I am reading a paper about layered materials. However, I am confused on the implementation of this paper. The following picture describe the layered material. enter image description here

r_ab is a complex reflection coeffcient when going from medium a to medium b.

And in the code, there is:

        float2 R12, phi12;
        fresnelDielectric(LdotH, 1.0, eta_2, R12, phi12);
        float2 R21 = R12;

I don't understand why is r_12 equal to r_21?


1 Answer 1


We have $t_{12} = t_{21}$, by the law of reciprocity. Also, $$r_{12} + t_{12} = 1\\r_{21} + t_{21} = 1$$ It follows that $r_{12} = r_{21}$ as well.

  • $\begingroup$ Ahh..I don't understand why t_12 = t_21... $\endgroup$ Commented Jan 20, 2019 at 5:03
  • $\begingroup$ @TIANLUNZHU It's because of the law of reciprocity, a fundamental principle of optics. It says if you swap the incoming and outgoing rays, the BSDF (reflectance or transmittance) doesn't change. Note from the diagram that the $t_{12}$ and $t_{21}$ cases are exactly symmetrical with each other, only with the rays going in the opposite directions. $\endgroup$ Commented Jan 21, 2019 at 5:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.