copies of some pages from Applied Optics and Optical Design by A.E. Conrady and I did find, on page 136 (Dover Publications, INC. New York, 1957) the following statement, under the heading “The Rayleigh Limit”: “… The first of these fundamental questions (edit effect of aberrations) was answered in 1878 (edit note incorrect date) by the Late Lord Rayleigh….to state as a general deduction from a small number of mathematically discussed test-cases that an optical instrument would not fall seriously short of the performance possible with an absolutely perfect system if the difference between the longest and the shortest optical paths leading to a selected focus did not exceed one quarter of a wave-length…”

(FOOTNOTE. Actually, his mathematics is initially nonsymmetrical in two dimensions. On Page 407 he states “…When the aberration is symmetrical about the centre of the beam…” discusses the changing complexity of the equations then says “…and requires for its calculation two integrations. These could be effected by quadratures; but the results would perhaps scarcely repay the labour, especially as the practical question differs somewhat from that here proposed..”)

Dick Parker

#2 mark cowan

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Posted 20 August 2012 - 08:13 PM

Amen to that. I did a similar search (albeit virtual) and found the same thing. Google books has it here.

But it (the criteria itself) has always been a bit of a judgment call. As forr the so-called "sensibly perfect" part, this only ever appeared in the title of a similar article, not in a conclusion.

Best,
Mark

#3 Dave O

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Posted 20 August 2012 - 10:50 PM

Wow -- great stuff there Dick! Thanks so much for the leg-work and for sharing your research. Dave O

#4 Mark Harry

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Posted 21 August 2012 - 06:04 AM

I might add, that with Rayleigh already having described the basic Strehl, there is reference in Dick's post of the D&C limitations.(!) Smart fellow.
Good research job, Mr. Parker!

#5 MKV

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Posted 21 August 2012 - 06:56 AM

Hint – he did NOT say that “..1/4 wave was sensibly perfect..”

Dick, even if Lord Rayleigh (John William Strutt) did not state it that way it was apparently understood that way by the professional community. As you yourself note, A. E. Conrady writes that the performance "would not fall seriously short of" that of an "absolutely perfect system" if the OPD did not exceed ¼ wavelength.

And Warren J. Smith (Modern Optical Engineering, McGraw-Hill, 1966, Ch. 11.4, pp .297-298) states that the Rayleigh Criterion "allows no ore than one quarter wavelength of OPD over the wavefront with respect to a reference sphere...that the iamge may be 'sensibly' perfect."

Technically, that's not what Lord Rayleight said, and technically Warren J. Smith is paraphrasing him, but the important thing is that this is what Lord Rayleigh meant. The professional community seems pretty much in full agreement on that.

I agree that, through repeated references to it, the exact wording of Lord Rayleigh become misquoted to variable degree, but I don't agree that as a result of that his observations became misunderstood.

If you take the words "decidedly prejudicial" and substitute them with modern-usage synonyms it is like saying "unquestionably unacceptable". So, what Lord Rayleigh seems to be saying is that the performance of an optical system becomes unquestionably unacceptable" when the wave-surface deviates from its proper place by about a quarter of a wavelength".

Assuming that by "proper place" he means "as it should be", or "sensibly perfect" for that matter, he is saying that one will not notice anything seriously detrimental in the image quality until the wavefront's optical path difference reaches ¼ wavelength.

And since he does use the term "sensibly perfect" in a related chapter on "Accuracy of Focus", to two statements became conflated over time as part of the general rule which has become known as the "Rayleigh criterion" and is easy to remember than in his long and antiquated form of writing.

I think you are absolutely right, however, to point out that Lord Rayleigh never did state his criterion the way he is most often quoted as saying, and that those who quote him (professionals and amateurs alike) should know and acknowledge that they are paraphrasing him.

If, as your post seems to suggest under the surface, the scientific community did indeed misunderstand what he was saying, from Conrady to modern day sources, then that doesn't reflect well of the community as a whole, does it? I don;t think that's the case.


