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1) The question "why should it be a polynomial?" was addressed to
Brian W.
2) Those who want to write their own digital convolution programs
would probably appreciate the answer. Consider my 20*20 pixels example
(each pixel emits 100 units of light). Geometry is defined below.
a) How many units of light arrive to the screen at x=7 cm and y= 10 cm?
b) How many units of light arrive to the screen at x=-7 cm and y=10 cm?
Ludwik
On May 1, 2009, at 4:15 PM, John Denker wrote:
On 05/01/2009 12:25 PM, ludwik kowalski wrote:
1) Suppose the object is a flat square (each side is 10 cm) in the z=0
plane. The center of the square, whose sides are parallel to axes, is
at the origin. Each "pixel" (small area) emits equal amount of light
(100 units) isotropically. THERE ARE 20*20=400 PIXELS
Write the "function representing the object." Why should it be a
polynomial?
It's not a polynomial. Why should it be a polynomial?
For that matter, why do we need to write down the function?
We have a perfectly good _optical computer_ that already has
a representation of the function, and is already doing the
convolution for us.
If you want to predict the results of the optical computer,
and you already have the object and kernel represented digitally
(in pixels) why not just do the convolution digitally?
2) Suppose the mask consists of a black paper located in the plane
z=10 cm, with three circular holes. The radium of each circle is 1
cm.
Centers of circles are specified as follows:
circle 1 (x=0, y=0); circle 2 (x=5 cm, y=5 cm); circle 3 (x=5 cm,
y=-5
cm)
Write the "function representing the mask." Why should it be a
polynomial?
It's not a polynomial. Why ask the question?
3) Suppose the resulting light spot is observed on a screen situated
in the plane z=30 cm
Show how to convolute the two functions in order to predict the
distribution of light on the screen (how many units of light per
square cm at a given x and y).
P.S.
This is probably far fro being trivial. I have no idea how to do
this.
Specific examples of that kind would probably be helpful.
It's trivial. Just code the convolution from the definition and
run the program. For extra credit there are at least five ways
to make the code more efficient, but this is far from necessary.
I already provided a mice simple one-dimensional example
http://www.av8n.com/physics/convolution-intro.xls
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Forum for Physics Educators
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- - - - - - - - - - - - - -
Ludwik Kowalski, a retired physics teacher and an amateur journalist.
Updated links to publications and reviews are at:
http://csam.montclair.edu/~kowalski/cf/ http://csam.montclair.edu/~kowalski/my_opeds.html
http://csam.montclair.edu/~kowalski/revcom.html
Also an ESSAY ON ECONOMICS at: http://csam.montclair.edu/~kowalski/economy/essay9.html
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Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
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