## Super-resolution photon-efficient imaging by nanometric double-helix point spread function localization of emitters (SPINDLE) |

Optics Express, Vol. 20, Issue 24, pp. 26681-26695 (2012)

http://dx.doi.org/10.1364/OE.20.026681

Acrobat PDF (2153 KB)

### Abstract

Super-resolution imaging with photo-activatable or photo-switchable probes is a promising tool in biological applications to reveal previously unresolved intra-cellular details with visible light. This field benefits from developments in the areas of molecular probes, optical systems, and computational post-processing of the data. The joint design of optics and reconstruction processes using double-helix point spread functions (DH-PSF) provides high resolution three-dimensional (3D) imaging over a long depth-of-field. We demonstrate for the first time a method integrating a Fisher information efficient DH-PSF design, a surface relief optical phase mask, and an optimal 3D localization estimator. 3D super-resolution imaging using photo-switchable dyes reveals the 3D microtubule network in mammalian cells with localization precision approaching the information theoretical limit over a depth of 1.2 µm.

© 2012 OSA

## 1. Introduction

1. E. Abbe, “Contributions to the theory of the microscope and microscopic observations (translated from German),” Archiv für Mikroskopische Anatomie **9**, 413–468 (1873). [CrossRef]

2. L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science **320**(5881), 1332–1336 (2008). [CrossRef] [PubMed]

3. R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods **5**(6), 539–544 (2008). [CrossRef] [PubMed]

4. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science **313**(5793), 1642–1645 (2006). [CrossRef] [PubMed]

5. S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. **91**(11), 4258–4272 (2006). [CrossRef] [PubMed]

6. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods **3**(10), 793–796 (2006). [CrossRef] [PubMed]

7. M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl. **47**(33), 6172–6176 (2008). [CrossRef] [PubMed]

8. J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods **5**(11), 943–945 (2008). [CrossRef] [PubMed]

9. B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science **319**(5864), 810–813 (2008). [CrossRef] [PubMed]

10. M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods **5**(6), 527–529 (2008). [CrossRef] [PubMed]

11. G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. **106**(9), 3125–3130 (2009). [CrossRef] [PubMed]

12. S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. **106**(9), 2995–2999 (2009). [CrossRef] [PubMed]

13. J. Tang, J. Akerboom, A. Vaziri, L. L. Looger, and C. V. Shank, “Near-isotropic 3D optical nanoscopy with photon-limited chromophores,” Proc. Natl. Acad. Sci. U.S.A. **107**(22), 10068–10073 (2010). [CrossRef] [PubMed]

14. D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Research **4**(6), 589–598 (2011). [CrossRef]

15. D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods **8**(4), 353–359 (2011). [CrossRef] [PubMed]

9. B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science **319**(5864), 810–813 (2008). [CrossRef] [PubMed]

10. M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods **5**(6), 527–529 (2008). [CrossRef] [PubMed]

12. S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. **106**(9), 2995–2999 (2009). [CrossRef] [PubMed]

16. S. A. Jones, S.-H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods **8**(6), 499–505 (2011). [CrossRef] [PubMed]

17. F. Cella Zanacchi, Z. Lavagnino, M. Perrone Donnorso, A. Del Bue, L. Furia, M. Faretta, and A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods **8**(12), 1047–1049 (2011). [CrossRef] [PubMed]

18. G. Grover, S. R. P. Pavani, and R. Piestun, “Performance limits on three-dimensional particle localization in photon-limited microscopy,” Opt. Lett. **35**(19), 3306–3308 (2010). [CrossRef] [PubMed]

18. G. Grover, S. R. P. Pavani, and R. Piestun, “Performance limits on three-dimensional particle localization in photon-limited microscopy,” Opt. Lett. **35**(19), 3306–3308 (2010). [CrossRef] [PubMed]

19. R. Piestun and J. Shamir, “Synthesis of three-dimensional light fields and applications,” Proc. IEEE **90**(2), 222–244 (2002). [CrossRef]

