Optical density is the base ten logarithm of the reciprocal of transmission, so each unit of OD removes another factor of ten from the light that gets through.

T is transmission as a fraction, so 0.001 for 0.1 %. Attenuation in decibels is the same quantity on a different logarithmic scale and is simply ten times the optical density, which is the convention used for fibre and for optical link budgets.

Reference points

• OD 1 is 10 % transmission, 10 dB. Around the density of a dark sunglass lens.
• OD 2 is 1 % transmission, 20 dB. Roughly welding shade 5 to 6.
• OD 4 is 0.01 % transmission, 40 dB. A common laser safety eyewear rating.
• OD 6 is 0.0001 % transmission, 60 dB. High power laser safety.

Optical density is wavelength dependent

A filter rated OD 6 is OD 6 only across the band it is specified for, and it can be close to transparent outside that band. Laser safety eyewear carries a rating tied to specific wavelengths for exactly this reason, and a rating quoted without a wavelength means nothing. This converter handles the arithmetic and says nothing about which wavelength the number applies at.

Optical density and absorbance

The same expression is called absorbance in spectroscopy, where it is the quantity that scales with concentration and path length through the Beer-Lambert relation. In that context it applies at one wavelength, usually at the peak of an absorption line, rather than across a band. An instrument reading an absorbance of 0.001 at a line centre is not measuring an OD 0.001 filter, it is measuring a trace amount of an absorbing gas.

What this does not account for

Reflection and scattering both remove light without absorbing it, and both count as blocked here. For a filter the OD figure normally includes reflection losses at the surfaces. The calculation also assumes the beam passes through once, so a double pass doubles the optical density.