Finesse

Finesse is defined as

where $\text{FSR}$ is the free spectral range and $\Delta \nu_{1/2}$ is the full-width half-maximum linewidth of one resonance. Both quantities must use matching units (frequency or wavelength).

Relation to quality factor:

Quality factor scales with resonator size (larger ring → higher $Q$ at fixed loss per unit length) but finesse does not: finesse is determined by per-round-trip loss alone.

For a Fabry–Pérot cavity with mirror power reflectivities $R_1$, $R_2$ and no other intracavity loss:

For $R_1 = R_2 = R$, this simplifies to $\mathcal{F} \approx \pi / (1 - R)$ when $R$ is close to 1.

Typical values:

Finesse rather than $Q$ is the relevant figure of merit when comparing resonators of different sizes — a longer ring has higher $Q$ at fixed loss simply because more photons fit in it, but finesse captures the intrinsic mirror or loss quality.