Analytic fourier ptychotomography for volumetric refractive index imaging
AssigneeCalifornia Institute of Technology
InventorsZhenyu Dong, Haowen Zhou, Ruizhi Cao, Changhuei Yang
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Abstract
Analytic Fourier ptychotomography techniques for analytically reconstructing a volumetric (3D) refractive index image based on NA-matching intensity measurements, darkfield intensity measurements, and a finite sample thickness (FST) prior where the FST prior is used for aberration correction and darkfield extension.
Claims20
An analytic Fourier ptychotomography imaging method, comprising:
- obtaining a plurality of NA-matching intensity measurements corresponding to plurality of NA-matching illumination angles and a plurality of darkfield intensity measurements corresponding to a plurality of darkfield illumination angles;
- determining an aberration-corrected NA-matching spectrum based at least in part on the plurality of NA-matching intensity measurements and a finite sample thickness (FST) prior;
- extending the aberration-corrected NA-matching spectrum using the plurality of darkfield intensity measurements;
- and
- reconstructing a volumetric refractive index distribution of a sample being imaged based at least in part on the extended aberration-corrected NA-matching spectrum.
The analytic Fourier ptychotomography imaging method of claim, wherein determining the aberration-corrected NA-matching spectrum comprises:
- recovering a plurality of NA-matching sub-spectrums from NA-matching intensity measurements using Kramers-Kronig (K-K) relation;
- solving for system aberration using a finite sample thickness (FST) prior;
- removing the system aberration from each of the NA-matching sub-spectrums to form a plurality of aberration-corrected NA-matching sub-spectrums;
- and
- stitching together the plurality of aberration-corrected NA-matching sub-spectrums to form an aberration-corrected NA-matching sample spectrum.
The analytic Fourier ptychotomography imaging method of claim, wherein recovering the plurality of NA-matching sub-spectrums comprises:
- for each NA-matching illumination angle, determining a 2D complex-valued Fourier spectrum from a corresponding NA-matching measurement using Kronig-Kramer relation to generate a plurality of 2D complex-valued Fourier spectrums;
- and
- mapping each of the 2D complex-valued Fourier spectrums onto an Ewald space to form a plurality of NA-matching sub-spectrums.
The analytic Fourier ptychotomography imaging method of claim, further comprising determining the FST prior based on thickness of the sample being imaged.
The analytic Fourier ptychotomography imaging method of claim, wherein solving for system aberration using the finite sample thickness (FST) prior comprises:
- determining the FST prior based on thickness of the sample being imaged;
- pairing the plurality of NA-matching sub-spectrums to from a plurality of sub-spectrum pairs;
- using the FST prior to extend an overlap region between each of the sub-spectrum pairs;
- using positions of the extended overlap regions to form a position matrix;
- subtracting phase of each of the sub-spectrum pairs within the extended overlap regions to generate a plurality of phase difference vectors;
- using the position matrix and phase difference vectors to form a set of linear equations;
- and
- solving for system aberration from the set of linear equations using least square solution.
The analytic Fourier ptychotomography imaging method of claim, wherein extending the aberration-corrected NA-matching spectrum comprises:
- for each darkfield illumination angle, extracting a known component of the aberration-corrected NA-matching sample spectrum;
- constructing a cross-correlation operator from the known components;
- using the cross-correlation operator to form a set of linear equations based on the known components;
- solving for unknown components with the set of linear equations using least squares relation to generate a plurality of darkfield sub-spectrums using least square solution;
- and
- ptychographically synthesizing darkfield sub-spectrums with NA-matching sub-spectrums to generate a darkfield-extended sample spectrum.
The analytic Fourier ptychotomography imaging method of claim, wherein reconstructing the volumetric refractive index distribution comprises:
- applying inverse Fourier transform to the darkfield extended spectrum;
- and
- applying linear transform to reconstruct the volumetric refractive index distribution.
The analytic Fourier ptychotomography imaging method of claim, wherein obtaining the plurality of NA-matching intensity measurements and the plurality of darkfield intensity measurements comprises causing an illumination source to deliver to the sample NA-matching illumination at the plurality of NA-matching illumination angles and darkfield illumination at the plurality of darkfield illumination angles.