It is much more important to state what he meant than how he wrote it, but it is definitely wrong to misquote him.

Regards,

Mladen

#6 wh48gs

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Posted 21 August 2012 - 07:13 AM

Dick,

Also in section 5, page 477 Lord Rayleigh translates the wave front limit which he presented in Sect 4 (previously discussed) to optical surfaces, Here he recognizes that “…In the case of perpendicular reflection from mirrors, the results of sect 4 lead to the conclusion that no considerable area of the surface should deviate from truth by more than one eighth of the wave-length…”



That is very interesting finding. It shows that Lord Rayleigh did address the extent of wavefront error, not only its nominal p-v. Yet, it is the nominal p-v alone which is notoriously presented as Rayleigh criterion, making it nearly meaningless. Implying that the limit is for the aberration affecting nearly all of the wavefront area makes it much more specific. There are still more than negligible variations with the aberration type (for instance, 1/4 wave p-v gives 0.70 Strehl for a wavy mirror with 2-3 1/4 wave zones, 0.80 for primary spherical, and 0.90 for primary astigmatism), but it does gravitate toward the right value.

I did check my copies of some pages from Applied Optics and Optical Design by A.E. Conrady and I did find, on page 136 (Dover Publications, INC. New York, 1957) the following statement, under the heading “The Rayleigh Limit”: “… The first of these fundamental questions (edit effect of aberrations) was answered in 1878 (edit note incorrect date) by the Late Lord Rayleigh….to state as a general deduction from a small number of mathematically discussed test-cases that an optical instrument would not fall seriously short of the performance possible with an absolutely perfect system if the difference between the longest and the shortest optical paths leading to a selected focus did not exceed one quarter of a wave-length…”



Conrady gives quite extensive coverage to it in the book 2 (p626-627). He made Rayleigh criterion specific by relating it to 1/4 wave p-v of primary spherical (later confirmed by Marechal's criterion, based on diffraction calculation). But Conrady says, very specifically: "We may, therefore, adopt it as a safe guide, but we should never draw upon it to save a little extra trouble in perfecting a permanent design."

Vla

#7 MKV

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Posted 21 August 2012 - 07:13 AM

If Lord Rayleigh did indeed hint at the Strehl ratio, as Dick's post suggests, then credit needs to go to him, as he precedes Karl Strehl by a few decades. Surely, Strehl had to be familiar with the work of Lord Rayleigh. I wonder if he references him in his work.

By the way, even though the Strehl ratio is something that has been around for a long time, obviously, it has come into use only relatively recently. You will not find in in professional books of the 60's or 70's. Not exactly sure when it started being promoted in general optics, but suffice it to say that there was life before Strehl became the faddish alpha and omega of optical quality! :)

Liewise, Strehl is not an absolute measure and is, like everything else, is subject to its own limitations. Here is a good link to more on this topic.

Mladen

#8 MKV

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Posted 21 August 2012 - 07:27 AM

Yet, it is the nominal p-v alone which is notoriously presented as Rayleigh criterion, making it nearly meaningless

The Rayleigh limit can be applied to any optical path difference. Its "meangfulness" or "menanglessness" depends on how applicable it is to an observer.

Notrmally, for observational purposes, the limit should be applied based to the residual spherical aberration at the best focus.

Mladen

#9 freestar8n

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Posted 21 August 2012 - 10:01 AM

In terms of what he actually said and thought, in his 1885 paper on "Accuracy of focus necessary for sensibly perfect definition" he imagines a perfect double convex lens forming a perfect focus and asks what would happen if the index of the lens changed slightly. The OPD of rays through the edge of the lens would be unchanged, while the central one through the thick part would change a bit. How much discrepancy between the two rays would be acceptable?

"This quantity tells us the discrepancy of phase; And we know that if it is less than [Lambda]/2 it is still good enough to give nearly perfect definition."

Note that he explicitly says lambda/2, not lambda/4, and he describes it as "nearly perfect definition."

