Why a Smartphone Cannot Replace the Touchstone for Assaying Gold

A new study published in Gold Bulletin asks whether that ancient practice could finally be retired in favor of something carried in billions of pockets: the smartphone camera. The answer, according to Arnaud Manas, the paper’s author, is a qualified no—at least not yet, and not without adding microscopy-grade magnification to the device.

The motivation is straightforward. Modern phones are far more precise than the human eye, which can distinguish between roughly 2 and 10 million colors. A standard JPEG image can encode up to 16 million colors, while newer smartphones shooting in DNG format can store hundreds of billions. Earlier authors had proposed building a database of photographs of gold objects of known composition, so that an unknown object could be assayed simply by matching its image against the records. That idea, however, was never implemented, and the new study set out to test whether it could actually work.

The proposed procedure sounds simple enough: photograph a gold sample, compute a look-up table of colors for ternary gold-silver-copper alloys on the phone, and match the measured color components to the prerecorded references while controlling the illumination. The experiment failed. It proved impossible to match the color of a gold object to its alloy composition, even with a controlled light source, because of many unknown factors. The core problem lies in the surface state of the metal, which induces multiple reflections and creates structural colors that overwhelm any composition-dependent signal.

The measurements were carried out with a Samsung S22 running an expert pro photo app, capturing native DNG files at 50 megapixels with a three-times zoom, and analyzed in Mathematica 13.0, which imports DNG files and works in the linear RGB color space. Illumination was handled with an LED ring light providing multidirectional, homogeneous lighting, together with automatic white balance correction using a white card. When photographs of gold samples were plotted in linear RGB space, they formed continuous, elongated shapes resembling feathers, stretching along the black-to-white diagonal and wide enough to indicate substantial hue variation. Crucially, the colors are relative to a scaling factor set by the photographic exposure value, meaning the absolute brightness of white cannot be determined by photography alone.

Even deciding which single number should represent an image proved problematic. The center of gravity of the feather, corresponding to the average color, has no actual physical meaning. The brightest pixel, or the modal value, might carry significance, but only up to that unknown scaling factor. Comparisons between measured values and theoretical colors computed from alloy compositions showed major discrepancies and turned out to be unreliable. Coins with the same alloy and the same design, minted on different presses—one steam operated, one electrical—display distinct colors, underscoring how strongly processing history shapes appearance.

The decisive obstacle is overlap among structural colors. For ternary alloys, the loci of colors produced by single and by double reflections overlap in color space. It is not possible, by color alone, to distinguish fine gold reflecting once from the ternary alloy Au61Ag26Cu13 reflecting twice, because both yield the same colorimetric coordinates up to a scaling factor. Multiple reflections give a redder hue, and these colors are not limited to discrete retroreflection modes. Worse, a single pixel can correspond to a combination of several different colors appearing on the same spot. Any progress therefore requires modeling both the gold surface and the camera.

Standard facet-based models of rough surfaces, whether in physical or geometrical optics, do not properly handle multiple reflections; some assume all multiple reflections are perfectly diffused. To overcome this, facets must be considered in pairs: a light ray hitting one facet may bounce off another, escape toward the observer, or be lost. Taking advantage of the reversibility of optics, rays can be traced backward from the camera pixel to the light source, with reflectance calculated at each step via the Fresnel equations. This stochastic backward raytracing model, however, proved too general, with too many parameters to yield significant results. The author’s earlier infinite vertical symmetrical dihedral model was, in turn, too crude for diffuse lighting.

The compromise is a finite asymmetrical dihedral facets model: pairs of equal-sized facets with different angles, each described by three parameters. This simple geometry generates complex hues combining between one and three colors. The inner and outer sides of each facet behave differently because of their finite size, and when the dihedral is tilted, each facet takes on its own color. The combined effect produces an asymmetric shape in RGB color space—not unlike Salvador Dali’s mustache—translating into yellow to brown and dark orange tones, with the largest color variations occurring where the angle of incidence approaches the pseudo-Brewster angle.

Connecting this theoretical mustache of dihedral colors to the empirical feathers of photographed gold is a statistical sampling problem governed by magnification. At low magnification, one pixel averages the colors of many facets, and variance across the image shrinks toward zero. When one pixel corresponds exactly to one facet, variance peaks. At high magnification, one facet spans several pixels, each showing a pure facet color, and image variance falls again because pixel colors are no longer independent. Assessing the color of a single facet would require optical magnification at the level of maximal variance—something colorimetric microscopy might achieve. Yet even that depends on facet size distribution: if facets share roughly one size, an optimal zoom may exist, but if sizes span orders of magnitude, as with the V-grooves on gold coins that follow a power law, the pixel color remains an average dependent on the distributions of facet angles and sizes.

The conventional assumption from tribology, that facet slopes follow a Gaussian distribution tied to roughness, also breaks down for gold. That assumption relies on a small-angle approximation that fails for the vertical or very steep facets found on gold surfaces, such as dendritic structures and grain boundaries. Microscopic observation shows ordinary gold surfaces are not homogeneous in optical response, presenting grooves, hills, pits, grain boundaries, and dendritic features side by side. The conclusion is that the link between gold color and surface state is complex and multi-dimensional, and that replacing the touchstone with the smartphone seems premature. The touchstone’s strength is precisely that it homogenizes surface states: rubbing both the object and a needle of known alloy on an abrasive medium equalizes their facet sizes and angle distributions, making the visual comparison unequivocal. Still, the study leaves a door open. Micro-photographing gold at several magnification factors, combined with a color-variance-maximizing heuristic, might recover facet colors, and it may even become possible to reconstruct a gold surface’s height map and power spectral density from an image alone, without profilometry.

Subject of Research: The relationship between gold surface state and colorimetry, and why smartphone photography cannot yet replace the touchstone for assaying gold alloys.

Article Title: Surface state and colorimetry—is it possible to assay gold with a smartphone?

Article References: Manas, A. (2025). Surface state and colorimetry—is it possible to assay gold with a smartphone?. Gold Bulletin, 58(1), Article 7. https://doi.org/10.1007/s13404-025-00360-2

Image Credits: AI Generated

DOI: 10.1007/s13404-025-00360-2

Keywords: gold assaying, touchstone, colorimetry, smartphone, surface state, structural colors, multiple reflections, raytracing model, dihedral facets, gold alloys, colorimetric microscopy, surface roughness