30. G. Grover, S. Quirin, C. Fiedler, and R. Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express **2**(11), 3010–3020 (2011). [CrossRef] [PubMed]

20. S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. **109**(3), 675–679 (2012). [CrossRef] [PubMed]

12. S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. **106**(9), 2995–2999 (2009). [CrossRef] [PubMed]

_{x}, σ

_{y}, σ

_{z}) = (2.5, 3.8, 16.5) nm with 6000 collected photons and (σ

_{x}, σ

_{y}, σ

_{z}) = (22, 29, 52) nm with 1100 photons. We further show that these numbers are very close to the theoretical precision limits.

## 2. An information optimized DH-PSF design

21. S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express **16**(5), 3484–3489 (2008). [CrossRef] [PubMed]

22. S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express **16**(26), 22048–22057 (2008). [CrossRef] [PubMed]

22. S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express **16**(26), 22048–22057 (2008). [CrossRef] [PubMed]

24. M. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. **107**(42), 17864–17871 (2010). [CrossRef] [PubMed]

**106**(9), 2995–2999 (2009). [CrossRef] [PubMed]

25. A. Greengard, Y. Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. **31**(2), 181–183 (2006). [CrossRef] [PubMed]

26. D. B. Conkey, R. P. Trivedi, S. R. P. Pavani, I. I. Smalyukh, and R. Piestun, “Three-dimensional parallel particle manipulation and tracking by integrating holographic optical tweezers and engineered point spread functions,” Opt. Express **19**(5), 3835–3842 (2011). [CrossRef] [PubMed]

18. G. Grover, S. R. P. Pavani, and R. Piestun, “Performance limits on three-dimensional particle localization in photon-limited microscopy,” Opt. Lett. **35**(19), 3306–3308 (2010). [CrossRef] [PubMed]

**35**(19), 3306–3308 (2010). [CrossRef] [PubMed]

21. S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express **16**(5), 3484–3489 (2008). [CrossRef] [PubMed]

_{3D}for a range exceeding 1µm. The resulting DH-PSF is specifically used for SPINDLE experiments so it is henceforth referred to as DH-PSF-S. The phase mask function is shown in Fig. 1(b) and the transverse cross-sections of the corresponding PSF for different defocus positions are shown in Fig. 1(d).

_{3D}of the DH-PSF-S (labeled as DH-S) with prior designs. The new DH-PSF-S not only provides the best precision for 3D localization experiments with high background but is also more confined transversely as shown in Fig. 1(d). This is advantageous for super-resolution because more particles per image can be detected. For super-resolution PALM/STORM experiments, the PSF confinement translates into faster data acquisition. Note that for experiments with backgrounds up to about 40 photons/pixel, the DH-PSF-S is best for 3D localization. Further, for different depth ranges such as 800 nm and 2 µm the behavior follows the same trend (see section 6.2). For instance, for a longer depth range of 2 µm, the crossing point is 50 photons/pixel. The loss of precision for DH-PSF in the high background regime is explained by the larger spread as compared to the astigmatic PSF, which leads to lower signal to background ratio. Note that these results are for the shot noise limited case only. For other noise sources like EMCCD gain noise, the results may vary but the general trend is preserved.

### 2.1 Analytic approach to Double-helix PSF generation

28. Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics **54**(1), R50–R53 (1996). [CrossRef] [PubMed]

29. G. Indebetouw, “Optical Vortices and Their Propagation,” J. Mod. Opt. **40**(1), 73–87 (1993). [CrossRef]

22. S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express **16**(26), 22048–22057 (2008). [CrossRef] [PubMed]

*r*,

*θ*) are the pupil plane co-ordinates,

*R*is the radius of the pupil aperture,

*M*= (

*N*-1)/2,

*N*is the number of vortices and (

*r*,

_{k}*θ*) is the location of the

_{k}*k*th vortex. For DH-PSF-S, we used the CRB

_{3D}metric and found the optimal number of vortices

*N*to be 9 with the distance between successive vortices a constant

*d*= 0.66

*R*(Fig. 1(b)). The phase mask has only three vortices located within the aperture while the other six are located outside but still have a significant effect on the phase in the aperture.

