Optical system for controlling a light beam

An optical system comprising:

• focusing optics comprising a set of focusing elements configured to produce a focusing beam, wherein the set of focusing elements comprise at least one spherical surface configured to introduce a respective set of spherical aberrations into the focusing beam, wherein the spherical aberrations are tuned to maximize a length of a focal region;
• beam steering optics comprising at least one rotatable element configured to receive the focusing beam with an angle of incidence, and redirect the focusing beam along a first beam direction, wherein the first beam direction has a first beam angle with respect to a central axis, wherein the central axis is perpendicular to a target plane, wherein the first beam angle is controllable by setting an angle of rotation of the rotatable element to change the angle of incidence;
• and
• a flat gradient index plate configured to receive the focusing beam along the first beam direction, and redirect the focusing beam along a second beam direction, wherein the second beam direction has a second beam angle with respect to the central axis, wherein the focusing beam redirected along the second beam direction has a focal region overlapping the target plane at a radial coordinate with respect to an intersection of the central axis with the target plane, wherein the gradient index plate is configured to linearize a dependence of the radial coordinate as function of the angle of rotation.