3 D superresolution imaging with a doublehelix microscope

3 D super-resolution imaging with a double-helix microscope Sri Rama Prasanna Pavani and Rafael Piestun Dept. of Electrical and Computer Engineering, Univ. of Colorado at Boulder M. A. Thompson, J. S. Biteen, and W. E. Moerner Dept. of Chemistry, Stanford University Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 1 4/27/2009

Why super-resolution imaging? Super-resolution: Resolving beyond the diffraction limit n Optical diffraction limit q q q Not all spatial frequencies participate in the far-field image formation Rayleigh limit: ~200 nm in visible wavelengths Visible light is gentle on living cells, unlike electrons or X-rays Decaying evanescent waves Blocked spatial frequencies Super-resolution techniques q q q STED Structured-illumination PALM, STORM, F-PALM Objective Object Intracellular structure Detected Image Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 2

Super-resolution by photoactivation and precise localization (PALM, STORM, F-PALM) n Diffraction-limited spot size much larger than a fluorescent molecule n Individual molecules cannot be resolved Reactivated Bleached Z 407 nm 514 nm n Active control q q Bleach all molecules with 514 nm Reactivate with 407 nm power chosen so only few molecules reactivate Excite reactivated molecules with 514 nm PSF Position X + Traditional 2 D 2 D image Superresolution image E. Betzig, et al. , "Imaging intracellular fluorescent proteins at nanometer resolution, " Science 313, 1642 -1645 (2006). M. J. Rust, et al. , "Sub-diffraction-limit imaging by stochastic optical reconstruction microsc. (STORM), " Nat Meth 3, 793 -795 (2006). Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford S. T. Hess, et al. , "Ultra-high resolution imaging by fluores. photoactivation localization microsc. , " Biophys J 91, 4258 -4272 (2006). 3

Computational Optical Imaging Object Unconventional Optics Masks Gratings Holograms Sub-apertures Active Illumination Detector Final image (optional) Post processing n n Improves performance by capturing information lost in traditional imaging Active Illumination and unconventional optics are application dependent Detected image is intermediate! Processing required to obtain final image and measurements Examples: Super-resolution, compressive sensing, 3 D imaging, extended depth of focus Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 4

Depth from diffracted rotation f Standard PSF Lens Double-helix PSF Slices Y Mask q q q Double-helix PSF q q X Generated by a mask in Fourier plane Exhibits two main lobes that rotate with defocus Depth is estimated from rotation angle “Axial super-resolution” q q q Rate of rotation maximum in focal plane! Standard PSF: constant within the depth of field Information theoretical analysis shows improved 3 D position estimation over standard PSF Z 400 nm X A. Greengard, Y. Schechner, and R. Piestun, "Depth from diffracted rotation, " Opt. Lett. 31, 181 -183 (2006). Pavani, Piestun, Thompson, Biteen, Moerner, Optics U. Colorado Stanford (2008) S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions, ” Express and 16, 3484 -3489 Y 5

Three-dimensional position localization Double-helix PSF image n Object: Discrete points in a volume n Phase mask in Fourier plane n Axial position estimated from PSF’s rotation angle n Transverse position is the midpoint of PSF lobes 3 D position localization of multiple object points with a single image! Standard PSF image S. R. P. Pavani et al, “ 3 D tracking of fluores. Micropart. using a phot. -lim. double-helix resp. system, " Opt. Express 16, 22048 (2008). Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 6

Information theoretical analysis Double-helix PSF carries more information about 3 D positions than standard PSF n Cramer-Rao bound of DH-PSF is lower (on an average) and more uniform than Std. PSF q q DH-PSF fundamentally provides better estimation accuracy than standard PSF! Estimation accuracy of DH-PSF essentially constant over a long axial range. S. R. P. Pavani et al, “ 3 D tracking of fluores. Micropart. using a phot. -lim. double-helix resp. system, " Opt. Express 16, 22048 (2008). Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 7

