Systematic Deviations

Systematic Deviations answers “what-if” questions where every layer drifts the same way at once: what if all layers ran 2 % thick, what if the coater is +5 nm long on every layer, or what if a material’s index shifted by Δn = +0.05? Unlike Monte Carlo, the error here is correlated: one deliberate offset applied across the design rather than an independent random draw per layer. Your design is never modified; the deviation is applied to a working copy and the result is overlaid against the unperturbed spectrum.

The analysis runs for the surface mode set in the Design Editor, shown as a badge on the window.

Each layer’s thickness becomes d′ = max(0, d · scale + offset). The scale is multiplicative (global scale × per-material scale) and the offset is additive (global offset + per-material offset). The offset can be entered in four units, converted to physical nanometres per layer at the design reference wavelength λ₀:

• nm: physical nanometres, used directly.
• OT: optical thickness in nm; divided by n(λ₀).
• QW: quarter-waves at λ₀.
• FW: full-waves at λ₀.

Settings

Single / Sweep: the two working modes (described below).

λ range / step: the wavelength grid, in nanometres.

AOI / pol: angle of incidence and polarization (s, p, or averaged).

T+R+A / T / R / A: which channel(s) to plot.

baseline: overlay the unperturbed spectrum behind the deviated one.

Deviations

The strip below the plot holds the deviations themselves, and follows the mode.

In Single mode you build one fixed deviation and overlay it on the baseline:

d × scale: the thickness multiplier.

d + offset: a flat thickness offset, with the nm / OT / QW / FW unit selector beside it.

Δn / Δk: additive shifts to the real and imaginary index (k stays ≥ 0).

These appear once as a Global deviation and again per material under Per-material. The global deviation acts on the coating layers only: its scale and offset change every layer’s thickness, and its Δn and Δk shift every layer’s index, while the incident medium, the substrate and the exit medium keep their own index. A deposition process running off nominal changes the films it grows, not the glass underneath or the air in front. Per-material values combine with the global ones (additively for Δn and Δk, multiplicatively for the scale), so you can say “everything +2 %, but TiO₂ also overshot by +3 nm”. Each per-material row lists every place that material appears, including the incident and exit media; a material in more than one role is shown once with all of them (for example, Air (incident, exit)), and editing it governs that material everywhere. A per-material Δn or Δk is therefore the way to shift a medium on purpose, such as a substrate glass whose index is off; it also shifts any layer made of the same material.

Reset deviations: return every control to its no-op value.

In Sweep mode you vary one parameter across a range and map the result:

Sweep parameter: any one of the global or per-material controls above.

from / to / steps: the range and resolution. The range re-seeds itself to sensible defaults when you switch parameter kinds, and stays fully editable. Offset parameters carry their own nm / OT / QW / FW unit selector.

Run sweep computes the map. The sweep is self-contained: it varies only the chosen parameter, starting from the unperturbed design, so the Global and Per-material fields are not shown in this mode. To combine a fixed deviation with a sweep, set the fixed part up in Single mode first.

How to read it

In Single mode the chart is in percent, with the baseline drawn dotted and the deviated spectrum solid on top. The gap between them is the cost of the deviation. If the design has a Specification, a live verdict tells you whether the deviated design still passes.

In Sweep mode the result is a heatmap of parameter value (vertical) against wavelength (horizontal), with the channel value as color (also in percent); choosing T+R+A stacks three maps. The vertical axis is labelled with the swept parameter and its unit. A broad, slowly-changing band means the design tolerates that error well; a narrow, fast-changing one means it is on a knife edge.

References

• H. A. Macleod, Thin-Film Optical Filters, 5th ed., §13.7.