## Novel perspectives for the application of total internal reflection microscopy

Optics Express, Vol. 17, Issue 26, pp. 23975-23985 (2009)

http://dx.doi.org/10.1364/OE.17.023975

Acrobat PDF (339 KB)

### Abstract

Total Internal Reflection Microscopy (TIRM) is a sensitive non-invasive technique to measure the interaction potentials between a colloidal particle and a wall with femtonewton resolution. The equilibrium distribution of the particle-wall separation distance *z* is sampled monitoring the intensity *I* scattered by the Brownian particle under evanescent illumination. Central to the data analysis is the knowledge of the relation between *I* and the corresponding *z*, which typically must be known *a priori*. This poses considerable constraints to the experimental conditions where TIRM can be applied (short penetration depth of the evanescent wave, transparent surfaces). Here, we introduce a method to experimentally determine *I*(*z*) by relying only on the distance-dependent particle-wall hydrodynamic interactions. We demonstrate that this method largely extends the range of conditions accessible with TIRM, and even allows measurements on highly reflecting gold surfaces where multiple reflections lead to a complex *I*(*z*).

© 2009 Optical Society of America

## 1. Introduction

1. J. Walz, “Measuring particle interactions with total internal reflection microscopy,” Curr. Opin. Colloid. Interface Sci. **2**, 600–606 (1997). [CrossRef]

2. D. C. Prieve, “Measurement of colloidal forces with TIRM,” Adv. Colloid. Interface Sci. **82**, –125 (1999). [CrossRef]

*U*(

*z*) of the particle-surface interactions with sub-

*k*resolution, where

_{B}T*k*is the thermal energy. Amongst various techniques available to probe the mechanical properties of microsystems, the strength of TIRM lies in its sensitivity to very weak interactions. Atomic Force Microscopy (AFM) [3

_{B}T3. G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Phys. Rev. Lett. **56**, 930–933 (1986). [CrossRef] [PubMed]

4. W. Ducker, T. Senden, and R. Pashley, “Direct measurement of colloidal forces using an atomic force micro-scope,” Nature **353**, 239–241 (1991). [CrossRef]

^{-12}

*N*); the sensitivity of Photonic Force Microscopy (PFM) [5

5. L. P. Ghislain and W. W. Webb, “Scanning-force microscope based on an optical trap,” Opt. Lett. **18**, 1678–1680 (1993). [CrossRef] [PubMed]

7. G. Volpe, G. Volpe, and D. Petrov, “Brownian motion in a nonhomogeneous force field and photonic force microscope,” Phys. Rev. E **76**, 061118 (2007). [CrossRef]

^{-15}

*N*), but this method is usually applied to bulk measurements far from any surface. TIRM, instead, can measure forces with femtonewton resolution acting on a particle near a surface. Over the last years, TIRM has been successfully applied to study electrostatic [8

8. S. G. Bike and D. C. Prieve, “Measurements of double-layer repulsion for slightly overlapping counterion clouds,” Int. J. Multiphase Flow **16**, 727–740 (1990). [CrossRef]

9. H. H. von Grünberg, L. Helden, P. Leiderer, and C. Bechinger, “Measurement of surface charge densities on Brownian particles using total internal reflection microscopy,” J. Chem. Phys. **114**, 10094–10104 (2001). [CrossRef]

10. M. A. Bevan and D. C. Prieve, “Direct measurement of retarded van der Waals attraction,” Langmuir **15**, 7925–7936 (1999). [CrossRef]

11. M. Piech, P. Weronski, X. Wu, and J. Y. Walz, “Prediction and measurement of the interparticle depletion interaction next to a flat wall,” J. Colloid Interface Sci. **247**, 327–341 (2002). [CrossRef]

14. D. Kleshchanok, R. Tuinier, and P. R. Lang, “Depletion interaction mediated by a polydisperse polymer studied with total internal reflection microscopy,” Langmuir **22**, 9121–9128 (2006). [CrossRef] [PubMed]

15. V. Blickle, D. Babic, and C. Bechinger, “Evanescent light scattering with magnetic colloids,” Appl. Phys. Lett. **87**, 101102 (2005). [CrossRef]

16. C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, “Direct measurement of critical Casimir forces,” Nature **451**, 172–175 (2008). [CrossRef] [PubMed]

*I*of a polystyrene particle with radius

_{t}*R*=1.45

*µm*in water.

