Place a red, a green, and a blue LED die a few millimeters apart on a shared board, aim them at a target plane, and the result is three overlapping colored patches rather than one white spot. The spatial separation between die produces color that shifts across the field, and the difference in emission angle between a Lambertian red die and a narrower blue die produces color that shifts with viewing angle. For a machine vision ring light, a horticulture panel, or an architectural wash fixture, that spatial and angular color separation is the difference between a usable product and a rejected prototype.
The design problem is to combine the flux from several die of different peak wavelengths into a single output with color uniformity held within a stated tolerance across both position and angle. TracePro handles this class of problem by modeling each die as a separate non-sequential source, tracing the combined flux through the mixing optics with Monte Carlo ray tracing, and reporting the color coordinate at every point on an analysis plane. This article walks through the LED color mixing design workflow in TracePro, from source setup to the chromaticity maps that tell you whether the mix meets spec.
Why Multi-LED Sources Separate in Color
Two independent mechanisms drive color separation, and an LED color mixing design has to address both. Spatial separation comes from die placement. A red die at one corner of the emitter and a blue die at the opposite corner illuminate slightly different regions of any downstream target. Near the source the two footprints barely overlap, so the near field shows distinct red and blue zones. The footprints converge with distance, but many products place the target close to the emitter where separation is still visible.
Angular separation comes from the emission profile of each die. A bare LED die follows a near-Lambertian intensity distribution, falling as the cosine of the angle from normal. Add a primary lens or a phosphor layer and the profile changes, and it changes differently for each color. A red AlInGaP die and a blue InGaN die rarely share the same angular distribution, so the ratio of red to blue flux varies with angle even when the die sit at the same point. The eye reads that ratio change as a color that drifts toward the edge of the beam.
Quantifying the target matters before any optics get designed. Color uniformity is usually stated as a maximum spread in the CIE 1976 u' v' coordinates, written as delta u' v'. A demanding machine vision application may call for delta u' v' below 0.004 across the working field. A general lighting product may accept 0.010. TracePro reports u' v' directly at each analysis point, so the design target becomes a number the simulation can check against, not a subjective judgment about whether the beam looks even.
Modeling Each LED Die as a Source
Accurate LED color mixing design starts with accurate sources. TracePro represents each die as its own emitter with its own spectral content, spatial extent, and angular distribution, so the combined output reflects the real physics of the array rather than an averaged approximation.
The most reliable source definition uses a measured ray file. Many LED vendors supply ray set files that encode the position, direction, and flux of a large sample of rays leaving the packaged die, measured on a goniophotometer. Importing the red, green, and blue ray files as three separate sources reproduces the true spatial and angular emission of each color. When a ray file is not available, a surface source on the die area with an assigned angular distribution and a spectral definition tied to the peak wavelength and spectral width gives a workable approximation.
Assigning spectral and flux data
Each source carries its own spectrum. A blue die might be defined at a 465 nm peak with a 25 nm spectral width, a green die at 525 nm, a red die at 625 nm. Setting the radiant or luminous flux per die to the drive current in the design lets the model predict the mix at the operating point, not at an arbitrary normalized level. When the product dims or shifts white point by adjusting per-color current, re-running with new flux values shows how the color coordinate moves without any change to the geometry.
Positioning die on the board
The die sit at their real board coordinates. A 2 by 2 millimeter emitter with four die on a 1 millimeter pitch behaves differently from the same four die spread across a 6 millimeter footprint. Because spatial separation scales with pitch, the source layout is itself a design variable, and TracePro lets you trace alternative arrangements against the same mixing optics to see which pitch the optics can actually correct.
Choosing and Modeling the Mixing Optics
The optics between the die and the target do the mixing. TracePro traces each candidate geometry and reports how well it collapses the separate colored footprints into one, so the choice among mixing approaches rests on simulated color uniformity rather than rules of thumb.
