Abstract

Precise positioning of nitrogen-vacancy (NV) centers is crucial for their application in sensing and quantum information. Here we present a new purely optical technique enabling determination of the NV position with nanometer resolution. We use a confocal microscope to determine the position of individual emitters along the optical axis. Using two separate detection channels, it is possible to simultaneously measure reflected light from the diamond surface and fluorescent light from the NV center and statistically evaluate both signals. An accuracy of 2.6 nm for shallow NV centers was achieved and is consistent with other techniques for depth determination.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]

2014 (2)

T. Rosskopf, A. Dussaux, K. Ohashi, M. Loretz, R. Schirhagl, H. Watanabe, S. Shikata, K. M. Itoh, and C. L. Degen, “Investigation of surface magnetic noise by shallow spins in diamond,” Phys. Rev. Lett. 112, 147602 (2014).
[Crossref] [PubMed]

L. J. Rogers, K. D. Jahnke, M. W. Doherty, A. Dietrich, L. P. McGuinness, C. Müller, T. Teraji, J. Isoya, N. B. Manson, and F. Jelezko, “Electronic structure of the negatively-charged silicon-vacancy center in diamond,” Phys. Rev. B 89, 235101 (2014).
[Crossref]

2013 (7)

J. Cai, A. Retzker, F. Jelezko, and M. B. Plenio, “A large-scale quantum simulator on a diamond surface at room temperature,” Nat. Phys. 9(3), 168–173 (2013).
[Crossref]

E. R. MacQuarrie, T. A. Gosavi, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, “Mechanical spin control of nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 111, 227602 (2013).
[Crossref] [PubMed]

T. Staudacher, F. Shi, S. Pezzagna, J. Meijer, J. Du, C. A. Meriles, F. Reinhard, and J. Wrachtrup, “Nuclear magnetic resonance spectroscopy on a (5-nanometer)3 sample volume,” Science 339(6119), 561–563 (2013).
[Crossref] [PubMed]

H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, and D. Rugar, “Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor,” Science 339(6119), 557–560 (2013).
[Crossref] [PubMed]

M. S. Grinolds, S. Hong, P. Maletinsky, L. Luan, M. D. Lukin, R. L. Walsworth, and A. Yacoby, “Nanoscale magnetic imaging of a single electron spin under ambient conditions,” Nat. Phys. 9, 215–219 (2013).
[Crossref]

L. P. McGuinness, L. T. Hall, A. Stacey, D. A. Simpson, C. D. Hill, J. H. Cole, K. Ganesan, B. C. Gibson, S. Prawer, P. Mulvaney, F. Jelezko, J. Wrachtrup, R. E. Scholten, and L. C. L. Hollenberg, “Ambient nanoscale sensing with single spins using quantum decoherence,” New J. Phys. 15, 073042 (2013).
[Crossref]

A. Ermakova, G. Pramanik, J. Cai, G. Algara-Siller, U. Kaiser, T. Weil, Y.-K. Tzeng, H.-C. Chang, L. P. McGuinness, M. B. Plenio, B. Naydenov, and F. Jelezko, “Detection of a few metallo-protein molecules using color centers in nanodiamonds,” Nano Lett. 13(7), 3305–3309 (2013).
[Crossref] [PubMed]

2012 (3)

M. A. Thompson, M. D. Lew, and W.E. Moerner, “Extending microscopic resolution with single-molecule imaging and active control,” Ann. Rev. Biophys. 41(1), 321–342 (2012).
[Crossref]

S. H. Lee, M. Baday, M. Tjioe, P. D. Simonson, R. Zhang, E. Cai, and P. R. Selvin, “Using fixed fiduciary markers for stage drift correction,” Opt. Express 20(11), 12177–12183 (2012).
[Crossref] [PubMed]

J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
[Crossref]

2011 (3)

A. Dupont and D. C. Lamb, “Nanoscale three-dimensional single particle tracking,” Nanoscale 3(11), 4532–4541 (2011).
[Crossref] [PubMed]

J. Tisler, R. Reuter, A. Lämmle, F. Jelezko, G. Balasubramanian, P. R. Hemmer, F. Reinhard, and J. Wrachtrup, “Highly efficient fret from a single nitrogen-vacancy center in nanodiamonds to a single organic molecule,” ACS Nano 5(10), 7893–7898 (2011).
[Crossref] [PubMed]

Y.-Y. Chen, H. Shu, Y. Kuo, Y.-K. Tzeng, and H.-C. Chang, “Measuring förster resonance energy transfer between fluorescent nanodiamonds and near-infrared dyes by acceptor photobleaching,” Diam. Relat. Mater. 20(5–6), 803–807 (2011).
[Crossref]

2010 (3)

K. Y. Han, S. K. Kim, C. Eggeling, and S. W. Hell, “Metastable dark states enable ground state depletion microscopy of nitrogen vacancy centers in diamond with diffraction-unlimited resolution,” Nano Lett 10(8), 3199–3203 (2010).
[Crossref] [PubMed]

