Laser focal shift monitor

A change in the collimation angle (describing the overall beam divergence or convergence) causes a corresponding change in the laser focal position. The collimation angle of a ray can be expressed in terms of the ratio alpha of its position to slope at the lens. Changes in beam collimation delta alpha can be accurately determined by passing the beam through an apertured mask and recording its image at a distant location. For a plano-convex lens of thickness t and refractive index n, the focal shift is given by delta f - ((f + (t/n)) squared)delta alpha. Shifts of a few micrometers can be measured when the distance between mask and image is sufficiently large.