Optical scattering: Converting BRDF to PSD

[mudkip9001]

edit: the TeX is still being screwy, not putting the equations in the right places. stay tuned.
editII: fixed, I think.

Homework Statement

I'm working on converting a BRDF to a PSD, S(f_x,f_y).

Homework Equations

In the book 'optical scatter: measurement and analysis', the BRDF is given as

$$BRDF(\theta_i,\theta_s,\phi_i)\propto S(f_x,f_y)$$

where f_x and f_y are evaluated at:

$$f_x=\frac{\sin{\theta_s}\cos{\phi_s}-\sin{\theta_i}}{\lambda}$$$$f_y=\frac{\sin{\theta_s}\sin{\phi_s}}{\lambda}$$

So

$$S(f_x,f_y) \propto BRDF(\theta_i,\theta_s,\phi_i)$$

I'm confused as to what angles correspond to what frequencies. i.e, what values for the angles should I plug into the BRDF for any given frequencies..

The Attempt at a Solution

It's probably quite simple, the book makes no mention of it, but my brain is failing me, I don't even know where to start. For example, the data I have is for only one angle of incidence, so that will be fixed, but f_x is a function of two varialbles (theta and phi), so I can't just solve for $$\theta_s$$

 

[mark726]

and \phi_s.

Hi there,

It sounds like you are on the right track! The angles \theta_s and \phi_s correspond to the direction of scattered light, while \theta_i and \phi_i correspond to the direction of incident light. So, in order to calculate the BRDF for a given frequency, you will need to know the angles of incidence and scattering for that frequency.

One way to do this is to use the equations for fx and fy that you provided. These equations relate the angles \theta_s and \phi_s to the frequency components fx and fy. So, for a given frequency, you can use these equations to calculate the corresponding angles \theta_s and \phi_s. Then, you can plug these values into the BRDF equation to calculate the BRDF for that frequency.

Another way to approach this is to use the data you have for only one angle of incidence. Since the angle of incidence is fixed, you can use this data to calculate the frequency components fx and fy for that angle. Then, you can use these frequency components in the BRDF equation to calculate the BRDF for that frequency.

I hope this helps! Let me know if you have any other questions.