Precision optical systems with performance characterization and uses thereof

A method of compensating for distortion errors in an optical system, comprising the steps of:

• a) determining the location of where collimated beams from a projector would be imaged by an image recording device incorporated into the optical system if the optical system were distortion free;
• b) obtaining an image of a scene along with an image of the collimated beams projected onto the image recording device by the projector and determining the location of the collimated beams in the image;
• c) determining transformation coefficients that map the locations of the image of the collimated beams determined in step b) to the locations determined in step a);
• and
• d) applying the transformation coefficients to at least a portion of the image of the scene in step b) such that the optical system distortions are corrected.

A method for compensating for distortion errors in a precision optical system, comprising the steps of:

• a) obtaining an image of a scene along with an image of collimated beams of light projected onto an image recording device by a projector;
• b) determining the locations on the image recording device of the collimated beams in the image and the associated true ray angles for the collimated beams;
• c) determining the apparent incoming ray angles θ of the collimated beams from the locations on the image recording device using the relation θ=arctan (r/f), where r is a scalar distance from the beams to the center of the image recording device and f is the focal length of the optical system;
• d) determining transformation coefficients that map the true incoming ray angles determined in step b) to the apparent incoming ray angles determined in step c);
• e) applying the transformation coefficients determined in step d) to at least a portion of the image to thereby correct optical system distortions.