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 | | From: | Gigi Loreti | | Subject: | Irregular gratings | | Date: | Tue, 11 Jan 2005 01:58:25 +0100 |
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 | The classic grating equation is well known D*sin(theta)=k*lambda
What happen to the equation if some lines of the grating are missing? i.e
some line is black or transparent.
When I say "some", I mean each 3rd line, or 4th or nth line a.s.o.
Any literature on this argument?
Thanks
Luigi
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| | From: | Timo Nieminen | | Subject: | Re: Irregular gratings | | Date: | Tue, 11 Jan 2005 11:26:13 +1000 |
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| On Tue, 11 Jan 2005, Gigi Loreti wrote:
> The classic grating equation is well known D*sin(theta)=k*lambda
>
> What happen to the equation if some lines of the grating are missing? i.e
> some line is black or transparent.
>
> When I say "some", I mean each 3rd line, or 4th or nth line a.s.o.
Then it's still regular.
If missing every nth ruling, then you have a combination of what you'd
get from the complete grating, with no missing rulings, and a grating with
a spacing of n times that of the original grating, illuminated out of
phase compared to the complete grating.
Since the phase is important, you have to think about the fields, not just
intensities.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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| | From: | Gigi Loreti | | Subject: | Re: Irregular gratings | | Date: | Tue, 11 Jan 2005 10:00:25 +0100 |
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"Timo Nieminen" ha scritto nel messaggio
news:Pine.LNX.4.50.0501111122310.1887-100000@localhost...
> > When I say "some", I mean each 3rd line, or 4th or nth line a.s.o.
>
> Then it's still regular.
>
> If missing every nth ruling, then you have a combination of what you'd
> get from the complete grating, with no missing rulings, and a grating with
> a spacing of n times that of the original grating, illuminated out of
> phase compared to the complete grating.
>
> Since the phase is important, you have to think about the fields, not just
> intensities.
So, it's right to say that if I have a grating with 1 missing line, the
total fase and intensity of the filed is the convolution of the regular
grating with the single line?
i.e. is like opening a fenditure on the grating, just quite a sampling of
the grating?
I'm asking this because I'm doing "virtual grating" with LCD (transmissive)
or with DLP (reflective) illuminated with coherent light and focused on the
image plane.
So my question is: given a grating distribution I can compute the phase &
intensity of the resulting field at a given distance (Fraunhofer approx).
Now, if I have a givendistribution of field & phase on the Fourier plane,
there exist (and is only one) a grating distribution which will give that
field & phase?
Matematically speaking, is the inverse of FdT (antitransform) biunivoque?
Thanks
Luigi
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| | From: | Gigi Loreti | | Subject: | Re: Irregular gratings | | Date: | Tue, 11 Jan 2005 13:41:58 +0100 |
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"Gigi Loreti" ha scritto nel messaggio
news:34hip7F4c5kjqU1@individual.net...
>
> Now, if I have a givendistribution of field & phase on the Fourier plane,
> there exist (and is only one) a grating distribution which will give that
> field & phase?
>
> Matematically speaking, is the inverse of FdT (antitransform) biunivoque?
ok, I found the answer on the Lipson (Optical Physics) which states that:
"Although in principle the phase problem can have no general solution
(there is an infinite number of mathematical function which give the same
diffraction pattern intensities), in practice the additition of some
reasonable constraints leads to a unique solution.. Hauptman and KArle were
awared the Nobel prize for this work..."..interesting..
Nice problem the "Phase retrieval" :-)) well trated on chapter 8.6 of
Lipson, Lipson & Tahnhauser..
Luigi
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| | From: | Repeating Rifle | | Subject: | Re: Irregular gratings | | Date: | Tue, 11 Jan 2005 01:54:17 GMT |
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| in article 34gmhgF4apdqgU1@individual.net, Gigi Loreti at gigilo@lcnet.it
wrote on 1/10/05 4:58 PM:
> The classic grating equation is well known D*sin(theta)=k*lambda
>
> What happen to the equation if some lines of the grating are missing? i.e
> some line is black or transparent.
>
> When I say "some", I mean each 3rd line, or 4th or nth line a.s.o.
>
> Any literature on this argument?
>
> Thanks
>
> Luigi
>
>
>
>
Look at the Fourier analysis of gratings or of almost periodic structures.
It also stries me as being similar to the scattering of electrons in
conducting crystals by impurities.
Bill
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| | From: | Gigi Loreti | | Subject: | Re: Irregular gratings | | Date: | Tue, 11 Jan 2005 13:43:32 +0100 |
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"Repeating Rifle" ha scritto nel messaggio
news:BE0871D5.2F44D%salmonegg@sbcglobal.net...
> in article 34gmhgF4apdqgU1@individual.net, Gigi Loreti at gigilo@lcnet.it
> Look at the Fourier analysis of gratings or of almost periodic structures.
> It also stries me as being similar to the scattering of electrons in
> conducting crystals by impurities.
Thanks for the answer, you gave me the idea to look on lattice
scattering...indeed the problem is that and it's not so simple..
Luigi
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| | From: | Spagyrique | | Subject: | Re: Irregular gratings | | Date: | Tue, 11 Jan 2005 10:39:40 -0500 |
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"Gigi Loreti" wrote
> The classic grating equation is well known D*sin(theta)=k*lambda
>
> What happen to the equation if some lines of the grating are missing? i.e
> some line is black or transparent.
>
> When I say "some", I mean each 3rd line, or 4th or nth line a.s.o.
>
> Any literature on this argument?
Well, yes, or at least 0n something highly similar.
Periodic errors are nothing new in gratings.
Such errors give rise to the so-called "ghosts".
Any good book on gratings should have some info on the topic.
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