[ { "topic": "Surface finish parameters and derived specular lobe widths for mirror-finish stainless steel, diamond-drag-burnished, and plastically torn surfaces (visible light, λ = 550 nm)", "confidence": "estimated", "values": [ { "quantity": "MODEL — step 0: reference wavelength", "value": "550", "unit": "nm", "note": "[CHOICE] Photopic peak. All angular results scale roughly linearly with λ in the smooth/physical-optics regime and are λ-independent in the geometric-optics regime. Blue (450 nm) halos are ~20% narrower than red (650 nm) ones; that chromatic spread is itself visible as a faint colored fringe on the halo of a No.8 surface." }, { "quantity": "MODEL — step 1: Ra to Rq conversion factor", "value": "1.4", "unit": "dimensionless (Rq/Ra)", "note": "[LIT] Eckhardt Optics, standard for near-Gaussian height distributions. Assumption: Gaussian heights. Mill finishes (2B, BA) satisfy this reasonably. Burnished and torn surfaces do NOT — they are skewed and leptokurtic (the diamond-burnishing literature reports Rsk/Rku explicitly for this reason), so 1.4 is the weakest link for the last two cases." }, { "quantity": "MODEL — step 2: Rayleigh smooth-surface criterion, σ_crit at normal incidence", "value": "44", "unit": "nm (Rq)", "note": "[LIT-derived] σ_crit = λ/(4π) = 550/(4π) = 43.8 nm. Below this the surface is optically smooth: a true specular SPIKE (delta function, mirror image) survives and roughness only removes energy from it into a halo. Above it there is no spike at all — only a broadened LOBE. This single threshold is what separates No.8 mirror from every other case here." }, { "quantity": "MODEL — step 3a: energy split in the smooth regime (Bennett–Porteus TIS)", "value": "TIS = 1 − exp(−(4π·Rq·cosθ_i/λ)²)", "unit": "fraction scattered out of the spike", "note": "[LIT] Bennett–Porteus / total-integrated-scatter. Gives HOW MUCH light leaves the mirror direction, not how far. Assumptions: single scattering, scalar diffraction, σ ≲ λ/(4π), clean front-surface reflector, no subsurface or contaminant scatter." }, { "quantity": "MODEL — step 3b: halo angular width in the smooth regime (grating equation + Gaussian PSD)", "value": "W_1/e = arcsin(λ/(π·T))", "unit": "degrees (half-width from specular direction)", "note": "[LIT-derived] Grating equation sinθ_s − sinθ_i = λ·f (Rayleigh-Rice / Harvey-Shack). For a Gaussian autocorrelation C(τ)=σ²exp(−τ²/T²) the PSD ∝ exp(−π²f²T²), whose 1/e point is f_c = 1/(πT). KEY CONSEQUENCE: in the smooth regime the halo WIDTH depends only on the lateral correlation length T, not on σ at all. σ sets brightness of the halo, T sets its size. Most rendering discussions get this backwards." }, { "quantity": "MODEL — step 3c: lobe width in the rough/geometric regime (microfacet)", "value": "W_1/e = 2·arctan(α), FWHM = 4·arctan(0.833·α), with α = Sdq = √2·Rq/T", "unit": "degrees", "note": "[LIT-derived] Beckmann/Cook-Torrance D ∝ exp(−tan²θ_h/α²); the microfacet roughness α equals the RMS surface slope Sdq. The factor 2 is the reflection law (a facet tilted by θ_h swings the reflected ray by 2θ_h). √2·Rq/T is the exact RMS slope for a Gaussian ACF. FWHM ≈ 1.67 × W_1/e. Assumptions: σ >> λ, geometric optics, single scattering, Gaussian slope statistics, no shadowing correction." }, { "quantity": "MODEL — step 4: relevant spatial-frequency band", "value": "0.63 to 32", "unit": "µm (surface wavelength) for scatter between 60° and 1°", "note": "[LIT-derived] From f = sinθ/λ. Lobe broadening you can see in a render comes only from surface wavelengths of roughly 0.6–30 µm. A stylus Ra taken with a 0.8 mm cutoff includes far longer wavelengths that produce sub-0.5° deviation — read as waviness/orange-peel, not lobe width. Every Ra-derived α below is therefore an OVERESTIMATE, possibly by 1.5–3x for the rolled finishes." }, { "quantity": "No. 8 / 8K mirror stainless — Ra", "value": "0.01 to 0.05 (typical 0.02–0.025)", "unit": "µm", "note": "[LIT] Multiple mill/supplier finish charts converge on Ra 0.01–0.05 µm for No.8/8K; 'super mirror' grades target the 0.01–0.02 end. The spec band is a factor of 5 wide and that matters enormously — see the TIS entries." }, { "quantity": "No. 8 / 8K mirror stainless — Rq", "value": "0.014 to 0.07 (typical 0.03)", "unit": "µm", "note": "[DERIVED from LIT] Rq = 1.4·Ra. Note that only the lower half of the band falls under the 44 nm Rayleigh threshold." }, { "quantity": "No. 8 / 8K mirror stainless — correlation length T", "value": "1 to 5 (typical 2–3)", "unit": "µm", "note": "[EST] Reasoned, not measured. Final 8K polishing uses ~1–3 µm diamond or alumina abrasive on a cloth/felt pad; the residual lateral feature scale tracks the abrasive and pad contact size. I found no published autocorrelation-length measurement for No.8 stainless specifically. This is the single largest uncertainty in the mirror case." }, { "quantity": "No. 8 / 8K mirror stainless — fraction of light scattered out of the mirror spike (TIS, normal incidence)", "value": "10% at Ra 0.01 / 38% at Ra 0.02 / 92% at Ra 0.05", "unit": "% of reflected energy", "note": "[DERIVED from LIT] Bennett–Porteus. This is the most actionable number here: 'No. 8 mirror finish' spans a genuine mirror (90% spike) to an essentially hazy surface with no spike at all (8% spike), all within one nominal spec. If simulating real fabricated panels rather than idealized ones, expect 30–60% haze." }, { "quantity": "No. 8 / 8K mirror stainless — SPECULAR LOBE WIDTH (halo around the spike)", "value": "2 to 5 (typical ~3); full plausible range 0.5 to 11", "unit": "degrees (half-width at 1/e from specular direction)", "note": "[EST, model-derived] Two independent routes agree, which is the main reason to trust the order of magnitude: physical optics arcsin(λ/πT) gives 10.1°/5.0°/3.3°/2.0° for T = 1/2/3/5 µm; microfacet 2·arctan(√2Rq/T) gives 0.45° (best case Rq 14 nm, T 5 µm), 2.4° (typical