Diffuser

A diffuser spreads light over a range of directions by scattering from a rough surface, from particles inside a material, or from designed surface microstructure. It is used to even out illumination, hide the structure of a lamp or LED array, or reduce the coherence of a laser beam. The main types differ in how widely they spread light and how much they transmit: ground glass scatters into a moderate cone with good transmission, opal glass scatters almost uniformly into the whole hemisphere with lower transmission, and engineered (holographic or microlens) diffusers put the light into a specified angular pattern, for example a 1°, 10° or 60° full width, with high efficiency.

Types

Ground glass is made by grinding a glass surface with abrasive grit, typically from about 120 grit (coarse) to 1500 grit (fine). The spread depends on grit and surface finish, and much of the light still travels near the original direction, so a bright spot of the source often remains visible.

Opal glass has a thin layer of milky glass containing scattering particles fused onto a clear substrate. The light is scattered many times inside the layer and leaves with nearly equal radiance in every direction, the Lambertian limit. The cost is transmission, which is considerably lower than that of ground glass.

Engineered diffusers use a surface relief pattern, either a recorded or computed random phase profile or an array of microlenses, to send light into a chosen angle with a sharp edge. Microlens array diffusers can form a flat-top angular distribution with a square or circular shape, useful for illuminating a rectangular sensor or target.

Reflective diffusers use the same principles: sintered polytetrafluoroethylene and barium-sulfate coatings are close to Lambertian with reflectance of about 97–99% in the visible, and they are used to line integrating spheres.

Lambertian spread and collection

A Lambertian diffuser emits intensity proportional to $\cos\theta$ about its normal. The fraction of the scattered power inside a cone of half-angle $\theta$ is then

$$F(\theta) = \sin^2\theta.$$

This gives 25% within 30°, 50% within 45° and 75% within 60°. A detector or fiber with numerical aperture 0.1 collects $0.1^2 = 1\%$ of the light a Lambertian diffuser sends into its hemisphere; diffused light couples poorly into small-aperture optics for this reason.

The loss follows from étendue: a diffuser increases the product of beam area and solid angle, and no passive optic downstream can reduce it again. A collimated laser beam, which has small étendue, cannot be recovered from a diffuser's output without discarding most of the power.

Diffusers and laser speckle

Laser light passing through a stationary diffuser acquires a random phase at every point, and the scattered waves interfere to form speckle, a granular pattern with contrast close to 1. At a distance $z$ from an illuminated patch of width $D$, the speckle grains are of order

$$\delta \approx 1.22\,\frac{\lambda z}{D}.$$

For 633 nm light, a 5 mm illuminated patch and $z = 1$ m, $\delta \approx 154$ µm. Moving the diffuser, usually by rotating it, changes the pattern over time; averaging $N$ independent patterns within the detector's integration time reduces the contrast to $1/\sqrt{N}$, 0.1 for $N = 100$. The same rotating diffuser, followed by a lens, is a standard way to make pseudo-thermal light with a controllable spatial coherence for coherence and ghost-imaging experiments.

Measurement

The angular distribution of a diffuser is measured by scanning a detector around it at fixed distance (a goniometer), or by imaging the scattered light on a screen or in the back focal plane of a lens. The result is usually reported as a full width at half maximum in degrees. Total transmission is measured with an integrating sphere, because a power meter with a small aperture misses light scattered to wide angles.

Pitfalls

• The spread of a diffuser depends on the input beam's divergence; a diffuser specified for collimated light gives a wider output when fed a diverging beam.
• A single diffuser seldom gives uniform illumination by itself: ground glass leaves a hot spot, and two diffusers separated by some distance, or a light pipe or integrating sphere, smooth it further.
• Surface-relief diffusers work less well when immersed in cement or oil, because the relief depends on the index step at the surface.

Common questions

What is the difference between ground glass and opal diffusers?

Ground glass scatters mainly forward, with high transmission and some residual image of the source. Opal glass scatters almost uniformly, close to Lambertian, and transmits less.

How does a rotating diffuser reduce speckle?

Rotation presents a changing random phase to the beam, so the speckle pattern changes many times during an exposure. The detector adds the patterns, and the contrast falls as $1/\sqrt{N}$ for $N$ independent patterns.

Does a diffuser reduce laser power?

A diffuser loses some light to absorption and back-scatter, but mainly it redistributes power over a larger solid angle, which lowers the irradiance at any given distance. The total power passing through may still be high.

References: J. W. Goodman, Speckle Phenomena in Optics, 2nd ed. (SPIE Press, 2020); E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 4; C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983); R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, 1983).