An analytic Fourier ptychotomography imaging system, comprising:
- an illumination system configured to provide NA-matching illumination at a plurality of NA-matching illumination angles and darkfield illumination at a plurality of darkfield illumination angles to a sample being imaged;
- an optical system comprising collection optics configured to collect light scattered by a sample being illuminated, wherein the NA-matching illumination angles are equal to, or nearly equal to, an acceptance angle of the collection optics and the darkfield illumination angles are greater than the acceptance angle of the collection optics;
- one or more light detectors in optical communication with the optical system, the one or more light detectors configured to acquire (i) a plurality of NA-matching intensity measurements corresponding to the NA-matching illumination angles and (i) a plurality of darkfield measurements corresponding to the darkfield illumination angles;
- and
- a computing device configured to reconstruct a volumetric refractive index distribution based at least in part on the plurality of NA-matching intensity measurements and the plurality of darkfield measurements.
The analytic Fourier ptychotomography imaging system of claim, wherein the computing device is configured to reconstruct the volumetric refractive index distribution by:
- obtaining a plurality of NA-matching intensity measurements corresponding to plurality of NA-matching illumination angles and a plurality of darkfield intensity measurements corresponding to a plurality of darkfield illumination angles;
- determining an aberration-corrected NA-matching spectrum based at least in part on the plurality of NA-matching intensity measurements and a finite sample thickness (FST) prior;
- extending the aberration-corrected NA-matching spectrum using the plurality of darkfield intensity measurements;
- and
- reconstructing the volumetric refractive index distribution based at least in part on the extended aberration-corrected NA-matching spectrum.
The analytic Fourier ptychotomography imaging system of claim, wherein the computing device is configured to determine the aberration-corrected NA-matching spectrum by:
- recovering a plurality of NA-matching sub-spectrums from NA-matching intensity measurements using Kramers-Kronig (K-K) relation;
- solving for system aberration using a finite sample thickness (FST) prior;
- removing the system aberration from each of the NA-matching sub-spectrums to form a plurality of aberration-corrected NA-matching sub-spectrums;
- and
- stitching together the plurality of aberration-corrected NA-matching sub-spectrums to form an aberration-corrected NA-matching sample spectrum.
The analytic Fourier ptychotomography imaging system of claim, wherein the illumination system comprises one or more light emitting diodes (LEDs).
The analytic Fourier ptychotomography imaging system of claim, wherein the illumination system comprises a circular or rectangular array of light emitting diodes (LEDs).
The analytic Fourier ptychotomography imaging system of claim, wherein the illumination system comprises a circular array of light emitting diodes (LEDs), the circular array comprising a ring of NA matching illumination sources configured to provide illumination at the plurality of NA-matching illumination angles.
The analytic Fourier ptychotomography imaging system of claim, wherein the illumination system comprises at least one laser source and a rotational mechanism configured rotate a laser beam from at least one laser source such that the laser beam is provided sequentially at the plurality of NA-matching illumination angles and the plurality of darkfield illumination angles.
The analytic Fourier ptychotomography imaging system of claim, wherein the rotational mechanism is a galvo mirror.
The analytic Fourier ptychotomography imaging system of claim, wherein the illumination system comprises:
- a rotational mechanism;
- and
- an illumination source mounted to the rotational mechanism.
A non-transitory machine-readable medium comprising instructions that, when executed by one or more processors, are configured to cause the one or more processors to perform operations comprising:
- obtaining a plurality of NA-matching intensity measurements corresponding to plurality of NA-matching illumination angles and a plurality of darkfield intensity measurements corresponding to a plurality of darkfield illumination angles;
- determining an aberration-corrected NA-matching spectrum based at least in part on the plurality of NA-matching intensity measurements and a finite sample thickness (FST) prior;
- extending the aberration-corrected NA-matching spectrum using the plurality of darkfield intensity measurements;
- and
- reconstructing a volumetric refractive index distribution based at least in part on the extended aberration-corrected NA-matching spectrum.
The non-transitory machine-readable medium of claim, wherein determining the aberration-corrected NA-matching spectrum comprises:
- recovering a plurality of NA-matching sub-spectrums from NA-matching intensity measurements using Kramers-Kronig (K-K) relation;
- solving for system aberration using a finite sample thickness (FST) prior;
- removing the system aberration from each of the NA-matching sub-spectrums to form a plurality of aberration-corrected NA-matching sub-spectrums;
- and
- stitching together the plurality of aberration-corrected NA-matching sub-spectrums to form an aberration-corrected NA-matching sample spectrum.
The non-transitory machine-readable medium of claim, further comprising determining the FST prior based on thickness of a sample being imaged.
Dependencies are inferred from the claim text.