3 D superresolution imaging Phase mask n DH-PSF+ Active control q q n Reactivated 3 D positions from each image Summation → 3 D superresolution Each 2 D image encodes the 3 D positions of multiple molecules Bleached Z 514 nm X PSF + Z X Y Superresolution 3 D image S. R. P. Pavani et al “Three-Dim. Single-Mol. Fluores. Imaging Beyond the Diff. Limit Using a DH-PSF, ” PNAS 106, 2995 (2009) Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 8

3 D super-resolution setup r to tec De f s( ) Object n Le er 1. 4 NA P riz ola Image plane Spatial Light Modulator Lens ( f ) n 1. 4 NA Inverted fluorescence microscope n Spatial light modulator implements phase mask n Cooled EMCCD detects the DH-PSF images Commercial microscope S. R. P. Pavani et al “Three-Dim. Single-Mol. Fluores. Imaging Beyond the Diff. Limit Using a DH-PSF, ” PNAS 106, 2995 (2009) Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 9

3 D localization of sparse molecules 3 D (x, y, z) molecule locations DH-PSF image Scale bar: 1μm n n Scale bar: 2μm DH-PSF offers a long axial range 3 D molecule localizations from a single image S. R. P. Pavani et al “Three-Dim. Single-Mol. Fluores. Imaging Beyond the Diff. Limit Using a DH-PSF, ” PNAS 106, 2995 (2009) Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 10

3 D superresolution imaging Scale bars: 1μm 20 nm n n Resolved two molecules separated by 14 nm (X), 26 nm (Y), and 21 nm (Z) [Euclidean dist: 36 nm] Localization precisions: Standard deviations x, y, and z are 13 nm, 14 nm, and 23 nm S. R. P. Pavani et al “Three-Dim. Single-Mol. Fluores. Imaging Beyond the Diff. Limit Using a DH-PSF, ” PNAS 106, 2995 (2009) Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 11

Fundamental limits of resolution n Standard deviations decrease with increase in photons n Fundamental limits of precision (Cramer Rao Bound) q q n Inevitability of noise 3 D PSF shape constrained by the wave equation Fundamental limits of resolution q q q Precision limit (Cramer Rao Bound) Inter-molecular fluorescence inhibition Molecule size (DCDHF-V-PF 4 -azide) molecules S. R. P. Pavani et al “Three-Dim. Single-Mol. Fluores. Imaging Beyond the Diff. Limit Using a DH-PSF, ” PNAS 106, 2995 (2009) Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 12

Conclusions n Double-helix PSF fundamentally improves the accuracy 3 D position localization n Demonstrated 3 D superresolution by using photoactivatable molecules in a DH-PSF microscope n Using a far-field optical microscope, resolved molecules as close as 14 nm (X), 26 nm (Y), and 21 nm (Z) Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 13

Acknowledgments § Piestun Group, Univ. of Colorado at Boulder § Moerner Group, Stanford University § Twieg Group, Kent State University CDMOptics Ph. D fellowship Stanford graduate fellowship National Science Foundation National Institute of General Medical Sciences Technology Transfer Office, University of Colorado Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 14

Rotating beams q q q n 5 Visualizing propagation-invariance Scaled self-imaging, rotating beams, modes Rotating beams q q q Basis set for paraxial fields Represented in GL modal plane Gauss Laguerre modal plane q q 10 Gauss Laguerre (GL) modes q q GL modal plane Superposition along a straight line Rotation rate related to slope of line Both intensity and phase rotate Maximum rotation rate in Rayleigh range 0 -10 -5 Intensity 0 m 5 10 Intensity Rotating point spread function q q q Implementation: mask encoding GL superposition Mask is extremely absorptive High-efficiency mask design using optimization R. Piestun, Y. Schechner, and J. Shamir, "Propagation-invariant wave fields with finite energy, " JOSA A 17, 294 -303 (2000). 15 Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions, ” Optics Express 16, 3484 -3489 (2008).

