Is optical path length (OPL) usually in units of length, or wavelength? When I do calculations, I usually define optical path length (OPL) of a path as the integral of index $n$ along a path divided by the vacuum wavelength, so that I can get the phase easily. So for a plane wave normal on a flat slab where $n$ only varies in the direction of propagation, I'd use:

my way:
$OPL={1 \over \lambda}\int{n(x) \ dx}$
$E=E_0 \ exp(i(\omega t - 2 \pi OPL))$

But I noticed that in Wikipedia article on optical path length it has units of length;

Wikipedia's way:
$OPL=\int{n(x) \ dx}$
$E=E_0 \ exp(i(\omega t - k \ OPL))$
$k=2\pi / \lambda$

If you use caution, either way will generally give you the same answer for $E$.
My question is, in optics discussions, if not otherwise noted, does OPL usually have dimensions of length (e.g. meters), or is it usually dimensionless, referenced to the vacuum wavelength, or are both roughly equally likely to be used?
 A: As in ptomato's answer optical path length is generally expressed with units of length.
However, a related quantity is optical path difference for a system or rays, which measures the degree of optical aberration (not to be confused with stellar aberration). Optical path difference is the RMS deviation of the optical path length of rays through a system's exit pupil from the mean optical path. This is most often written in wavelengths, i.e. normalized with respect to the wavelength, because a given aberration distribution with the same normalized optical path difference will give rise to the same proportional intensity drop in the focus, i.e. the same decrease in Strehl ratio. In fact, to first order, we have Maréchal's formula:
$$\mathcal{S} = \frac{I_f}{I_0} \approx 1 - 4\,\pi^2\,\sigma^2$$
where $I_f$ is the peak intensity of the focus, $I_0$ would be the intensity were the light field aberration free and $\sigma$ is the RMS optical path difference normalized with respect to wavelength.
Note that the Ruze / Mahajan formula $\mathcal{S} = e^{-4\,\pi^2\,\sigma^2}$ is widely quoted and only approximately true. It is actually a cludge: Strehl ratio is observed experimentally to decrease very swiftly with increasing $\sigma$, so the Ruze-Mahajan formula fits the exponential with the same first order behavior as Maréchal's formula (which can be straightforwardly derived from a diffraction integral). The Ruze Mahajan formula is unreliable for Strehl ratios much less than 0.5.
A: Optical path length generally has units of length, as its name implies. I haven't seen the dimensionless quantity $OPL/\lambda_0$ referred to as optical path length.
