Re: PSF function.. and convolution help needed

On Apr 20, 9:38 pm, Phil Hobbs
<pcdhSpamMeSensel...@xxxxxxxxxxxxxxxxxx> wrote:
odprt...@xxxxxxxxx wrote:
On Apr 20, 3:10 pm, Phil Hobbs <pcdhSpamMeSensel...@xxxxxxxxxxxx>
wrote:
odprt...@xxxxxxxxx wrote:
On Apr 16, 9:46 pm, "odprt...@xxxxxxxxx" <odprt...@xxxxxxxxx> wrote:
On Apr 16, 9:39 pm, "odprt...@xxxxxxxxx" <odprt...@xxxxxxxxx> wrote:
    F( X Y ) = F( X * Y )  and F( X * Y ) = F( X Y )  where * indicates the
convolution.
So, the amplitude of the light at the image plane is the Fourier transform
of the light at the pupil plane:
    Image(x,y) = F( L1(x,y) ) = F( L0(x,y) A(x,y) ) = F( L0(x,y) ) * F(
A(x,y) )
 something is not right in this equations, I think there is a mistake,
tell me if I am wrong here...
it should be :
  F( X)F( Y ) = F( X * Y )
what do u say?
also after reading few things, and reading this comment again.
in the end the PSF is nothing but a simple transform Fourier over the
aperture , and the light that hit it, no ?
also tell me if i understand what u say correctly
if you have the PSF of a system, then you can calculate how any signal
will look, by convulting this signal with the transform the PSF .
is that right? :)
thanks
meant:
if you have the PSF of a system, then you can calculate how any signal
 will look, by convulting this signal with  the PSF .
anyone ?
Convolution in the space domain is multiplication in the spatial
frequency domain, and vice versa.  So your first set of equations should
read

F(X*Y) = F(X)F(Y)    and F(XY) = F(X)*F(Y).

You have to be very careful to distinguish between the coherent transfer
function (CTF), which operates on field amplitudes, and the less well
defined and less well behaved optical transfer function (OTF), which
operates on intensity.  See lots of earlier threads on this newsgroup..

Cheers,

Phil Hobbs

 correct me if I am wrong here , but the first equation is much more
useful no ?

also I will be very glad if you can  tell me if this two saying is
true :

in the end the PSF is nothing but a simple transform Fourier over the
aperture , and the light that hit it, no ?

if you have the PSF of a system, then you can calculate how any signal
will look, by convulting this signal with the transform the PSF .

is that right? :)

Both equations are important.  In a typical imaging system, the first
one tells you about your resolution, and the second tells about your
illumination.  You have to use both for a complete description of your
imaging system.

You need to read the archived discussions from this group (start fromhttp://groups.google.com/advanced_search?num=100and search on OTF and
CTF).  There's not much point in rehashing this, since many of them are
quite recent.

Cheers,

Phil Hobbs

you didn't notice my firs t paragraph when I asked if :

in the end the PSF is nothing but a simple transform Fourier over the
aperture , and the light that hit it, ?


what do you say ?

Thanks

.

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