Ellipse-Oval Illuminated at plane

[DT1010]

Hello to everyone,

Imagine that you have a source of illumination where the light footprint lies on a rectangular plane. Assume that if you move the source, in every light-foorprint the center of the footprint remains the same.If the source is at the center of the plane and has a distance from the plane equal to d, the footprint is an ellipse. However if you move the source, the shape becomes more like an oval(a_left!=aright & b_up!= b_down).

Imagine that for some reason the source fluctuates from its position (e.g wind blows) so the center of the footprint will move.


I have modeled the problem without fluctuations and i know exactly the area of the plane which is illuminated wherever i place the source. Can anyone help me with the fluctuation case?

 

[Dr.Peterson]

Imagine that you have a source of illumination where the light footprint lies on a rectangular plane. Assume that if you move the source, in every light-foorprint the center of the footprint remains the same.If the source is at the center of the plane and has a distance from the plane equal to d, the footprint is an ellipse. However if you move the source, the shape becomes more like an oval(a_left!=aright & b_up!= b_down).

Imagine that for some reason the source fluctuates from its position (e.g wind blows) so the center of the footprint will move.

I have modeled the problem without fluctuations and i know exactly the area of the plane which is illuminated wherever i place the source. Can anyone help me with the fluctuation case?

I'm not at all sure what this means. What is a light footprint? What is a rectangular plane (as opposed to a mere rectangle)? How can something be at the center of a plane yet at some distance from it? How is the source allowed to move? What sort of fluctuations are allowed?

Some pictures and a fuller explanation might help.

 

[DT1010]

By rectangular plane i mean a finite size plane.The UAV is the source and the ellipse is the footprint.As the UAV moves the shape inside the plane changes. The UAV is assumed to point at the center of the plane wherever you place it. However if the wind blows the UAV will fluctuate. So i want to find how tge illuminated area will change if we assume that tge UAV fluctuates at the x axis with normal distribution~(0,σ^2) and the same in y axis