How it is calculated
Optical density is the base-10 logarithm of the attenuation. Decibels use ten times the same logarithm:
Because these are logarithms, filters in series add: \(\mathrm{OD}_\text{total} = \sum \mathrm{OD}_i\), equivalent to multiplying their transmittances. The OD needed to bring a beam from \(P_\text{in}\) down to \(P_\text{target}\) is \(\log_{10}(P_\text{in}/P_\text{target})\). Laser-safety eyewear uses the same formula with the exposure and the maximum permissible exposure (MPE) from ANSI Z136.1 or IEC 60825-1 in place of the powers.
| OD | Transmission | Attenuation |
|---|---|---|
| 0.1 | 79.4 % | 1 dB |
| 0.3 | 50.1 % | 3 dB |
| 0.5 | 31.6 % | 5 dB |
| 1 | 10 % | 10 dB |
| 2 | 1 % | 20 dB |
| 3 | 0.1 % | 30 dB |
| 4 | 0.01 % | 40 dB |
| 6 | 0.0001 % | 60 dB |
OD is not always absorbance
For an absorptive ND filter (colored glass), OD is close to the absorbance of the glass plus small surface-reflection losses. A reflective ND filter (a thin metal or dielectric coating) attenuates mainly by reflecting light. Its OD describes transmission only. The "missing" power goes back toward the source, which can disturb the laser or create ghost beams. In spectroscopy, absorbance \(A = -\log_{10}(I/I_0)\) means the same thing when \(I_0\) is measured through a reference that cancels reflection losses.
Practical cautions
- OD depends on wavelength. Absorptive ND glass is often far less dense in the near-IR than in the visible. Check the vendor's OD curve at your wavelength rather than the nominal value.
- Stacking reflective filters creates multiple reflections between them. Tilt them by a few degrees so back-reflections leave the beam path, and don't let them return into the laser.
- High power. An absorptive filter at the front of a stack absorbs almost all the power and can crack or thermally lens. Put a reflective filter, beam sampler, or beam dump first, and keep within each filter's damage threshold.
- High OD is hard to verify. Above OD 4–5, scattered and leaked light around the filter often dominates the measured transmission.
Worked example
A 2 W beam needs to be at or below 1 mW for a camera. The required OD is \(\log_{10}(2\,\text{W}/1\,\text{mW}) = 3.30\). Stacking OD 1 + OD 2 + OD 0.5 = OD 3.5 transmits \(2\,\text{W}\times10^{-3.5} = 0.63\) mW, which meets the target. Nearly the full 2 W is absorbed or reflected by the first filter, so make it a reflective filter or one with a suitable damage threshold.
References
- ANSI Z136.1-2022, American National Standard for Safe Use of Lasers, Laser Institute of America.
- IEC 60825-1:2014, Safety of laser products — Part 1: Equipment classification and requirements.
- E. Hecht, Optics, 5th ed., Pearson (2017).