Nano position sensing and surface estimation in scanning probe microscopes using reference estimation

A controller apparatus with integral action and output error for a scanning probe microscope comprising:

• a summing block that is operable to output a controller output signal to said scanning probe microscope;
• an estimator coupled to said summing block, said estimator operable to directly receive a first input signal that depends on an optical error signal and on a substitute reference signal and a second input signal that depends on an actuator position signal, said estimator operable to use said first and said second input signal to generate a state estimate that is communicated to said summing block;
• and
• a reference input gain matrix coupled to said summing block, said reference input gain matrix operable to directly receive said substitute reference signal and operable to use said substitute reference signal to generate a scaled and vectorized substitute reference signal that is directly communicated to said summing block.