Formula and Method for Optical Density
Optical density (OD), also called absorbance in spectrophotometry, is a logarithmic measure of how strongly a medium — a filter, solution, or window — attenuates light passing through it. It is defined as OD = log₁₀(I₀ / I), where I₀ is the incident (input) light intensity and I is the transmitted (output) intensity. This calculator turns that ratio into OD, percent transmittance, the linear attenuation coefficient, and the equivalent number of photographic "stops" of light reduction.
Deriving OD from intensity
Enter the incident intensity I₀ and the transmitted intensity I in any consistent unit — because OD is a ratio, the units cancel as long as both values are measured the same way (for example, both in W/m² or both as raw detector counts). The calculator forms I₀/I and takes its base-10 logarithm to get OD, then inverts the ratio to report percent transmittance (%T = 100 × I/I₀). If you supply a path length l through the medium, it also computes the linear (base-e) attenuation coefficient from the Beer-Lambert relation OD = αl / ln(10), solved as α = OD × ln(10) / l.
Reading OD values
OD is a log scale, so it behaves multiplicatively: OD = 0 is 100% transmission, OD = 1 lets through 10% of the light, OD = 2 lets through 1%, and OD = 3 lets through just 0.1%. Neutral-density (ND) camera filters and laser safety eyewear are rated on this same scale. For photographers, one "stop" of light is a factor of 2, so stops = OD / log₁₀(2) ≈ 3.3219 × OD.
Common mistakes and practical notes
- Mixing intensity units: I₀ and I must be measured the same way (same detector, same units) or the ratio — and therefore OD — is meaningless.
- Forgetting OD is wavelength-dependent: absorbing media rarely attenuate all wavelengths equally, so an OD value usually applies to a specific wavelength (or a stated "visual density" averaged over the visible spectrum) unless noted otherwise.
- Stacking filters: optical densities add when layers are stacked (OD_total = OD1 + OD2), which is equivalent to multiplying the transmittances — do not add the percent-transmittance values directly.
- Surface reflections: a filter's measured OD often includes Fresnel reflection losses at each surface in addition to bulk absorption, so it can differ slightly from a value computed purely from a material's absorption coefficient.