System and method for optical three-dimensional particle localization

摘要

Embodiments include methods that may be used to optically obtain the precise three-dimensional location of multiple objects from one or more two dimensional images. An optical point spread function having a transverse shape which varies with axial distance may be implemented to obtain depth information. The transverse variation in the PSF with depth may be produced using a cylindrical lens. The objects may be imaged by a focal plane array detector. One or more 2D images may be used to find the 3D location of the objects using sparse signal reconstruction methods.

主权项

1. A method for localizing an object containing an ensemble of light-switchable elements in three-dimensional space comprising the steps of:
causing a first sparse subset of the elements to illuminate; acquiring a first image b having dimensions m(1/2)×m(1/2) of said activated first sparse subset through optics having a point spread function (PSF) that varies predictably with axial object distance; causing said first sparse subset of the elements to extinguish; repeating the previous three steps for different sparse subsets of elements; defining a sensing array Φ=m×n×l which represents a discrete set of possible PSF's that any of said elements can generate within a given volume having dimensions n(1/2)×n(1/2)×l; and creating a three dimensional image of said elements by solving the following linear programming problem:
min Σl∥xln∥1 subject to ∥Σl(Φlmnlxln)−bm∥2≦ε(Σmbmm)1/2 and xln≧0, where: x=l-many n×1 image vectors comprising said n(1/2)×n(1/2)×l three dimensional volume and ε=user set tolerance on convergence and where: m is the number of pixels in each image b, n is the total number of possible transverse locations in which a light-switchable element may localized and l is the number of planes of images.