J. F. Ziegler, M. D. Ziegler, and J. P. Biersack, “Srim–the stopping and range of ions in matter (2010),” Nucl. Instrum. Meth. B 268(11), 1818–1823 (2010).
[Crossref]

A. Pertsinidis, Y. Zhang, and S. Chu, “Subnanometre single-molecule localization, registration and distance measurements,” Nature 466, 647–651 (2010).
[Crossref] [PubMed]

2009 (4)

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,” P. Natl. Acad. Sci. USA 106(9), 2995–2999 (2009).
[Crossref]

E. Rittweger, D. Wildanger, and S. W. Hell, “Far-field fluorescence nanoscopy of diamond color centers by ground state depletion,” Europhys. Lett. 86(1), 14001 (2009).
[Crossref]

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “Sted microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3(3), 144–147 (2009).
[Crossref]

K. Y. Han, K. I. Willig, E. Rittweger, F. Jelezko, C. Eggeling, and S. W. Hell, “Three-dimensional stimulated emission depletion microscopy of nitrogen-vacancy centers in diamond using continuous-wave light,” Nano Lett. 9(9), 3323–3329 (2009).
[Crossref] [PubMed]

2008 (2)

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]

J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, “High-sensitivity diamond magnetometer with nanoscale resolution,” Nat. Phys. 4(10), 810–816 (2008).
[Crossref]

2007 (2)

S. S. Rogers, T. A. Waigh, X. Zhao, and J. R. Lu, “Precise particle tracking against a complicated background: polynomial fitting with gaussian weight,” Phys. Biol. 4(3), 220 (2007).
[Crossref] [PubMed]

J. Keller, A. Schönle, and S. W. Hell, “Efficient fluorescence inhibition patterns for resolft microscopy,” Opt. Express 15(6), 3361–3371 (2007).
[Crossref] [PubMed]

2006 (3)

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]

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]

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]

2005 (2)

A. Yildiz and P. R. Selvin, “Fluorescence imaging with one nanometer accuracy: Application to molecular motors,” Accounts Chem. Res. 38(7), 574–582 (2005).
[Crossref]

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94, 143903 (2005).
[Crossref] [PubMed]

2004 (1)

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

2003 (2)

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin v walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

S. W. Hell, “Toward fluorescence nanoscopy,” Nat. Biotechnol. 21(11), 1347–1355 (2003).
[Crossref] [PubMed]

2002 (1)

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

2001 (2)

A. D. Dinsmore, E. R. Weeks, V. Prasad, A. C. Levitt, and D. A. Weitz, “Three-dimensional confocal microscopy of colloids,” Appl. Optics 40(24), 4152–4159 (2001).
[Crossref]

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81(4), 2378–2388 (2001).
[Crossref] [PubMed]

1995 (1)

S. W. Hell and M. Kroug, “Ground-state-depletion fluorscence microscopy: A concept for breaking the diffraction resolution limit,” Appl. Phys. B 60(5), 495–497 (1995).
[Crossref]

1986 (1)

N. Bobroff, “Position measurement with a resolution and noise limited instrument,” Rev. Sci. Instrum. 57(6), 1152–1157 (1986).
[Crossref]

Algara-Siller, G.

A. Ermakova, G. Pramanik, J. Cai, G. Algara-Siller, U. Kaiser, T. Weil, Y.-K. Tzeng, H.-C. Chang, L. P. McGuinness, M. B. Plenio, B. Naydenov, and F. Jelezko, “Detection of a few metallo-protein molecules using color centers in nanodiamonds,” Nano Lett. 13(7), 3305–3309 (2013).
[Crossref] [PubMed]

Awschalom, D. D.

H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, and D. Rugar, “Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor,” Science 339(6119), 557–560 (2013).
[Crossref] [PubMed]

Baday, M.

Balasubramanian, G.

J. Tisler, R. Reuter, A. Lämmle, F. Jelezko, G. Balasubramanian, P. R. Hemmer, F. Reinhard, and J. Wrachtrup, “Highly efficient fret from a single nitrogen-vacancy center in nanodiamonds to a single organic molecule,” ACS Nano 5(10), 7893–7898 (2011).
[Crossref] [PubMed]

Bates, M.

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]

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]

Betzig, E.

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]

Bhave, S. A.

E. R. MacQuarrie, T. A. Gosavi, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, “Mechanical spin control of nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 111, 227602 (2013).
[Crossref] [PubMed]

Biersack, J. P.

J. F. Ziegler, M. D. Ziegler, and J. P. Biersack, “Srim–the stopping and range of ions in matter (2010),” Nucl. Instrum. Meth. B 268(11), 1818–1823 (2010).
[Crossref]

Biteen, J. S.

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,” P. Natl. Acad. Sci. USA 106(9), 2995–2999 (2009).
[Crossref]

Bobroff, N.

