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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?

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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.

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  • $\begingroup$ Ahh..I don't understand why t_12 = t_21... $\endgroup$
    – TIANLUN ZHU
    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. $\endgroup$
    – Nathan Reed
    Commented Jan 21, 2019 at 5:38

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