Three-dimensional single-molecule fluorescence imaging beyond the diffraction limit using a double-helix point spread function
Embodiments of the present invention can resolve molecules beyond the optical diffraction limit in three dimensions. A double-helix point spread function can be used to in conjunction with a microscope to provide dual-lobed images of a molecule. Based on the rotation of the dual-lobed image, the axial position of the molecule can be estimated or determined. In some embodiments, the angular rotation of the dual-lobed imaged can be determined using a centroid fit calculation or by finding the midpoints of the centers of the two lobes. Regardless of the technique, the correspondence between the rotation and axial position can be utilized. A double-helix point spread function can also be used to determine the lateral positions of molecules and hence their three-dimensional location.
1. A method comprising:
illuminating with an illumination system of an imaging system a molecule within a sample near a focal plane of the imaging system;
directing light from the molecule toward an optical element comprising a double-helix point spread function;
imaging a point spread produced by the double-helix point spread function as a response to the molecule's emission;
determining, with a processor, an angular rotation of the point spread relative to a baseline rotation;
determining, with a processor, the distance between the molecule and the focal plane from the angular rotation; and
generating an output that when displayed specifies an estimated position of the molecule within the sample.
2. The method according to claim 1 wherein the double-helix point spread function is created using an iterative optimization procedure operating in more than one domain.
3. The method according to claim 2 , wherein the domains comprise the GL modal plane, the Fourier plane, and the spatial plane.
4. The method according to claim 1 further comprising determining the lateral location relative to an optical axis from the centroid of the point spread.
5. The method according to claim 1 , wherein the determining an angular rotation comprises:
finding a center of each of two lobes of the point spread function using a least-squares fit;
determining the midpoint between the two lobe centers; and
determining the angle between the two centers.
6. The method according to claim 1 , wherein the determining an angular rotation comprises determining the center of two lobes of the point spread function using one of either a centroid calculation or a Gaussian fit.
7. The method according to claim 1 , wherein the distance between the molecule and the focal plane can be determined with an accuracy of about 5-50 nm.
8. The method according to claim 1 , wherein the point spread function is a double-helix point spread function.
9. The method according to claim 1 , wherein the determining the angular rotation of the point spread determines the rotation of one or more lobes of the point spread.
10. The method according to claim 1 wherein the double-helix point spread function comprises a phase mask.
11. The method according to claim 1 further comprising fluorescent molecules.
12. A fluorescence microscope comprising:
an illumination system configured to illuminate a fluorescing molecule at an illumination wavelength;
an optical system configured to image the fluorescing molecule at an imaging wavelength, wherein the imaging wavelength is different than the illumination wavelength;
a double-helix point spread function disposed within the optical system, the double-helix point spread function configured to produce a double-helix point spread that rotates as a function of the fluorescing material's distance from a focal plane;
an imager configured to produce an image of the double helix point spread; and
a processor configured to:
determine an angular rotation of a double-helix point spread in the image,
determine a distance between the fluorescing material and an focal plane using the angular rotation; and
output the distance between the fluorescing material and the focal plane.
13. The fluorescence microscope according to claim 12 , wherein the double-helix point spread function is created using an iterative optimization procedure operating in more than one domain.
14. The fluorescence microscope according to claim 13 , wherein the three domains comprise the GL modal plane, the Fourier plane, and the spatial plane.
15. The fluorescence microscope according to claim 12 wherein the double-helix point spread function is disposed within either or both of a phase mask or a spatial light modulator.
16. The fluorescence microscope according to claim 12 further comprising a polarizer disposed between the double-helix point spread function and the imaging device.
17. A method comprising:
receiving from an imager of an optical system a dual lobe image of a molecule through a double helix point spread function disposed within the optical system;
determining a point of maximum intensity of each lobe;
determining, with a processor, the angular rotation of the lobes using the center point;
determining, with a processor, the position of the molecule from the angular rotation of the lobes; and
outputting at least one of an x-coordinate, a y-coordinate, and a z-coordinate that specifies the position of the molecule.
18. The method according to claim 17 , wherein the determining the center point of the lobes comprises finding the midpoint between the two center points.
19. The method according to claim 17 , wherein the determining the center point of the lobes comprises using a centroid fit algorithm.