Furthermore, he uses this lamba/2 to calculate the allowed depth of focus and gets:

df < f^2 lambda / y^2

where y is the lens semi-diameter. This translates to an allowed defocus of:

df = +/- 4 lambda fnum^2

Meanwhile, contemporary texts will calculate the depth of focus and apply "Rayleigh's 1/4 wave criterion" to get a value of:

df = +/- 2 lambda fnum^2

But Rayleigh himself, in his own paper, uses twice that allowed wavefront error and ends up with twice the allowed depth of focus for "nearly perfect definition" and, presumably given the title of that same article, "sensibly perfect definition."

So it looks to me like he did state a criterion pretty clearly in 1885, and it is lambda/2 for sensibly perfect definition. He even did experiments with his own eyes in that paper to confirm it.

Frank

#10 MKV

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Posted 21 August 2012 - 01:12 PM

Note that he explicitly says lambda/2, not lambda/4, and he describes it as "nearly perfect definition."

For light encountering a surface suqarely, the surface error doubles on reflection and is halved on refraction. Thus, you want a minimum 1/8 wave error on a mirror or 1/2 wave error on a lens, for a minimum 1/4 wave error on the wavefront.

In any case, it is clear that Lord Rayleigh did indeed consider 1/4 wave OPD at the focus as "nearly [ed note or 'sensibly'] perfect."

Mladen

#11 freestar8n

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Posted 22 August 2012 - 02:04 AM

No - nothing to do with mirrors or surface error - that should be clear from his expression for focus tolerance, which is too large by a factor of two. I think it is also wrong to suggest he attached the words "sensibly perfect" to 1/4 wave error - because I am only aware of him associating those words with 1/2 wave of defocus error.

In answer to Dick Parker's first post - I can believe that there is nothing up to 1880 by Rayleigh that says 1/4 wave is sensibly perfect - but in 1885 he has a paper where he says up to 1/2 wave of defocus is sensibly perfect. If he has another paper where he associates a different wavefront error tolerance with the term, "sensibly perfect," that would also be interesting.

In a nutshell, Rayleigh said 1/4 wave spherical led to 20% drop in peak intensity, which can usually be tolerated. This became Rayleigh's 1/4 wave rule. Rayleigh also, later, said that 1/2 wave defocus was needed for sensibly perfect definition. Two different statements and two different criteria - from the same guy at two different times. Only one of the criteria "stuck" as a convention - but his descriptions of the second criterion have been incorrectly attributed to the first.

It's clear that Rayleigh, in his own writing, refers to 1/4 wave tolerance in most cases, but for defocus he allows 1/2 wave - and he mentions this both in 1885 and 1888, with both citations mentioning experimental verification. My interpretation is that he regarded 1/4 wave as a form of theoretical perfection, while 1/2 wave (of defocus anyway) empirically did not show much degredation, i.e. "sensibly perfect definition." Perhaps he did not allow for visual accommodation in his experiment - I don't know.

It's ironic that today people will calculate depth of focus and apply the 1/4 wave Rayleigh criterion in his honor - without realizing that he did the same calculation and chose 1/2 wave as the relevant allowed error - and got a value twice as big.

Frank

#12 dave brock

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Posted 22 August 2012 - 02:54 AM

If you take the words "decidedly prejudicial" and substitute them with modern-usage synonyms it is like saying "unquestionably unacceptable". So, what Lord Rayleigh seems to be saying is that the performance of an optical system becomes unquestionably unacceptable" when the wave-surface deviates from its proper place by about a quarter of a wavelength".

Assuming that by "proper place" he means "as it should be", or "sensibly perfect" for that matter, he is saying that one will not notice anything seriously detrimental in the image quality until the wavefront's optical path difference reaches ¼ wavelength.


To me, these two paragraphs don't fit together. Are you suggesting that he's saying that nothing detrimental will be noticed in the image up to 1/4 wave then at the very instant it hits 1/4 wave it suddenly becomes unquestionably unacceptable?

Dave

#13 MKV

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Posted 22 August 2012 - 07:09 AM

Are you suggesting that he's saying that nothing detrimental will be noticed in the image up to 1/4 wave then at the very instant it hits 1/4 wave it suddenly becomes unquestionably unacceptable?