N. Bobroff, “Position measurement with a resolution and noise limited instrument,” Rev. Sci. Instrum. 57(6), 1152–1157 (1986).
[Crossref]

Bonifacino, J. S.

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]

Budker, D.

J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, “High-sensitivity diamond magnetometer with nanoscale resolution,” Nat. Phys. 4(10), 810–816 (2008).
[Crossref]

Cai, E.

Cai, J.

J. Cai, A. Retzker, F. Jelezko, and M. B. Plenio, “A large-scale quantum simulator on a diamond surface at room temperature,” Nat. Phys. 9(3), 168–173 (2013).
[Crossref]

A. Ermakova, G. Pramanik, J. Cai, G. Algara-Siller, U. Kaiser, T. Weil, Y.-K. Tzeng, H.-C. Chang, L. P. McGuinness, M. B. Plenio, B. Naydenov, and F. Jelezko, “Detection of a few metallo-protein molecules using color centers in nanodiamonds,” Nano Lett. 13(7), 3305–3309 (2013).
[Crossref] [PubMed]

Cappellaro, P.

J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, “High-sensitivity diamond magnetometer with nanoscale resolution,” Nat. Phys. 4(10), 810–816 (2008).
[Crossref]

Chang, H.-C.

A. Ermakova, G. Pramanik, J. Cai, G. Algara-Siller, U. Kaiser, T. Weil, Y.-K. Tzeng, H.-C. Chang, L. P. McGuinness, M. B. Plenio, B. Naydenov, and F. Jelezko, “Detection of a few metallo-protein molecules using color centers in nanodiamonds,” Nano Lett. 13(7), 3305–3309 (2013).
[Crossref] [PubMed]

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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).
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T. Rosskopf, A. Dussaux, K. Ohashi, M. Loretz, R. Schirhagl, H. Watanabe, S. Shikata, K. M. Itoh, and C. L. Degen, “Investigation of surface magnetic noise by shallow spins in diamond,” Phys. Rev. Lett. 112, 147602 (2014).
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J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, “High-sensitivity diamond magnetometer with nanoscale resolution,” Nat. Phys. 4(10), 810–816 (2008).
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E. R. MacQuarrie, T. A. Gosavi, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, “Mechanical spin control of nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 111, 227602 (2013).
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H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, and D. Rugar, “Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor,” Science 339(6119), 557–560 (2013).
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K. Y. Han, S. K. Kim, C. Eggeling, and S. W. Hell, “Metastable dark states enable ground state depletion microscopy of nitrogen vacancy centers in diamond with diffraction-unlimited resolution,” Nano Lett 10(8), 3199–3203 (2010).
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S. W. Hell and M. Kroug, “Ground-state-depletion fluorscence microscopy: A concept for breaking the diffraction resolution limit,” Appl. Phys. B 60(5), 495–497 (1995).
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Y.-Y. Chen, H. Shu, Y. Kuo, Y.-K. Tzeng, and H.-C. Chang, “Measuring förster resonance energy transfer between fluorescent nanodiamonds and near-infrared dyes by acceptor photobleaching,” Diam. Relat. Mater. 20(5–6), 803–807 (2011).
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T. Rosskopf, A. Dussaux, K. Ohashi, M. Loretz, R. Schirhagl, H. Watanabe, S. Shikata, K. M. Itoh, and C. L. Degen, “Investigation of surface magnetic noise by shallow spins in diamond,” Phys. Rev. Lett. 112, 147602 (2014).
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M. S. Grinolds, S. Hong, P. Maletinsky, L. Luan, M. D. Lukin, R. L. Walsworth, and A. Yacoby, “Nanoscale magnetic imaging of a single electron spin under ambient conditions,” Nat. Phys. 9, 215–219 (2013).
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E. R. MacQuarrie, T. A. Gosavi, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, “Mechanical spin control of nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 111, 227602 (2013).
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M. S. Grinolds, S. Hong, P. Maletinsky, L. Luan, M. D. Lukin, R. L. Walsworth, and A. Yacoby, “Nanoscale magnetic imaging of a single electron spin under ambient conditions,” Nat. Phys. 9, 215–219 (2013).
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H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, and D. Rugar, “Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor,” Science 339(6119), 557–560 (2013).
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L. J. Rogers, K. D. Jahnke, M. W. Doherty, A. Dietrich, L. P. McGuinness, C. Müller, T. Teraji, J. Isoya, N. B. Manson, and F. Jelezko, “Electronic structure of the negatively-charged silicon-vacancy center in diamond,” Phys. Rev. B 89, 235101 (2014).
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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]

McGuinness, L. P.

