A collimator specified for a 1064 nm fiber laser passes acceptance on a beam profiler, then produces a far-field pattern with 9 % of the total power sitting in rings outside the central lobe. Nothing in the lens prescription predicts it. The cause is the aperture: the designer sized the collimator clear aperture at 1.5 times the beam waist radius, which truncates the Gaussian at a level that puts measurable energy into diffraction rings and raises the risk of damage at the aperture edge. Apodization describes how the amplitude of a beam varies across the aperture, and truncation describes where that aperture cuts the beam off. Together they set the far-field irradiance distribution, the encircled energy, and the amount of flux landing on mechanical surfaces where it becomes both a stray light source and a thermal load.
TracePro models both directly. A grid source can carry a Gaussian amplitude profile, apertures in the imported mechanical assembly truncate it exactly where the hardware will, and the resulting irradiance map at any downstream plane reports what the profile actually looks like after the beam has passed through the real barrel. This article covers how to set the profile up correctly, how truncation ratio drives the result, and how to read the outputs that matter for a laser delivery system.
What Apodization Means in a Ray Trace
Ray tracing distributes flux across rays. In a uniform source, every ray carries the same flux and the rays are distributed evenly across the emitting area, so the irradiance profile is flat. Apodization changes that: the flux per ray, or the spatial density of rays, is weighted so that the aggregate profile matches a target function.
For a Gaussian source the weighting follows the standard intensity relationship, where irradiance falls to 1/e² of the peak at a radius equal to the beam waist. A ray launched at the beam waist radius therefore carries about 13.5 % of the flux carried by a ray launched on axis, assuming equal-area sampling. This matters because the two common sampling approaches give different statistical behavior. Weighting flux per ray on a uniform spatial grid keeps ray density constant and makes the outer wings well sampled, which is what you want when the question is how much energy lands outside the clear aperture. Weighting ray density instead, so that every ray carries equal flux and rays are concentrated toward the axis, gives lower variance in the bright center and poor statistics in the wings.
For stray light and damage-threshold work, sample the wings well. The engineering question in those studies is almost always about the small fraction of power far from the axis, and a sampling scheme that puts few rays there produces a confident-looking answer built on a handful of ray hits.
Truncation Ratio Sets the Far-Field Result
The truncation ratio is the aperture radius divided by the Gaussian beam waist radius. It is the single number that determines how a real aperture modifies an ideal Gaussian, and design decisions across the whole beam path follow from it. At a truncation ratio of 1.0, the aperture sits at the 1/e² radius and passes about 86.5 % of the total power. The 13.5 % that is lost lands on the aperture edge and whatever sits behind it. In a 40 W system that is 5.4 W deposited on a mechanical part, which is a thermal problem before it is an optical one. At a truncation ratio of 1.5, transmission rises to roughly 98.9 % and the far field begins to resemble an unclipped Gaussian, though diffraction rings are still measurable. At 2.0, transmission exceeds 99.96 % and the far-field pattern is Gaussian to within the noise floor of most profilers. Past 2.0 the optical return is negligible and the cost is a larger, heavier, more expensive lens. Most beam delivery designs settle between 1.5 and 2.0 for this reason. Below 1.5, the combination of power loss, edge heating, and ring structure in the far field usually outweighs the size saving. TracePro lets you test the specific tradeoff for your geometry rather than relying on the textbook curve, because it reports where the truncated power actually goes in your assembly rather than simply subtracting it from the total.
Where truncated power lands
Subtracting 13.5 % from a throughput budget is easy. Predicting the consequences is not. Trace the truncated case in TracePro with the aperture assigned a realistic surface property and inspect where those rays terminate. Some are absorbed at the aperture edge, some reflect at grazing incidence down the barrel toward the detector or the workpiece, and some scatter into the beam path from the machined edge. A collimator that passes 86.5 % of the power on axis may deliver an additional 0.4 % of the total as scattered light spread across the field, which in a laser scanning or metrology system sets the noise floor.
