Transmission and optical density describe the same thing on two scales: how much radiation a material lets through. Transmission states the transmitted fraction linearly in per cent, optical density states it logarithmically – an OD of 1 means 10 % transmission, an OD of 3 means 0.1 %. Because protective filters, laser safety eyewear and neutral density filters are specified in OD while instruments report per cent, converting in both directions is everyday work.
This calculator covers three tasks: optical density from a measured transmission, transmission from a stated optical density, and the combined attenuation when several components sit in the beam path – window, filter, sight glass. For the combination, transmissions are multiplied, not added; on the OD scale the values add up instead, which is what makes the logarithmic scale attractive.
The calculation applies to one wavelength and assumes that the transmission values refer to that same wavelength. Transmission is measured with a photometer or a spectrometer – Opsytec manufactures both and calibrates them in its own laboratory.
All further radiometric conversions are collected in the radiometry calculator.
The calculation applies to a single wavelength and to ideal, non-scattering samples. Reflection losses at the interfaces are already contained in a measured transmission, but not in a pure material figure. Safety-related assessments – of protective filters, for instance – must be verified by suitable, calibrated measurements.
Fundamentals
Optical density is the negative decadic logarithm of transmission: OD = −log₁₀(T), with T as a fraction between 0 and 1. If transmission is given in per cent as usual, then OD = −log₁₀(T[%] / 100). The reverse is T = 10^(−OD) or T[%] = 10^(−OD) · 100. Optical density is dimensionless. In chemistry the same quantity is called absorbance or extinction.
If several components follow one another, transmissions multiply: T_total = T₁ · T₂ · … · Tₙ. On the OD scale this becomes an addition: OD_total = OD₁ + OD₂ + … + ODₙ.
A filter transmits 1 %: OD = −log₁₀(0.01) = 2. Three components with 90 %, 75 % and 60 % give T_total = 0.90 · 0.75 · 0.60 = 0.405 = 40.5 %, corresponding to OD_total = 0.392.
Optical density depends strongly on wavelength. A figure of “OD 4” without a wavelength range is worthless — the same material may have OD 5 at 254 nm and OD 0.5 at 365 nm. For scattering or turbid samples a simple setup collects too little light and reports too high an optical density; that calls for an integrating sphere. And multiplying transmissions neglects multiple reflections between closely spaced surfaces.
Frequently asked questions
OD = −log₁₀(T/100) when T is given in per cent. 10 % transmission gives OD 1, 1 % gives OD 2, 0.1 % gives OD 3. Each further OD step means a factor of ten less transmitted radiation.
One ten-thousandth of the incident radiation is transmitted, that is 0.01 %. Accordingly, OD 6 attenuates to one millionth.
Arithmetically yes — all three are −log₁₀(T). The terms come from different fields: optical density from filter technology, absorbance and extinction from spectroscopy.
Multiply the transmissions or add the optical densities — both give the same result. Two filters with OD 2 and OD 3 together give OD 5, that is 0.001 % transmission.
Because the absorption of a material varies strongly across the spectrum. A UV protective glass can be highly absorbing in the UV-C and clear in the visible. Without a wavelength, an OD is not comparable — it is measured spectrally, see spectrometers.
A photometer for single wavelengths or a spectrometer for the whole curve. For scattering samples an integrating sphere is added so that scattered light is captured as well.
For the conversion yes, for the assessment no. Laser protection filters are classified by their own standards with protection levels; a plain OD conversion does not replace that assessment. For transmission testing in laser processes see laser processes & transmission testing.
Author: Dr. Mark Paravia
Dr.-Ing. Mark Paravia is the managing director of Opsytec Dr. Gröbel GmbH in Ettlingen and heads the accredited calibration laboratory. Following his research on pulsed xenon excimer discharges at the Institute of Lighting Technology at KIT, his current focus is on optical radiation measurement technology. He is vice-chair of the DIN Standards Committee FNL 7 “Optical Radiation” and a member of the DVGW Project Group on UV Disinfection.