I believe that's exactly what he was saying. In the image below, top row , left to right, 0 waves, 1/4 wave; bottom row, left to right, 1/3 wave, 1/2 wave. Clearly the bottom row is "decidedly prejudicial".

That's pretty keen observation he made without computers you must admit.

Doesn't anyone here think that the professional community over all these years tried to test and verify Lord Rayleigh's criterion, and why has the 1/4 wave limit been accepted all this time? Sometimes, I think, we're trying to reinvent the wheel.

Mladen

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#14 wh48gs

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Posted 22 August 2012 - 07:28 AM

In a nutshell, Rayleigh said 1/4 wave spherical led to 20% drop in peak intensity, which can usually be tolerated. This became Rayleigh's 1/4 wave rule. Rayleigh also, later, said that 1/2 wave defocus was needed for sensibly perfect definition. Two different statements and two different criteria - from the same guy at two different times. Only one of the criteria "stuck" as a convention - but his descriptions of the second criterion have been incorrectly attributed to the first.



Lord Rayleigh never specified the form of aberration; that's what Conrady did. Rayleigh seemed to be content with defining it as a departure from perfect affecting most or all of the wavefront area.

As for the 1/2 wave p-v defocus limit to "sensibly perfect definition", it seems to be taken out of context. Lord Rayleigh specifies the test object as a slit backed by soda flame, observed with high-power eyepiece, adjusting the focus until the edge of the slit and the wire at the eyepiece focus were seen both well defined.

What seems safe to assume is that he observed definition of brightly illuminated high-contrast line-like objects, as a function of defocus. Obviously, this cannot be applied as a general rule for all types of details, and certainly not for low-contrast detail definition. Although Rayleigh does use word "definition", considering the object observed, it is probably more related to the "resolution" limit. Anyway, it shouldn't be too hard for anyone to test how much of defocus takes to cause noticeable blurring of the edge of a brightly illuminated slit.

Vla

#15 freestar8n

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Posted 22 August 2012 - 08:04 AM

Lord Rayleigh never specified the form of aberration; that's what Conrady did. Rayleigh seemed to be content with defining it as a departure from perfect affecting most or all of the wavefront area.



Here I was summarizing things in a nutshell to point out the differences in the two criteria and their contexts. Rayleigh uses the calculated peak intensity as a function of *spherical* aberration and shows a drop off beyond 1/4 wave. He doesn't use the words "sensibly perfect" at all with the 1/4 wave criterion.

As for the 1/2 wave p-v defocus limit to "sensibly perfect definition", it seems to be taken out of context. Lord Rayleigh specifies the test object as a slit backed by soda flame, observed with high-power eyepiece, adjusting the focus until the edge of the slit and the wire at the eyepiece focus were seen both well defined.



I don't think there can be any doubt of the interpretation since he states it clearly, both in the text and in the title, and he backs it with his own experiment and general formula. Although he is studying a slit, he is using his own eyes in a controlled experiment to assess when he can actually see the *image* degraded - and for defocus it is lambda/2. This is written *after* the earlier work, and he cites it again in 1888.

Note that the lambda/4 writing is in the context of spectroscopy, *not* imaging, and is more theoretically based - whereas the defocus work pertains to how much aberration you can actually notice when you are looking in an eyepiece - and his value is clearly lambda/2. He then uses that tolerance to find the depth of focus over which *an image* will be sensibly perfect to the eye - and it is twice the value typically stated based on lambda/4.

I'm just going by what the guy said and did. It may be that he regarded defocus as a special case of aberration and was allowed greater tolerance - but either way he says lambda/2 defocus yields "sensibly perfect definition" [in the title] or "will not impair definition" [in the text].

In 1888 he restates this result and says his formula for depth of focus, based on lambda/2 tolerance, is "confirmed by experiment."

You may quibble about his result and his choice of objects for the test - but the point of this thread is to determine what he actually said - and his short little paper on defocus makes this pretty clear.

