OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 7 — Jun. 25, 2012

Optimized back-focal-plane interferometry directly measures forces of optically trapped particles

Arnau Farré, Ferran Marsà, and Mario Montes-Usategui  »View Author Affiliations

Optics Express, Vol. 20, Issue 11, pp. 12270-12291 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (4179 KB) Open Access

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Back-focal-plane interferometry is used to measure displacements of optically trapped samples with very high spatial and temporal resolution. However, the technique is closely related to a method that measures the rate of change in light momentum. It has long been known that displacements of the interference pattern at the back focal plane may be used to track the optical force directly, provided that a considerable fraction of the light is effectively monitored. Nonetheless, the practical application of this idea has been limited to counter-propagating, low-aperture beams where the accurate momentum measurements are possible. Here, we experimentally show that the connection can be extended to single-beam optical traps. In particular, we show that, in a gradient trap, the calibration product κ·β (where κ is the trap stiffness and 1/β is the position sensitivity) corresponds to the factor that converts detector signals into momentum changes; this factor is uniquely determined by three construction features of the detection instrument and does not depend, therefore, on the specific conditions of the experiment. Then, we find that force measurements obtained from back-focal-plane displacements are in practice not restricted to a linear relationship with position and hence they can be extended outside that regime. Finally, and more importantly, we show that these properties are still recognizable even when the system is not fully optimized for light collection. These results should enable a more general use of back-focal-plane interferometry whenever the ultimate goal is the measurement of the forces exerted by an optical trap.

© 2012 OSA

OCIS Codes
(120.1880) Instrumentation, measurement, and metrology : Detection
(120.4640) Instrumentation, measurement, and metrology : Optical instruments
(140.7010) Lasers and laser optics : Laser trapping
(170.1420) Medical optics and biotechnology : Biology
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Optical Trapping and Manipulation

Original Manuscript: April 26, 2012
Manuscript Accepted: April 27, 2012
Published: May 15, 2012

