[ATM] astigmatism question

[Dale Eason]

Once more I get the following error when using yahoo (my email system) to send mail to Vlad sacek.

-----------------
Hi. This is the qmail-send program at yahoo.com.
I'm afraid I wasn't able to deliver your message to the following addresses.
This is a permanent error; I've given up. Sorry it didn't work out.

<vla at coppert.net>:
Sorry, I couldn't find any host named coppert.net. (#5.1.2)
-------------------------------------------------------------



>>my response to Vlad
Thank you Vlad,

I did not realize the 1/4 rule only applied to SA.  I should have however.
I will update the pictures I posted earlier in a few days.

This time I used OpenFringe to modify the Y astig zernike value until the RMS value was .075 and sure enough the PV astig value was .365.  Thank you for correcting me.

Dale Eason 


--- On Wed, 3/11/09, vladimir sacek <vla at coppert.net> wrote:

> From: vladimir sacek <vla at coppert.net>
> Subject: Re: [ATM] astigmatism question
> To: atmpob at yahoo.com
> Date: Wednesday, March 11, 2009, 10:10 PM
> If Y is the Zernike aberration term for primary astigmatism,
> it can be written as:
> 
> Y= z√24(cos2θ-0.5)ρ2  =  A(cos2θ-0.5)ρ2
> 
> where "z" is usually termed Zernike expansion
> coefficient, "A" is the peak aberration
> coefficient for primary astigmatism (equaling 1/2 the P-V
> wavefront error), "θ" is the
> pupil angle and "ρ" is the height in the pupil
> normalized to 1 for pupil radius. Setting θ
> to 0 and ρ to 1, gives the maximum aberration value (along
> the axis of aberration) as
> 
> Y= 0.5z√24 = A/2
> 
> with "z" effectively equaling the RMS wavefront
> error. As you know, diffraction limited
> RMS - regardless of the type of aberration - is 0.0745 in
> units of the wavelength (exactly
> 1/√180). The corresponding peak aberration coefficient -
> and PV - is thus A=0.0745√24
> or 0.365, also in the units of the wavelength.
> 
> Diffraction limited PV wavefront for coma is 0.42 wave, and
> so on. The 0.25 wave PV is
> "diffraction limited" only for primary spherical
> aberration.
> 
> Vlad
> 
> ----- Original Message ----- From: "Dale Eason"
> <atmpob at yahoo.com>
> To: <atm at atmlist.net>
> Sent: Wednesday, March 11, 2009 9:47 PM
> Subject: Re: [ATM] astigmatism question
> 
> 
> Vladimir sacek sent me the email below. I tried to reply to
> him but it bounced.
> 
> I use the Y zernike term for atsitg and adjust it until the
> worst case PV on a surface profile graphs is as stated in
> the images. Then use the rule that 1/8 wave PV on the
> surface (1/4 wave on the wavefront) is a good approximation
> for diffraction limited. Does that help explain my
> statements and under those assumptions are my statements
> correct?
> 
> Dale Eason
> 
> --- On Wed, 3/11/09, vladimir sacek <vla at coppert.net>
> wrote:
> 
> From: vladimir sacek <vla at coppert.net>
> Subject: Re: [ATM] astigmatism question
> To: "Dale Eason" <atmpob at yahoo.com>
> Date: Wednesday, March 11, 2009, 7:27 PM
> 
> (off list)
> 
> Hope you don't mind; I've sent reply to the list
> earlier today, which
> has never made it.
> Some glitch with new email account that seems to be working
> well with everyone
> else.
> 
> Visual simulations, like those you posted, are the best way
> to get to the core
> of this.
> But there are some numerical inconsistencies. Since surface
> astigmatism doubles
> in the
> wavefront, and the PV-to-RMS ratio for primary astigmatism
> is sq.rt.24,
> "diffraction
> limited" PV (based on 0.0745 diffraction-limited RMS
> error in units of the
> wavelength)
> is 0.365 on the wavefront, and half as much on the surface.
> 
> Regards,
> 
> Vladimir Sacek
> 
> 
> 
> 
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