High-efficiency rotating PSFs n Design Method q q Iterative optimization in 3 domains n Gauss Laguerre modal plane n Fourier domain n 3 D spatial domain n Estimate 1 q Phase only transfer function q Lobes rotate with defocus q Minimal side lobes No! Yes! 2π High-efficiency phase mask q Obtained from optimization q Exhibits 7 phase singularities Generates double-helix PSF N Good ? Exact rotating PSF Desired features q 2 Initial estimate n n Constraints Optimal Exact rotating PSF Double-helix PSF 0 Phase only mask 1. 84% 57. 01% 30 times higher efficiency S. R. P. Pavani and R. Piestun, rotating point spread. U. functions, ” Optics Express 16, 3484 -3489 (2008) 16 Pavani, “High-efficiency Piestun, Thompson, Biteen, Moerner, Colorado and Stanford

Information theoretical analysis Double-helix PSF carries more information about 3 D positions than standard PSF NA = 0. 45 SNR = 30 n NA = 0. 45 SNR = 30 Cramer-Rao bound of DH-PSF is lower and more uniform than Std. PSF in three dimensions q q n NA = 0. 45 SNR = 30 DH-PSF fundamentally provides better estimation accuracy than standard PSF! Estimation accuracy of DH-PSF essentially constant over a long axial range DH-PSF estimator variance is lower than standard PSF Cramer-Rao bound. S. R. P. Pavani, et al, “ 3 D position localization with nanometer accuracy using a double-helix system, ” (submitted)17 Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford

Brightfield experimental results Standard PSF image n Standard PSF image blurs with defocus n Double-helix PSF image encodes depth in PSF’s rotation angle n 1 rotation every 35 nm n Standard deviations calculated from 100 successive estimations with 239 ms exposure 1 m 100 images 3 5 1 m 3 D positions Standard deviations 1 2 Double-helix PSF image 4 1 m X : 8 nm Y : 4 nm Z : 8 nm 3 5 2 1 Nanometer scale accuracy in 3 D! Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford S. R. P. Pavani, et al, “ 3 D position localization with nanometer accuracy using a double-helix system, ” (submitted) 4 18

Fluorescent particle tracking n Microspheres moving in water, which is trapped inside cured optical cement voids Standard PSF image Double-helix PSF image 1 2 3 4 S. R. P. Pavani et al, “ 3 D tracking of fluores. Micropart. using a phot. -lim. double-helix resp. system, " Opt. Express 16, 22048 (2008). Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 19

Velocity measurements n Three-dimensional time-varying velocities q q Microsphere 1 exhibits low velocities → bound to optical cement Microspheres 2 and 3 have relatively higher velocities S. R. P. Pavani et al, “ 3 D tracking of fluores. Micropart. using a phot. -lim. double-helix resp. system, " Opt. Express 16, 22048 (2008). Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 20

In-vivo superresolution imaging n In-vivo experiment q q Caulobacter cell 15 cycles of activation n 40 nm spatial resolution in a living cell n Periodic structures in 2 D suggest helix n 3 D superresolution imaging required to confirm helix Julie S Biteen, et al “Super-resolution imaging in live Caulobacter crescentus cells using photoswitchable EYFP, ” Nature Methods 5, 947 - 949 (2008) Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 21

Photoactivable molecule (E)-2 -(4 -(4 -Azido-2, 3, 5, 6 -tetrafluorostyryl)-3 -cyano-5, 5 -dimethylfuran-2(5 H)-ylidene)malononitrile (DCDHF-V-PF 4 -azide) Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 22

Drift correction Before drift correction Fiduciary drift After drift correction Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 23

3 D super-resolution setup Experimental DH-PSF 1. 4 NA Illumination Imaging path n 1. 4 NA Inverted fluorescence microscope n Spatial light modulator implements phase mask n Cooled EMCCD detects the DH-PSF images Pavani, Piestun, Thompson, Biteen, Moerner, U. Colorado and Stanford 24