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

["Richard Schwartz" <richas@earthlink.net>]

One wave OPD?    I would be delighted with an optical system that had
exactly one-wave OPD at all points in the focal plane.


> [Original Message]
> From: Vladimir Sacek <vladis.2@juno.com>
> To: <atm@atmlist.net>
> Date: 6/26/2004 6:12:57 AM
> Subject: [ATM] Re:Satisfying "Millies-Lacroix" is neither necessary
norsufficient for "diffraction-limited" performance
>
> Nils, 
>
> >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.<
>
> Then it was lord Rayleigh; I'm almost sure Conrady used "decidedly
> prejudicial"
> phrase somewhere, and that's why I thought it was him. I'd say the
> criterion was for optical instruments in general. But what is really
> intriguing is that his treatment for s.a.
> wavefront error was at the paraxial focus. And there is no doubt abot it,
> because Conrady directly states, analyzing s.a. defocus: "It is very
> remarkable that this great reduction in the value of OPD' at the
> mid-focus completely escaped previous investigators, including Lord
> Rayleigh, and that as a consequence they put the limit of admissible
> spherical aberration at one quarter of its true value" (Applied Optics,
> p631).
>
> The "true value" is, of course, 1/4 wave at the best focus, or 1 wave at
> the paraxial. Direct implication is that the original Rayleigh criterion
> for spherical aberration was 1/4 wave at the paraxial, and 1/16 wave at
> the best focus (the second part being the one he wasn't aware of).
>
> >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<
>
> Yes, it makes it even simpler when the root is expanded to include the
> free factor.
> Thanks for the tip. 
>
> >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.<
>
> What I'm sure of is that it doesn't represent essentially perfect optics.
> I'm less sure of  what  Rayleigh criterion originaly meant - or, in other
> words, how exactly it was derived - but there are strong indications that
> it was more demanding than 0.80 Strehl. 
>
> Vlad
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