*I*(

*z*) is known (and monotonic), the vertical component of the particles trajectory

*z*can be deduced from

_{t}*I*. To obtain

_{t}*I*(

*z*), it is in principle required to solve a rather complex Mie scattering problem, i.e. the scattering of a micron-sized colloidal particle under evanescent illumination close to a surface [17

17. H. Chew, D.-S. Wang, and M. Kerker, “Elastic scattering of evanescent electromagnetic waves,” Appl. Opt. **18**, 2679–2687 (1979). [CrossRef] [PubMed]

18. C. C. Liu, T. Kaiser, S. Lange, and G. Schweiger, “Structural resonances in a dielectric sphere illuminated by an evanescent wave,” Opt. Commun. **117**, 521–531 (1995). [CrossRef]

19. R. Wannemacher, A. Pack, and M. Quinten, “Resonant absorption and scattering in evanescent fields,” Appl. Phys. B **68**, 225–232 (1999). [CrossRef]

22. N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, “Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy,” J. Quantum Spectr. Rad. Transfer **106**, 464–474 (2007). [CrossRef]

*I*(

*z*)=

*I*

_{0}e

^{-z/β}[1

1. J. Walz, “Measuring particle interactions with total internal reflection microscopy,” Curr. Opin. Colloid. Interface Sci. **2**, 600–606 (1997). [CrossRef]

2. D. C. Prieve, “Measurement of colloidal forces with TIRM,” Adv. Colloid. Interface Sci. **82**, –125 (1999). [CrossRef]

17. H. Chew, D.-S. Wang, and M. Kerker, “Elastic scattering of evanescent electromagnetic waves,” Appl. Opt. **18**, 2679–2687 (1979). [CrossRef] [PubMed]

18. C. C. Liu, T. Kaiser, S. Lange, and G. Schweiger, “Structural resonances in a dielectric sphere illuminated by an evanescent wave,” Opt. Commun. **117**, 521–531 (1995). [CrossRef]

23. D. C. Prieve and J. Y. Walz, “Scattering of an evanescent surface wave by a microscopic dielectric sphere,” Appl. Opt. **32**, 1629–1641 (1993). [CrossRef] [PubMed]

*n*the substrate refractive index,

_{s}*n*the liquid medium refractive index, and

_{m}*θ*the incidence angle, which must be larger than the critical angle

*θ*=arcsin(

_{c}*n*/

_{m}*n*).

_{s}*I*

_{0}is the scattering intensity at the wall, which can be determined e.g. using a hydrodynamic method proposed in Ref. [24

24. M. A. Bevan and D. C. Prieve, “Hindered diffusion of colloidal particles very near to a wall: Revisited,” J. Chem. Phys. **113**, 1228–1236 (2000). [CrossRef]

*z*the particle-wall interaction potential

_{t}*U*(

*z*) is easily derived by applying the Boltzmann factor

*U*(

*z*)=-kBT ln p(z) to the calculated position distribution

*p*(

*z*) [Fig. 1(d), 1(e)]. For an electrically charged dielectric particle suspended in a solvent, the interaction potential typically corresponds to

*κ*

^{-1}the Debye length and

*B*a prefactor depending on the surface charge densities of the particle and the wall [1

1. J. Walz, “Measuring particle interactions with total internal reflection microscopy,” Curr. Opin. Colloid. Interface Sci. **2**, 600–606 (1997). [CrossRef]

2. D. C. Prieve, “Measurement of colloidal forces with TIRM,” Adv. Colloid. Interface Sci. **82**, –125 (1999). [CrossRef]

9. H. H. von Grünberg, L. Helden, P. Leiderer, and C. Bechinger, “Measurement of surface charge densities on Brownian particles using total internal reflection microscopy,” J. Chem. Phys. **114**, 10094–10104 (2001). [CrossRef]

*ρ*and

_{p}*ρ*the particle and solvent density and

_{m}*g*the gravitational acceleration constant;

*F*takes into account additional optical forces, which may result from a vertically incident laser beam often employed as a two-dimensional optical trap to reduce the lateral motion of the particle [25

_{s}25. J. Y. Walz and D. C. Prieve, “Prediction and measurement of the optical trapping forces on a dielectric sphere,” Langmuir **8**, 3073–3082 (1992). [CrossRef]

*β*≈100

*nm*), and have therefore been limited to rather small particle-substrate distances

