Spectroscope

The Spectroscope shows what a hand spectroscope shows when white light passes through one of our seven gemstones: the spectrum from violet to red, with dark lines and bands where the stone absorbs. The spectrum is computed from the same measured absorption spectra as the Dichroscope; nothing is drawn by hand. It is a teaching model of the instrument. It does not measure or identify any real stone.

The instrument

A hand spectroscope is a short tube with a narrow slit at the far end and a prism or a diffraction grating inside. Strong white light passes through the stone (or reflects from inside it) into the slit, and the prism or grating spreads it into a band of colors, violet at one end and red at the other. Where the stone absorbs, its part of the band goes dark: a sharp absorption line where an ion absorbs one narrow wavelength, a broad band where it absorbs a wide stretch. A spectroscope with a scale lets you read each line’s wavelength in nanometers (nm).

A grating spreads the wavelengths evenly. A prism does not: glass bends violet much more than red, so the red end is squeezed into a short stretch and the violet end drawn out. The same light spread over a longer stretch also looks dimmer, so the violet end of a prism’s spectrum is fainter than a grating’s.

The model

The light

A strong incandescent lamp, CIE illuminant A (2856 K), the classic hand set-up, or daylight, CIE D65. Illuminant A is computed from its CIE definition, Planck’s law at 2848 K with c₂ = 1.435 × 10⁷ nm K, set to 100 at 560 nm; D65 comes from the CIE table. Either is a relative spectral power S(λ).

The stone

One straight path of d from 1 to 10 mm (5 mm to start, as in the Dichroscope), across the optic axis, as the side view draws it, in unpolarized light. A doubly refractive stone splits the light into two rays that share it equally, the o-ray (ordinary) vibrating across the axis and the e-ray (extraordinary) along it, and each is absorbed by its own spectrum:
T(λ) = ½ [exp(−α_o d) + exp(−α_e d)].
An isotropic stone has one spectrum. The shape you choose changes only the drawing.

Fluorescence

Under strong light the chromium in ruby and emerald glows red in its R lines, so these lines can look bright instead of dark. With Fluorescence on, each R line is added as a Gaussian 1 nm wide, as tall as a fixed gain times the share of the lamp’s light from 380 to 620 nm the stone absorbs, times the lamp’s own level at the line, seen through half the path. This part is illustrative: we hold no measured fluorescence spectrum, so its heights are not measured.

The prism

A 60° prism of SCHOTT N-SF11 dense flint, set at minimum deviation for the sodium D line (589.3 nm). Its index comes from SCHOTT’s published Sellmeier fit,
n² − 1 = Σ B_i λ² / (λ² − C_i), with B = 1.73759695, 0.313747346, 1.89878101 and C = 0.013188707, 0.0623068142, 155.23629 µm²; it gives n_d 1.78472 and an Abbe number of 25.68, as the datasheet does. A wavelength’s place across the eyepiece follows its deviation, from 75.5° at 400 nm to 64.7° at 700 nm. The grating’s place is simply proportional to the wavelength. Both views show 400 to 700 nm.

The spectra

The absorption comes from the shared spectral registry, the measured polarized spectra the Dichroscope uses: ruby from GIA’s published Cr³⁺ absorption cross-sections, blue sapphire, emerald and amethyst from G.R. Rossman’s measured files (amethyst’s e-ray derived and provisional), as set out on the Dichroscope page. The Dichroscope reads them on a 5 nm grid, fine for color but too coarse for lines. For the Spectroscope the registry also holds the same spectra on a 1 nm grid, made from the same files by the same steps (the same baseline, a 1 nm bin instead of 5). The files are sampled every 0.6 to 1.2 nm (Rossman) and every 1 nm (GIA), so 1 nm keeps what they resolve. Averaged back over 5 nm, the fine spectra give the Dichroscope’s exactly (case S5).

One sample per variety means one stone’s lines. Ruby’s close pair of R lines, 1.4 nm apart, is resolved in neither source, so it shows as one line near 693 nm. In this sapphire the iron line sits at 451.4 nm in the o-ray and 453.2 nm in the e-ray, so in unpolarized light it falls near 452 nm, and its weaker iron lines near 460 and 471 nm are too faint to show. In this emerald the e-ray absorbs so much more than the o-ray that, through more than a few millimeters, the light that reaches the eye is almost all o-ray: the e-ray’s lines (684, 662 and 646 nm) fade, and a shorter path brings them back.

