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03 / 06   Light & materials

Application note

Additive Light and Subtractive Materials

Predict how emitted spectra combine and how materials reshape incident light.

An illuminated part, a display, and a printed label can look similar while producing very different spectra. Their behavior under a lighting change follows from how they generate, scatter, transmit, and absorb light. The useful distinction is between adding radiant contributions and selectively attenuating an incident spectrum.

Identify the physical mechanism

Emission creates outgoing light from an energy source. Gas discharges can produce narrow spectral lines associated with atomic transitions. Direct-emitting LEDs produce finite spectral bands; phosphor-converted LEDs combine excitation light with broader converted emission. A thermal emitter produces a continuous spectrum whose distribution changes with temperature.

For an ideal blackbody, the wavelength of maximum spectral radiance follows Wien’s displacement law:

λmax⁡T≈2.898×10−3 m K\lambda_{\max}T\approx2.898\times10^{-3}\ \mathrm{m\,K}

At 3000 K, that peak lies near 966 nm, outside the visible band. Visible appearance depends on the visible portion of the entire spectrum, not simply its peak wavelength. A quoted color temperature also does not identify a unique LED spectrum.

Idealized emission examples compare spectral lines, a phosphor-converted LED shape, and normalized blackbody spectra at 3000 K and 6000 K.

View diagram at full size

Ordinary reflection redirects incident radiation; it need not involve absorption followed by lower-energy re-emission. Fluorescence is a distinct process that couples excitation and emission wavelengths. Scattering can also select wavelengths: for particles much smaller than the wavelength, the Rayleigh model predicts a strong inverse-fourth-power wavelength dependence. Interference and refraction provide other routes to selective color.

Add light before encoding it

Independent, mutually incoherent sources contribute additive spectral power:

Pmix(λ)=aP1(λ)+bP2(λ),a,b≥0P_{\mathrm{mix}}(\lambda)=aP_1(\lambda)+bP_2(\lambda),\qquad a,b\geq0

The same addition applies to linear XYZ values or correctly defined linear-light RGB components. Coherent fields may interfere and require a field-based treatment. Encoded image values must be decoded before a physical light mixture is calculated.

An RGB display controls three primary contributions. Their spectra and usable intensities define its gamut; the letters alone do not establish a standardized color. In an LCD, the backlight and subpixel filters jointly shape those primary spectra. In an emissive display, each primary directly supplies its outgoing light.

Multiply ideal filter transmissions

For two independent, nonfluorescent filters with negligible interreflection:

Pout(λ)=Pin(λ)T1(λ)T2(λ)P_{\mathrm{out}}(\lambda) =P_{\mathrm{in}}(\lambda)T_1(\lambda)T_2(\lambda)

A band transmitted by one filter can be removed by the other. In a three-band teaching model, ideal cyan transmits green and blue, while ideal yellow transmits red and green. Their overlap passes green. Real filter edges, leakage, angle dependence, and surface reflections determine the actual result.

Additive mixing sums independent light contributions; an ideal cyan and yellow filter stack multiplies wavelength-dependent transmission and retains their common band.

View diagram at full size

Printing is also subtractive, but multiplying three RGB numbers is not a predictive ink model. Ink absorption, particle scattering, paper reflectance, layer thickness, and spatial halftones all contribute. CMYK adds a black channel to control dark reproduction and ink use; process characterization remains necessary.

For color inspection, stabilize the source spectrum as well as its output level. A camera can report different channel values from the same coating when the source changes, even after a neutral reference appears balanced. The calculators below separate linear-light mixing from an ideal filter-stack calculation at one selected wavelength.

Explore the model

Mix light in linear sRGB

Decode two sRGB colors, average their light contributions, then encode the result.

Change the values to update the results and visualization.

Linear-light mixture
#bcbc00
Encoded-value average
#808000

All swatches are sRGB previews on your current display.

Mix light in linear sRGB: First #FF0000, Second #00FF00, Linear-light result #bcbc00, Code-value average #808000First#FF0000Second#00FF00Linear-light result#BCBC00Code-value average#808000
Display previews; appearance depends on your screen and viewing conditions.
Formula & assumptions

Cout = encode[p decode(C₁) + (1−p) decode(C₂)].

A normalized mixture in the same ideal sRGB/D65 system. Swatches illustrate display encoding, not paint mixing or spectral reconstruction. The encoded-value average is shown only to reveal the difference between arithmetic in code values and in light.

Explore the model

Stack ideal filters

Estimate power transmission at one wavelength through two independent filters.

Change the values to update the results and visualization.

Stack transmittance
25 %
Stack optical density
0.60206
Stack ideal filters: interactive plotRemaining power / % against Optical path stage. Curves: Input → first filter → stack. 000.4200.8401.2601.6802100Optical path stageRemaining power / %
Input → first filter → stack
Formula & assumptions

Ttotal = T₁T₂; OD = −log₁₀(Ttotal), with T expressed as a fraction.

Same wavelength and geometry; no fluorescence, coherent interference, multiple reflections, or changes in polarization. This is not a model of mixed pigments. Zero transmission gives infinite optical density.

From estimate to application

Evaluate the spectrum your system actually delivers.

Bring the source, filter, coating, or sample you need to evaluate. We can help separate material behavior from illumination and collection effects.

Discuss your optical material