Virtual Issues
Vol. 7, Iss. 7 Virtual Journal for Biomedical Optics

Arnau Farré, Ferran Marsà, and Mario Montes-Usategui, "Optimized back-focal-plane interferometry directly measures forces of optically trapped particles," Opt. Express 20, 12270-12291 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett.11(5), 288–290 (1986). [CrossRef] [PubMed]
  2. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J.61(2), 569–582 (1992). [CrossRef] [PubMed]
  3. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct.23(1), 247–285 (1994). [CrossRef] [PubMed]
  4. S. C. Kuo and M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science260(5105), 232–234 (1993). [CrossRef] [PubMed]
  5. J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature368(6467), 113–119 (1994). [CrossRef] [PubMed]
  6. K. Svoboda and S. M. Block, “Force and velocity measured for single kinesin molecules,” Cell77(5), 773–784 (1994). [CrossRef] [PubMed]
  7. S. Kamimura and R. Kamiya, “High-frequency vibration in flagellar axonemes with amplitudes reflecting the size of tubulin,” J. Cell Biol.116(6), 1443–1454 (1992). [CrossRef] [PubMed]
  8. K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature365(6448), 721–727 (1993). [CrossRef] [PubMed]
  9. W. Denk and W. W. Webb, “Optical measurement of picometer displacements of transparent microscopic objects,” Appl. Opt.29(16), 2382–2391 (1990). [CrossRef] [PubMed]
  10. L. P. Ghislain and W. W. Webb, “Scanning-force microscope based on an optical trap,” Opt. Lett.18(19), 1678–1680 (1993). [CrossRef] [PubMed]
  11. L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum.65(9), 2762–2768 (1994). [CrossRef]
  12. S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science271(5250), 795–799 (1996). [CrossRef] [PubMed]
  13. S. B. Smith, “Stretch transitions observed in single biopolymer molecules (DNA or protein) using laser tweezers,” Doctoral Thesis, University of Twente, The Netherlands (1998).
  14. W. Grange, S. Husale, H.-J. Güntherodt, and M. Hegner, “Optical tweezers system measuring the change in light momentum flux,” Rev. Sci. Instrum.73(6), 2308–2316 (2002). [CrossRef]
  15. S. B. Smith, Y. Cui, and C. Bustamante, “Optical-trap force transducer that operates by direct measurement of light momentum,” Methods Enzymol.361, 134–162 (2003). [CrossRef] [PubMed]
  16. K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron.2(4), 1066–1076 (1996). [CrossRef]
  17. F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett.23(1), 7–9 (1998). [CrossRef] [PubMed]
  18. P. Bartlett and S. Henderson, “Three-dimensional force calibration of a single-beam optical gradient trap,” J. Phys. Condens. Matter14(33), 7757–7768 (2002). [CrossRef]
  19. M. Jahnel, M. Behrndt, A. Jannasch, E. Schäffer, and S. W. Grill, “Measuring the complete force field of an optical trap,” Opt. Lett.36(7), 1260–1262 (2011). [CrossRef] [PubMed]
  20. A. Farré and M. Montes-Usategui, “A force detection technique for single-beam optical traps based on direct measurement of light momentum changes,” Opt. Express18(11), 11955–11968 (2010). [CrossRef] [PubMed]
  21. M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J.83(1), 491–501 (2002). [CrossRef] [PubMed]
  22. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum.75(9), 2787–2809 (2004). [CrossRef] [PubMed]
  23. A. Rohrbach, H. Kress, and E. H. K. Stelzer, “Three-dimensional tracking of small spheres in focused laser beams: influence of the detection angular aperture,” Opt. Lett.28(6), 411–413 (2003). [CrossRef] [PubMed]
  24. S. Perrone, G. Volpe, and D. Petrov, “10-fold detection range increase in quadrant-photodiode position sensing for photonic force microscope,” Rev. Sci. Instrum.79(10), 106101 (2008). [CrossRef] [PubMed]
  25. T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt.9(8), S196–S203 (2007). [CrossRef]
  26. J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, “Differential detection of dual traps improves the spatial resolution of optical tweezers,” Proc. Natl. Acad. Sci. U.S.A.103(24), 9006–9011 (2006). [CrossRef] [PubMed]
  27. T. Godazgar, R. Shokri, and S. N. S. Reihani, “Potential mapping of optical tweezers,” Opt. Lett.36(16), 3284–3286 (2011). [CrossRef] [PubMed]
  28. K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum.75(3), 594–612 (2004). [CrossRef]
  29. I.-M. Tolić-Nørrelykke, K. Berg-Sørensen, and H. Flyvbjerg, “MatLab program for precision calibration of optical tweezers,” Comput. Phys. Commun.159(3), 225–240 (2004). [CrossRef]
  30. See Table 1 in: A. Wozniak, “Characterizing quantitative measurements of force and displacement with optical tweezers on the NanotrackerTM,” JPK Instruments Technical Report, http://www.jpk.com/optical-tweezers.233.en.html ; the product of stiffness and parameter β changes by a factor of more than two, for polystyrene beads between 100 nm and 4260 nm (similarly for silica beads, Table 2). Also, in Table 1 and Fig. 5 in: A. Buosciolo, G. Pesce, and A. Sasso, “New calibration method for position detector for simultaneous measurements of force constants and local viscosity in optical tweezers,” Opt. Commun. 230, 375–368 (2004), a factor of two or more is observed between the values of κ·β obtained for different positions of the trap. Finally, Fig. 9 in: M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, “Calibration of optical tweezers with differential interference contrast signals,” Rev. Sci. Instrum. 73, 1687–1696 (2002), shows a product factor κ·β that apparently changes more than sevenfold for beads between 500 and 5000 nm in size (position detection is through DIC interferometry).
  31. E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 349–357 (1959). [CrossRef]
  32. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959). [CrossRef]
  33. S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc.169(3), 391–405 (1993). [CrossRef]
  34. A. Rohrbach and E. H. K. Stelzer, “Optical trapping of dielectric particles in arbitrary fields,” J. Opt. Soc. Am. A18(4), 839–853 (2001). [CrossRef] [PubMed]
  35. K. von Bieren, “Lens design for optical Fourier transform systems,” Appl. Opt.10(12), 2739–2742 (1971). [CrossRef] [PubMed]
  36. C. J. R. Sheppard and M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt.40(8), 1631–1651 (1993). [CrossRef]
  37. A. Rohrbach and E. H. K. Stelzer, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys.91(8), 5474–5488 (2002). [CrossRef]
  38. K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, “Characterization of photodamage to Escherichia coli in optical traps,” Biophys. J.77(5), 2856–2863 (1999). [CrossRef] [PubMed]
  39. N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, and P. A. Maia Neto, “Characterization of objective transmittance for optical tweezers,” Appl. Opt.45(18), 4263–4269 (2006). [CrossRef] [PubMed]
  40. J. Mas, A. Farré, C. López-Quesada, X. Fernández, E. Martín-Badosa, and M. Montes-Usategui, “Measuring stall forces in vivo with optical tweezers through light momentum changes,” Proc. SPIE8097, 809726, 809726-10 (2011). [CrossRef]
  41. I. Verdeny, A.-S. Fontaine, A. Farré, M. Montes-Usategui, and E. Martín-Badosa, “Heating effects on NG108 cells induced by laser trapping,” Proc. SPIE8097, 809724, 809724-12 (2011). [CrossRef]
  42. S. P. Gross, “Application of optical traps in vivo,” Methods Enzymol.361, 162–174 (2003). [CrossRef] [PubMed]
  43. M. P. Landry, P. M. McCall, Z. Qi, and Y. R. Chemla, “Characterization of photoactivated singlet oxygen damage in single-molecule optical trap experiments,” Biophys. J.97(8), 2128–2136 (2009). [CrossRef] [PubMed]
  44. J. Dong, C. E. Castro, M. C. Boyce, M. J. Lang, and S. Lindquist, “Optical trapping with high forces reveals unexpected behaviors of prion fibrils,” Nat. Struct. Mol. Biol.17(12), 1422–1430 (2010). [CrossRef] [PubMed]
  45. E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir23(7), 3654–3665 (2007). [CrossRef] [PubMed]
  46. A. H. Firester, M. E. Heller, and P. Sheng, “Knife-edge scanning measurements of subwavelength focused light beams,” Appl. Opt.16(7), 1971–1974 (1977). [CrossRef] [PubMed]
  47. W. H. Wright, G. J. Sonek, and M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett.63(6), 715–717 (1993). [CrossRef]
  48. M. Mahamdeh, C. P. Campos, and E. Schäffer, “Under-filling trapping objectives optimizes the use of the available laser power in optical tweezers,” Opt. Express19(12), 11759–11768 (2011). [CrossRef] [PubMed]
  49. A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech.44(5), 378–386 (1999). [CrossRef] [PubMed]
  50. K. Berg-Sørensen, L. Oddershede, E.-L. Florin, and H. Flyvbjerg, “Unintended filtering in a typical photodiode detection system for optical tweezers,” J. Appl. Phys.93(6), 3167–3176 (2003). [CrossRef]
  51. T. Otaki, “Condenser lens system for use in a microscope,” US Patent no. 5657166 (1997).
  52. T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4(6), 388–394 (2010). [CrossRef]
  53. W. M. Lee, P. J. Reece, R. F. Marchington, N. K. Metzger, and K. Dholakia, “Construction and calibration of an optical trap on a fluorescence optical microscope,” Nat. Protoc.2(12), 3226–3238 (2007). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited