Rotating point-spread function (PSF) design for three-dimensional imaging
An optical imaging system having an aperture comprised of a plurality of concentric annuli. The outer radius of each annulus is proportional to the square root of the number of annuli. Each annulus also having an azimuthally linearly increasing phase profile comprising for a given light wavelength. The system also includes a birefringent plate and the aperture and birefringent plate are adapted to jointly encode the full spatial and polarimetric degrees of freedom of a point source.
1. An optical imaging system comprising:
an aperture comprising a plurality of concentric annuli numbered from a first annulus at a center of the aperture to an L-th annulus at an outside edge of the aperture, each l-th annulus of the plurality of annuli for l=1,2, . . . , L comprising an outer radius proportional to the square root of l, each l-th annulus of the plurality of annuli for l=1,2, . . . , L comprising an azimuthally linearly increasing phase profile comprising l complete cycles for a given light wavelength;
a birefringent plate:
said aperture and said birefringent plate adapted to jointly encode the full spatial and polarimetric degrees of freedom of the point source.
2. The imaging system of claim 1 wherein said imaging system is a three-dimensional imaging system.
3. The imaging system of claim 1 wherein said imaging system is an object tracking system.
4. The imaging system of claim 1 wherein said imaging system is a microscope.
5. The imaging system of claim 1 wherein said birefringent plate performs a phase retardation between the parallel and perpendicular polarizations that is different from the half-wave phase retardation of amount π by an amount β.
6. An optical imaging system comprising:
an aperture comprising a circular pupil having an optical axis and a plurality of successive Fresnel zones at the entrance of said pupil;
each of said successive Fresnel zones having a spiral phase profile;
each successive spiral phase profile having a successively larger topological winding number from one zone to the next; and
a birefringent plate:
said aperture and said birefringent plate adapted to jointly encode the full spatial and polarimetric degrees of freedom of the point source.
7. The imaging system of claim 6 wherein said birefringent plate performs a relative phase retardation between the parallel and perpendicular polarizations that is different from the half-wave phase retardation of amount π by an amount β.
8. The optical imaging system of claim 6 wherein said circular pupil has a radius R that is segmented into L different contiguous annular successive Fresnel zones with the lth zone having an outer radius equal to R√{square root over (l/L)}.
9. The optical imaging system of claim 6 wherein said topological winding number of the optical phase retardation increases from one zone to the next outer zone as the azimuthal angle makes a complete rotation about said optical axis of said pupil by an index of l.
10. The optical imaging system of claim 6 wherein said lth zone has a spiral optical-phase profile of form lφ that completes l complete phase cycles as the azimuthal angle φ completes a single rotation about said optical axis of said pupil.
11. The optical imaging system of claim 6 wherein the height of each said lth zone steadily increases in height to a maximum height of αl, with α equal to λ/(r−1), λ equal to the wavelength used with the device, r equal to the index of refraction of the device, and l equal to the zone index.
12. The optical imaging system of claim 6 wherein said circular pupil has a radius R that is segmented into L different contiguous annular successive Fresnel zones with the lth zone having an outer radius equal to l and having a rotating PSF that changes with the spherical aberration.
13. A method for locating a point source and estimating its polarimetric degrees of freedom in three-dimensions with an optical system having a circular pupil aperture, the method comprising:
generating a rotating point spread function (PSF) that maintains its shape and size in the image plane of said circular pupil aperture by rotating relative to its in-focus form by an angle that is proportional to the source defocus and using said PSF to determine the three-dimensional coordinates of said point source and modifying said PSF polarimetrically.
14. The method of claim 13 wherein said PSF is modified polarimetrically by a birefringent plate.
15. The method of claim 13 wherein said PSF is modified polarimetrically by a birefringent plate that converts the spin angular momentum of a photon to its orbital angular momentum.
16. The method of claim 15 wherein said PSF is modified polarimetrically by a birefringent plate that converts the spin angular momentum of a photon to orbital angular momentum in a single snapshot over a 3D field.
17. The method of claim 15 wherein said PSF is modified polarimetrically by a birefringent plate that converts the spin angular momentum of a photon to orbital angular momenta in a plurality of snapshots.
18. The method of claim 13 wherein said PSF continuously rotates with a changing defocus.
19. The method of claim 16 wherein said PSF maintains its shape and size while rotating uniformly with changing defocus over a narrow plurality of light wavelengths at said circular pupil aperture.
20. The method of claim 13 wherein said circular pupil aperture is divided into L Fresnel zones, with the lth zone having an outer radius proportional to √{square root over (l)} and having a spiral phase profile of form lφ on a light wavelength, where φ is the azimuthal angle coordinate measured from a fixed x axis in the plane of said pupil.