L. J. Rogers, K. D. Jahnke, M. W. Doherty, A. Dietrich, L. P. McGuinness, C. Müller, T. Teraji, J. Isoya, N. B. Manson, and F. Jelezko, “Electronic structure of the negatively-charged silicon-vacancy center in diamond,” Phys. Rev. B 89, 235101 (2014).
[Crossref]

A. Ermakova, G. Pramanik, J. Cai, G. Algara-Siller, U. Kaiser, T. Weil, Y.-K. Tzeng, H.-C. Chang, L. P. McGuinness, M. B. Plenio, B. Naydenov, and F. Jelezko, “Detection of a few metallo-protein molecules using color centers in nanodiamonds,” Nano Lett. 13(7), 3305–3309 (2013).
[Crossref] [PubMed]

L. P. McGuinness, L. T. Hall, A. Stacey, D. A. Simpson, C. D. Hill, J. H. Cole, K. Ganesan, B. C. Gibson, S. Prawer, P. Mulvaney, F. Jelezko, J. Wrachtrup, R. E. Scholten, and L. C. L. Hollenberg, “Ambient nanoscale sensing with single spins using quantum decoherence,” New J. Phys. 15, 073042 (2013).
[Crossref]

McKinney, S. A.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin v walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

Meijer, J.

T. Staudacher, F. Shi, S. Pezzagna, J. Meijer, J. Du, C. A. Meriles, F. Reinhard, and J. Wrachtrup, “Nuclear magnetic resonance spectroscopy on a (5-nanometer)3 sample volume,” Science 339(6119), 561–563 (2013).
[Crossref] [PubMed]

Meriles, C. A.

T. Staudacher, F. Shi, S. Pezzagna, J. Meijer, J. Du, C. A. Meriles, F. Reinhard, and J. Wrachtrup, “Nuclear magnetic resonance spectroscopy on a (5-nanometer)3 sample volume,” Science 339(6119), 561–563 (2013).
[Crossref] [PubMed]

Moerner, W. E.

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,” P. Natl. Acad. Sci. USA 106(9), 2995–2999 (2009).
[Crossref]

Moerner, W.E.

M. A. Thompson, M. D. Lew, and W.E. Moerner, “Extending microscopic resolution with single-molecule imaging and active control,” Ann. Rev. Biophys. 41(1), 321–342 (2012).
[Crossref]

Müller, C.

L. J. Rogers, K. D. Jahnke, M. W. Doherty, A. Dietrich, L. P. McGuinness, C. Müller, T. Teraji, J. Isoya, N. B. Manson, and F. Jelezko, “Electronic structure of the negatively-charged silicon-vacancy center in diamond,” Phys. Rev. B 89, 235101 (2014).
[Crossref]

Mulvaney, P.

L. P. McGuinness, L. T. Hall, A. Stacey, D. A. Simpson, C. D. Hill, J. H. Cole, K. Ganesan, B. C. Gibson, S. Prawer, P. Mulvaney, F. Jelezko, J. Wrachtrup, R. E. Scholten, and L. C. L. Hollenberg, “Ambient nanoscale sensing with single spins using quantum decoherence,” New J. Phys. 15, 073042 (2013).
[Crossref]

Naydenov, B.

A. Ermakova, G. Pramanik, J. Cai, G. Algara-Siller, U. Kaiser, T. Weil, Y.-K. Tzeng, H.-C. Chang, L. P. McGuinness, M. B. Plenio, B. Naydenov, and F. Jelezko, “Detection of a few metallo-protein molecules using color centers in nanodiamonds,” Nano Lett. 13(7), 3305–3309 (2013).
[Crossref] [PubMed]

Ober, R. J.

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

Ohashi, K.

T. Rosskopf, A. Dussaux, K. Ohashi, M. Loretz, R. Schirhagl, H. Watanabe, S. Shikata, K. M. Itoh, and C. L. Degen, “Investigation of surface magnetic noise by shallow spins in diamond,” Phys. Rev. Lett. 112, 147602 (2014).
[Crossref] [PubMed]

Ohno, K.

H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, and D. Rugar, “Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor,” Science 339(6119), 557–560 (2013).
[Crossref] [PubMed]

Olenych, S.

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]

Patterson, G. H.

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]

Pavani, S. R. P.

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,” P. Natl. Acad. Sci. USA 106(9), 2995–2999 (2009).
[Crossref]

Pertsinidis, A.

A. Pertsinidis, Y. Zhang, and S. Chu, “Subnanometre single-molecule localization, registration and distance measurements,” Nature 466, 647–651 (2010).
[Crossref] [PubMed]

Pezzagna, S.

T. Staudacher, F. Shi, S. Pezzagna, J. Meijer, J. Du, C. A. Meriles, F. Reinhard, and J. Wrachtrup, “Nuclear magnetic resonance spectroscopy on a (5-nanometer)3 sample volume,” Science 339(6119), 561–563 (2013).
[Crossref] [PubMed]

Piestun, R.

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,” P. Natl. Acad. Sci. USA 106(9), 2995–2999 (2009).
[Crossref]

Plenio, M. B.

