Lensfree method for imaging biological samples in three dimensions

1. A method for three-dimensional imaging of a sample, said method comprising:

receiving a plurality of interference patterns acquired using light-detecting elements for detecting incident light, wherein each interference pattern is formed by scattered light scattered from the sample in three dimensions and non-scattered light from a light source, wherein the interference patterns are acquired using different angles between the sample and the light source, wherein the plurality of interference patterns includes at least four interference patterns;

determining a scattering potential of the sample measured in each of three dimensions based on the received interference patterns;

applying an iterative algorithm to change the three-dimensional scattering potential of the sample by calculating a data fidelity term representing a difference between the received interference patterns represented by a measured amplitude of an optical field forming the interference patterns and predicted interference patterns based on the determined three-dimensional scattering potential formed by a light propagation model that maps the three-dimensional scattering potential of the sample to a scattered optical field in a sensor plane of the light-detecting elements and an incident optical field from the light source which is superposed with the scattered optical field to form the predicted interference patterns, wherein the iterative algorithm reduces a sum of the data fidelity term and a non-differentiable regularization term and wherein the iterative algorithm includes a forward-backward splitting method alternating between forward gradient descent on the data fidelity term and backward gradient descent on the regularization term;

performing digital holographic reconstruction on the received interference patterns based on the applying; and

reconstructing a three-dimensional image representation of the sample based on the digital holographic reconstruction.

2. The method according to claim 1 , wherein the iterative algorithm includes a primal-dual splitting method for reducing the regularization term.

3. The method according to claim 1 , wherein the forward-backward splitting method comprises a fast iterative shrinkage-thresholding algorithm, FISTA.

4. The method according to claim 1 , wherein the forward gradient descent on the data fidelity term comprises solving a phase retrieval problem using Wirtinger derivatives.

5. The method according to claim 1 , wherein the plurality of interference patterns comprises four to ten interference patterns.

6. The method according to claim 1 , wherein the regularization terms are set for reducing artifacts and shape distortion in the holographic reconstruction caused by a limited number of illumination angles and lack of phase information of a diffracted optical field.

7. The method according to claim 6 , wherein the regularization term comprises at least one of a L1 norm, a L2 norm, total variation or bound constraint.

8. The method according to claim 1 , wherein the iterative algorithm is applied until a stopping criterion is met.

9. The method according to claim 1 , wherein the sample is a three-dimensional organoid.

10. A computer program product comprising computer-readable instructions such that when executed on a processing unit the computer-readable instructions will cause the processing unit to perform the method according to claim 1 .

11. A device for three-dimensional imaging of a sample, said device comprising:

at least one light source configured to illuminate a sample from a plurality of different angles;

at least one image sensor, each comprising an array of light-detecting elements for detecting incident light, wherein the at least one image sensor is configured to acquire a plurality of interference patterns, wherein each interference pattern is formed by scattered light scattered from the sample in three dimensions and non-scattered light from the light source and each interference pattern is acquired for a different angle between the sample and the light source, wherein the plurality of interference patterns includes at least four interference patterns;

a processing unit configured to determine a scattering potential of the sample measured in each of three dimensions based on the received interference patterns and apply an iterative algorithm to change the three-dimensional scattering potential of the sample by calculating a data fidelity term representing a difference between the acquired interference patterns represented by a measured amplitude of an optical field forming the interference patterns and predicted interference patterns based on the determined three-dimensional scattering potential formed by a light propagation model that maps the three-dimensional scattering potential of the sample to a scattered optical field in a sensor plane of the light-detecting elements and an incident optical field from the light source which is superposed with the scattered optical field to form the predicted interference patterns, wherein the iterative algorithm reduces a sum of the data fidelity term and a non-differentiable regularization term and wherein the iterative algorithm includes a forward-backward splitting method alternating between forward gradient descent on the data fidelity term and backward gradient descent on the regularization term;

a processing unit configured to perform digital holographic reconstruction on the acquired interference patterns based on the application of the iterative algorithm; and

a reconstructing unit configured to reconstruct a three-dimensional image representation of the sample based on the digital holographic reconstruction.

12. The device according to claim 11 , wherein the device comprises a plurality of fixed light sources for illuminating the sample from the plurality of different angles.

13. The device according to claim 11 , wherein the device comprises a movable light source, which is movable between a plurality of positions for illuminating the sample from the plurality of different angles.

14. The device according to claim 11 , wherein the device comprises a single image sensor for acquiring the plurality of interference patterns.

15. A method for three-dimensional imaging of a sample, said method comprising:

receiving a plurality of interference patterns acquired using light-detecting elements for detecting incident light, wherein each interference pattern is formed by scattered light scattered from the sample in three dimensions and non-scattered light from a light source interfering at the light-detecting elements for acquisition by the light-detecting elements, and wherein the interference patterns are acquired using different angles between the sample and the light source, wherein the plurality of interference patterns includes at least four interference patterns;

determining a scattering potential of the sample measured in each of three dimensions based on the received interference patterns;

applying an iterative algorithm to change the three-dimensional scattering potential of the sample by calculating a data fidelity term representing a difference between the received interference patterns represented by a measured amplitude of an optical field forming the interference patterns and predicted interference patterns based on the determined three-dimensional scattering potential formed by a light propagation model that maps the three-dimensional scattering potential of the sample to a scattered optical field in a sensor plane of the light-detecting elements and an incident optical field from the light source which is superposed with the scattered optical field to form the predicted interference patterns, wherein the iterative algorithm reduces a sum of the data fidelity term and a non-differentiable regularization term and wherein the iterative algorithm includes a forward-backward splitting method alternating between forward gradient descent on the data fidelity term and backward gradient descent on the regularization term; and

performing digital holographic reconstruction on the received interference patterns based on applying the iterative algorithm.

16. A device for three-dimensional imaging of a sample, said device comprising:

at least one light source configured to illuminate a sample from a plurality of different angles;

at least one image sensor, each comprising an array of light-detecting elements for detecting incident light, wherein the at least one image sensor is configured to acquire a plurality of interference patterns formed at the at least one image sensor, wherein each interference pattern is formed by scattered light scattered from the sample in three dimensions and non-scattered light from a light source interfering at the light-detecting elements for acquisition by the at least one image sensor, wherein the plurality of interference patterns includes at least four interference patterns; and

a processing unit configured to determine a scattering potential of the sample measured in at least three dimensions based on the received interference patterns and apply an iterative algorithm to change the three-dimensional scattering potential of the sample by calculating a data fidelity term representing a difference between the acquired interference patterns represented by a measured amplitude of an optical field forming the interference patterns and predicted interference patterns based on the determined three-dimensional scattering potential formed by a light propagation model that maps the three-dimensional scattering potential of the sample to a scattered optical field in a sensor plane of the light-detecting elements and an incident optical field from the light source which is superposed with the scattered optical field to form the predicted interference patterns, wherein the iterative algorithm reduces a sum of the data fidelity term and a non-differentiable regularization term and wherein the iterative algorithm includes a forward-backward splitting method alternating between forward gradient descent on the data fidelity term and backward gradient descent on the regularization term; and

a processing unit configured to perform digital holographic reconstruction on the acquired interference patterns based on the application of the iterative algorithm.