Rq 30 nm, T 2 µm), 11.3° (worst case Rq 70 nm, T 1 µm). FWHM ≈ 1.67x these. RENDER AS: bright mirror spike + a broad low-amplitude halo of ~3° half-width carrying 10–40% of the energy. GGX α ≈ 0.005–0.03 for the halo lobe." }, { "quantity": "BA / 2R bright annealed — Ra", "value": "0.05 to 0.2 (typical 0.1)", "unit": "µm", "note": "[LIT] Supplier charts give 0.05–0.2 µm; some give a tighter 0.05–0.1 µm, and some mills claim 0.02–0.05 for premium 2R. The spread between sources is real disagreement, not measurement noise — BA quality varies by mill." }, { "quantity": "BA / 2R bright annealed — Rq and correlation length T", "value": "Rq 0.07–0.28 (typ 0.14) µm; T 5–20 (typ ~7) µm", "unit": "µm", "note": "Rq [DERIVED from LIT]; T [EST]. BA texture is imprinted by a mirror-finish work roll and then bright-annealed in reducing atmosphere, so the lateral scale is set by the roll finish and is longer-wavelength and smoother than an abrasive-polished surface — hence the larger T estimate than No.8. No published measurement found." }, { "quantity": "BA / 2R bright annealed — specular spike survival", "value": "0 (no spike)", "unit": "fraction of energy in a true mirror spike", "note": "[DERIVED from LIT] Rq ≈ 140 nm is 3.2x the 44 nm Rayleigh threshold; TIS ≈ 1.0000. This is the physical reason BA looks bright and reflective but cannot form a sharp image the way No.8 can: all of its energy sits in a narrow LOBE, none in a SPIKE. Gloss meters (which integrate a few degrees around specular) rate BA close to No.8; a camera resolving a reflected edge does not." }, { "quantity": "BA / 2R bright annealed — SPECULAR LOBE WIDTH", "value": "2 to 5 (typical ~3.2); full plausible range 0.6 to 9", "unit": "degrees (half-width at 1/e from specular direction)", "note": "[EST, model-derived] Microfacet: α = √2·Rq/T gives 0.0049 → 0.57° (Rq 0.07, T 20), 0.0283 → 3.24° (typical), 0.0792 → 9.1° (Rq 0.28, T 5). FWHM ≈ 5.4° typical. GGX α ≈ 0.02–0.04. Note the width is comparable to No.8's halo — the difference between the two finishes in a render is the presence/absence of the spike, not the lobe width." }, { "quantity": "2B mill finish — Ra", "value": "0.1 to 0.5 (typical 0.3)", "unit": "µm", "note": "[LIT] Charts give 0.1–0.5 µm; some narrow it to 0.2–0.5 µm. Cold rolled, annealed, pickled, then skin-passed on polished rolls." }, { "quantity": "2B mill finish — Rq and correlation length T", "value": "Rq 0.14–0.7 (typ 0.42) µm; T 5–30 (typ ~10) µm", "unit": "µm", "note": "Rq [DERIVED from LIT]; T [EST]. Skin-pass rolling texture is relatively long-wavelength. No published autocorrelation measurement found." }, { "quantity": "2B mill finish — SPECULAR LOBE WIDTH", "value": "5 to 10 (typical ~7); full plausible range 0.8 to 22", "unit": "degrees (half-width at 1/e from specular direction)", "note": "[EST, model-derived] α = √2·Rq/T: 0.0066 → 0.76° (best), 0.0594 → 6.8° (typical), 0.198 → 22.4° (worst). FWHM ≈ 11° typical. CROSS-CHECK against measured Sdq: the Frontiers Sdq-Sdr study reports Sdq 0.039–0.268 for oriented topographies (turned/ground/milled), i.e. lobe half-widths 4.5–30°; our typical 0.059 sits at the low end of that measured band, which is where a rolled-and-skin-passed finish belongs. GGX α ≈ 0.06 (0.01–0.2). Reads as a blurry but recognizable reflection." }, { "quantity": "Diamond-drag burnished land — Ra (literature anchors)", "value": "0.054 minimum reported; 0.137 to 0.225 measured range on 42CrMo4 from Ra 2.6 initial", "unit": "µm", "note": "[LIT] Slide/diamond burnishing studies: 42CrMo4 shafts went from turned Ra 2.6 µm to Ra 0.137–0.225 µm across 11 experiments (best: 0.032 mm/rev, 130 N, 180 rpm), with a regression-predicted optimum of 0.104 µm; a separate diamond-burnishing study reports a minimum Ra of 0.054 µm. General practice figure for burnish-plus-mild-abrasive is Ra 0.05–0.2 µm on most metals." }, { "quantity": "Diamond-drag burnished land — Ra (adjusted for a plotter drag tip)", "value": "0.1 to 0.3 (typical 0.2)", "unit": "µm", "note": "[EST, extrapolated from LIT] IMPORTANT CAVEAT: the literature above is lathe burnishing — a spherical polycrystalline diamond insert of ~2 mm radius, 130–600 N, flood lubrication, controlled feed, often multiple passes. A spring-loaded conical diamond DRAG tip on a plotter is a different regime: small tip radius, low and less controlled normal force, single pass, dry. I have shifted the estimate to the coarse end of the burnishing band. Do not treat 0.2 µm as a measured value for a drag tip." }, { "quantity": "Diamond-drag burnished land — anisotropy: correlation lengths", "value": "T_parallel 30–200 (typ 50) µm along the drag direction; T_perpendicular 1–5 (typ 2) µm across it", "unit": "µm", "note": "[EST] This is the defining feature of the case. The tip smears material continuously along its path, so along-lay correlation is long and broken only by tip defects and stick-slip; across the lay, the tip's own facet-scale asperities plough micro-grooves at the 1–5 µm scale. Expect Str < 0.3 (strongly anisotropic by the ISO 25178 texture-aspect-ratio criterion)." }, { "quantity": "Diamond-drag burnished land — SPECULAR LOBE WIDTH (anisotropic)", "value": "0.7 along the drag direction x 16 across it (typical); ranges 0.2–2.3 along, 4.5–61 across", "unit": "degrees (half-width at 1/e from specular direction)", "note": "[EST, model-derived] α_parallel = √2·0.2/50 = 0.0057 → 0.65°; α_perpendicular = √2·0.2/2 = 0.141 → 16.1°. Anisotropy ratio ~25:1. RENDER AS: anisotropic GGX/Ward with α_x ≈ 0.006, α_y ≈ 0.14, tangent frame aligned to the toolpath. Geometrically unambiguous statement: the lobe is WIDE in the plane containing the surface normal and the across-lay axis, NARROW in the plane containing the normal and the lay direction. (I am deliberately not asserting which way the on-screen streak points — that depends on view and light geometry and is easy to