Transmittance

Transmittance is the fraction of the optical power incident on a sample that emerges on the other side: $T = P_t / P_i$, a number between 0 and 1, often quoted as a percentage and usually as a function of wavelength. A clean uncoated glass window transmits about 92% of visible light, the rest being lost mostly to reflection at its two surfaces; an anti-reflection-coated window transmits 98 to 99.5%; a neutral-density filter of optical density 3 transmits 0.1%. Energy conservation links it to reflectance $R$, absorptance $A$ and scattered fraction $S$:

$$T + R + A + S = 1 .$$

Internal and external transmittance

Glass catalogs and filter data distinguish two quantities. External transmittance is what a power meter records: it includes the surface reflections. Internal transmittance $T_i$ excludes them and describes only attenuation in the bulk, which follows the Beer–Lambert law,

$$T_i = e^{-\alpha d},$$

with $\alpha$ the absorption coefficient and $d$ the thickness. A sample with $\alpha = 0.1\ \text{cm}^{-1}$ and $d = 1$ cm has $T_i = 90.5\%$. For a slab with equal surface reflectance $R$ at each face and incoherent multiple reflections, the external value is

$$T = \frac{(1-R)^2\,T_i}{1 - R^2 T_i^2} .$$

For a non-absorbing window ($T_i = 1$) this reduces to $(1-R)/(1+R)$, which with $R = 4.0\%$ at $n = 1.5$ gives 92.3%.

Logarithmic forms

Because transmittances of elements in series multiply, they are often expressed on a log scale, where they add. Optical density is $\text{OD} = -\log_{10} T$: OD 1 is 10%, OD 3 is 0.1%, OD 6 is one part per million. Chemists call the same quantity absorbance. In fiber optics and telecom the loss in decibels is $-10\log_{10} T$: a transmittance of 50% is a loss of 3.01 dB, and 100 km of fiber at 0.2 dB/km has 20 dB of loss, a transmittance of 1%. The insertion loss of a component is its transmittance expressed this way.

Measurement

A spectrophotometer measures transmittance by dividing the signal with the sample in the beam by a baseline recorded without it, wavelength by wavelength. A laser and a power meter do the same at a single wavelength. Several details decide the accuracy. The detector must capture the whole transmitted beam, including any lateral shift a thick tilted sample introduces. Its response must be uniform across its area, or a sample that moves or refocuses the beam changes the reading without changing the power. Source drift between the baseline and the sample measurement enters directly, so a reference detector on a split-off beam is used when better than about 1% is required. Values below $10^{-4}$ are hard to measure in a single pass because stray light and detector offset dominate; high-OD filters are characterized by stacking calibrated attenuators or by using a source with more dynamic range.

Where it matters

Transmittance curves are the primary specification for filters, windows, lens materials and coatings, and they decide what a system can see: fused silica transmits from about 180 nm into the near infrared, while ordinary soda-lime glass absorbs strongly below about 300 nm. Laser safety eyewear is specified by optical density at the laser wavelength. In a lens system with many elements, total transmittance is the product of every surface and bulk contribution, so ten uncoated surfaces at 4% each already remove a third of the light, which is the practical case for anti-reflection coatings.

Pitfalls

Transmittance depends on angle and polarization, and filter curves are specified at a stated incidence, usually 0°; interference filters shift toward shorter wavelengths when tilted. A scattering sample can appear more or less transmissive depending on how much forward-scattered light the detector accepts, so diffuse transmittance and specular (regular) transmittance are different quantities and are measured with and without an integrating sphere. Thin, parallel samples measured with a narrow-linewidth laser show interference fringes that are absent in a broadband measurement.

Common questions

What is the difference between transmittance and transmission?

Transmittance is the defined ratio of transmitted to incident power, a dimensionless number. Transmission is the general word for the process of light passing through, though it is often used loosely to mean the same ratio. Standards documents prefer transmittance for the quantity.

How is transmittance converted to absorbance?

Absorbance, or optical density, is $-\log_{10} T$. A transmittance of 90% is an absorbance of 0.046; 1% is 2.0. A measured absorbance includes reflection and scattering losses unless the baseline removes them, for example by using a matched reference cuvette.

What is a good transmittance for an optical window?

Uncoated glass or fused silica in the visible gives about 92–93%, limited by reflection. With a single-layer or multilayer AR coating on both sides, 98–99.5% is typical over the design band.

References: E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 4; B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019), Ch. 6; ISO 80000-7:2019, Quantities and units, Part 7: Light and radiation.