What is the exact meaning of this integral on this page? I can understand that we are integrating the proportion over solid angle, but I don't think this result is the final proportion of L_o comparing to L_i (since L_i varies between solid angles)

yongchi1

I found that on wikipedia the integration is on w_o not w_i, which makes more sense. I think you made a typo here.

mdsavage

It makes sense that Helmholtz reciprocity should generally hold, but is it a physical truth across all surfaces? A quick Google search seems to indicate that perhaps there are some cases in which it does not, though there aren't a lot of details about why these cases cause it to be violated. (For example, the Wikipedia article makes an allusion to a magnetic field causing the optical medium to "depart from linearity", though I don't really follow what it's talking about.)

riceroll

To my understanding, only for glass surface, the distribution function would equal to one, otherwise, there would be energy reflected to other directions.

keenan

@yongchi1 Yes, thanks; that's a typo indeed.

keenan

@mdsavage Right; a general rule about physics is that you can always cook up exotic scenarios where some assumption doesn't hold. There's a very nice discussion of Helmholtz reciprocity, as well as a good list of references, in Chapter 6 of Eric Veach's (Academy Award-winning) PhD thesis.

keenan

@riceroll If you correct the typo mentioned above, then you can have a material that reflects 100% of the light, but not necessarily in the specular direction.

What is the exact meaning of this integral on this page? I can understand that we are integrating the proportion over solid angle, but I don't think this result is the final proportion of L_o comparing to L_i (since L_i varies between solid angles)

I found that on wikipedia the integration is on w_o not w_i, which makes more sense. I think you made a typo here.

It makes sense that Helmholtz reciprocity should generally hold, but is it a physical truth across all surfaces? A quick Google search seems to indicate that perhaps there are some cases in which it does not, though there aren't a lot of details about

whythese cases cause it to be violated. (For example, the Wikipedia article makes an allusion to a magnetic field causing the optical medium to "depart from linearity", though I don't really follow what it's talking about.)To my understanding, only for glass surface, the distribution function would equal to one, otherwise, there would be energy reflected to other directions.

@yongchi1 Yes, thanks; that's a typo indeed.

@mdsavage Right; a general rule about physics is that you can always cook up exotic scenarios where some assumption doesn't hold. There's a very nice discussion of Helmholtz reciprocity, as well as a good list of references, in Chapter 6 of Eric Veach's (Academy Award-winning) PhD thesis.

@riceroll If you correct the typo mentioned above, then you can have a material that reflects 100% of the light, but not necessarily in the specular direction.