A. Ermakova, G. Pramanik, J. Cai, G. Algara-Siller, U. Kaiser, T. Weil, Y.-K. Tzeng, H.-C. Chang, L. P. McGuinness, M. B. Plenio, B. Naydenov, and F. Jelezko, “Detection of a few metallo-protein molecules using color centers in nanodiamonds,” Nano Lett. 13(7), 3305–3309 (2013).
[Crossref] [PubMed]

J. Cai, A. Retzker, F. Jelezko, and M. B. Plenio, “A large-scale quantum simulator on a diamond surface at room temperature,” Nat. Phys. 9(3), 168–173 (2013).
[Crossref]

Pramanik, G.

A. Ermakova, G. Pramanik, J. Cai, G. Algara-Siller, U. Kaiser, T. Weil, Y.-K. Tzeng, H.-C. Chang, L. P. McGuinness, M. B. Plenio, B. Naydenov, and F. Jelezko, “Detection of a few metallo-protein molecules using color centers in nanodiamonds,” Nano Lett. 13(7), 3305–3309 (2013).
[Crossref] [PubMed]

Prasad, V.

A. D. Dinsmore, E. R. Weeks, V. Prasad, A. C. Levitt, and D. A. Weitz, “Three-dimensional confocal microscopy of colloids,” Appl. Optics 40(24), 4152–4159 (2001).
[Crossref]

Prawer, S.

L. P. McGuinness, L. T. Hall, A. Stacey, D. A. Simpson, C. D. Hill, J. H. Cole, K. Ganesan, B. C. Gibson, S. Prawer, P. Mulvaney, F. Jelezko, J. Wrachtrup, R. E. Scholten, and L. C. L. Hollenberg, “Ambient nanoscale sensing with single spins using quantum decoherence,” New J. Phys. 15, 073042 (2013).
[Crossref]

Ram, S.

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

Reinhard, F.

T. Staudacher, F. Shi, S. Pezzagna, J. Meijer, J. Du, C. A. Meriles, F. Reinhard, and J. Wrachtrup, “Nuclear magnetic resonance spectroscopy on a (5-nanometer)3 sample volume,” Science 339(6119), 561–563 (2013).
[Crossref] [PubMed]

J. Tisler, R. Reuter, A. Lämmle, F. Jelezko, G. Balasubramanian, P. R. Hemmer, F. Reinhard, and J. Wrachtrup, “Highly efficient fret from a single nitrogen-vacancy center in nanodiamonds to a single organic molecule,” ACS Nano 5(10), 7893–7898 (2011).
[Crossref] [PubMed]

Rettner, C. T.

H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, and D. Rugar, “Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor,” Science 339(6119), 557–560 (2013).
[Crossref] [PubMed]

Retzker, A.

J. Cai, A. Retzker, F. Jelezko, and M. B. Plenio, “A large-scale quantum simulator on a diamond surface at room temperature,” Nat. Phys. 9(3), 168–173 (2013).
[Crossref]

Reuter, R.

J. Tisler, R. Reuter, A. Lämmle, F. Jelezko, G. Balasubramanian, P. R. Hemmer, F. Reinhard, and J. Wrachtrup, “Highly efficient fret from a single nitrogen-vacancy center in nanodiamonds to a single organic molecule,” ACS Nano 5(10), 7893–7898 (2011).
[Crossref] [PubMed]

Rittweger, E.

E. Rittweger, D. Wildanger, and S. W. Hell, “Far-field fluorescence nanoscopy of diamond color centers by ground state depletion,” Europhys. Lett. 86(1), 14001 (2009).
[Crossref]

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “Sted microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3(3), 144–147 (2009).
[Crossref]

K. Y. Han, K. I. Willig, E. Rittweger, F. Jelezko, C. Eggeling, and S. W. Hell, “Three-dimensional stimulated emission depletion microscopy of nitrogen-vacancy centers in diamond using continuous-wave light,” Nano Lett. 9(9), 3323–3329 (2009).
[Crossref] [PubMed]

Rogers, L. J.

L. J. Rogers, K. D. Jahnke, M. W. Doherty, A. Dietrich, L. P. McGuinness, C. Müller, T. Teraji, J. Isoya, N. B. Manson, and F. Jelezko, “Electronic structure of the negatively-charged silicon-vacancy center in diamond,” Phys. Rev. B 89, 235101 (2014).
[Crossref]

Rogers, S. S.

S. S. Rogers, T. A. Waigh, X. Zhao, and J. R. Lu, “Precise particle tracking against a complicated background: polynomial fitting with gaussian weight,” Phys. Biol. 4(3), 220 (2007).
[Crossref] [PubMed]

Rosskopf, T.

T. Rosskopf, A. Dussaux, K. Ohashi, M. Loretz, R. Schirhagl, H. Watanabe, S. Shikata, K. M. Itoh, and C. L. Degen, “Investigation of surface magnetic noise by shallow spins in diamond,” Phys. Rev. Lett. 112, 147602 (2014).
[Crossref] [PubMed]

Rugar, D.