*z*. In addition, no TIRM studies on highly reflecting walls, e.g. gold surfaces, have been reported, although such surfaces are interesting since they can support surface plasmons enhancing the evanescent field [26

26. O. Marti, H. Bielefeldt, B. Hecht, S. Herminghaus, P. Leiderer, and J. Mlynek, “Near-field optical measurement of the surface plasmon field,” Opt. Commun. **96**, 225–228 (1993). [CrossRef]

27. G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett. **96**, 238101 (2006). [CrossRef] [PubMed]

29. M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femto-newton range,” Phys. Rev. Lett. **100**, 186804 (2008). [CrossRef] [PubMed]

30. A. Ulman, “Formation and structure of self-assembled monolayers,” Chem. Rev. **96**, 1533–1554 (1996). [CrossRef] [PubMed]

*I*(

*z*) relationship under these conditions. For example, it has been demonstrated that large penetration depths (e.g. above ≈200

*nm*in Ref. [31

31. C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, “Experimental verification of an exact evanescent light scattering model for TIRM,” Langmuir **24**, 1–4 (2008). [CrossRef]

*I*(

*z*) [21

21. L. Helden, E. Eremina, N. Riefler, C. Hertlein, C. Bechinger, Y. Eremin, and T. Wriedt, “Single-particle evanescent light scattering simulations for total internal reflection microscopy,” Appl. Opt. **45**, 7299–7308 (2006). [CrossRef] [PubMed]

31. C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, “Experimental verification of an exact evanescent light scattering model for TIRM,” Langmuir **24**, 1–4 (2008). [CrossRef]

32. C. T. McKee, S. C. Clark, J. Y. Walz, and W. A. Ducker, “Relationship between scattered intensity and separation for particles in an evanescent field,” Langmuir **21**, 5783–5789 (2005). [CrossRef] [PubMed]

31. C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, “Experimental verification of an exact evanescent light scattering model for TIRM,” Langmuir **24**, 1–4 (2008). [CrossRef]

*I*(

*z*) by making solely use of the experimentally acquired

*I*and of the distance-dependent hydrodynamic interactions between the particle and the wall. In particular, no knowledge about the shape of the potential

_{t}*U*(

*z*) is required. We demonstrate the capability of this method by experiments and simulations, and we also apply it to experimental conditions with long penetration depths (

*β*=720

*nm*) and even with highly reflective gold surfaces.

## 2. Theory

### 2.1. Diffusion coefficient and skewness of Brownian motion near a wall

*D*=

_{SE}*k*/6

_{B}T*πηR*, where

*η*is the shear viscosity of the liquid. It is well known that this bulk diffusion coefficient decreases close to a wall due to hydrodynamic interactions. From the solution of the creeping flow equations for a spherical particle in motion near a wall assuming nonslip boundary conditions and negligible inertial effects, one obtains for the diffusion coefficient in the vertical direction [33

33. H. Brenner, “The slow motion of a sphere through a viscous fluid towards a plane surface,” Chem. Eng. Sci. **16**, 242–251 (1961). [CrossRef]

*D*

_{⊥}first increases with

*z*approaching the corresponding bulk value at a distance of several particle radii away from the wall.

*z*-component this reads 〈(

*z*+Δ

_{t}*t*-

*z*)

^{t}^{2}〉=2

*D*Δ

_{SE}*t*, where 〈…〉 indicates average over time

*t*. To account for a

*z*-dependent diffusion coefficient close to a wall, one has to calculate the conditional MSD given that the particle is at time

*t*at position

*z*, i.e. 〈(

*z*+Δ

_{t}*-*

_{t}*z*)

_{t}^{2}|

*z*=

_{t}*z*〉=2

*D*

_{⊥}(

*z*)Δ

*t*where the equality is valid for Δ

*t*→0; in such limit, this expression is only determined by the particle diffusion even if the particle is exposed to an external potential

*U*(

*z*). From this follows that

*D*

_{⊥}(

*z*) can be directly obtained from the particle’s trajectory

34. R. J. Oetama and J. Y. Walz, “A new approach for analyzing particle motion near an interface using total internal reflection microscopy,” J. Colloid. Interface Sci. **284**, 323–331 (2005). [CrossRef] [PubMed]

35. M. D. Carbajal-Tinoco, R. Lopez-Fernandez, and J. L. Arauz-Lara, “Asymmetry in colloidal diffusion near a rigid wall,” Phys. Rev. Lett. **99**, 138303 (2007). [CrossRef] [PubMed]

*h*(

*z*;

*z*

_{0},Δ

*t*) around a given distance

*z*

_{0}converges to a gaussian for Δ

*t*→0 and therefore its

*skewness*– i.e. the normalized third central moment – converges to zero. Accordingly,

*M*(

*z*,Δ

*t*)=〈

*z*+Δ

_{t}*t*-

*z*|

_{t}*z*=

_{t}*z*〉=arg

_{ẑ}max

*h*(ẑ;

*z*,Δ

*t*), where arg

_{ẑ}max indicates the argument that maximize the given function.