29. G. Indebetouw, “Optical Vortices and Their Propagation,” J. Mod. Opt. **40**(1), 73–87 (1993). [CrossRef]

*r*,

_{k}*θ*) and their number

_{k}*N*is constant along the axial direction of the PSF.

*N*, the number of vortex singularities, on the in-focus PSF. As

*N*grows the diffracted energy is more confined in the two lobes of the PSF. On the other hand, Fig. 2(b) shows the effect of increasing the distance

*d*among the vortex singularities. As

*d*increases the two lobes of the PSF become closer, a direct result of the Fourier transform properties of wave propagation.

29. G. Indebetouw, “Optical Vortices and Their Propagation,” J. Mod. Opt. **40**(1), 73–87 (1993). [CrossRef]

*N*and

*d/R*. Therefore, varying the number and spacing of singularities provides two significant degrees of freedom that enable flexibility in the design of the DH-PSF. Moreover, if desired, a nonperiodic array of vortices provides additional design freedom. The new flexibility in DH-PSF design makes these microscope systems well suited for a variety of biological applications.

## 3. SPINDLE imaging - experimental details

^{2}and activation power density of < 2 W/cm

^{2}was used. A polychroic mirror from Semrock (Di01-R405/488/561/635) was used to separate excitation and emission light. The emission was further filtered by two stacked dual-band filters (Semrock DBP FF01-538/685-25 and Omega XF3470 540-700DBEM, Brattleboro, VT, USA). The dual-band filters allow detection of emission of reporter dye Alexa-647 and the activator dye Alexa-488.

*x*-

*y*-

*z*translation stage. The DH mask was mounted on a magnetic kinematic mount to easily convert between a conventional and a DH-PSF microscope. The DH mask has a diameter of 2.7 mm and acts as the limiting aperture therefore reducing the effective NA of the system to 1.35. The mask was fabricated by the gray-scale lithography process described in Ref [30

30. G. Grover, S. Quirin, C. Fiedler, and R. Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express **2**(11), 3010–3020 (2011). [CrossRef] [PubMed]

20. S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. **109**(3), 675–679 (2012). [CrossRef] [PubMed]

*x*-

*z*and

*y*-

*z*plots for the recovered 3D PSF are shown in Fig. 4(b). These complex fields in each transverse plane are then used by the maximum likelihood position estimation algorithm.

31. S. Wolter, M. Schüttpelz, M. Tscherepanow, S. VAN DE Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. **237**(1), 12–22 (2010). [CrossRef] [PubMed]

20. S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. **109**(3), 675–679 (2012). [CrossRef] [PubMed]

*x*,

*y*and

*z*position [20

**109**(3), 675–679 (2012). [CrossRef] [PubMed]

9. B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science **319**(5864), 810–813 (2008). [CrossRef] [PubMed]

_{x}, σ

_{y}, σ

_{z}) = (21,20,51) nm and for 6000 photons the precision is (σ

_{x}, σ

_{y}, σ

_{z}) = (8,9,18).

## 4. 3D super-resolution imaging of microtubules with SPINDLE

*z*dimension. The SPINDLE mask and experimental setup allow imaging over a depth of 1.2 µm.

*z*) direction, as shown in Figs. 5(e) and 5(f). Third, the SPINDLE image has a longer depth of field as illustrated by comparison of the upper left corners of Figs. 5(a) and 5(b).