H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, and D. Rugar, “Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor,” Science 339(6119), 557–560 (2013).
[Crossref] [PubMed]

Rust, M. J.

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]

Schirhagl, R.

T. Rosskopf, A. Dussaux, K. Ohashi, M. Loretz, R. Schirhagl, H. Watanabe, S. Shikata, K. M. Itoh, and C. L. Degen, “Investigation of surface magnetic noise by shallow spins in diamond,” Phys. Rev. Lett. 112, 147602 (2014).
[Crossref] [PubMed]

Scholten, R. E.

L. P. McGuinness, L. T. Hall, A. Stacey, D. A. Simpson, C. D. Hill, J. H. Cole, K. Ganesan, B. C. Gibson, S. Prawer, P. Mulvaney, F. Jelezko, J. Wrachtrup, R. E. Scholten, and L. C. L. Hollenberg, “Ambient nanoscale sensing with single spins using quantum decoherence,” New J. Phys. 15, 073042 (2013).
[Crossref]

Schönle, A.

Selvin, P. R.

S. H. Lee, M. Baday, M. Tjioe, P. D. Simonson, R. Zhang, E. Cai, and P. R. Selvin, “Using fixed fiduciary markers for stage drift correction,” Opt. Express 20(11), 12177–12183 (2012).
[Crossref] [PubMed]

A. Yildiz and P. R. Selvin, “Fluorescence imaging with one nanometer accuracy: Application to molecular motors,” Accounts Chem. Res. 38(7), 574–582 (2005).
[Crossref]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin v walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

Sherwood, M. H.

H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, and D. Rugar, “Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor,” Science 339(6119), 557–560 (2013).
[Crossref] [PubMed]

Shi, F.

T. Staudacher, F. Shi, S. Pezzagna, J. Meijer, J. Du, C. A. Meriles, F. Reinhard, and J. Wrachtrup, “Nuclear magnetic resonance spectroscopy on a (5-nanometer)3 sample volume,” Science 339(6119), 561–563 (2013).
[Crossref] [PubMed]

Shikata, S.

T. Rosskopf, A. Dussaux, K. Ohashi, M. Loretz, R. Schirhagl, H. Watanabe, S. Shikata, K. M. Itoh, and C. L. Degen, “Investigation of surface magnetic noise by shallow spins in diamond,” Phys. Rev. Lett. 112, 147602 (2014).
[Crossref] [PubMed]

Shu, H.

Y.-Y. Chen, H. Shu, Y. Kuo, Y.-K. Tzeng, and H.-C. Chang, “Measuring förster resonance energy transfer between fluorescent nanodiamonds and near-infrared dyes by acceptor photobleaching,” Diam. Relat. Mater. 20(5–6), 803–807 (2011).
[Crossref]

Simonson, P. D.

Simpson, D. A.

L. P. McGuinness, L. T. Hall, A. Stacey, D. A. Simpson, C. D. Hill, J. H. Cole, K. Ganesan, B. C. Gibson, S. Prawer, P. Mulvaney, F. Jelezko, J. Wrachtrup, R. E. Scholten, and L. C. L. Hollenberg, “Ambient nanoscale sensing with single spins using quantum decoherence,” New J. Phys. 15, 073042 (2013).
[Crossref]

Sougrat, R.

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]

Stacey, A.

L. P. McGuinness, L. T. Hall, A. Stacey, D. A. Simpson, C. D. Hill, J. H. Cole, K. Ganesan, B. C. Gibson, S. Prawer, P. Mulvaney, F. Jelezko, J. Wrachtrup, R. E. Scholten, and L. C. L. Hollenberg, “Ambient nanoscale sensing with single spins using quantum decoherence,” New J. Phys. 15, 073042 (2013).
[Crossref]

Staudacher, T.

T. Staudacher, F. Shi, S. Pezzagna, J. Meijer, J. Du, C. A. Meriles, F. Reinhard, and J. Wrachtrup, “Nuclear magnetic resonance spectroscopy on a (5-nanometer)3 sample volume,” Science 339(6119), 561–563 (2013).
[Crossref] [PubMed]

Taylor, J. M.

J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, “High-sensitivity diamond magnetometer with nanoscale resolution,” Nat. Phys. 4(10), 810–816 (2008).
[Crossref]

Teraji, T.

L. J. Rogers, K. D. Jahnke, M. W. Doherty, A. Dietrich, L. P. McGuinness, C. Müller, T. Teraji, J. Isoya, N. B. Manson, and F. Jelezko, “Electronic structure of the negatively-charged silicon-vacancy center in diamond,” Phys. Rev. B 89, 235101 (2014).
[Crossref]

Thompson, M. A.

M. A. Thompson, M. D. Lew, and W.E. Moerner, “Extending microscopic resolution with single-molecule imaging and active control,” Ann. Rev. Biophys. 41(1), 321–342 (2012).
[Crossref]

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,” P. Natl. Acad. Sci. USA 106(9), 2995–2999 (2009).
[Crossref]

Thompson, R. E.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

Tisler, J.

