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We show that narrow filaments or sheets of over- or under-dense plasma, or"noodles," with fluctuations of scattering phase of less than a radian, canform the scintillation arcs seen for many pulsars. The required localfluctuations of electron density are indefinitely small. We assume a cosineprofile for the electron column and find the scattered field by analyticKirchhoff integration. For a large electron column, corresponding to largeamplitude of phase variation, the stationary-phase approximation is accurate;we call this regime "ray optics". For smaller-amplitude phase variation, thestationary-phase approximation is inaccurate or inapplicable; we call thisregime "wave optics". We show that scattering is most efficient when the widthof the strip equals that of one pair of Fresnel zones, and in the wave-opticsregime. We show that the resolution of present observations is about 100Fresnel zones on the scattering screen. Incoherent superposition of stripswithin a resolution element tends to increase the scattered field. We find thatobservations match a single noodle per resolution element with phase of up to12 radians; or many noodles per resolution element with arbitrarily small phasevariation each, for net phase of less than a radian. Observations suggest aminimum radius for noodles of about 650 km, comparable to the ion inertialscale or the ion cyclotron radius in the scattering plasma.

Scintillation Arc Brightness and Electron Density for an Analytical Noodle Model