### 2.2. Mean square displacement and skewness of the scattering intensity

*h*(

*z*;

*z*

_{0},Δ

*t*) is translated into a corresponding intensity distribution

*h*(

*I*;

*I*

_{0},Δ

*t*) around intensity

*I*

_{0}=

*I*(

*z*

_{0}), whose shape strongly depends on

*I*(

*z*). In Fig. 3 we demonstrate how a particle displacement distribution

*h*(

*z*;

*z*

_{0},Δ

*t*), which is gaussian for small Δt, translates into the corresponding scattered intensity distribution

*h*(

*I*;

*I*

_{0},Δt) for an arbitrary non-exponential

*I*(

*z*) dependence. In the linear regions of

*I*(

*z*), the corresponding

*h*(

*I*;

*I*

_{0},Δ

*t*) are also gaussian with the half-width determined by the slope of the

*I*(

*z*) curve. In the non-linear part of

*I*(

*z*), however, a non-gaussian intensity histogram with finite skewness is obtained.

*h*(

*I*;

*I*

_{0},Δ

*t*) for an arbitrary I(z), which we assume to be a continuous function with well defined first and second derivates

*I*′ and

*I*″. In the vicinity of

*z*

_{0},

*I*(

*z*) can be therefore expanded in a Taylor series

*h*(

*I*;

*I*

_{0},Δ

*t*) is

*I*+Δ

_{t}*t*-

*I*)

_{t}^{2}|

*I*=

_{t}*I*〉=

*I*′

^{2}〈(

*z*+Δ

_{t}*t*-

*z*)

_{t}^{2}|

*I*=

_{t}*I*〉 for Δ

*t*→0 and Eq. (2) has been used. The skewness of

*h*(

*I*;

*I*

_{0},Δ

*t*) is

*M*(

*I*,Δ

*t*)=arg

_{Î}max

*h*(

*Î*;

*I*,Δ

*t*) and

*t*→0 where the first term is null because of Eq. (3), and the second term is calculated using the properties of the momenta of a gaussian distribution 〈(…)

^{4}〉=3〈(…)

^{2}〉

^{2}.

*I*(

*z*) [Fig. 4(a), 4(c), 4(e)]. The solid lines in Fig. 4(b), 4(d), 4(f) show the theoretical MSD(

*I*) (black) and S(

*I*) (red) and the dots the ones obtained from the simulations. When

*I*(

*z*) is linear [Fig. 4(a)], MSD(

*I*) is proportional to Eq. (1) and S(

*I*) vanishes [Fig. 4(b)]. When

*I*(

*z*) is exponential [Fig. 4(c)] or a sinusoidally modulated exponential [Fig. 4(e)], MSD(

*I*) is not proportional to Eq. (1) and large values of the skewness occur as shown in Figs. 4(d), 4(f). Small deviations between the theoretical curves and the numerical data can be observed for intensities where the particle drift becomes large in comparison to the time-step (Δ

*t*=2

*ms*); in our case this corresponds to a slope of the potential of about 1

*pN*/

*µm*, which is close to the upper force limit of typical TIRM measurements. If necessary such deviations can be reduced employing shorter time-steps.

### 2.3. Obtaining I(z) from It

*I*(

*z*) satisfies the conditions

*I*) and S(

*I*) are calculated from an experimental

*I*. Thus, the problem of determining

_{t}*I*(

*z*) can be regarded as a functional optimization problem, where Eqs. (6) have to be fulfilled.

## 3. Analysis workflow

*z*from the experimental It by finding the

_{t}*I*(

*z*) that satisfies Eqs. (6). To do so, we will construct a series of approximations

*I*

^{(i)}(

*z*) indexed by

*i*converging to

*I*(

*z*).

