Merit Function Editor

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
Phase / field	PSI DEL TANPSI COSDEL PR PT DPR DPT GD* GDD* TOD* EFMX	phase, ellipsometry, dispersion, peak |E|²
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 and stress	TT STR MNT MXT	total / per-layer thickness, film force on the substrate
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.

The wizard

The wizard sits above the table. Its bar carries the Optimize and Eval badges and the current MF and OMF; the chevron at the left folds the form away and brings it back. Under the bar are three boxes:

• Preset: the coating category (AR, mirror, beamsplitter, edge filter, bandpass or notch, gradient, integral or worst-case, custom target), the type within it, and the type’s own values, the wavelength range first. The Custom target type generates a single target of your own: a channel (T/R/A), a comparison (=, ≤, ≥), a value and a range.
• Angle and target: the angle of incidence, or a range of angles with the number of steps, the polarization, and whether the target is a continuous line or discrete points. A type that sets polarization itself, such as the polarizing beamsplitter, shows no polarization control.
• Thickness limits: minimum and maximum layer thickness (MNT/MXT) and a total thickness cap, each behind a checkbox.

The line under the boxes says how many rows the wizard will add and of which types. Start at row is where the block goes; Generate adds it. The form keeps its values while the window is closed and reopened.

The table

One row per operand. The table works like a spreadsheet:

• Click a cell to focus it, type to replace its value, or press Enter or double-click to edit it. Enter commits and moves down, Tab moves right, Escape cancels.
• The Type cell holds the operand code. Typing a letter opens the operand picker searching for it; Enter or a double-click opens it on the current type. The Pol cell shows a chevron while it is focused; the chevron, Enter or a double-click opens its three values as a list, and a, s or p typed straight in sets it without the list.
• Drag across cells, or hold Shift, to select a rectangle; hold Ctrl to add single cells. Ctrl+C copies the selection as tab-separated text, Ctrl+V pastes text over it: one value fills every selected cell, a block of values is laid out from the focused cell. Text that came from copying rows is inserted as rows.
• Rows are selected from the row-number column at the left: click one, drag down the column for a run, Shift for a run, Ctrl to add. A comment or header row is selected by a click anywhere on it. Delete, Ctrl+X and Ctrl+D act on selected rows; Insert adds a row above the focused one, Shift+Insert below.
• Right-click opens the same actions as a menu: copy and paste of the cell or cells, cut, copy and paste of operands, insert, duplicate and delete.

Load MF and Save MF in the table’s bar load and save the whole table as a named merit function you can reuse in another design.

Constraints: 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. An MXT row is the only upper limit on a layer’s thickness; without one the optimizers let a layer grow as thick as the merit asks.

MF vs OMF

The header shows two numbers:

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

They separate two questions the plain MF blurs together: how good is the spectrum? (OMF) versus how good is the spectrum while honoring what I can build? (MF). When MF is high but OMF is low, the optical performance is fine and it is a constraint costing you, not the optics: a too-thin or too-thick layer, a thickness budget, or a coating that bends its substrate too far.

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).