System and method for optical three-dimensional particle localization
AssigneeRoper Scientific, Inc.
InventorJason McClure
Life of this patent
Estimating the term…
Abstract
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.
Claims8
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 Σi∥xln∥1 subject to ∥Σl(Φ1mnlx1n)−bm∥2≦ε(Σmbmm)1/2 and xin≧0,
- where:
- x=l-many n×1 image vectors comprising said n(1/2)×n(1/2)×l three dimensional volume and c=user set tolerance on convergence.
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:
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- where:
- x=l-many n×1 image vectors comprising said n(1/2)×n(1/2)×l three dimensional volume,
- ε=user set tolerance on convergence and
- weighting factors are defined for n-many transverse locations each of said elements can occupy for each axial plane l, and wherein said weighing factors are represented by the equation
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A system for creating an image of an object comprising an ensemble of light-switchable elements, the system comprising:
- an image sensor;
- optics having a point spread function (PSF) that varies predictably with axial object distance;
- an energy source;
- and
- a computer;
- wherein
- said computer:
- controls said energy source to illuminate a first portion of said light-switchable elements;
- controls said image sensor to acquire a first image of said light-switchable elements;
- controls said energy source to illuminate a second portion of said light-switchable elements;
- controls said image sensor to acquire a second image of said light-switchable elements and
- defines 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
- creates a three dimensional image of said elements by solving the following linear programming problem:
- min Σl∥xin∥1 subject to ∥Σl(Φ1mnlx1n)−bm∥2≦ε(Σmbmm)1/2 and xin≧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.
Dependencies are inferred from the claim text.