Didn't Ray Rogers provide a definitive answer about paint?
Yes. He wrote:
The primary goal of STURP was to test the hypothesis that the Shroud's image was painted, as claimed by Bishop d'Arcis in 1389. If it had been painted, some colored material had to be added to the cloth, but the colored material would have gone through the fire of 1532. The pigments and vehicles would have suffered changes in response to the heating, the pyrolysis products, and the water used to put the fire out. No changes in image color could be observed at scorch margins.
We tested all pigments and media that were known to have been used before 1532 by heating them on linen up to the temperature of char formation. All of the materials were changed by heat and/or the chemically reducing and reactive pyrolysis products. Some Medieval painting materials become water soluble, and they would have moved with the water that diffused through parts of the cloth as the fire was being extinguished. Observations of the Shroud in 1978 showed that nothing in the image moved with the water.
The Shroud was observed by visible and ultraviolet spectrometry, infrared spectrometry, x-ray fluorescence spectrometry, and thermography. Later observations were made by pyrolysis-mass-spectrometry, lasermicroprobe Raman analyses, and microchemical testing. No evidence for pigments or media was found.
Your eye sees colors when the surface absorbs some wavelengths of light and reflects others. A red surface absorbs all visible wavelengths other than red. Each chemical compound absorbs wavelengths that are characteristic of its chemical structure. The best way to determine the properties of a color is by measuring its spectrum. Reflectance spectrometry was one of the most important contributions of the STURP observations.
The reflectance spectra in the visible range for the image, blood, and hematite are shown in the figure. The image could not have been painted with hematite or any of the other known pigments. The spectrum of the image color does not show any specific features: it gradually changes through the spectrum. This proves that it is composed of many different light-absorbing chemical structures. It has the properties of a dehydrated carbohydrate.
There is no evidence for significant amounts of any of the many pigments and/or dyes that could have been used to paint or touch up the blood stains. We had considered and studied Tyrian purple (6,6'-dibromoindigo) and Madder root dye on an aluminum and/or chromium mordant as well as cinnabar (mercuric sulfide) and ferric oxide pigments.
During and before the 14th Century, gold metal was the most important yellow. That would easily be detected by x-ray fluorescence. Other pigments in common use were yellow ocher (hydrated Fe2O3), burnt ocher (hematite Fe2O3) and other ochers, orpiment (As2S3), realgar (AsS), Naples Yellow (Pb3[SbO4]), massicot (PbO), and mosaic gold (SnS2). Organic dyes included saffron, bile yellow, buckthorn, and weld. Madder root began appearing in Europe from the Near East about that time. Many of the dyes required mordants, which are hydrated oxides of several metals (e.g., aluminum, iron, and chromium). In order to produce the shadings observed in the Shroud's image, the concentrations of pigments would have to vary across the image. No variations in any pigment were observed by x-ray fluorescence spectrometry. The image was not painted with any inorganic pigment of an appropriate color.