Re: [ATM] Re: Satisfying "Millies-Lacroix" is neither necessarynorsufficient for "diffraction-limited" performance?"

["Nils Olof Carlin" <nilsolof.carlin@telia.com>]

Vladimir,


The only thing I have to go by is this quotation from lord Rayleigh, out of
its context:

"aberration begins to become decidedly prejudicial when the wave-surface
deviates from its proper
place by about a quarter of a wavelength."

 I don't even know if he referred to astronomical optics or optics in
general. Even so, a telescope with 1/4 wave of low-order sph ab would be
useful, if noticeably imperfect. But what the "proper place" is, considering
paraxial or best focus, I have no idea.

As a coincidence, I found that quotation yesterday in precognition (?) of
your message -and also my own calculations from a few years back of P-V to
RMS ratios:

Low (3rd) order sph ab: 1.5*sqrt(5)=3.35
Defocus: sqrt(12)=3.46
astig: sqrt(24)=4.90
high (5th) order sph.ab: sqrt(28)=5.29
coma: sqrt(32)=5.66

Anyway, the idea that <1/4 wave P-V should mean essentially perfect optics
seems to be widespread still, but I think this is a misrepresentation of
Rayleigh - and I take it you agree.

> Actually, larger and fainter blur is more desirable for general
> observing, since it likely less affects contrast of smaller details near
> the limit of low-contrast resolution. But, again, the difference is
> rather slight for good (or better) mirrors.

I have the impression that people may object to the wide scatter on esthetic
grounds - just like spider diffraction, even if its effect on image contrast
is negligible. But I suspect that it would be hard to find actual mirrors
with equal RMS errors and widely different RTAs, for actual comparison.


> This sounds more like Conrady than lord Rayleigh. As I gather, the
> original Rayleigh's criterion was derived from  a number of empirical
> test for spherical aberration *at the paraxial focus", coma and
> astigmatism (Applied Optics II, p626). The 1/4 wave wavefront error
> criterion was generalized, and it was assumed that it causes
> approximately 20% fainter central disc. After Airy made it possible to
> calculate the actual values, it turned out that actual energy losses
> under the original Rayleigh formulation are widely different for 1/4 wave
> of various aberrations, as well as for different locations within the
> s.a. defocus.  For the coma, the p-v error "p" translates into RMS
> through RMS=p/4(sq.rt.2), which for 1/4 wave p-v error gives 1/22.6 wave
> RMS and corresponding 0.926 Strehl: less than 8% loss in central
> intensity. For the astigmatism,
> RMS=p/2(sq.rt.6), so that 1/4 wave p-v error translates into 1/19.6 wave
> RMS, and 0.90 Strehl, with 10%  central intensity loss.
>
> For spherical aberration (also primary), RMS=2p/3(sq.rt.5) for the p-v
> wavefront error at  best focus, which is four times smaller than the
> error at the paraxial focus. If lord Rayleigh was counting with the p-v
> error at the paraxial focus (which is double the surface error for near
> perfect conic), while testing - inevitably - at the best focus - his
> actual toerance for spherical aberration (assuming near-perfect conic)
> would be extraordinary low: RMS~p/6(sq.rt.5), which for p=1/4 wave comes
> to ~1/50 wave RMS,  0.984 Strehl and less than 2% central intensity loss!
>
> Of course, this part is little hard to swallow, besides it all being
> rather speculative not knowing the exact details. But indications are
> there that the original Rayleigh criterion was more demanding than
> nowdays accepted conventional "diffraction limited" standard of 0.80
> Strehl. Most likely, the approximate level it was originally set at was
> appropriate to 0.90 Strehl, possibly better.
>
> >My simplified view is that the RMS says how much of the light is within
> the
> Airy disk and how much in the rings, but the RTA says something about how
> wide the light is scattered in the rings. A small amount that is widely
> scattered may be objectionable in much the same sense that the spikes
> from
> the spider vanes are.<
>
> Yes, it is a piece of information that gives some general implications.
> Hope my categorization of it as "meaningless" was clearly enough in the
> context of  the size of aberration, not its particular effect on image
> contrast. However, assuming nearly identical amount of energy out of the
> Airy disc, there won't be significant difference in performance - in
> general terms - between good mirror producing larger, fainter blur, and
> one producing smaller brighter blur. The reason is that they both have
> nearly identical RMS and Strehl, which means that their average contrast
> drop over all frequencies will be also neraly identical. In other words,
> if they both are 1/20 wave RMS and 0.9 Strehl, they will both have 10%
> average contrast drop over the frequency range. The one with larger,
> fainter blur, will have slightly lower contrast for larger details; the
> other will have it slightly lower for smaller details. Quid pro quo.
> Actually, larger and fainter blur is more desirable for general
> observing, since it likely less affects contrast of smaller details near
> the limit of low-contrast resolution. But, again, the difference is
> rather slight for good (or better) mirrors.
>
> In fact, real effect of an aberrated blur can't be reliably predicted -
> even in general terms - based on its size alone. What matters is also
> intensity distribution within the blur, as well as type of defocus. For
> instance, when smallest astigmatic blur is about equal to the Airy disc,
> astigmatic p-v error is 1/1.64 wave (comparable to 1/2.4 wave s.a.
> contrast-wise), and cross-like intensity redistribution is readily
> visible in the pattern seemingly out of the reach of the blur itself.
> Mother Nature keeps on being tough on us: it would be too easy to know it
> just by the geometric blur size; instead, we really have to do
> diffraction calculation and MTF to find out.
>
> Vlad
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