Building the Source in TracePro
TracePro grid sources support the geometry and profile control this analysis requires. The setup below covers a collimated Gaussian beam entering a lens assembly, which is the common case for fiber-coupled and free-space laser delivery.
Grid geometry and extent
Define the grid source as a circular grid centered on the optical axis. Set the grid radius to at least 2.5 times the beam waist radius, not to the aperture radius. The grid must extend past the aperture so that TracePro traces the rays that will be clipped, since rays that are never launched cannot be shown landing on a retainer. A grid radius of 2.5 waists captures more than 99.999 % of the Gaussian energy, which is sufficient for any practical power accounting.
Applying the Gaussian profile
Set the source spatial profile to Gaussian and specify the 1/e² beam radius that matches the measured beam. If the beam profiler reports a D4 sigma diameter, divide by two to get the radius used here, since D4 sigma diameter and 1/e² diameter coincide for a clean Gaussian. For a beam with a measured M squared of 1.3, model the Gaussian at the physical waist and treat the divergence separately, since a ray trace propagates geometrically and will not reproduce M squared behavior on its own.
Ray count and convergence
Start at 500,000 rays for throughput and irradiance profile work. Move to five million when the question is edge scatter or ring structure, because those signals sit three to four orders of magnitude below the peak and need the statistics. Confirm convergence by running the same case at two ray counts and comparing the quantity you care about. If total transmitted flux changes by less than 0.1 % between one million and five million rays, the throughput answer has converged even though the scatter tail may not have.
Reading the Outputs That Matter
Two TracePro outputs carry most of the engineering content in an apodization study. The irradiance map at the exit plane gives the beam profile after truncation. Compare the traced profile to the ideal Gaussian at the same waist. The difference at the aperture radius shows the hard edge introduced by clipping, and the profile flatness across the central region indicates how much of the beam the system is actually using.
The flux report on individual mechanical surfaces gives the thermal and stray light picture. Select the aperture retainer, the barrel inner wall, and any baffle, and read absorbed flux on each. This converts an abstract 13.5 % loss into watts on a named part, which is the number a thermal analyst can use. For a 40 W beam truncated at a ratio of 1.2, expect roughly 1.5 W distributed on the aperture edge, concentrated in a narrow annulus where the local flux density can exceed 10 W per square centimeter even though the average across the part looks harmless.
Common Modeling Errors
Several mistakes recur in apodization models and each one produces a plausible but wrong answer. Launching the grid source at the aperture radius rather than past it removes the clipped rays from the simulation entirely. Throughput then reads 100 % and no flux appears on the mechanics. The model is self-consistent and completely misleading. Confusing beam diameter with beam radius shifts the truncation ratio by a factor of two, which moves a design from a safe 2.0 to a marginal 1.0. Check the profiler convention before entering numbers.
Assigning a perfect absorber to the aperture edge hides the grazing-incidence reflection that often dominates downstream stray light. Aluminum machined to a 0.8 micron finish reflects strongly at angles above 80 degrees from normal, and that reflection travels down the barrel. Use a measured BSDF for the actual finish. Tracing a single wavelength when the source has spectral width is usually acceptable for apodization work, since the profile is geometric, but it becomes wrong as soon as the analysis includes a coating or a diffractive element whose efficiency varies across the band.
Modeling the beam as collimated through the entire assembly ignores that a truncated Gaussian diverges differently from an unclipped one. If the beam path includes a long free-space section after the aperture, the truncation-modified divergence changes the spot at the target. Apodization and truncation determine how much of a laser beam reaches the target, what the far-field pattern looks like, and how many watts land on mechanical parts that were never intended to absorb them. The truncation ratio is the number that controls all three, and the useful design range for most beam delivery systems runs from 1.5 to 2.0.
TracePro models the effect end to end. Launch a Gaussian grid source that overfills the aperture, trace it through the imported assembly, and read the irradiance map for beam profile, the radiant intensity plot for far-field ring structure, and per-surface absorbed flux for the thermal and stray light consequences. The result is a defensible aperture specification rather than a rule of thumb.
Contact Lambda Research to request a TracePro demo built around your own laser source and beam delivery geometry.