Fast feature identification for holographic tracking and characterization of colloidal particles
A method and system for identification of holographic tracking and identification of features of an object. A holograph is created from scattering off the object, intensity gradients are established for a plurality of pixels in the holograms, the direction of the intensity gradient is determined and those directions analyzed to identify features of the object and enables tracking of the object. Machine learning devices can be trained to estimate particle properties from holographic information.
1. A method of feature identification in holographic tracking and identification for features of a spherical object, comprising the steps of:
inputting a collimated laser beam;
scattering the collimated laser beam from the object to generate a scattered beam;
recording a hologram characteristic of the interference between the scattering beam and the input beam;
determining, using an orientational alignment transform, from the recorded hologram an estimate of a two-dimensional position of the spherical object; and
determining, using the two-dimensional position of the spherical object and a machine learning algorithm an estimate of an axial position of the object and a size of the spherical object and a refractive index of the spherical object.
2. The method of claim 1 , wherein determining, using the orientational alignment transform, from the recorded hologram an estimate of a two-dimensional position of the spherical object further comprises:
establishing intensity gradients for pixels in the hologram;
determining direction for the intensity gradients for each of the pixels; and
analyzing the direction of the intensity gradients to identify centers of rotational symmetry.
3. The method of claim 2 , further comprising transforming each of the center of rotational symmetry into a centers of brightness.
4. The method of claim 2 , wherein determining the object's position in a plane of the hologram comprises coalescing ring-like features into centers of brightness with a circular Hough transform and then locating the centers of brightness.
5. The method of claim 1 , wherein further comprising:
applying Lorenz-Mie solution to the recorded scattering; and
determining the estimate of the axial position as well as object size and refractive index from the application of the Lorenz-Mie solution to the recorded scattering.
6. The method of claim 5 , wherein the determination of the axial position, object size and refractive index is obtained with a machine learning algorithm, and wherein determining the estimate comprises comparing the hologram to a set of learned models in the machine learning algorithm.
7. The method in claim 6 , wherein the machine learning algorithm consists of a support vector machine.
8. The method of claim 7 , wherein the machine learning device is a neural network and determining the estimate comprises comparing the hologram to a set of learned models in the neural network.
9. A method of feature identification in holographic tracking and identification for features of an object, comprising the steps of:
inputting a collimated laser beam;
scattering the collimated laser beam from the object to generate a scattered beam;
recording a hologram characteristic of the scattering beam;
establishing intensity gradients with an orientational alignment transform for a plurality of pixels in the hologram;
determining direction for the intensity gradients for each of the pixels; and
analyzing the direction of the intensity gradients to identify features of the object.
10. The method as defined in claim 9 wherein the direction of the intensity gradients is associated with a direction analysis,
ϕ
(
r
)
=
tan
-
1
(
∂
y
b
(
r
)
∂
x
b
(
r
)
)
where r is a radial distance from a center of the object's hologram, b(r) is a gradient image, {circumflex over (x)} is one image axis and ŷ is another image axis perpendicular to {circumflex over (x)}.
11. The method as defined in claim 10 wherein the direction of the intensity gradients derived from ϕ(r) is determined by applying the step of performing a voting analysis.
12. The method as defined in claim 11 wherein the voting analysis comprises the step of establishing votes for each of the pixels along a preferred direction with votes tallied.
13. The method as defined in claim 12 wherein the votes tallied are evaluated to determine most votes, thereby establishing candidates for a center position of the object.
14. The method as defined in claim 12 wherein the votes tallied for each of the pixels are calculated directly as a solution of a set of simultaneous equations.
15. The method as defined in claim 12 further including the step of identifying the pixels having background intensity contributions, thereby removing those pixels from the voting analysis.
16. The method as defined in claim 11 wherein the ϕ(r) is determined by the step of applying a continuous transform of local orientation field.
17. The method as defined in claim 16 wherein the continuous transform of the local orientation field includes determining a gradient image using a two-fold orientation order parameter,
Ψ( r )=|∇ b ( r )| 2 e 2iϕ(r) ,
wherein the factor of 2 multiplying ϕ(r) accounts for the bidirectionality of orientation information obtained from the intensity gradients.