From spectrum to what you see

No screen can show the color of a single wavelength: every spectral color lies outside its gamut. Each wavelength is drawn in the most saturated screen color of that light: its CIE 1931 color converted to linear sRGB (the IEC 61966-2-1 matrix), the negative primaries set to zero, and scaled until its strongest primary is at full strength.

Its brightness is that of the empty spectroscope, compressed the way the eye adapts to a bright spectrum, times the light the stone lets through. With u(λ) = 0.08 × S(λ) × ȳ(λ) × p(λ) / Y_c(λ), where ȳ is the CIE luminosity function, p how tightly the view packs that light (1 for the grating) and Y_c the luminance of the drawn color, the brightness is [1 − exp(−u)] × T(λ). The compression keeps both ends of the spectrum visible, as they are to an eye looking into a bright spectroscope; multiplying by T keeps every line’s contrast exactly as the stone makes it. The stone’s own color in the side view is computed from the 5 nm spectra through the same path in daylight, with the shared colorimetry.

Reading the lines

The page names each line and band of the stone’s reference list and measures it in the model. A line is the darkest point in its window, placed between grid points by a parabola through the absorbance, and its contrast is c = 1 − T/T_c against the light 2.5 to 7 nm either side. A band’s contrast is against the brighter of the two 12 nm stretches just outside it, and its span is where it is more than half as deep as at its darkest. A line under 0.04 is too faint to see, under 0.15 weak, under 0.4 distinct, and strong above; a broad band needs a deeper dip to be seen, so its steps are 0.1, 0.35 and 0.7. These steps are our own choice, not a published scale. The reading names the coloring element when lines show: chromium for ruby and emerald, iron for sapphire. Wavelengths are given to the whole nanometer, as a hand spectroscope is read.

What the model leaves out

• A yellow (Cape) diamond’s spectrum. Its N3 line at 415.5 nm, with weaker lines at 478, 465, 452, 435 and 423 nm, is the classic diamond reading, but we hold no measured spectrum of a yellow diamond, so the model shows colorless diamond only.
• Moissanite that absorbs toward the violet: the simulator’s moissanite is colorless.
• Fluorescence, except as the illustration described above; and light reflected from inside the stone, which a real set-up often uses.
• One sample per variety: another ruby or sapphire, with more or less chromium or iron, shows the same lines stronger or weaker.
• The instrument’s own blur: each line is as sharp as its 1 nm data, where a real hand spectroscope blurs more in the red, most of all a prism.
• Reflection losses at the surfaces, which dim every color almost alike.
• The straight path across the optic axis: tilted, the e-ray’s share of absorption changes, as the Dichroscope shows.

Validation

These cases run on the page’s own data each time the site is built, and the build stops if one fails. The reference positions are the standard hand-spectroscope values; where the model differs by more than 1 nm, or a value has no source we hold, it is marked for checking rather than changed.

Every reference feature against the model, in nm. A line agrees when it is within 1 nm of each reference value; a band when its darkest point is inside its range. “To check” marks a value we could not back with a source we hold, listed for review.

Sources

We are not affiliated with any of these publishers.

• G.R. Rossman, Mineral Spectroscopy Server, California Institute of Technology: polarized visible spectra of corundum (GRR 1843, GRR 1020a), beryl (GRR 3570) and quartz (amethyst, Anahí Mine).
• E.V. Dubinsky, J. Stone-Sundberg and J.L. Emmett, Gems & Gemology 56(1), 2 to 28, 2020, and its absorption cross-section data file.
• F. Hassan and A.J. Cohen, American Mineralogist 59, 1974; A.J. Cohen, “Color centers in the α-quartz called amethyst”, American Mineralogist 41, 874 to 891, 1956.
• SCHOTT AG, optical glass datasheet and Zemax catalog (2017): N-SF11, its Sellmeier coefficients, n_d and Abbe number.
• CIE, “Colour-matching functions of CIE 1931 standard colorimetric observer” (CIE 018:2019, DOI 10.25039/CIE.DS.xvudnb9b), “CIE standard illuminant D65” (DOI 10.25039/CIE.DS.hjfjmt59), and CIE 15, Colorimetry, for the definition of illuminant A.
• IEC 61966-2-1:1999, the sRGB color space.