get backwards.) Worth noting for the artwork case: a burnished line on 2B stock can be GLOSSIER than its surround along the favorable azimuth, because burnishing reduces Rq while the anisotropy concentrates energy into one plane." }, { "quantity": "Plastically torn ridge material — Ra / Rq", "value": "Ra 0.5–3 (typ 1.4) µm; Rq 0.7–4 (typ 2) µm", "unit": "µm", "note": "[EST, bracketed by LIT] No direct published Ra for scribe-ridge tear-out found. Bracketed from: (a) over-burnishing literature — burnishing force above ~400 N causes flaking of the burnished surface on AISI 1010, and roughness passes a minimum then rises again with increasing force, i.e. torn surfaces return toward or above the pre-finish level; (b) the pre-burnish turned datum of Ra 2.6 µm; (c) an AISI 1010 ball-burnishing study reporting Ra 2.48 → 1.75 µm. Torn/fractured material is at or above these values." }, { "quantity": "Plastically torn ridge material — RMS slope α", "value": "0.4 to 0.8 (typical ~0.6)", "unit": "dimensionless (= Sdq = tan of RMS slope angle)", "note": "[EST, anchored to LIT] The σ/T route gives α = √2·2/3 ≈ 0.94, which is beyond model validity. Better anchored to measured Sdq: the Frontiers study reports Sdq 0.182–0.521 (10.4–29.9° RMS slope) for non-oriented topographies (honed, EDM, sintered), and a plated surface measured Sdq 22.4° before polishing. Ductile tear-out should sit at or slightly above the top of that measured band, hence 0.4–0.8." }, { "quantity": "Plastically torn ridge material — SPECULAR LOBE WIDTH", "value": "45 to 75 (typical ~60)", "unit": "degrees (half-width at 1/e from specular direction)", "note": "[EST, model-derived] 2·arctan(0.4) = 43.6°, 2·arctan(0.6) = 61.9°, 2·arctan(0.8) = 77.3°. At these widths the lobe fills most of the hemisphere and the concept of a 'lobe' stops being useful — render as effectively diffuse with a broad grazing sheen. MANDATORY at this roughness: single-scatter GGX/Beckmann loses roughly 40–50% of its energy at α ≈ 0.6, so use a multiple-scattering or energy-compensated (Kulla-Conty / Turquin) formulation, or the torn ridge will render conspicuously too dark relative to the burnished land beside it." }, { "quantity": "Plastically torn ridge — separate MACRO-geometry highlight (not a roughness effect)", "value": "crest radius ~1–10 µm", "unit": "µm", "note": "[EST] Distinct effect worth modeling separately: a torn ridge is a physical convex crest. Independent of its microroughness, that curvature produces a sharp specular LINE highlight along the ridge — a cylindrical-mirror effect. This, not the roughness, is what makes a scribed line read as a bright thread against the substrate. If the ridge is modeled as a flat rough band it will look wrong no matter what α is used." }, { "quantity": "Stainless steel normal-incidence reflectance, visible", "value": "~55 to 65", "unit": "% ", "note": "[textbook-typical, NOT verified in this search] Out of the requested scope (lobe shape) but needed for amplitude: the analysis above governs lobe SHAPE only. Amplitude requires the complex index of the Fe-Cr-Ni alloy with a conductor Fresnel term. Look up n,k for 304/316 before trusting this figure." }, { "quantity": "SUMMARY TABLE — lobe half-width at 1/e, all six cases", "value": "No.8 mirror: spike + 3° halo | BA/2R: 3.2° lobe, no spike | 2B: 7° | drag-burnished: 0.7° x 16° anisotropic | torn ridge: 60° (≈diffuse) | (measured Sdq band for machined metals: 4.5–30°)", "unit": "degrees", "note": "[MIXED — Ra values are LIT, all angular values are model-derived EST] Corresponding GGX α: 0.005–0.03 / 0.02–0.04 / 0.06 / α_x 0.006 & α_y 0.14 / 0.4–0.8. Multiply by 1.67 for FWHM. Ordering and ratios between cases are more trustworthy than absolute values, because the same estimated correlation lengths propagate through all of them." } ], "sources": [ "https://www.eckop.com/resources/scatterometer-resources/optical-scattering-versus-surface-roughness/ — Bennett-Porteus TIS formula, Rq ≈ 1.4 Ra, reference roughness/scatter pairs (Rq 25 nm ≈ 10% scatter at 60°, λ 500 nm)", "https://xrtgsteel.com/stainless-steel-surface-finish-chart/ — Ra table: 2B 0.2–0.5 µm, BA 0.05–0.2 µm, No.4 0.4–0.8 µm, 8K/No.8 0.01–0.05 µm", "https://sanmeimetal.com/stainless-steel-2b-vs-ba-finish/ — 2B Ra 0.1–0.5 µm, BA Ra 0.05–0.1 µm", "https://fotslittingline.com/industry-news/understanding-8k-mirror-finish-compared-to-other-stainless-steel-finishes/ — 8K vs BA vs 2B smoothness and reflectivity comparison", "https://pmc.ncbi.nlm.nih.gov/articles/PMC7958946/ — Modelling the Influence of Slide Burnishing Parameters on Surface Roughness of 42CrMo4 Shafts: Ra 2.6 µm → 0.137–0.225 µm, predicted optimum 0.104 µm", "https://learning-gate.com/index.php/2576-8484/article/view/6174 — Effects of diamond burnishing parameters on surface roughness of AISI 304 (2 mm PCD insert, 250 HB, flood lubrication); abstract only, numeric results behind PDF", "https://www.frontiersin.org/journals/mechanical-engineering/articles/10.3389/fmech.2020.00050/full — Sdq-Sdr Topological Map of Surface Topographies: measured Sdq by process (turned 0.071–0.247, ground 0.039–0.237, milled 0.064–0.268, honed 0.192–0.521, EDM 0.182–0.459, sintered 0.213–0.372); oriented 0.039–0.268 (2.23–15.35°), non-oriented 0.182–0.521 (10.43–29.85°)", "https://www.keyence.com/ss/products/microscope/roughness/surface/sdq-root-mean-square-gradient.jsp — Sdq definition (ISO 25178 rms gradient)", "https://michmet.com/glossary-term/root-mean-square-surface-slope/ — Sdq vs gloss; polished plated surface Sdq 22.441° → 7.563°", "https://michmet.com/glossary-term/autocorrelation-length/ — autocorrelation length (Sal) definition, 1/e decay convention", "https://www.researchgate.net/publication/253218746_Limitations_of_Rayleigh_Rice_Perturbation_Theory_for_describing_surface_scatter — grating equation sinθ_s = kλ linking surface spatial frequency to scatter