A total internal reflection mixing rod is the most common approach. A straight rod of PMMA or polycarbonate carries rays from all die through repeated internal reflections, and each reflection folds the angular and spatial distribution back on itself. The mixing improves with the ratio of rod length to cross-section width. A square rod with a length near six to eight times its width typically brings a three-color mix into a tight delta u' v' at the exit face. TracePro models the rod as a solid with the correct refractive index and traces the TIR interactions directly, so the exit-face color map shows the actual residual separation for a given length.
A diffuser is the second lever. A surface or volume scatter model spreads each ray into a distribution of directions, blending colors at the cost of some flux lost to wider angles. TracePro applies a bidirectional scattering distribution function, the BSDF, to represent the diffuser. A Gaussian BSDF with a scatter half-angle of 10 to 20 degrees mixes color effectively while keeping most of the flux within a usable cone. Because the BSDF is a measured or fitted property, the model reflects the real diffuser rather than an idealized one.
Lenslet arrays and reflective color-mixing chambers are two further options TracePro can trace. A lenslet array on the exit optic subdivides and overlaps the beam, and a diffusely reflecting chamber randomizes ray direction before the light exits an aperture. In every case the value of the simulation is the same. It converts a geometry choice into a color uniformity number before anyone cuts a part.
Quantifying Color Uniformity with Irradiance and Chromaticity Maps
The output of the trace is where the design gets judged. TracePro generates an irradiance or illuminance map on any analysis plane, and it computes the color coordinate at each cell of that map, so the residual color separation is visible as data rather than as a rendered guess.
The irradiance map shows total flux distribution and reveals brightness roll-off toward the field edge. The candela or luminance plot shows angular distribution and reveals whether the beam holds its shape. The color map, plotted in CIE 1931 x y or CIE 1976 u' v', shows where the mix succeeds and where a fringe of uncorrected color remains. Reading delta u' v' across the working field against the design target confirms whether the mixing optics are long enough, the diffuser strong enough, or the die pitch tight enough.
Separating spatial from angular residuals
Because the two separation mechanisms respond to different fixes, it helps to measure them separately. A near-field color map at the exit face of the mixing rod isolates spatial residual. A far-field color map, or an angular color plot, isolates angular residual. A design that passes at the exit face but fails in the far field points to angular separation the rod did not correct, which usually calls for a diffuser or a change in the exit optic rather than a longer rod. TracePro produces both maps from the same trace, so the diagnosis does not require a second model.
Iterating Toward a Passing Mix
LED color mixing design is a loop, and the loop closes fastest when each iteration changes one variable and the simulation reports the effect on delta u' v'. TracePro supports that loop by making the color metric a direct output of every trace.
Ray count sets the confidence of the color numbers. Color coordinates computed from too few rays carry statistical noise that can hide or fake a passing result. Monte Carlo ray tracing converges as the square root of ray count, so a color map that still flickers between runs needs more rays, often several million across the array, before the delta u' v' figure is trustworthy. Multi-threaded tracing in TracePro spreads that ray count across processor cores, keeping a converged color map within a practical run time.
The design variables are the rod length, the die pitch, the diffuser strength, and the exit optic. Changing one at a time and re-tracing builds a clear picture of which lever moves the color metric and by how much. A design that reaches delta u' v' below the target across the full working field, at the real drive currents and with converged ray statistics, is ready to prototype with confidence that the physical part will match the model.
From Model to Product
Multi-LED color mixing is a problem of combining sources that separate in both position and angle, and it yields to a workflow that models each die honestly, traces real mixing optics, and reads color uniformity as a number. TracePro carries that workflow from measured ray files through TIR mixing rods and BSDF diffusers to the chromaticity maps that decide whether a mix passes. The result is a design validated against a delta u' v' target before the first board is populated, which cuts the number of physical iterations a color-critical product usually demands.
Request a TracePro trial and build a multi-LED color mixing model with your own ray files, or contact us to request a demo focused on color uniformity analysis for your application.