I assume that paper is overlooked and I don't know if anyone cited it or referred to his formula for defocus - but I do find it telling that he wasn't locked into lambda/4 as a rigid limit. And it ties together the words, "sensibly perfect" with a defocus tolerance of lambda/2.

Did anyone here know he put a lambda/2 tolerance on allowed defocus? It surprised me - but there it is in writing.

Frank

#16 Ed Jones

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Posted 22 August 2012 - 09:11 AM

Regardless of what Rayleigh said or how he said it the 1/4 wave rule is now a defacto diffraction limit attributed to him.

Texereau says "in fact the uncorrected spherical mirror may satisfy Rayleigh's rule and give a practically perfect star image" (with focal lengths >= to thse in his table 1). He does say Francon states on planetary detail 1/16 wave begins to be objectionable. My first mirror was 6 inch I made with a 50.5 focal length and I was quite happy with it not having looked through anything better. I suppose it's all a matter of what you are used to seeing.

#17 freestar8n

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Posted 22 August 2012 - 10:09 AM

Regardless of what Rayleigh said or how he said it the 1/4 wave rule is now a defacto diffraction limit attributed to him.



I don't think anyone here disputes that at all. Of course, if someone does I'd be interested to hear why. In terms of the rule itself and how it is attached to his name, I mean.

But I do like a thread like this that goes to primary sources (the guy's actual papers) and figures out what he really said.

The whole separate issue of how useful and meaningful the rule is by itself is a separate topic - and I'd be happy to cite sources along those lines - but that would be a different thread since the OP wanted the topic limited to his actual writings.

Regardless of the rule, you can cite with confidence a writing by Rayleigh in which he says 1/2 wave P-V on the wavefront provides sensibly perfect definition. Although the specific aberration is defocus in that case, it is still Rayleigh himself departing from current interpretations of his quarter-wave rule in a very ATM context of a guy lookin' in an eyepiece.

Frank

#18 MKV

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Posted 22 August 2012 - 10:19 AM

Regardless of the rule, you can cite with confidence a writing by Rayleigh in which he says 1/2 wave P-V on the wavefront provides sensibly perfect definition.

I think Vla's reminder that his work in this instance had to do with a slit and the wire and [linear] resolution is the crux of the matter.

A slit is not a point source but a series of Airy discs stacked in a linear fashion, which modifies the whole spatial picture. I believe there is a distinct difference in spatial frequency resolution for lines as opposed to point sources, and that mixing his lambda/4 and lambda/2 rule is mixing apples and oranges.

Mladen

#19 wh48gs

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Posted 22 August 2012 - 11:38 AM

Here I was summarizing things in a nutshell to point out the differences in the two criteria and their contexts. Rayleigh uses the calculated peak intensity as a function of *spherical* aberration and shows a drop off beyond 1/4 wave.



The simplest way to show that Rayleigh did specify spherical aberration, as you say, is to specify where he did it.

Note that the lambda/4 writing is in the context of spectroscopy, *not* imaging, and is more theoretically based - whereas the defocus work pertains to how much aberration you can actually notice when you are looking in an eyepiece - and his value is clearly lambda/2.



The tolerance will vary widely with what one looks at in an eyepiece. It is obvious from Rayleigh's description of the experiment that this specific tolerance cannot be applied as a general rule. He didn't really need to acknowledge that.

Vla

#20 freestar8n

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Posted 22 August 2012 - 12:46 PM

I personally give the guy credit and praise for attempting to empirically verify a theoretical result. He did it somewhat crudely but I think it is a sound attempt to use defocus as a controllable proxy for general wavefront error - along with a well-defined object as a test subject.

The fact that his setup and object were not ideal viewed from a modern day perspective is separate from the claim he published - which is that up to 1/2 wave of defocus was not noticeable to him based on the repeatability of his focus positions.

Confirmed by experiment - as he says.

If there are other published reports from the time that confirm at what level aberration shows in an image - to a guy looking in an eyepiece as part of a controlled experiment - I would be interested to see them.

