System and method for autofocusing an optical system through image spectral analysis

An apparatus for autofocusing an optical system, comprising:

• a detector configured to capture images formed by the optical system;
• an actuator configured to move the detector and optical system relative to each other;
• and
• a processor for directing movement of the actuator based at least upon calculating a transform and a blur spread parameter of the images at a first position and a second position relative to the optical system,
• a memory,
• wherein the memory stores a lookup table of ratios of transforms of a test image indexed by radial spatial frequency and positions of the optical system relative to the detector.

An apparatus for autofocusing an optical system, comprising:

• a detector configured to capture images formed by the optical system;
• an actuator configured to move the detector and optical system relative to each other;
• a processor for directing movement of the actuator based at least upon calculating a transform and a blur spread parameter of the images at a first position and a second position relative to the optical system;
• and
• a memory,
• wherein the memory stores a lookup table of move distances for the detector indexed by radial spatial frequency and ratios of transforms of a test image.

An apparatus for autofocusing an optical system, comprising:

• a detector configured to capture images formed by the optical system;
• an actuator configured to move the detector and optical system relative to each other;
• a processor for directing movement of the actuator based at least upon calculating a transform and a blur spread parameter of the images at a first position and a second position relative to the optical system;
• and
• a memory,
• wherein the memory stores a lookup table of move distances for the detector indexed by radial spatial frequency and a continuous monotonic transformation of ratios of transforms of a test image.

A computer-implemented method of autofocusing an optical system, comprising:

• applying a spectral transform to a first image formed by the optical system and captured by an imager, wherein the first image is formed at a first position relative to the optical system;
• applying the spectral transform to a second image formed by the optical system and captured by the imager, wherein the second image is formed at a second position relative to the optical system;
• determining a difference of squared blur spread values from the transformed first image and the transformed second image;
• and
• autofocusing the optical system based on the difference of squared blur spread values.

A computer-readable medium storing instructions for autofocusing an optical system, wherein the instructions comprise:

• applying a transform to a first image formed by the optical system and captured by a detector, wherein the first image is formed at a first location relative to the optical system;
• applying the transform to a second image formed by the optical system and captured by the detector, wherein the second image is formed at a second location relative to the optical system;
• determining a difference of squared blur spread values from the transformed first image and the transformed second image;
• and
• autofocusing the optical system based on a mathematical function between the squared blur spread values.

A method of autofocusing an optical system, comprising:

• positioning a detector at a first position along an optical axis of the optical system;
• calculating a transform of a first image formed by the optical system at the first position;
• moving the detector along the optical axis of the optical system to a second position;
• calculating a transform of a second image formed by the optical system at the second position;
• calculating from the transform of the first image and the transform of the second image, a first parameter and a second parameter, wherein the first parameter is given by (σ12−σ22), wherein σ1 is a first blur spread value for the first image, and σ2 is a second blur spread value for the second image, and a second parameter is given by the first parameter divided by Δs, wherein Δs is given by a difference between the first position and the second position;
• based upon signs of the first parameter and the second parameter, determining how far and in which direction to move the detector along the optical axis and moving the detector accordingly to a third position;
• and
• if the second parameter has converged to a predetermined value, stop moving the detector, otherwise
• based upon signs of the first parameter and the second parameter, determining whether to discard the first image or the second image;
• calculating a transform of a third image formed by the optical system at the third position, wherein the third image replaces the discarded image;
• calculating from the transform of the third image and the undiscarded transform, a new first parameter and a new second parameter;
• and
• based upon signs of the new first parameter and the new second parameter, determining how far and in which direction to move the detector along the optical axis and moving the detector accordingly to a new position.