A center wavelength tolerance holds at one temperature

The number

A filter datasheet gives the center wavelength (CWL) with a tolerance, for example 532.0 ± 1.0 nm, measured at a reference temperature. A separate line gives the temperature coefficient of the CWL in pm/K. The two belong together: the tolerance holds at the reference temperature only.

The datasheet of the fictional NB-532-3-B filter, Rev B, gives the coefficient as 4 pm/K typical and 6 pm/K maximum, with a note that the CWL tolerance applies at 23 °C.

What it means

Over an operating range from $T_\mathrm{min}$ to $T_\mathrm{max}$, with tolerance limits $L$ and $U$ at $T_\mathrm{ref}$ and the maximum coefficient $c_\mathrm{max}$, the window that can hold the CWL is

The coefficient is applied linearly on both sides of the reference temperature, at its maximum value. That is a conservative assumption when the datasheet states the coefficient over a narrower range than the operating range.

For ±1 nm at 23 °C, 6 pm/K and −20 to +70 °C, the window runs from 530.742 to 533.282 nm: 2.54 nm wide against 2.0 nm at 23 °C. At the typical 4 pm/K one part moves 0.36 nm over the 90 K range.

The margin of a laser line inside the half-maximum band at each edge of the window is $m = \mathrm{FWHM}/2 - \lvert \lambda_\mathrm{edge} - \lambda_\mathrm{line} \rvert$. A 532.0 nm line in a 3.0 nm filter keeps 0.24 nm at the low edge and 0.22 nm at the high edge.

Compute it

Where it misleads

A ±1 nm tolerance reads as a 2 nm window. Over −20 to +70 °C it is 2.54 nm, and a design that budgets 2 nm for the CWL is short by about a quarter of a nanometer at each end.

The coefficient depends on the coating. Dense, energetically deposited coatings shift far less with temperature than porous evaporated ones, which also shift with humidity as water enters the pores (Macleod 2017). A typical coefficient says nothing about the spread between coating runs, and a coefficient measured from 20 to 50 °C is an extrapolation at −20 °C.

Temperature is one term in the CWL budget. Angle of incidence and a converging beam move the center further; FWHM in a cone computes those terms.

What to specify

• Whether the CWL limits apply at 23 °C only or over the operating range.
• The temperature coefficient as typical and maximum values, with the temperature range it was measured over.
• The operating and storage temperature ranges, and the humidity range for coatings that are not dense.
• The margin required between the line and the half-maximum points at both edges of the full window.

References

• Macleod, H. A. (2017). Thin-Film Optical Filters, 5th ed. CRC Press, Boca Raton.