Re: [Phys-l] Sun's image due to reflection by not a pinhole.

[ludwik kowalski <kowalskil@mail.montclair.edu>]

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 2 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. [P.S. 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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- - - - - - - - - - - - - -
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