*I*

^{(0)}(

*z*)=

*I*

_{0}exp(-

*z*/

*β*)+

*b*, where

_{s}*β*,

*I*

_{0}and

*b*are parameters chosen to optimize Eqs. (6). Often some initial estimates are available from the experimental conditions:

_{s}*β*can be taken as the evanescent field penetration depth,

*I*

_{0}as the scattering intensity at the wall, and

*b*as the background scattering in the absence of the Brownian particle. While

_{s}*β*is typically well known,

*I*

_{0}and

*b*are prone to large experimental systematic errors and uncertainties.

_{s}*I*

^{(1)}(

*z*)=

*I*

^{(0)}(

*z*)[1-

*G*(

*I*

^{(0)}(

*z*),

*µ*

^{(1)},

*σ*

^{(1)},

*A*

^{(1)})], where

*G*(

*x*,

*µ,σ,A*)=

*A*exp(-(

*x*-

*µ*)

^{2}/

*σ*

^{2}) is a gaussian, and the parameters

*µ*

^{(1)},

*σ*

^{(1)}, and

*A*

^{(1)}optimize Eqs. (6). Gaussian functions were chosen because they have smooth derivatives and quickly tend to zero at infinite. Notice that the choice of a Gaussian is unessential for the working of the algorithm.

*I*

^{(0)}with

*I*

^{(i)}and

*I*

^{(1)}with

*I*

^{(i+1)}, until Eqs. (6) are satisfied within the required precision.

*I*

^{(i+1)}(

*z*), i.e. numerically construct

*z*

^{(i+1)}(

*I*).

*z*=

_{t}*z*

^{(i+1)}(

*I*).

_{t}## 4. Experimental case studies

### 4.1. Validation of the technique

*R*=1.45

*µm*near a glass-water interface kept in place by a vertically incident laser beam [25

25. J. Y. Walz and D. C. Prieve, “Prediction and measurement of the optical trapping forces on a dielectric sphere,” Langmuir **8**, 3073–3082 (1992). [CrossRef]

*z*) is justified (

*β*=120

*nm*, λ=658

*nm*) [31

**24**, 1–4 (2008). [CrossRef]

*I*(

*z*) in Eqs. (6) are already fulfilled after

*I*

_{0}and

*b*have been optimized in the first step of the analysis workflow in the previous section. As shown in Fig. 5(b), the experimental MSD(

_{s}*I*) (black dots) and skewness S(

*I*) (red dots) fit Eqs. (4) and (5) (solid lines).

### 4.2. TIRM with large penetration depth

*I*(

*z*) is not valid, i.e. for large penetration depth as mentioned above. Figure 6 shows the potential obtained for the same particle as in Fig. 5 but for a penetration depth (

*β*=720

*nm*). Note, that compared to Fig. 5 the potential extends over a much larger distance range since the particle’s motion can be tracked from hundreds of nanometers to microns. The green data points show the faulty interaction potential that is obtained when assuming an exponential

*I*(

*z*). Since the only difference is in the illumination, the same potential as in Fig. 5 should be retrieved [solid line in Fig. 6(a)]. However, applying an exponential

*I*(

*z*) [green line in Fig. 6(b)] wiggles appear in the potential [green dots in Fig. 6(a)]. Their origin is due to multiple reflections between the particle and the wall as discussed in detail in [21

21. L. Helden, E. Eremina, N. Riefler, C. Hertlein, C. Bechinger, Y. Eremin, and T. Wriedt, “Single-particle evanescent light scattering simulations for total internal reflection microscopy,” Appl. Opt. **45**, 7299–7308 (2006). [CrossRef] [PubMed]

*I*(

*z*) [black line in Fig. 6(b)] is obtained with the algorithm proposed in the previous section: after 9 iterations the conditions in Eqs. (6) appear reasonably satisfied, as shown in Fig. 6(c). With this

*I*(

*z*), we reconstructed the potential represented by the black dots in Fig. 6(a), in good agreement with the one in Fig. 5. It should be noticed that, even though the deviations of the correct

*I*(

*z*) from an exponential function are quite small, this is enough to significantly alter the measurement of the potential. This again demonstrates the importance of obtaining the correct

*I*(

*z*) for the analysis of TIRM experiments.