34. M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science **317**(5845), 1749–1753 (2007). [CrossRef] [PubMed]

**319**(5864), 810–813 (2008). [CrossRef] [PubMed]

**319**(5864), 810–813 (2008). [CrossRef] [PubMed]

11. G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. **106**(9), 3125–3130 (2009). [CrossRef] [PubMed]

## 5. Conclusions

30. G. Grover, S. Quirin, C. Fiedler, and R. Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express **2**(11), 3010–3020 (2011). [CrossRef] [PubMed]

**109**(3), 675–679 (2012). [CrossRef] [PubMed]

**35**(19), 3306–3308 (2010). [CrossRef] [PubMed]

34. M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science **317**(5845), 1749–1753 (2007). [CrossRef] [PubMed]

## 6. Appendix

### 6.1 PSF calculation

*u*,

*v*) are normalized pupil plane co-ordinates and

*H*(

*u*,

*v*) is the pupil function,

*NA*is the numerical aperture of the objective,

*n*is the refractive index of the oil and

_{oil}*dz*is the defocus distance and

_{ℑ}is the 2D Fourier transform operator.

### 6.2 CRB comparison of different PSFs

*x*,

*y*and

*z*directions with varying axial position of the emitter. CRB

_{3D}is the average of CRB for

*x*,

*y*and

*z*. It is seen that the CRB for transverse dimensions are relatively flat as compared to the axial CRB. It is important to achieve a flat and uniform CRB

_{z}over the entire depth but we have observed that some loss of flatness is required to achieve a lower CRB by concentrating more energy in the two lobes [18

**35**(19), 3306–3308 (2010). [CrossRef] [PubMed]

19. R. Piestun and J. Shamir, “Synthesis of three-dimensional light fields and applications,” Proc. IEEE **90**(2), 222–244 (2002). [CrossRef]

_{z}while still achieving a low CRB

_{3D}.

### 6.3 Labeling of PtK1 cells with photoswitching probes

34. M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science **317**(5845), 1749–1753 (2007). [CrossRef] [PubMed]

### 6.4 Fiduciary beads on cell slides

### 6.5 Calibration beads

### 6.6 Camera calibration

*m*between photons and camera counts was determined. The obtained count value for each pixel is divided by

*m*to determine the number of photons. This was done by two methods which gave the same value for

*m*. The experimental setup for both methods was the same which was to put a diffused light source in front of the objective to capture a uniform illumination on the camera. The light source is then turned off and camera shutter closed to capture dark/offset value with EM gain on and EM gain off.

37. M. Newberry, “CCD camera gain measurement,” http://www.mirametrics.com/tech_note_ccdgain.htm.

_{EMon}-Dark

_{EMon})/(Signal

_{EMoff}-Dark

_{EMoff}) then gives the EM gain value. So the conversion value from counts to photons was

*m*= 300/10.69 = 28 counts/photons.

38. M. H. Ulbrich and E. Y. Isacoff, “Subunit counting in membrane-bound proteins,” Nat. Methods **4**(4), 319–321 (2007). [PubMed]

39. K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods **7**(5), 377–381 (2010). [CrossRef] [PubMed]

*c*is given bywhere

*p*is the number of photons hitting the pixel,

*m*is the camera conversion factor (counts/photons) and

*BesselI*is the first order modified Bessel function of first kind. Uniform illumination images were acquired and offset corrected to plot the distribution of pixel values as shown in Fig. 8 . By fitting the histogram with the probability distribution functions in Eq. (3), value of conversion factor

_{1}*m*was obtained to be 27.4 counts/photons. The value of

*m*is approximately the same for a camera with given settings independent of the illumination.

### 6.7 Precision analysis and experimental CRB calculation

*x*,

*y*and

*z*positions with varying number of photons was done by assuming the probability distribution function in Eq. (2) and experimentally determined value of

*m*. The σ values in Fig. 6 are √Avg(CRB) for 1.2 µm range around focus. The CRB calculation was done by method explained in Ref [40

40. S. R. P. Pavani, A. Greengard, and R. Piestun, “Three-dimensional localization with nanometer accuracy using a detector-limited double-helix point spread function system,” Appl. Phys. Lett. **95**(2), 021103 (2009). [CrossRef]

**109**(3), 675–679 (2012). [CrossRef] [PubMed]

## Acknowledgments

## References and Links

1. | E. Abbe, “Contributions to the theory of the microscope and microscopic observations (translated from German),” Archiv für Mikroskopische Anatomie |

