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Thread Subject:
Super-position of light elements

Subject: Super-position of light elements

From: Ron

Date: 5 Sep, 2010 10:44:05

Message: 1 of 3

Have a point source of light projecting a full circle on a flat surface (with light intensity changing with distance^2 from source). When having a whole "room" lit, with elements spaced uniformly along lines and few lines in parallel, I'd like to show the light patches on the surface as well as calculate overlapping between beams and later, distribution uniformity. Is there a "nice" way to do so?

Subject: Super-position of light elements

From: Roger Stafford

Date: 5 Sep, 2010 19:57:05

Message: 2 of 3

"Ron " <ron.seligmann@gmail.com> wrote in message <i5vs9l$gal$1@fred.mathworks.com>...
> Have a point source of light projecting a full circle on a flat surface (with light intensity changing with distance^2 from source). When having a whole "room" lit, with elements spaced uniformly along lines and few lines in parallel, I'd like to show the light patches on the surface as well as calculate overlapping between beams and later, distribution uniformity. Is there a "nice" way to do so?
- - - - - - - - - -
  One thing to remember is that, while light intensity varies as the inverse square of the distance from its point source, this is intensity as measured on a surface orthogonal to the light ray. In your case when the light is cast onto a surface at a slant from the orthogonal direction, the intensity on the surface will be further reduced by the cosine of the angle between the surface normal and the ray.

  If h is the orthogonal distance from the light source to the surface and d the distance along the surface from the surface point at the base of this orthogonal line and the surface point where intensity is to be determined, then the intensity there would be proportional to:

 I = 1/r^2*cos(theta) = 1/(h^2+d^2)*(h/sqrt(h^2+d^2) =
     h/(h^2+d^2)^(3/2)

where r is the diagonal distance from the light to the surface point where intensity is determined.

  What you have to do is make a summation of all such quantities for the different light sources. At any given point on the surface the d quantity will accordingly be different for each light source. That will make a good exercise for you in the use of matlab, so I leave that to you.

Roger Stafford

Subject: Super-position of light elements

From: Ron Seligmann

Date: 5 Sep, 2010 20:48:04

Message: 3 of 3

"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <i60smh$r8e$1@fred.mathworks.com>...
> "Ron " <ron.seligmann@gmail.com> wrote in message <i5vs9l$gal$1@fred.mathworks.com>...
> > Have a point source of light projecting a full circle on a flat surface (with light intensity changing with distance^2 from source). When having a whole "room" lit, with elements spaced uniformly along lines and few lines in parallel, I'd like to show the light patches on the surface as well as calculate overlapping between beams and later, distribution uniformity. Is there a "nice" way to do so?
> - - - - - - - - - -
> One thing to remember is that, while light intensity varies as the inverse square of the distance from its point source, this is intensity as measured on a surface orthogonal to the light ray. In your case when the light is cast onto a surface at a slant from the orthogonal direction, the intensity on the surface will be further reduced by the cosine of the angle between the surface normal and the ray.
>
> If h is the orthogonal distance from the light source to the surface and d the distance along the surface from the surface point at the base of this orthogonal line and the surface point where intensity is to be determined, then the intensity there would be proportional to:
>
> I = 1/r^2*cos(theta) = 1/(h^2+d^2)*(h/sqrt(h^2+d^2) =
> h/(h^2+d^2)^(3/2)
>
> where r is the diagonal distance from the light to the surface point where intensity is determined.
>
> What you have to do is make a summation of all such quantities for the different light sources. At any given point on the surface the d quantity will accordingly be different for each light source. That will make a good exercise for you in the use of matlab, so I leave that to you.
>
> Roger Stafford

Thanks Roger.

Since posted I've managed to create a reflector to project the light onto a plane and calculate the distance to each point. You are right and the forgotten cosine will be added to intensity calc. By saying good excercise you mean create a "large room" zeros matrix and "dump" my projected matrices in specific locations on it? Is that the best there is?

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