J. Tisler, R. Reuter, A. Lämmle, F. Jelezko, G. Balasubramanian, P. R. Hemmer, F. Reinhard, and J. Wrachtrup, “Highly efficient fret from a single nitrogen-vacancy center in nanodiamonds to a single organic molecule,” ACS Nano 5(10), 7893–7898 (2011).
[Crossref] [PubMed]

Tjioe, M.

Twieg, R. J.

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,” P. Natl. Acad. Sci. USA 106(9), 2995–2999 (2009).
[Crossref]

Tzeng, Y.-K.

A. Ermakova, G. Pramanik, J. Cai, G. Algara-Siller, U. Kaiser, T. Weil, Y.-K. Tzeng, H.-C. Chang, L. P. McGuinness, M. B. Plenio, B. Naydenov, and F. Jelezko, “Detection of a few metallo-protein molecules using color centers in nanodiamonds,” Nano Lett. 13(7), 3305–3309 (2013).
[Crossref] [PubMed]

Y.-Y. Chen, H. Shu, Y. Kuo, Y.-K. Tzeng, and H.-C. Chang, “Measuring förster resonance energy transfer between fluorescent nanodiamonds and near-infrared dyes by acceptor photobleaching,” Diam. Relat. Mater. 20(5–6), 803–807 (2011).
[Crossref]

Waigh, T. A.

S. S. Rogers, T. A. Waigh, X. Zhao, and J. R. Lu, “Precise particle tracking against a complicated background: polynomial fitting with gaussian weight,” Phys. Biol. 4(3), 220 (2007).
[Crossref] [PubMed]

Walker, W. F.

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81(4), 2378–2388 (2001).
[Crossref] [PubMed]

Walsworth, R.

J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, “High-sensitivity diamond magnetometer with nanoscale resolution,” Nat. Phys. 4(10), 810–816 (2008).
[Crossref]

Walsworth, R. L.

M. S. Grinolds, S. Hong, P. Maletinsky, L. Luan, M. D. Lukin, R. L. Walsworth, and A. Yacoby, “Nanoscale magnetic imaging of a single electron spin under ambient conditions,” Nat. Phys. 9, 215–219 (2013).
[Crossref]

Wang, W.

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]

Ward, E. S.

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

Watanabe, H.

T. Rosskopf, A. Dussaux, K. Ohashi, M. Loretz, R. Schirhagl, H. Watanabe, S. Shikata, K. M. Itoh, and C. L. Degen, “Investigation of surface magnetic noise by shallow spins in diamond,” Phys. Rev. Lett. 112, 147602 (2014).
[Crossref] [PubMed]

Webb, W. W.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

Weeks, E. R.

A. D. Dinsmore, E. R. Weeks, V. Prasad, A. C. Levitt, and D. A. Weitz, “Three-dimensional confocal microscopy of colloids,” Appl. Optics 40(24), 4152–4159 (2001).
[Crossref]

Weil, T.

A. Ermakova, G. Pramanik, J. Cai, G. Algara-Siller, U. Kaiser, T. Weil, Y.-K. Tzeng, H.-C. Chang, L. P. McGuinness, M. B. Plenio, B. Naydenov, and F. Jelezko, “Detection of a few metallo-protein molecules using color centers in nanodiamonds,” Nano Lett. 13(7), 3305–3309 (2013).
[Crossref] [PubMed]

Weitz, D. A.

A. D. Dinsmore, E. R. Weeks, V. Prasad, A. C. Levitt, and D. A. Weitz, “Three-dimensional confocal microscopy of colloids,” Appl. Optics 40(24), 4152–4159 (2001).
[Crossref]

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V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94, 143903 (2005).
[Crossref] [PubMed]

Wildanger, D.

E. Rittweger, D. Wildanger, and S. W. Hell, “Far-field fluorescence nanoscopy of diamond color centers by ground state depletion,” Europhys. Lett. 86(1), 14001 (2009).
[Crossref]

Willig, K. I.

K. Y. Han, K. I. Willig, E. Rittweger, F. Jelezko, C. Eggeling, and S. W. Hell, “Three-dimensional stimulated emission depletion microscopy of nitrogen-vacancy centers in diamond using continuous-wave light,” Nano Lett. 9(9), 3323–3329 (2009).
[Crossref] [PubMed]

Wrachtrup, J.