angle; validity limits of Rayleigh-Rice", "https://www.researchgate.net/publication/252638337_Calculating_BRDFs_from_surface_PSDs_for_moderately_rough_optical_surfaces — BRDF from surface PSD, generalized Harvey-Shack; RR proportionality fails for slightly rough surfaces", "https://www.researchgate.net/publication/235998985_Beckmann_formulation_for_accurate_determination_of_submicron_surface_roughness_and_correlation_length — Beckmann σ, correlation length T, RMS slope m relation for Gaussian ACF (any two determine the third)", "https://journals.sagepub.com/doi/full/10.1177/16878132231201794 — slide burnishing: excessive burnishing force deteriorates surface finish", "https://www.researchgate.net/publication/226228158_Effect_of_Ball_Burnishing_Process_on_the_Surface_Quality_and_Microstructure_Properties_of_AISI_1010_Steel_Plates — force >400 N causes flaking; Ra 2.48 → 1.75 µm; roughness passes a minimum then rises with force" ], "warnings": [ "PROVENANCE SPLIT — the Ra values for 2B, BA and No.8, the Sdq ranges by machining process, the burnishing Ra results, and the TIS/grating-equation formulas are all literature. EVERY lobe width in degrees is a reasoned estimate derived by me from those inputs. I found no published measurement of specular lobe width in degrees for any of these six surfaces.", "CORRELATION LENGTH IS THE WEAK LINK — no published autocorrelation length (Sal or Beckmann T) was found for No.8, BA, 2B, drag-burnished, or torn stainless. Every T value is reasoned from the process physics (abrasive grit size, roll finish, tip geometry, grain/tear scale). Since lobe width scales as 1/T, a 3x error in T is a 3x error in every angle reported. The estimates for No.8 and BA cluster around 2–7 µm and are the least constrained.", "Ra ALONE CANNOT DETERMINE LOBE WIDTH — this is the central methodological point. Ra is a height statistic; lobe width is a slope statistic. Two surfaces with identical Ra and 10x different correlation length have 10x different lobe widths. If measured data can be obtained, ask for Sdq (ISO 25178 rms gradient) or a PSD, not Ra — Sdq IS the microfacet α and needs no conversion or assumption at all. The Michigan Metrology example of Sdq dropping 22.4° → 7.6° with Sa barely changing shows exactly this failure mode.", "BANDWIDTH MISMATCH BIASES EVERY NUMBER HIGH — visible-light lobe broadening comes only from surface wavelengths of ~0.6–30 µm. Stylus Ra with a standard 0.8 mm cutoff includes much longer wavelengths that contribute sub-0.5° deviation (waviness, orange-peel) rather than lobe width. The Ra-derived α values are therefore systematic overestimates, plausibly by 1.5–3x for the rolled finishes (2B, BA). Correct by band-limiting the PSD to f = sinθ/λ over the angular range being rendered.", "'No. 8 MIRROR FINISH' IS NOT A SINGLE OPTICAL STATE — across its own Ra 0.01–0.05 µm spec band the specular spike goes from ~90% to ~8% of reflected energy. A render targeting 'mirror stainless' must pick a point in that band deliberately. Real fabricated architectural panels are usually well short of the 0.01 µm end.", "GAUSSIAN HEIGHT AND SLOPE STATISTICS ARE ASSUMED THROUGHOUT — and are demonstrably wrong for the last two cases. Burnished and torn surfaces are strongly skewed and leptokurtic (the diamond-burnishing literature reports Rsk and Rku precisely because Ra is insufficient). This invalidates both Rq = 1.4 Ra and the Beckmann slope distribution for the drag-burnished and torn-ridge cases. Expect the real lobes there to have heavier tails than the Gaussian model predicts — a GGX/Trowbridge-Reitz tail is the better choice than Beckmann for those two.", "ENERGY LOSS ABOVE α ≈ 0.3 — single-scattering microfacet BRDFs lose roughly 40–50% of their energy at α ≈ 0.6 (the torn-ridge case). Without multiple-scattering compensation the torn ridge will render markedly too dark next to the burnished land, producing exactly the wrong contrast between groove and surround.", "DIAMOND DRAG TIP ≠ DIAMOND BURNISHING INSERT — all burnishing Ra literature found is lathe burnishing with a ~2 mm spherical PCD insert at 130–700 N under flood lubrication. A spring-loaded conical drag tip on a plotter is a different mechanical regime (small tip radius, low uncontrolled force, single dry pass). The Ra 0.1–0.3 µm figure used for the burnished land is my extrapolation, not a measurement of a drag tip, and could easily be off by 2x in either direction.", "LOBE WIDTHS BELOW ~1° ARE PRACTICALLY UNOBSERVABLE — the visible highlight is the lobe convolved with the light source's angular size. Under a source subtending more than ~1°, the 0.45° best-case No.8 halo and the 0.65° along-lay burnished lobe are indistinguishable from a perfect mirror. Do not spend render budget resolving them unless the source is a point or a distant sun.", "TORN-RIDGE GEOMETRY MATTERS MORE THAN ITS ROUGHNESS — the ~1–10 µm convex crest produces a sharp cylindrical specular line highlight that dominates the appearance of a scribed line. Modeling the ridge as a flat rough band will look wrong for any choice of α. Model the crest geometry explicitly, or bake an anisotropic line highlight.", "AMPLITUDE NOT COVERED — this analysis fixes lobe shape only. The ~55–65% reflectance figure for stainless is textbook-typical and was NOT verified in this search; look up complex n,k for 304/316 in the visible and use a conductor Fresnel term before trusting reflected brightness.", "RELATIVE ORDERING IS MORE RELIABLE THAN ABSOLUTE VALUES — because the same estimated correlation lengths propagate through all six cases, the ratios between them (No.8 narrowest, then BA, then 2B, then anisotropic burnished, then near-diffuse torn) are considerably more trustworthy than any individual degree figure. Treat the absolute angles as good to roughly a factor of 2." ] }, { "topic": "Optical constants and reflectance of polished 304 