wiki:PolarizationMaps

Version 5 (modified by Jonathan, 7 years ago) ( diff )

Goal is to integrate various functions along lines of sight which is constrained to be in the y-z plane and has components and

is the tilt angle of the jet towards the observer

so

Each pixel in the resulting image will be given by the integral of the function along the path

where corresponds to crossing of the plane

and we have and

and

For 3D we just need to create the expressions in visit, create the lineouts, and then integrate the resulting query for each x_i and y_i

For 2.5D, we need to transform the integral along (normally in the yz plane) into an integral in the plane.

Since everything is axi-symmetric, the value at can be inferred by rotating the corresponding solution at

by an angle

.

So our new path is in the xy plane and is given by

And we have

so we can write the integral as

$\int F(x'(s)

and we have

which under the substitution gives

Assume jet is oriented along and that we are integrating along the direction

where is the angle of inclination.

We are interested in calculating the integral of , , and where

If this is just , , and

If then we have to tilt the integral and calculate using the expression above.

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