How this instrument works
Optical density measures how thoroughly a material blocks light, on a logarithmic scale rather than as a plain fraction. Transmittance, T, is the share of incident light that makes it through — 0.1 means one tenth gets out the far side, 0.01 means one hundredth. Optical density is OD = −log₁₀(T); the minus sign flips the naturally negative logarithm of a fraction below one into a positive, readable number. A transmittance of 0.1 becomes an OD of exactly 1; drop to 0.01 and OD becomes 2.
The logarithm is not decoration; it is the entire point of rating filters this way. Light crossing two filters in series has its transmittances multiply, T₁ × T₂, because the second filter only ever sees what the first one let through. Take logarithms of both sides and that multiplication turns into addition: OD₁ + OD₂. That single fact is why welding lenses, laser safety eyewear, and photographic neutral-density filters are all rated in OD rather than percent transmission — a welder combining a shade-10 lens with a shade-5 cover plate can add the two OD ratings directly, with no decimals to multiply.
The scale has a hard floor and no ceiling. OD = 0 marks perfect transmittance, T = 1, and nothing blocks less than that — a negative optical density would mean a passive filter emits more light than it receives, which none do. A laser beam block, by contrast, can carry OD 7 or higher, a transmittance of one part in ten million. What OD never tells you is where the missing light went; absorbed as heat, reflected off a coated surface, or scattered sideways all read identically on this scale.
- Enter Transmittance (fraction, 0-1) — the share of incident light that exits the filter, sample, or lens. A pane passing 40% of light is entered as 0.4, not 40.
- Use a decimal above zero and up to 1.0; the field will not accept zero or a negative value because log₁₀(0) is undefined.
- Read Optical density (absorbance) — the instrument computes OD = −log₁₀(T) instantly, shown to six decimal places.
- To rate a stack of filters, work out each one's OD separately and add the results by hand — the entire reason the scale is logarithmic.
Worked example — rating a 10%-transmittance filter
A photographer holds a neutral-density filter up to a light meter and measures that it passes exactly 10% of the incident light — a transmittance of 0.1. Entering 0.1 into Transmittance (fraction, 0-1) returns Optical density (absorbance) = −log₁₀(0.1) = 1.0 exactly, since log₁₀(0.1) equals −1 precisely. That single digit is the filter's OD rating: OD 1.
Stack a second, identical OD-1 filter behind the first and the combined transmittance becomes 0.1 × 0.1 = 0.01, exactly 1% of the original light. Rather than multiplying those decimals, the OD scale just adds: 1.0 + 1.0 = 2.0, matching −log₁₀(0.01) = 2 exactly. That shortcut is why camera stores, welding-supply catalogues, and laser-safety eyewear specs all print OD numbers instead of percentages — three OD-1 filters in series give OD 3, a transmittance of exactly 0.1%, without a calculator in sight.
Questions
Why is optical density logarithmic instead of a simple percentage?
Because filters in series multiply their transmittances rather than add them, and a logarithm is the one operation that turns multiplication into addition. Rating filters in OD lets you add two numbers to find a stack's combined effect instead of multiplying decimals — 90% transmittance stacked with another 90% gives 81%, but OD 0.046 stacked with OD 0.046 simply sums to about 0.092.
What is the difference between optical density and transmittance?
Transmittance (T) is a plain fraction: the share of light that gets through, from 0 to 1. Optical density is −log₁₀(T) — a filter transmitting 50% of light has OD ≈ 0.301, while one transmitting 1% has OD = 2. The relationship is one-to-one but not linear: small changes in T near zero swing OD sharply, while the same size change near T = 1 barely moves it.
Can transmittance be entered as a percentage instead of a fraction?
No — the Transmittance (fraction, 0-1) field expects a decimal, not a percentage. A filter rated 25% transmittance goes in as 0.25; typing 25 by mistake computes −log₁₀(25) = −1.398, a negative optical density with no physical meaning for a filter that only blocks light. Divide any percentage figure by 100 before entering it.
How does optical density relate to absorbance in chemistry?
They are the same formula under two names. Spectrophotometry calls −log₁₀(T) 'absorbance' and uses it in the Beer–Lambert law to find a solution's concentration from how much light a sample cell absorbs. Optics and photography call the identical quantity 'optical density' when describing filters, lenses, and coatings. A cuvette reading of A = 1.0 describes exactly the same 10%-transmittance situation as an OD-1 camera filter.
What optical density do laser safety glasses need?
Enough to bring the beam below the exposure limit for its specific wavelength and power, which is why eyewear is rated per wavelength band rather than with one universal number. An OD-4 lens transmits only 10⁻⁴ of incident light, or 0.01%, and standards such as ANSI Z136.1 specify the minimum OD a given laser class requires — using the wrong wavelength rating can leave eyes unprotected even when the printed OD number looks high enough.
Why can't transmittance be zero or negative?
Because log₁₀(0) is undefined, and negative transmittance would describe light arriving before it left, which nothing physical does. This calculator requires a value greater than zero; a near-opaque material should be entered as a very small decimal, such as 0.0000001, rather than zero, and the resulting optical density climbs without any fixed upper limit as transmittance approaches it.