10.5 - Spot distortion during gradient deflection of focused laser beams

A generalized expression is developed for the differential scan angle in terms of the gradient of wavelengths in the medium, and thus the gradient of the index of refraction in optical media. This large class of nonmechanical deflectors is shown to impose aberrations upon convergent light flux which are directly related to the magnitude of scan angle and the number of the focusing bundle. A uniform gradient case is analyzed and magnitudes of distortions are evaluted. Distortion is shown to increase rapidly as the number is reduced. Since diffraction limitations dominate at high numbers, an optimum number exists at which the maximum number of spots may be subtended per scan increment. This optimum is shown to be where is the refractive index, is the scan length, is an aperture shape factor ( ), and λ is the wavelength (in same units as ). The maximum spots per scan, is independent of the dimensions of the deflector and may be further constrained by the boundaries of the cell. This problem may be further generalized for all ray-like flux tubes, such as electron beams. Possibilities for the control of aberrations by gradient shaping are considered.