Three-dimensional interferometric microscopy

An apparatus comprising:

• an optical actuation system configured to cause an optical source in a sample that extends generally along a sample plane to emit optical beams in a plurality of optical paths;
• an interference system configured to receive first and second optical beams emitted from the optical source, divide each of the optical beams into two or more divided beams, and combine at least two or more of the divided beams to form a plurality of combined beams, wherein each of the combined beams includes an interference between the two or more divided beams caused at least in part by a difference in a source phase between the optical beams due to a difference in the optical path length of the optical beams relative to the location of the optical source;
• at least two detectors configured to separately detect one or more of an intensity and a profile of each of the combined beams output from the interference system;
• and
• a processor configured to:
• receive the output from the at least two detectors;
• calculate a position of the optical source in the sample plane to sub-diffractive accuracy based on a center region of an image of each combined beam;
• calculate a set of possible positions of the optical source in a third orthogonal dimension that is perpendicular to the sample plane based on separately detected intensities of each combined beam;
• analyze the shape of an image of one or more of an optical beam and a combined beam based on a wavefront modification that varies with the position of the optical source in the third orthogonal dimension, wherein the wavefront modification is a modification of one or more of a curvature and a shape of a wavefront of at least one optical beam emitted from the optical source;
• and
• determine the position of the optical source in the third orthogonal dimension out of the set of possible positions based on the analyzed shape.

A method comprising:

• activating a statistically sparse subset of switchable optical sources in a sample;
• exciting the activated switchable optical sources such that optical beams are emitted from the activated switchable optical sources along at least two optical paths;
• introducing a first wavefront modification in a first optical beam emitted from the activated switchable optical sources along a first optical path and introducing a second wavefront modification in a second optical beam emitted from the activated switchable optical sources along a second optical path, the second wavefront modification being distinct from the first wavefront modification;
• interfering the first and second optical beams to produce a plurality of output beams;
• and
• determining three-dimensional position information of the optical sources based on an intensity of each output beam from the plurality of output beams.

A method comprising:

• directing first and second optical beams emitted from an optical point source along first and second distinct directions associated with respective first and second distinct optical paths;
• shifting by a first shift value focal planes for transverse directions of the first optical beam in the first optical path and shifting by a second shift value focal planes for transverse directions of the second optical beam in the second optical path, in which the second shift value is opposite to the first shift value;
• after shifting the focal planes of the first and second optical beams, dividing each of the first and second optical beams into two or more divided beams and combining at least two or more of the divided beams to form a plurality of combined beams, in which each of the combined beams includes an interference between the two or more divided beams caused at least in part by a difference in the lengths of the optical paths of the first and second optical beams;
• separately detecting an image of each of the combined beams;
• determining a position of the optical source in a first orthogonal dimension and a second orthogonal dimension;
• and
• determining a position of the optical source in a third orthogonal dimension based on the separately detected images of each of the combined beams.