Optics in three-dimensional printing

An apparatus for printing at least one three-dimensional (3D) object comprising at least one controller configured to:

• (a) couple to an electrical power source and operatively couple to (i) an energy source configured to generate an energy beam that transforms at least a portion of a material bed to print the at least one 3D object, the material bed having an exposed surface having a roughness, (ii) a scanner configured to propagate the energy beam along the exposed surface, and (iii) a detector configured to detect a reflected radiation from the exposed surface;
• (b) direct the energy source to generate the energy beam configured to irradiate at least a portion of the exposed surface and form a footprint on the exposed surface, the footprint emitting the reflected radiation from the exposed surface;
• (c) direct the scanner to propagate the energy beam along the exposed surface to cause the footprint of the energy beam to propagate along the exposed surface while emitting the reflected radiation from the exposed surface;
• (d) direct the detector to detect the reflected radiation from the footprint at the exposed surface during propagation of the energy beam along the exposed surface, to generate associated signals;
• and
• (e) direct a signal analysis of the associated signals to determine an exposed surface signal component, the signal analysis comprising determining an optical variability of the associated signals from the reflected radiation, the optical variability indicating at least in part a degree of focus of the energy beam such that the optical variability increases as the focus of the energy beam increases, wherein the optical variability is determined by analyzing variations in the reflected radiation signals from the footprint of the energy beam on the exposed surface.