{"id":39766,"date":"2018-07-18T07:15:49","date_gmt":"2018-07-18T07:15:49","guid":{"rendered":"http:\/\/www.labri.fr\/perso\/barla\/blog\/?p=39766"},"modified":"2019-08-14T15:47:50","modified_gmt":"2019-08-14T15:47:50","slug":"diffraction-w-b-walter","status":"publish","type":"post","link":"https:\/\/www.labri.fr\/perso\/barla\/blog\/?p=39766","title":{"rendered":"Diffraction w\/ B. Walter"},"content":{"rendered":"<p id=\"top\" \/><p>I have recently read your review of diffraction models, which appeared as supplemental material of the Siggraph 2018 paper by Ling Qi et al.<\/p>\n<p>I&#8217;d first like to thank you for having synthesized this body of research from the Optics literature. I had read some references: Beckmann&#8217;s half of his book, Krywonos&#8217; thesis, some courses on Fourier Optics. But every time I went back to the topic of diffraction, it seemed I had forgotten half of it, which is frustrating.<\/p>\n<p>Thanks to your comprehensive review, I now have a much more solid understanding of the different models. The fact that it&#8217;s &#8220;restricted&#8221; to explicit height fields actually made it much simpler for me to understand! I also found the reciprocity and geometric term interesting, even though the latter is skipped in practice if I understand well.<\/p>\n<p>Something was still bugging me: I thought the Generalized Harvey-Shack (GHS) approach was superior to Beckamm-Kirchoff (BK)&#8230; I went back to Krywonos&#8217; thesis, and remembered that this is the case only if one drops the far-field assumption. One might think (as I did) that for BRDFs, only the far-field condition matters; but Krywonos argues to the contrary. He writes on pages 26 and 27 of his thesis that not only does the near field then becomes excluded, but a paraxial limitation is also imposed. As far as I understand, this affects the tails of the resulting BRDF lobes; this means that GHS should be superior to BK toward grazing angles&#8230;<\/p>\n<p>I was wondering whether you had investigated these non-paraxial\u00a0 considerations of diffraction and their impact on the BRDF. I should re-read Krywonos&#8217; thesis in details to better understand the importance of dealing with near-field diffraction patterns. He mentions that they are aberrated Fraunhofer diffraction patterns, but I am not sure of the visual impact of such aberrations.<\/p>\n<p>\u00a0<\/p>\n<p style=\"padding-left: 60px;\">I&#8217;m glad you found the diffraction writeup useful.\u00a0 I&#8217;m not an expert in optics and I had a lot of trouble matching terminology across papers and keeping track of what approximations and assumptions were used in each diffraction method.\u00a0 The diffraction literature covers a lot of different models and application areas, and simplifying it to the just parts relevant for diffractive BRDF from surfaces of known geometry, really helped me and hopefully can be useful for others as well.<\/p>\n<p style=\"padding-left: 60px;\">You are right that we are not using the geometric masking term in this siggraph paper.\u00a0 I had used a geometric shadowing\/masking term in an earlier paper on brushed metals but didn&#8217;t have a good justification for it until now, so I wanted to include that in the writeup.\u00a0 We do use the reciprocity which turned out to be pretty simple once I understood how similar the Kirchhof and Harvey-Shack approaches are theoretically.<\/p>\n<p style=\"padding-left: 60px;\">I found Krywonos&#8217; thesis to be very useful though not always easy to follow.\u00a0 Sometimes I have trouble figuring out which conditions and assumptions are used in some of his claims.\u00a0 As far as I can tell, Kirchhoff theory and Generaiized-Harvey-Shack are actually quite similar and Kirchhoff might be more accurate in some cases because it does not require the planar proxy approximation used in the Harvey-Shack reflection-phase-shift function.<\/p>\n<p style=\"padding-left: 60px;\">Specific Beckman-Kirchhoff models however may contain paraxial or other approximations that reduce their accuracy.\u00a0 My impression of his section 2.1 discussion on pages 26-27 is that he is using the terms &#8220;Fresnel&#8221; and &#8220;Fraunhofer&#8221; to refer to specific paraxial approximations and claiming (quite reasonably) that the Generalized-Harvey-Shack method does not require using those paraxial approximations and thus is more accurate than methods that do use them.\u00a0 However Kirchhoff, at least in the way we use it in the paper, also does not use those paraxial approximations, so that is not an advantage for either approach over the other in our case.\u00a0 So I don&#8217;t think his claim in that part applies to the Kirchhoff method as used in our paper.<\/p>\n<p style=\"padding-left: 60px;\">I have not tried to test the accuracy of Kirchhoff versus Generalized-Harvey-Shack so I can&#8217;t say anything definitive about their relative accuracy, but my impression so far has been that they often produce very similar results such that its often hard to tell them apart.\u00a0 My personal guess is that the Kirchhoff is perhaps slightly more accurate.\u00a0 Though I have not included or analyzed the energy renormalization term in Generalized-Harvey-Shack model which Krywonos says improves its accuracy when significant amounts of energy end up in the non-propagating or evanescent modes, so perhaps that would tilt the accuracy comparison in GHS&#8217;s favor.<\/p>\n<p>\u00a0<\/p>\n<p>My understanding of the usefulness of near-field diffraction is that it depends on the size of the diffracting surface under consideration. By this I mean the size of the aperture for instance or, more relevant to graphics, the size of the ray or pixel footprint on a surface. With large-enough sizes, the phase of waves &#8220;emitted&#8221; at one end of the footprint might significantly differ from that at the other end. This phase difference is ignored by far-field approximations, even though it may be important, especially towards grazing angles as shown by Krywonos.<\/p>\n<p>The reason why your approach might not suffer from ignoring these near-field diffraction effects is that you consider an infinitesimal neighborhood on the surface. Or said differently, you only consider the Kirchoff approach with an explicit height field, not Beckmann-Kirchoff where the paraxial approximation is effectively made. However, in practice, in the Siggraph paper, you do consider extended neighborhoods, right? You may thus want to consider near-field diffraction at some point&#8230;<\/p>\n<p>That being said, I don&#8217;t know whether there&#8217;s a practical way to take these near-field diffraction effects into account; at least your current approach works efficiently! I&#8217;ll try to find some time to read Krywonos&#8217; thesis (once again) with the questions above in mind; if I get an epiphany, I&#8217;ll get back to you.<\/p>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I have recently read your review of diffraction models, which appeared as supplemental material of the Siggraph 2018 paper by Ling Qi et al. I&#8217;d first like to thank you for having synthesized this body of research from the Optics literature. I had read some references: Beckmann&#8217;s half of his book, Krywonos&#8217; thesis, some courses &#8230; <a title=\"Diffraction w\/ B. Walter\" class=\"read-more\" href=\"https:\/\/www.labri.fr\/perso\/barla\/blog\/?p=39766\" aria-label=\"Read more about Diffraction w\/ B. Walter\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21],"tags":[],"class_list":["post-39766","post","type-post","status-publish","format-standard","hentry","category-discuss"],"_links":{"self":[{"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/posts\/39766","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=39766"}],"version-history":[{"count":3,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/posts\/39766\/revisions"}],"predecessor-version":[{"id":40134,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/posts\/39766\/revisions\/40134"}],"wp:attachment":[{"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=39766"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=39766"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=39766"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}