Glossary entry

Spatial filter

A lens that focuses a laser beam onto a pinhole, which passes the smooth Gaussian core and blocks the scattered light that makes a beam noisy. A pinhole about 1.5 times the focused 1/e² diameter passes 98.9% of an ideal Gaussian beam.

Optics & beams Lab practiceUpdated September 2026

A laser beam that has passed through dusty or scratched optics picks up fine speckle and fringes, and the beam from many lasers carries some light in higher-order transverse modes. A spatial filter cleans it. A lens focuses the beam, and in its focal plane the light is sorted by direction: the smooth Gaussian part comes to a small central spot, while light scattered by small defects travels at larger angles and lands farther out. A pinhole at the focus passes the central spot and blocks the rest, and a second lens recollimates the output, usually at a larger diameter. The arrangement is a Keplerian beam expander with a pinhole at its internal focus, and the output approaches a pure TEM₀₀ mode.

Choosing the pinhole

A collimated Gaussian beam of radius $w_{in}$ focused by a lens of focal length $f$ has a focal spot of $1/e^2$ radius $w_f = \lambda f/(\pi w_{in})$ . The fraction of power passed by a pinhole of radius $a$ is

T = 1 - \exp\left(-\frac{2a^2}{w_f^2}\right),

and the usual choice, a pinhole diameter about 1.5 times the focused $1/e^2$ diameter ( $a = 1.5\,w_f$ ), transmits 98.9% of an ideal beam. A smaller pinhole removes more noise but starts to clip the Gaussian itself, which adds diffraction rings to the output; a larger one passes more of the scattered light. As an example, a helium-neon beam of 1 mm $1/e^2$ diameter focused by a 16 mm focal length microscope objective (a traditional 10× objective) makes a 12.9 µm spot, and a pinhole of about 20 µm is the nearest standard size.

Alignment

The pinhole sits on an XYZ mount. With the pinhole well out of focus, it is centred in X and Y on the transmitted light, then moved toward focus in small steps, recentring each time, until the transmitted power is at its maximum and the output shows a clean central disk with no rings. The final adjustments are a few micrometres, and thermal drift of the mount or the laser pointing can undo them over hours, so critical setups use a larger pinhole than the ideal.

References: E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 11; J. W. Goodman, Introduction to Fourier Optics, 4th ed. (W. H. Freeman, 2017).