Methods and systems for three dimensional optical imaging, sensing, particle localization and manipulation

A method for locating an object in three-dimensions with an optical system, the method comprising:

• generating one or more 3D point spread functions (PSF);
• generating one or more experimental images of the object using the one or more 3D PSF of the optical system;
• taking a set of calibration images separated by an axial distance;
• generating the one or more 3D PSF from the set of calibration images by numerically propagating the set of calibration images with defocus;
• searching for a location of the object in an axial direction by numerically propagating the one or more experimental images with an axial shift to generate an axial position estimate and by transversely shifting the axial position estimate to correlate with the one or more experimental images to find transverse position estimates;
• and
• generating a 3D position of the object by increasing a probability of matching the experimental image to the PSF in the presence of noise.

A method for locating an object in three-dimensions with an optical system, the method comprising:

• generating one or more 3D point spread functions (PSF);
• generating one or more experimental images of the object using the one or more 3D PSF of the optical system;
• and
• generating a 3D position of the object by increasing a probability of matching the experimental image to the PSF in the presence of noise;
• wherein a set of initial coordinates is generated by searching for the object location in the axial plane by propagating the experimental image with an axial shift to generate an axial position estimate and transversely cross correlating the axial position estimate with the experimental image to find the transverse position estimates.

A method for locating an object in three-dimensions with an optical system, the method comprising:

• generating one or more 3D point spread functions (PSF);
• generating one or more experimental images of the object using the one or more 3D PSF of the optical system;
• generating a 3D position of the object by increasing a probability of matching the experimental image to the PSF in the presence of noise;
• wherein generating the 3D position of the object by increasing a probability of matching the experimental image to the PSF in the presence of noise includes a phase retrieval (PR) enabled maximum likelihood estimator (MLE) that models the noise by Poisson, Gaussian, or a mixture distribution.

A ranging system, comprising:

• a calibration module arranged to take a set of calibration images separated by an axial distance;
• an imaging module arranged to take an experimental image of an object, wherein the imaging module is arranged to adjust a focus of the axial ranging system by an axial shift;
• a search module arranged to search for an object location within an axial plane by propagating a representation of the experimental image by an axial shift to generate an axial position estimate and by transversely shifting the axial position estimate with the experimental image to find transverse position estimates;
• and an estimation module coupled to the calibration module, the imaging module, and the search module, wherein the estimation module is configured to receive the set of calibration images and the experimental image and generate an estimate of a position of the object using a maximum likelihood estimator.

A method for locating an object in three-dimensions with an optical system, the method comprising:

• generating one or more 3D point spread functions (PSF) by control of one or more associated pupil functions of the optical system;
• generating one or more experimental images of the object using the one or more 3D PSF of the optical system;
• generating a model of the one or more 3D PSF and a model of noise;
• generating a 3D position of the object by increasing a probability of matching the experimental image to the PSF in the presence of the noise.