Spatial Filters

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Spatial filters provide a convenient way to remove random fluctuations from the intensity profile of a laser beam. This greatly improves resolution — which is especially critical for applications like holography and optical data processing.
Laser beams pick up intensity variations from scattering by optical defects and particles in the air. You can view this by expanding a laser beam onto a card: the whorls, holes and rings superimposed on the ideal pattern of uniform speckles are spatial noise.
Spatial filtering is conceptually simple: an ideal coherent, collimated laser beam behaves as if generated by a distant point source. Spatial filtering involves focusing the beam, producing an image of the “source” with all imperfections in the optical path defocused in an annulus about the axis. A pinhole blocks most of the noise.
The ideal Gaussian laser beam profile, I(r), is contaminated by intensity fluctuations, δΙ, caused by scattering. δΙ varies rapidly over an average distance dn, which is much smaller than the beam radius, a. The distance dn is then known as the average spatial wavelength of the laser beam noise.
When a positive lens of focal length F focuses a Gaussian beam, the image at the focal plane (the Optical Power Spectrum, or OPS) will be an inverted “map” of spatial wavelengths present in the beam. Short wavelength noise (dn) will appear in an annulus of radius Fλ/dn centered on the optic axis. The long spatial wavelength of an ideal Gaussian profile will form an image directly on the optic axis.
A pinhole centered on the axis can block the unwanted noise annulus while passing most of the laser’s energy. The fraction of power passed by a pinhole of diameter D is:

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and the minimum noise wavelength transmitted by the pinhole is

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Newport recommends a pinhole of diameter Dopt:

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This passes 99.3% of the total beam energy and blocks spatial wavelengths smaller than 2a, the diameter of the initial beam. Since dn is always much smaller than the beam diameter, the filtered beam is very close to the ideal profile.
For convenience, optimal pinhole/objective combinations have been tabulated in a Selection Guide, Three-Axis Spatial Filters and Compact Five-Axis Spatial Filters .

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