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# Re: Photo Image out of focus

I looked through undergrad notes more than a generation old,
without finding the photo image correction example that I wanted
to share. So I need to speak from memory, and I will be glad if
what I say can be corrected, or updated with more recent technique.

The approach discussed then, depended on detailed knowledge of the image
distortion introduced by the original image generating method.
A 2-dimensional array is generated of digital values of the original
image. And a 2-dimensional array is produced
from (say) the distorted image of a point source through the same
defocussed camera.
The two arrays are convoluted (I say 'convolved') together so as to
produce an array which evaluates the intensity of a point source
from the spread representation of this point at all positions on
the image. You will recall that the Fourier transform of a point
is an array of infinite extent in two dimensions, so the computational
chore could formerly occupy a mainframe for more than trivial time;
in other words, a fast Pentium would be needed to handle the
computation now.

I probably glossed over the numerical massaging involved somewhat.
Applications to spy satellite imagery remediation are so obvious I
expect some relevant research is not on the open shelf.
So the answer to the question, 'is there a purely optical method?'
is, 'I don't think so....'

Brian

At 17:18 6/19/01 -0400, you wrote:

Hi Everyone,

A parent of one of my students sent me the following question:

At Lower School graduation, I took a great photo of a friend of mine
and his son. But it's somewhat out of focus. I want to print it,
but in focus. My intuition tells me that all the various light
rays hit the film -- but not quite in the right place.
So it seems to me that all the data for a good
print must be there on the emulsion. And if I could only bend the
light rays in the printing process (whether before or after it goes
through the negative, I'm not sure), it should be possible to
correct the error and make
the print come out in focus. (After all, they fixed the Hubble
telescope, right?)

I responded as follows:

My first thought is that you are seeking an analog solution to a
digital problem.
You're probably right that all the necessary data is there, just
not in the right place. And your photography friends may also be
right that there are no photographic techniques available at the
developer to move those data around. The easy fluidity of data is
a digital reality, not an
analog one or we would have had it sooner, I imagine.

Is anyone on this list a knowledgeable photographer who can resolve
this question one way or the other. I'm not sufficiently aware of
the optics of the development process to answer directly.
Is there an optical solution to the focus problem?