stainless steel in the visible (400-700 nm), plus estimated reflectance reduction for a diamond-ploughed groove interior and its torn/smeared ridges", "confidence": "measured-literature", "values": [ { "quantity": "Normal-incidence reflectance, visible average (polished 304, ideal smooth surface)", "value": "62", "unit": "% (flat mean over 400-700 nm); photopic-weighted 62.4%", "note": "[LITERATURE - COMPUTED FROM LITERATURE n,k] Fresnel R0=((n-1)^2+k^2)/((n+1)^2+k^2) evaluated on the Castelli et al. 2006 dispersion fit that is explicitly labelled for 304. The alternative (Karlsson & Ribbing austenitic) dataset gives 63.6% flat mean / 64.4% photopic. So: 62-64% for an ideal surface. Real diamond-polished 304 measures LOWER (see the 35 nm roughness entry) and trade literature quotes 49-60% for commercially polished stainless; 54% was measured on polished stainless mirror blanks. Use 62% as the ideal-surface Fresnel value and expect ~55% on an actual polished coupon." }, { "quantity": "Spectral variation of R0 across the visible (non-neutrality)", "value": "400 nm: 60.6% -> 700 nm: 64.5% (ratio 1.065)", "unit": "% reflectance", "note": "[LITERATURE - COMPUTED] From the 304-labelled Castelli fit. Monotonic rise toward red, no features. The Karlsson austenitic dataset gives a stronger tilt: 57.0% at 400 nm -> 67.6% at 700 nm (ratio 1.19). The two literature sets bracket the tilt at +6% to +19% relative across the band. Steel is warm-tilted but only weakly; there is no dip or peak anywhere in 400-700 nm, so a linear ramp in wavelength is an adequate model." }, { "quantity": "Perceptual tint of polished 304 (linear sRGB, white-point normalized, one bounce)", "value": "R:G:B = 1 : 0.979 : 0.959 (Castelli 304 fit) / 1 : 0.959 : 0.896 (Karlsson austenitic)", "unit": "linear sRGB ratio", "note": "[LITERATURE - COMPUTED] CIE 1931 integration of the Fresnel R0 spectrum under an equal-energy illuminant, converted to linear sRGB and divided by the perfect-white response so a neutral spectrum returns 1:1:1. A faint straw/warm-grey cast. For rendering, a linear specular color of about (0.634, 0.621, 0.608) reproduces the Castelli 304 spectrum; (0.667, 0.639, 0.597) reproduces Karlsson austenitic. The tint is subtle enough that many renders get away with neutral 0.62 grey, but it is real and it compounds with each bounce (see the multi-bounce colour entry)." }, { "quantity": "n, k at 450 nm", "value": "n = 1.360, k = 2.894 (Castelli 304 fit) | n = 1.678, k = 3.117 (Karlsson austenitic)", "unit": "dimensionless (N = n + ik)", "note": "[LITERATURE] Two independent literature sources, both valid, differing mainly in n. Castelli et al. 2006 give closed-form fits stated to apply to 304 over 400-800 nm: n = 0.0028*lambda + 0.100 and k = 0.0033*lambda + 1.4088 with lambda in nm; they state these are consistent with their own ellipsometric measurements on the 304 substrates used. Karlsson & Ribbing 1982 is a tabulated Kramers-Kronig dataset on Avesta 832 MV, which is 316-like (Cr 18.5 / Ni 9.3 / Mo 0.44), not 304, and refractiveindex.info notes the data were extracted from a figure. Prefer Castelli for 304 specifically; use the pair as an uncertainty band of roughly +/-0.3 in n and +/-0.25 in k." }, { "quantity": "n, k at 550 nm", "value": "n = 1.640, k = 3.224 (Castelli 304 fit) | n = 2.044, k = 3.673 (Karlsson austenitic)", "unit": "dimensionless (N = n + ik)", "note": "[LITERATURE] Same two sources. A commonly circulated single-point value for stainless steel is n = 1.580, k = 3.413 at 500 nm, which sits between these two sets (Castelli at 500 nm: 1.500 / 3.059; Karlsson at 500 nm: 1.864 / 3.401) and corroborates the band." }, { "quantity": "n, k at 650 nm", "value": "n = 1.920, k = 3.554 (Castelli 304 fit) | n = 2.440, k = 4.182 (Karlsson austenitic)", "unit": "dimensionless (N = n + ik)", "note": "[LITERATURE] Same two sources. Both n and k rise monotonically and roughly linearly with wavelength through the whole visible band; the Castelli linear fit is a good enough description that you can evaluate it per-wavelength in a spectral renderer without a table." }, { "quantity": "Fresnel unpolarized reflectance vs incidence angle at 450 nm (n=1.360, k=2.894)", "value": "0 deg: 61.0% | 45 deg: 60.6% | 70 deg: 61.3% | 85 deg: 79.3%", "unit": "% reflectance, unpolarized (Rs+Rp)/2", "note": "[LITERATURE - COMPUTED] Exact complex Fresnel with cos(theta_t) = sqrt(1 - (sin(theta_i)/N)^2). Component values at 85 deg: Rs = 95.9%, Rp = 62.6%. Note the reflectance is essentially FLAT from 0 to 70 deg and dips very slightly below R0 in between - it does not rise smoothly toward grazing the way a dielectric does." }, { "quantity": "Fresnel unpolarized reflectance vs incidence angle at 550 nm (n=1.640, k=3.224)", "value": "0 deg: 62.2% | 45 deg: 61.7% | 70 deg: 60.8% | 85 deg: 76.8%", "unit": "% reflectance, unpolarized (Rs+Rp)/2", "note": "[LITERATURE - COMPUTED] Components at 85 deg: Rs = 96.1%, Rp = 57.5%. At 45 deg: Rs = 71.8%, Rp = 51.6%. At 70 deg: Rs = 85.4%, Rp = 36.3%. The s/p split is large well before grazing, so if you care about polarization at all (glancing light along a groove wall), you cannot use the unpolarized average." }, { "quantity": "Fresnel unpolarized reflectance vs incidence angle at 650 nm (n=1.920, k=3.554)", "value": "0 deg: 63.7% | 45 deg: 63.1% | 70 deg: 60.9% | 85 deg: 74.6%", "unit": "% reflectance, unpolarized (Rs+Rp)/2", "note": "[LITERATURE - COMPUTED] Components at 85 deg: Rs = 96.2%, Rp = 53.0%. Note the ordering inverts with angle: at normal incidence red is the most reflective, but at 85 deg blue is (79.3% vs 74.6%). Grazing-lit steel edges therefore go slightly COOLER, not warmer. This is a real, renderable effect on the groove ridges." }, { "quantity": "Pseudo-Brewster angle and the reflectance minimum", "value": "Rp minimum at 71.5 deg (450 nm) / 73.8 deg (550 nm) / 75.5 deg (650 