2. | L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science |

3. | R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods |

4. | E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science |

5. | S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. |

6. | M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods |

7. | M. Heilemann, S. van de Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. Engl. |

8. | J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods |

9. | B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science |

10. | M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods |

11. | G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. |

12. | S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. |

13. | J. Tang, J. Akerboom, A. Vaziri, L. L. Looger, and C. V. Shank, “Near-isotropic 3D optical nanoscopy with photon-limited chromophores,” Proc. Natl. Acad. Sci. U.S.A. |

14. | D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Research |

15. | D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods |

16. | S. A. Jones, S.-H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods |

17. | F. Cella Zanacchi, Z. Lavagnino, M. Perrone Donnorso, A. Del Bue, L. Furia, M. Faretta, and A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods |

18. | G. Grover, S. R. P. Pavani, and R. Piestun, “Performance limits on three-dimensional particle localization in photon-limited microscopy,” Opt. Lett. |

19. | R. Piestun and J. Shamir, “Synthesis of three-dimensional light fields and applications,” Proc. IEEE |

20. | S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. |

21. | S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express |

22. | S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express |

23. | M. A. Thompson, M. D. Lew, M. Badieirostami, and W. E. Moerner, “Localizing and tracking single nanoscale emitters in three dimensions with high spatiotemporal resolution using a double-helix point spread function,” Nano Lett. |

24. | M. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. |

25. | A. Greengard, Y. Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. |

26. | D. B. Conkey, R. P. Trivedi, S. R. P. Pavani, I. I. Smalyukh, and R. Piestun, “Three-dimensional parallel particle manipulation and tracking by integrating holographic optical tweezers and engineered point spread functions,” Opt. Express |

27. | S. Ram, J. Chao, P. Prabhat, E. S. Ward, and R. J. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 64430D, 64430D-7 (2007). [CrossRef] |

28. | Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics |

29. | G. Indebetouw, “Optical Vortices and Their Propagation,” J. Mod. Opt. |

30. | G. Grover, S. Quirin, C. Fiedler, and R. Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express |

31. | S. Wolter, M. Schüttpelz, M. Tscherepanow, S. VAN DE Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. |

32. | A. Neubeck and L. Van Gool, “Efficient non-maximum suppression,” in |

33. | A. Egner and S. W. Hell, “Aberrations in Confocal and Multi-Photon Fluorescence Microscopy Induced by Refractive Index Mismatch,” in |

34. | M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science |

35. | J. F. Kenney and E. S. Keeping, “The distribution of the standard deviation,” in |

36. | L. Novotny and B. Hecht, “Chapter 4,” in |

37. | M. Newberry, “CCD camera gain measurement,” http://www.mirametrics.com/tech_note_ccdgain.htm. |

38. | M. H. Ulbrich and E. Y. Isacoff, “Subunit counting in membrane-bound proteins,” Nat. Methods |

39. | K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods |

40. | S. R. P. Pavani, A. Greengard, and R. Piestun, “Three-dimensional localization with nanometer accuracy using a detector-limited double-helix point spread function system,” Appl. Phys. Lett. |

**OCIS Codes**

(110.4850) Imaging systems : Optical transfer functions

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(180.2520) Microscopy : Fluorescence microscopy

(180.6900) Microscopy : Three-dimensional microscopy

(110.1758) Imaging systems : Computational imaging

(050.4865) Diffraction and gratings : Optical vortices

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: August 6, 2012

Revised Manuscript: October 16, 2012

Manuscript Accepted: November 5, 2012

Published: November 12, 2012

**Virtual Issues**

Vol. 7, Iss. 12 *Virtual Journal for Biomedical Optics*

**Citation**

Ginni Grover, Keith DeLuca, Sean Quirin, Jennifer DeLuca, and Rafael Piestun, "Super-resolution photon-efficient imaging by nanometric double-helix point spread function localization of emitters (SPINDLE)," Opt. Express **20**, 26681-26695 (2012)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-24-26681

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