L. P. McGuinness, L. T. Hall, A. Stacey, D. A. Simpson, C. D. Hill, J. H. Cole, K. Ganesan, B. C. Gibson, S. Prawer, P. Mulvaney, F. Jelezko, J. Wrachtrup, R. E. Scholten, and L. C. L. Hollenberg, “Ambient nanoscale sensing with single spins using quantum decoherence,” New J. Phys. 15, 073042 (2013).
[Crossref]

T. Staudacher, F. Shi, S. Pezzagna, J. Meijer, J. Du, C. A. Meriles, F. Reinhard, and J. Wrachtrup, “Nuclear magnetic resonance spectroscopy on a (5-nanometer)3 sample volume,” Science 339(6119), 561–563 (2013).
[Crossref] [PubMed]

J. Tisler, R. Reuter, A. Lämmle, F. Jelezko, G. Balasubramanian, P. R. Hemmer, F. Reinhard, and J. Wrachtrup, “Highly efficient fret from a single nitrogen-vacancy center in nanodiamonds to a single organic molecule,” ACS Nano 5(10), 7893–7898 (2011).
[Crossref] [PubMed]

Yacoby, A.

M. S. Grinolds, S. Hong, P. Maletinsky, L. Luan, M. D. Lukin, R. L. Walsworth, and A. Yacoby, “Nanoscale magnetic imaging of a single electron spin under ambient conditions,” Nat. Phys. 9, 215–219 (2013).
[Crossref]

J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, “High-sensitivity diamond magnetometer with nanoscale resolution,” Nat. Phys. 4(10), 810–816 (2008).
[Crossref]

Yildiz, A.

A. Yildiz and P. R. Selvin, “Fluorescence imaging with one nanometer accuracy: Application to molecular motors,” Accounts Chem. Res. 38(7), 574–582 (2005).
[Crossref]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin v walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

Zhang, R.

Zhang, Y.

A. Pertsinidis, Y. Zhang, and S. Chu, “Subnanometre single-molecule localization, registration and distance measurements,” Nature 466, 647–651 (2010).
[Crossref] [PubMed]

Zhao, X.

S. S. Rogers, T. A. Waigh, X. Zhao, and J. R. Lu, “Precise particle tracking against a complicated background: polynomial fitting with gaussian weight,” Phys. Biol. 4(3), 220 (2007).
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Figures (6)

Fig. 1
Fig. 1

Schematic confocal microscope with two separated detection channels for the fluorescent red light and the reflected green light. An exemplary x-y-scan is shown. The scanning position for the later performed z-scans is determined by a 2D-Gaussian fit. The x-z-profile of the NV center was then recorded at the calculated position of the emitter.

Fig. 2
Fig. 2

Signals of the reflected light from the surface (green) and the fluorescent light from the NV center (red) in a scan along the optical axis. The maximum positions have been determined by an optimized polynomial fit of the central peak with a maximum at 2.992 μm for the reflection and 3.214 μm for the fluorescence.

Fig. 3
Fig. 3

Determination of the shot noise limit of the measurements. The binning of determined maximum position differences between the reflected and fluorescent light signal shows a steadily decreasing standard deviation for a higher number of binned measurements with shot noise scaling. We see a noise limit below of 0.9 nm is achieved at about 500 measurements. The highly wavering behavior of the standard deviation for high binning numbers can be explained by the limited amount of measurements as the total number of measurements is not perfectly divisible by the binning number. The volatility is exaggerated due to logarithmic scaling.

Fig. 4
Fig. 4

The maximum positions of the reflected light from the surface and the fluorescent light of the NV center show a strong linear correlation. Due to the focal shift in the diamond the slope differs from 1. Here 500 single measurements show a slope of 0.76 at a average position difference of 236 ± 1 nm.

Fig. 5
Fig. 5

The linear correlation and thus the focal shift factor increases for deeper emitters. Shallow implanted NV centers show a position difference of about 170±3 nm at a minimal shift factor of 1.3±0.3. The measurements show a steadily increasing focal shift for deeper NV centers. The dashed lines compare the evaluated values to a geometrical optics model (green, [30]) and a simple approach to a focal shift calculation for shallow emitters (blue, see appendix)

Fig. 6
Fig. 6

Comparison of SRIM simulation of NV depth distribution (red line) with calculated depth distribution (blue histogram) for (a) 101 NV centers of an implantation energy of 2.4 keV and (b) 49 NV centers of an implantation energy 50 keV. Both implantation distributions show a good agreement with the theoretical expectation of implanted nitrogen.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

δ x = Δ N
VD = z 0 s + c
y i ( z ) = a i z 2 + b i z + c i ,
F ( z ) = H ( h z ) y 1 + H ( z h ) y 2 .
Δ z 0 = Δ s ( VD c ) + Δ VD s + Δ c s
w ( z ) = w 0 ( 1 + ( z z R ) 2 ) 1 / 2
w 0 = λ π α λ π arcsin ( NA / n 1 )
w ( z ) = w 0 z z 0 2 ( 1 + ( z z 0 ) 2 ) 1 / 2
s exc ( z ) = w ( z ) tan arcsin ( n 1 n 2 sin ( arctan w ( z ) ) )
f ( z ) = f 0 exp ( z 2 2 σ 2 )
s = CDF ( z , 0 , σ ) s exc ( z ) + ( 1 CDF ( z , 0 , σ ) )

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