nm); unpolarized minimum at 59-70 deg", "unit": "degrees / % reflectance", "note": "[LITERATURE - COMPUTED] Rp bottoms out at 37.6% / 35.4% / 33.7% at 450 / 550 / 650 nm. The unpolarized minimum is shallow: 60.3% at 59 deg (450 nm), 60.6% at 66 deg (550 nm), 60.9% at 70 deg (650 nm) - i.e. about 1-3% relative BELOW the normal-incidence value. The steep rise only begins past about 80 deg: at 88 deg unpolarized R is 88-90% and at 89 deg it is 92-94%. This corrects the premise in the question: metal reflectance does not 'rise toward grazing incidence' through the mid angles, it sags slightly and then rises very abruptly in the last 5-10 degrees." }, { "quantity": "Specular retention of a real diamond-paste-polished 304 coupon (roughness penalty already present before any ploughing)", "value": "0.53 at 550 nm (best-fit rms microroughness 35 nm)", "unit": "fraction of ideal-surface specular reflectance", "note": "[LITERATURE] Castelli et al. found the measured specular reflectivity of an uncorroded, diamond-paste-polished 304 coupon was significantly below the ideal-surface theory, and the discrepancy was best fitted by 35 nm rms microroughness using Rd/Ro = 1 - exp(-(4*pi*delta/lambda)^2). Evaluating exp(-(4*pi*35nm/lambda)^2) gives retention 0.385 / 0.528 / 0.633 at 450 / 550 / 650 nm - strongly wavelength dependent, so even a good polish looks blue-deficient in the specular lobe. This is the single most useful literature anchor for the groove question: it says the baseline is already only about half of ideal, and it gives you the calibrated scattering law to extrapolate with." }, { "quantity": "Groove interior (ploughed + burnished by the diamond flank) - SPECULAR reflectance factor", "value": "0.00 (use <= 0.01; absolute upper bound 0.2 for a flawlessly burnished wall)", "unit": "multiplier on the polished-land specular reflectance", "note": "[ESTIMATE, but built on a literature scattering law and a literature Ra] Diamond burnishing of AISI 304 under controlled low-load smoothing reaches Ra ~ 0.10-0.11 um (Maximov et al. 2022). Your process is not smoothing burnishing: it is a 120 deg cone with R 12.5 um tip ploughing 17.8 um deep at 300 gf, with prow formation and lateral flow (only 35% of the displaced steel leaves as chip). I take Ra 0.15-0.40 um inside the groove, i.e. rms sigma ~ 0.19-0.50 um (sigma ~ 1.25*Ra for a Gaussian surface). Substituting into the same exp(-(4*pi*sigma/lambda)^2) law that Castelli calibrated gives retention below 1e-8 at 550 nm. Even the most generous case, a perfectly burnished sigma = 60 nm wall, gives only 0.14-0.39. Conclusion: the groove has NO mirror lobe at visible wavelengths. It is a fully diffuse/scattering surface. This is the dominant visual difference and it is robust - it does not depend on my Ra estimate being right, because sigma would have to fall below about 25 nm to recover any specular at all, which no ploughing process achieves." }, { "quantity": "Groove interior - TOTAL HEMISPHERICAL reflectance factor", "value": "0.90 (defensible range 0.85 - 0.97)", "unit": "multiplier on the polished-land hemispherical reflectance", "note": "[ESTIMATE] Roughening a metal redistributes light without absorbing much of it; the only real loss channel is multiple bounces inside the microtexture, each costing a factor R ~ 0.62. Modelling this as R_eff = R*(1 - f*(1-R)) where f is the fraction of rays taking a second bounce: the burnished groove wall has fine-amplitude, LOW-SLOPE roughness (0.2-0.4 um amplitude over 2-5 um lateral -> rms slope 0.05-0.2, i.e. 3-11 deg), so f ~ 0.05-0.15, giving factors 0.94-0.98. I round DOWN to 0.90 to absorb the sub-grain tearing and any embedded debris that the slope model does not capture. So: about 56% absolute versus 62% for the land. The groove is only ~10% darker in total light, while being 100% darker in mirror terms." }, { "quantity": "Groove interior - GEOMETRIC redirection (do not confuse this with a reflectance drop)", "value": "wall inclined 29.9 deg from the plate surface; normal-incidence light hits it at 29.9 deg local incidence, R = 62.1% (essentially unchanged), and leaves at 59.9 deg from vertical", "unit": "degrees / % reflectance", "note": "[COMPUTED FROM YOUR OWN GEOMETRY] Derived from the groove dimensions already in your README (w = 61.8 um, d = 17.8 um -> arctan(17.8/30.9) = 29.9 deg, consistent with the 120 deg cone). Two consequences. (1) The local Fresnel value on the wall is 62.1% versus 62.2% at normal incidence - the tilt costs you nothing in reflectance. (2) A 120 deg V-groove is the special case where the once-reflected ray runs exactly PARALLEL to the opposite face (reflected direction slope 0.577 vs opposite wall slope 0.576), so it escapes after a single bounce. There is no cavity self-trapping and no cavity darkening. What makes the groove read dark to a near-normal camera is purely that the specular lobe is aimed 60 deg away, not that the metal reflects less. IMPORTANT: if your renderer already resolves the 61.8 um groove geometry and uses a real microfacet BRDF, apply only the 0.90 hemispherical factor and let the geometry do the rest - applying a large extra darkening on top would double-count." }, { "quantity": "Ridges (torn/smeared pile-up) - SPECULAR reflectance factor", "value": "0.00", "unit": "multiplier on the polished-land specular reflectance", "note": "[ESTIMATE] The ridges are 7.9 um high folded/torn lamellae; the feature scale is micrometres, i.e. sigma >> lambda. exp(-(4*pi*sigma/lambda)^2) is identically zero for sigma above ~150 nm at every visible wavelength. Fully diffuse, no mirror component. High confidence in this one despite being an estimate - it is scale-of-magnitude safe." }, { "quantity": "Ridges - TOTAL HEMISPHERICAL reflectance factor", "value": "0.75 (defensible range 0.65 - 0.85)", "unit": "multiplier on the polished-land hemispherical reflectance", "note": "[ESTIMATE] Same