Stray light

Stray light is any light that arrives at a detector or image plane by a route other than the one the optical design intends. It adds a background that carries no information: a haze over an image, a floor under a spectrum, an offset under a weak signal. Typical magnitudes are small fractions of the main beam, from about $10^{-3}$ to $10^{-5}$ of the incident power inside a single-grating spectrometer, but they decide the weakest signal that can be measured next to a strong one.

Sources

Scattering from optical surfaces. Residual roughness on a polished surface scatters light out of the specular beam. For a smooth surface with RMS roughness $\sigma$ at normal incidence, the total integrated scatter is approximately

$$\text{TIS} \approx \left(\frac{4\pi\sigma}{\lambda}\right)^2,$$

which for $\sigma = 1$ nm at 633 nm is $3.9 \times 10^{-4}$; doubling the roughness quadruples it. Dust, scratches and illuminated mechanical surfaces add to this.

Ghost reflections. Each uncoated glass surface ($n = 1.5$) reflects 4.0% at normal incidence. A pair of surfaces sends $0.04 \times 0.04 = 0.16\%$ of the light forward again after two reflections, a ghost 28 dB below the main beam. With an anti-reflection coating of 0.25% on both surfaces the ghost falls to $6.25 \times 10^{-6}$, or 52 dB below.

Diffraction. Apertures, lens edges and mounts diffract light outside the geometric beam.

Grating effects. A diffraction grating scatters light from groove errors and surface roughness, and its other diffraction orders overlap the wanted one: second-order light at 400 nm leaves the grating at the same angle as first-order light at 800 nm, which is why spectrometers covering an octave use order-sorting filters. Holographic gratings generally scatter less than ruled ones.

Ambient and out-of-field light. Room lights and sources outside the field of view reach the detector through gaps in an enclosure or by scattering inside it.

Effect on spectrophotometry

In a spectrometer set to one wavelength, stray light is the fraction $s$ of the reference signal that arrives at other wavelengths. A sample of true transmittance $T$ is then measured as

$$T_\text{meas} = \frac{T + s}{1 + s},$$

assuming the sample transmits the stray light, which lies at other wavelengths, without loss. With $s = 10^{-3}$, a sample of true optical density 1 reads 1.00, OD 2 reads 1.96, OD 3 reads 2.70 and OD 4 reads 2.96, and a sample opaque only at the set wavelength reads 3.00. The calibration curve bends over and flattens at $-\log_{10} s$, so a 0.1% stray-light ratio caps the measured OD near 3, and $10^{-4}$ caps it near 4. The procedure for measuring beyond that floor is described in Measuring optical density beyond OD 4.

The same floor limits how close to a strong line a weak one can be seen; in an optical spectrum analyzer it sets the close-in dynamic range and so the largest OSNR the instrument can report.

Raman spectroscopy and cameras

In Raman spectroscopy the elastically scattered laser light is roughly a million times stronger than the Raman bands. If a spectrometer passed it unfiltered and scattered $10^{-4}$ of it internally, the stray Rayleigh light alone would carry about 100 times the power of the Raman signal. A notch filter or long-pass edge filter of OD 6 or more removes the laser line before the light enters the spectrometer; double and triple monochromators reduce the internal stray light further.

In cameras and telescopes stray light appears as veiling glare, a haze that lowers the contrast of dark regions, and as ghost images of bright sources.

Control

Stray-light control is designed in and then checked on the bench:

• Baffles and vanes, so that no surface the detector can see is directly illuminated.
• Field stops and Lyot stops at intermediate images and pupils.
• Black coatings, anodizing and flocked materials on interior surfaces, with the caveat that many black finishes reflect more strongly in the near infrared than in the visible.
• AR coatings on all transmissive surfaces, and wedged or tilted windows so that their reflections leave the beam path.
• Beam dumps for unused beam-splitter ports, grating zero orders and back-reflections.
• An enclosure, and modulation of the source with lock-in detection, to reject ambient light.

On the bench, blocking the beam just before the sample and reading what remains separates stray light from the signal.

Common questions

What is the difference between stray light and background?

Background includes detector dark signal and electronic offset, present with no light at all. Stray light is optical: it scales with the source power and disappears when the source is blocked.

How is stray light measured in a spectrophotometer?

By measuring a sharp cut-off filter or solution that is opaque at the test wavelength and transparent elsewhere. Any signal recorded at the test wavelength is stray light, and its ratio to the reference signal is the stray-light ratio.

References: E. C. Fest, Stray Light Analysis and Control (SPIE Press, 2013); J. C. Stover, Optical Scattering: Measurement and Analysis, 3rd ed. (SPIE Press, 2012); H. E. Bennett and J. O. Porteus, "Relation between surface roughness and specular reflectance at normal incidence," J. Opt. Soc. Am. 51, 123 (1961); E. Hecht, Optics, 5th ed. (Pearson, 2017).