### 4.3. TIRM in front of a reflective surface

*nm*gold-layer, reflectivity ≈60%, β=244

*nm*). The experimental conditions are similar to the previous experiments. Only the salt concentration was lowered to avoid sticking of the particle to the gold surface due to van der Waals forces, leading to a larger electrostatic particle-surface repulsion, and the optical trap was not used. Using an exponential

*I*(

*z*) [green line in Fig. 7(b)], we obtain the potential represented by the green dots in Fig. 7(a), which clearly features unphysical artifacts, e.g. spurious potential minima. After 27 iterations of the data analysis algorithm, the black

*I*(

*z*) in Fig. 7(b) is obtained, which reasonably satisfies the criteria in Eqs. (6) [Fig. 7(c)]. The reconstructed potential [black dots in Fig. 7(a)] fits well to theoretical predictions (solid line); in particular the unphysical minima disappear.

## 5. Conclusions & Outlook

*a priori*knowledge of the intensity-distance relation.

*I*(

*z*) ∝ exp(-

*z*/

*β*) can safely be assumed only for short penetration depths of the evanescent field and transparent surfaces. This, however, poses considerable constraints to the experimental conditions and the range of forces where TIRM can be applied. Here, we have proposed a technique to determine

*I*(

*z*) that relies only on the hydrodynamic particle-surface interaction [Eq. (1)] and, differently from existing data evaluation schemes, makes no assumption on the functional form of

*I*(

*z*) or on the wall-particle potential. This technique will particularly be beneficial for the extension of TIRM to new domains. Here, we have demonstrated TIRM with a very large penetration depth, which allows one to bridge the gap between surface measurements and bulk measurements, and TIRM in front of a reflecting (gold-coated) surface, which allows plasmonic and biological applications.

*in situ*[24

24. M. A. Bevan and D. C. Prieve, “Hindered diffusion of colloidal particles very near to a wall: Revisited,” J. Chem. Phys. **113**, 1228–1236 (2000). [CrossRef]

*I*(

*z*). Were

*I*(

*z*) not monotonous, as it might happen for a metallic particle in front of a reflective surface, the technique can be adapted to use the information from two non-monotonous signals, e.g. the scattering from two evanescent fields with different wavelength [31

**24**, 1–4 (2008). [CrossRef]

*I*(

*z*), they permit a self-consistency check on the data analysis. Even when an exponential

*I*(

*z*) is justified, errors that arise from the estimation of some parameters (e.g. the zero-intensity

*I*

_{0}and the background intensity

*b*) can be easily avoided by checking the consistency of the analyzed data with the aforementioned criteria. In principle, the analysis of TIRM data can be completely automatized, possibly providing the missing link for a widespread application of TIRM to fields, such as biology, where automated analysis techniques are highly appreciated.

_{s}36. G. Volpe, G. Kozyreff, and D. Petrov, “Backscattering position detection for photonic force microscopy,” J. Appl. Phys. **102**, 084701 (2007). [CrossRef]

## References and links

1. | J. Walz, “Measuring particle interactions with total internal reflection microscopy,” Curr. Opin. Colloid. Interface Sci. |

2. | D. C. Prieve, “Measurement of colloidal forces with TIRM,” Adv. Colloid. Interface Sci. |

3. | G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Phys. Rev. Lett. |

4. | W. Ducker, T. Senden, and R. Pashley, “Direct measurement of colloidal forces using an atomic force micro-scope,” Nature |

5. | L. P. Ghislain and W. W. Webb, “Scanning-force microscope based on an optical trap,” Opt. Lett. |

6. | K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. |

7. | G. Volpe, G. Volpe, and D. Petrov, “Brownian motion in a nonhomogeneous force field and photonic force microscope,” Phys. Rev. E |

8. | S. G. Bike and D. C. Prieve, “Measurements of double-layer repulsion for slightly overlapping counterion clouds,” Int. J. Multiphase Flow |

9. | H. H. von Grünberg, L. Helden, P. Leiderer, and C. Bechinger, “Measurement of surface charge densities on Brownian particles using total internal reflection microscopy,” J. Chem. Phys. |

10. | M. A. Bevan and D. C. Prieve, “Direct measurement of retarded van der Waals attraction,” Langmuir |

11. | M. Piech, P. Weronski, X. Wu, and J. Y. Walz, “Prediction and measurement of the interparticle depletion interaction next to a flat wall,” J. Colloid Interface Sci. |

12. | M. A. Bevan and P. J. Scales, “Solvent quality dependent interactions and phase behavior of polystyrene particles with physisorbed PEO-PPO-PEO,” Langmuir |