multiple-bounce model, but torn/smeared metal has steep and partly re-entrant structure (laps, folds, overhangs), so the second-bounce fraction f rises to ~0.3-0.5, giving factors 0.89-0.81. I take 0.75 to also account for genuine light-trapping in the re-entrant folds, which the two-bounce model understates, and for possible embedded debris. Anchored between two literature endpoints: burnished/polished stainless measures ~55-60% total, while heavily roughened/blasted stainless samples measure ~40% (a factor 0.67). Torn ploughing ridges sit between those, hence 0.75. Absolute value: about 46% versus 62% for the land." }, { "quantity": "Effect of work hardening (200 HV -> 450 HV) on optical constants", "value": "negligible; below 2% change in R", "unit": "% relative", "note": "[ESTIMATE, physically grounded - state plainly that this is NOT a source of darkening] Optical response in the visible is set by free-electron density plus interband transitions, neither of which changes with plastic strain. Cold work raises the defect density, which slightly raises the Drude scattering rate and so nudges k, but the effect on R is well under a couple of percent. Do not model it. If someone attributes groove darkness to work hardening, that is wrong - it is roughness and geometry." }, { "quantity": "Effect of exposing fresh metal (loss of the original passive film)", "value": "negligible; below 1% change in R", "unit": "% relative", "note": "[ESTIMATE, physically grounded - also NOT a source of darkening] Castelli et al. report the polished 304 surface carries only about 30 Angstrom (3 nm) of Cr-depleted oxide. A freshly ploughed 304 surface re-passivates in air within seconds to minutes to a comparable 2-3 nm film. A 3 nm film on a metal with k ~ 3 changes normal-incidence R by well under 1% and produces no visible interference colour (first-order colour needs tens of nm). Only if the piece is later heat-tinted or genuinely corroded does the oxide matter, and then it matters enormously - Castelli shows corrosion films driving 304 reflectance down to near zero across the visible." }, { "quantity": "Colour shift from multiple bounces (why grooves and ridges read warmer)", "value": "1 bounce R:G:B = 1 : 0.979 : 0.959 | 2 bounces = 1 : 0.959 : 0.920 | 3 bounces = 1 : 0.939 : 0.882 (Castelli 304 fit)", "unit": "linear sRGB ratio", "note": "[LITERATURE - COMPUTED] Because R(lambda) is warm-tilted, every extra bounce multiplies the tilt. Karlsson austenitic, being more strongly tilted, gives a bigger effect: 1 : 0.959 : 0.896 -> 1 : 0.920 : 0.802 -> 1 : 0.883 : 0.718. Practical upshot: the ridges (most multiple bounces) should render slightly warmer/browner than the untouched mirror land, and the groove walls sit between. This is a small but genuine and free piece of realism if your renderer is spectral or does per-channel energy tracking." }, { "quantity": "Area-weighted hemispherical reflectance of a fully ploughed region (your measured 2 mm window: 34% mirror / 47% groove / 19% ridge)", "value": "56% absolute, i.e. factor 0.90 relative to the untouched land", "unit": "% reflectance / multiplier", "note": "[ESTIMATE, built from your own measured area fractions in README plus the factors above] 0.34*0.62 + 0.47*(0.90*0.62) + 0.19*(0.75*0.62) = 0.561. The headline: a fully worked area loses only about 10% of its TOTAL reflectance but retains only about 34% of its MIRROR area (and that 34% is the untouched land, not the worked metal). If your render currently darkens the ploughed region by a lot in diffuse terms, that is too much; if it keeps a mirror lobe over the groove area, that is far too much. Suggested practical GGX/Disney parameters if you cannot resolve the microtexture: land roughness 0.05-0.10, groove wall roughness 0.30-0.40 (alpha ~ 0.10-0.16, from rms slope 0.05-0.2), ridge roughness 0.70-0.90 (alpha ~ 0.5-0.8). Those roughness numbers are ESTIMATES derived from the Ra estimates above." } ], "sources": [ "[Karlsson & Ribbing (1982), Optical constants and spectral selectivity of stainless steel and its oxides, J. Appl. Phys. 53, 6340-6346](https://doi.org/10.1063/1.331503) - the primary tabulated n,k dataset (0.20-2.50 um). Sample is Avesta 832 MV austenitic SS, similar to SS316 (Cr 18.5 / Ni 9.3 / Mo 0.44 / Mn 1.61 / Si 0.64), NOT 304.", "[refractiveindex.info: Stainless steel, Karlsson-austenitic](https://refractiveindex.info/?shelf=other&book=stainless_steel&page=Karlsson-austenitic) - machine-readable form of the above; note the page states 'Data extracted from a figure'. Raw file: https://raw.githubusercontent.com/polyanskiy/refractiveindex.info-database/main/database/data/other/alloys/stainless%20steel/nk/Karlsson-austenitic.yml (public domain, CC0). Local copy saved at {temporary_worktree}/scratchpad/aust.yml", "[refractiveindex.info: Stainless steel, Karlsson-ferritic](https://refractiveindex.info/?shelf=other&book=stainless_steel&page=Karlsson-ferritic) - companion ferritic dataset (Avesta 393 M, Cr 13.5), useful as a lower bound: R0 rises 55.5% -> 61.7% across 400-700 nm.", "[Castelli, Persans, Strohmayer & Parkinson (2006), Optical Reflection Spectroscopy of Thick Corrosion Layers on 304 Stainless Steel, LM-06K035, Lockheed Martin KAPL / Rensselaer](https://www.osti.gov/servlets/purl/881303) - THE 304-specific source. Gives n = 0.0028*lambda + 0.100 and k = 0.0033*lambda + 1.4088 (lambda in nm, valid 400-800 nm), states these are consistent with their own ellipsometry on the 304 substrates; gives the roughness scattering law Rd/Ro = 1 - exp(-(4*pi*delta/lambda)^2); reports that a diamond-paste-polished 304 coupon fits 35 nm rms microroughness and measures well below ideal-surface theory; reports ~30 Angstrom oxide on the polished surface.", "[Maximov et al. (2022), Effect of Diamond Burnishing on Fatigue Behaviour of AISI 304 Chromium-Nickel Austenitic Stainless Steel, Materials 