The Merit Function Editor is where you tell the optimizer what “good” looks like. Every target the design should hit and every constraint on the layer stack lives here, expressed as a list of operands. Each operand is a single number the optimizer tries to drive toward a target value, and the merit function (MF) is the weighted root-mean-square of how far each operand misses:

MF = √( Σ_i  w_i · residual_i²  /  Σ_i w_i )

The weight w_i enters linearly. The residual is value − target for an equality target, or a one-sided max(0, …) term for an inequality or constraint (so a satisfied constraint drops out of the sum entirely). Wavelength-valued residuals are rescaled to optical scale first so they don’t dominate. A smaller MF is better; the optimizers — Refinement, Needle and Gradual Evolution — move layer thicknesses to reduce it.

Operand types

The table below is a quick orientation. The full catalog — every type, its arguments, its output value and unit, and how it forms a residual — is on the Operand Reference page.

Group	Types	Output
Single-λ optical	T R A	T/R/A at one λ
Band average	TAV RAV AAV	mean T/R/A over a band
Spectral target	TGT RGT AGT	deviation from a flat/ramp line
Weighted integral	TIW RIW AIW	source × detector weighted mean
Worst-case	TMN RMN AMN TMX RMX AMX	band extremum of T/R/A
Argmax/min λ	MXWT MXWR MXWA MNWT MNWR MNWA	wavelength of the extremum
Math (reference rows)	OPGT OPLT OPVA ABSO ABGT ABLT DIFF SUMM PROD	derived from other rows
Thickness	TT MNT MXT	total / per-layer thickness
Comment	BLNK DMFS	inert

Reflection and transmission targets are typically generated in paired rows by the filter-type wizard so the optimizer can’t trade absorption for an easy win.

Settings

Filter-type wizard — at the top, a set of coating categories (AR, HR, bandpass, notch, edge filters, ramps). Pick the goal and the wizard fills in sensible weights and operands you can then refine.

Operand table — one row per operand; edit any cell inline. The advanced columns set each operand’s weight, angle of incidence, polarization and an optional surface-mode override.

Constraints — set minimum and maximum layer-thickness bounds (MNT/MXT) per layer or per material. A bound can be written to cover layers that synthesis will add later.

MF vs OMF

The header shows two numbers:

• MF — the full merit function, including the manufacturing and thickness constraints (MNT, MXT, TT).
• OMF — the optical merit function: the same RMS but counting only the optical operands (T/R/A targets, bands, and so on), with the thickness constraints dropped.

They separate two questions the plain MF blurs together: how good is the spectrum? (OMF) versus how good is the spectrum while honoring my thickness limits? (MF). When MF is high but OMF is low, the optical performance is fine and it is a constraint — a too-thin or too-thick layer — costing you, not the optics.

How to read it

Each operand row shows its current value and its residual, so you can see at a glance which targets are met and which are dragging the merit up. Bigger weights make an operand count for more; bumping the stopband weight on an HR design is the most common tweak.

The operand list is saved with the design and is read by every optimizer: Refinement, Needle, Gradual Evolution and the Structural Optimizer. The synthesis tools optimize against the optical operands only while they build the stack, then the thickness constraints are enforced during Refinement — a good final sequence is Refinement, then Cleaner, then Refinement again.

References

• A. V. Tikhonravov, M. K. Trubetskov, G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493 (1996).
• J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876 (1990).