Frank

#21 Mark Harry

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Posted 22 August 2012 - 04:27 PM

It must be remembered in his day,any verification must have been done with relatively small achromats or small reflectors (diminutve for our time).
Enough said,
M.

#22 freestar8n

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Posted 23 August 2012 - 02:16 AM

His "day" was 1885 when he published what I would call his "Half-wave rule for perfectly sensible definition." That was just before the death of Alvan Clark, and first light for the 36" refractor at Lick observatory. It was also around the time Common was doing long exposure astrophotography with a 36" silvered mirror, and working on a 60-inch - all near London not far from Rayleigh in Cambridge. Lord Rosse's 72" speculum was already 40 years old then, just across the Irish Sea.

So - rather than being the dawn of little achromatic lenses, I would call that time the beginning of the end for large achromats - as silvered mirrors and imaging took over.

Once again - whether or not you agree with his assessment, techniques, and methodology is not relevant to what he actually said. His writings show confidence both in his theoretical results and in his acumen as an experimentalist to verify them.

Frank

#23 Mark Harry

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Posted 23 August 2012 - 08:26 AM

****
I have had optics forwarded to me by quite a few owners, and I can't for the life of me see how anyone can call an optic with such an error, as "perfectly sensible". The cross section of owners varies from relative newcomers, to very experienced observers, and all highly suspected, or downright knew that such optics were substandard while in use. This is based on hundreds of tests, and observations done first hand. No theorizing or experimentation whatsoever. Personally, I feel that this information has a high degree of relevance, and certainly negates this claim (lam/2 rule as being sensibly perfect) directly and irrefutably. But of course he could have stated such; that is not being questioned. Whether or not it's correct in validating a standard is another matter.
M.

#24 Pinbout

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Posted 23 August 2012 - 09:46 AM

Hey Mark,

I really appreciate Mr. Praker's post, but isn't there too many more interesting opportunities to invest our creative intellegence than to argue over +100 year old concepts.

doing the right thing vs doing it right.


like if the parabolic mirror was as big as North America, it would be required to only have a peak/valley as small +/- 1in.

Mirror Lab

doesn't it look like that huge mirror has an edge issue judging by the way their figuring it? :grin:

#25 freestar8n

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Posted 23 August 2012 - 01:05 PM

I have just been focused on what he wrote and how he interpreted his own experiments to get the main point across that he did use lambda/2 as a tolerance for defocus pertaining to "the least visible displacement of the eyepiece of a telescope focused upon a distant object..." This nails down that he did not hold fast to lambda/4, and it also spells out what he meant by, "sensibly perfect definition." It meant - when you focus as critically as possible and get the image perfect to your eye - what is the range of defocus, in terms of wavefront error, that will be present in the image?

In terms of whether I agree with him or not, which is a separate issue - no, I don't, but I'm not a big fan of setting hard thresholds and tolerances that are expected to have general application in the first place.

I interpret it as Rayleigh being somewhat flexible on a tolerance from 1/4 to 1/2 wave, and based on his experiment he realized that his measurements were outside a limit allowed by 1/4 wave - so he adjusted.

I actually like the design and intent of his experiment, but I think his implementation is critically flawed by using a very coarse measuring device coupled with a relatively fast 12" fl, 1 1/8" diameter (f/10.7) lens of his own creation - and for which he doesn't give details of how its quality was assessed. This is particularly odd since he starts his paper saying that a plano-convex lens about 2" f/18 will have "unimportant" aberration present. But then he uses one at f/10.7...

The measurement is also limited by his own visual acuity. It also requires the experimentalist to be accurately co-focused on the reticle and the image at the same time.

I would have done multiple trials with different lenses of varying f/ratios - especially longer ones so that the displacement measurement was less critical.

So I can see many reasons why he would have gotten an empirical result larger than current expectations - but my main point in this thread is to convey that he did put a rather large wavefront error tolerance on sensibly perfect definition that departs from the quarter-wave rule named for him.

Frank


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