13. | L. Helden, R. Roth, G. H. Koenderink, P. Leiderer, and C. Bechinger, “Direct measurement of entropic forces induced by rigid rods,” Phys. Rev. Lett. |

14. | D. Kleshchanok, R. Tuinier, and P. R. Lang, “Depletion interaction mediated by a polydisperse polymer studied with total internal reflection microscopy,” Langmuir |

15. | V. Blickle, D. Babic, and C. Bechinger, “Evanescent light scattering with magnetic colloids,” Appl. Phys. Lett. |

16. | C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, “Direct measurement of critical Casimir forces,” Nature |

17. | H. Chew, D.-S. Wang, and M. Kerker, “Elastic scattering of evanescent electromagnetic waves,” Appl. Opt. |

18. | C. C. Liu, T. Kaiser, S. Lange, and G. Schweiger, “Structural resonances in a dielectric sphere illuminated by an evanescent wave,” Opt. Commun. |

19. | R. Wannemacher, A. Pack, and M. Quinten, “Resonant absorption and scattering in evanescent fields,” Appl. Phys. B |

20. | C. Liu, T. Weigel, and G. Schweiger, “Structural resonances in a dielectric sphere on a dielectric surface illuminated by an evanescent wave,” Opt. Commun. |

21. | L. Helden, E. Eremina, N. Riefler, C. Hertlein, C. Bechinger, Y. Eremin, and T. Wriedt, “Single-particle evanescent light scattering simulations for total internal reflection microscopy,” Appl. Opt. |

22. | N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, “Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy,” J. Quantum Spectr. Rad. Transfer |

23. | D. C. Prieve and J. Y. Walz, “Scattering of an evanescent surface wave by a microscopic dielectric sphere,” Appl. Opt. |

24. | M. A. Bevan and D. C. Prieve, “Hindered diffusion of colloidal particles very near to a wall: Revisited,” J. Chem. Phys. |

25. | J. Y. Walz and D. C. Prieve, “Prediction and measurement of the optical trapping forces on a dielectric sphere,” Langmuir |

26. | O. Marti, H. Bielefeldt, B. Hecht, S. Herminghaus, P. Leiderer, and J. Mlynek, “Near-field optical measurement of the surface plasmon field,” Opt. Commun. |

27. | G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett. |

28. | M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys. |

29. | M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femto-newton range,” Phys. Rev. Lett. |

30. | A. Ulman, “Formation and structure of self-assembled monolayers,” Chem. Rev. |

31. | C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, “Experimental verification of an exact evanescent light scattering model for TIRM,” Langmuir |

32. | C. T. McKee, S. C. Clark, J. Y. Walz, and W. A. Ducker, “Relationship between scattered intensity and separation for particles in an evanescent field,” Langmuir |

33. | H. Brenner, “The slow motion of a sphere through a viscous fluid towards a plane surface,” Chem. Eng. Sci. |

34. | R. J. Oetama and J. Y. Walz, “A new approach for analyzing particle motion near an interface using total internal reflection microscopy,” J. Colloid. Interface Sci. |

35. | M. D. Carbajal-Tinoco, R. Lopez-Fernandez, and J. L. Arauz-Lara, “Asymmetry in colloidal diffusion near a rigid wall,” Phys. Rev. Lett. |

36. | G. Volpe, G. Kozyreff, and D. Petrov, “Backscattering position detection for photonic force microscopy,” J. Appl. Phys. |

**OCIS Codes**

(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology

(120.5820) Instrumentation, measurement, and metrology : Scattering measurements

(180.0180) Microscopy : Microscopy

(240.0240) Optics at surfaces : Optics at surfaces

(240.6690) Optics at surfaces : Surface waves

(260.6970) Physical optics : Total internal reflection

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: September 29, 2009

Revised Manuscript: November 19, 2009

Manuscript Accepted: November 20, 2009

Published: December 16, 2009

**Virtual Issues**

Vol. 5, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

Giovanni Volpe, Thomas Brettschneider, Laurent Helden, and Clemens Bechinger, "Novel perspectives for the application of total internal reflection microscopy," Opt. Express **17**, 23975-23985 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23975

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### References

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- G. Volpe, G. Kozyreff, and D. Petrov, "Backscattering position detection for photonic force microscopy," J. Appl. Phys. 102, 084701 (2007). [CrossRef]

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