15, 4768](https://doi.org/10.3390/ma15144768) - Ra anchor for diamond-tip contact on 304: Ra 0.423-0.685 um after fine turning, reduced to Ra ~0.10-0.11 um by diamond burnishing (300-600 N, r = 2-3 mm).", "[Birkebak & Eckert, Hemispherical reflectance of metal surfaces as a function of wavelength and surface roughness, Int. J. Heat Mass Transfer (1967)](https://www.sciencedirect.com/science/article/abs/pii/0017931067900865) - establishes that hemispherical reflectance of metals collapses onto a single curve in sigma/lambda, and that peak steepness (rms slope), not Ra alone, controls the multiple-reflection loss. Full text was not retrievable (403 on the DTIC mirror AD0472767), so it is cited for the qualitative scaling only, not for a specific number.", "[Surface Properties of Polished Stainless Steel, CIRP Annals / ScienceDirect](https://www.sciencedirect.com/science/article/abs/pii/S0007850607613614) - reflectance of polished stainless is strongly dependent on wavelength and surface roughness and increases as sub-surface damage decreases; ~40% reflectance cited for real (non-ideal) UV-VIS samples.", "[Zahner, Stainless Steel material reference](https://www.azahner.com/materials/stainless-steel) - trade-practice figures for architectural stainless: ~60% reflectance for polished, ~49% attributed to the chromium content. Used only as a reality check on the ideal-surface Fresnel value.", "Working scripts and the derived tables are in {temporary_worktree}/scratchpad/ (fresnel.py, fres2.py, final.py, extra.py, tint.py), with the Castelli report text at osti.txt.", "Groove geometry (w = 61.8 um, d = 17.8 um, 7.9 um ridges, 47% ploughed / 19% ridge / 34% mirror in the 2 mm window) was taken from {repo_path}/README.md around line 286, not from external literature." ], "warnings": [ "MIXED PROVENANCE. Everything about the smooth polished surface (n, k, all Fresnel angular values, the spectral tilt, the tint, the per-bounce colour shift) is LITERATURE or directly computed from literature n,k. Everything about the groove interior and the ridges is an ESTIMATE. There is no published measurement of the reflectance inside a diamond-ploughed groove in 304, and I did not find one. The estimates are grounded in a literature scattering law (Castelli), a literature Ra for diamond-tip contact on 304 (Maximov), and your own measured groove geometry - but they are estimates and should be labelled as such in anything you publish.", "The two literature n,k sets disagree noticeably. At 650 nm Karlsson gives n = 2.44 while the Castelli 304 fit gives n = 1.92. R0 differs less (66.7% vs 63.7%) because k dominates, but the angular curves and the strength of the warm tilt differ meaningfully. Karlsson is a real Kramers-Kronig dataset but on a 316-like alloy and digitised from a printed figure; Castelli is explicitly labelled 304 and cross-checked against their own ellipsometry but is only a two-parameter linear fit. Use Castelli for 304 and treat the pair as your error bar; do not present either as exact.", "THE PREMISE THAT REFLECTANCE RISES TOWARD GRAZING IS WRONG FOR METAL IN THE MID ANGLES. Unpolarized R is flat or very slightly DECREASING from 0 to 70 degrees (62.2% -> 60.8% at 550 nm), passes a shallow pseudo-Brewster minimum around 60-75 degrees, and only rises steeply past about 80 degrees. If you have a Schlick/Fresnel approximation in the renderer it will get this wrong, because Schlick is monotonic by construction and cannot reproduce the sag or the correct Rp minimum. Use the exact complex Fresnel expression if grazing angles matter.", "Distinguish specular from hemispherical reflectance or the groove numbers will be badly wrong. The specular factor for both the groove and the ridges is effectively ZERO, while the hemispherical factors are only 0.90 and 0.75. Applying a single scalar 'the groove is X% as reflective' conflates these and will either over-darken the diffuse response or leave a mirror lobe where physically none exists.", "DO NOT DOUBLE-COUNT GEOMETRY. If the render resolves the actual 61.8 um V-groove profile, the darkening from the 60-degree specular redirection emerges from the geometry itself. Adding a large reflectance penalty on top of resolved geometry will over-darken. Apply only the 0.90 / 0.75 hemispherical factors plus appropriate surface roughness in that case.", "The Castelli n,k fit is stated valid over 400-800 nm only, and the Karlsson data below 400 nm and above 700 nm change character quickly. Do not extrapolate either into the UV or the near-IR from the values given here.", "The Karlsson n,k values for wavelengths not on the 0.02 um grid were obtained by linear interpolation of the tabulated data, which adds a small additional error on top of the figure-digitisation error already noted by refractiveindex.info.", "Work hardening and loss of the original passive film are NOT causes of groove darkening (both under 2% and under 1% respectively). If the project's write-up currently attributes any of the visual darkening to hardness or fresh metal, that attribution is physically wrong - the causes are microroughness (kills specular) and wall tilt (aims the lobe away).", "These numbers assume clean, unoxidised, room-temperature metal. Heat tint or genuine corrosion changes the picture completely: Castelli shows 304 reflectance falling toward near zero across the visible once oxide layers reach a few hundred nm, with strong interference colour in between. If the ploughing generates enough local heating to tint the steel, none of the above applies to the tinted regions.", "The area fractions used for the combined 56% figure (34% mirror / 47% groove / 19% ridge) come from a single 2 mm measurement window at the outer radius of your own dataset and will differ elsewhere on the disc where pass density differs. Recompute the weighting per region rather than applying 56% globally." ] } ]