field confinement with aberration correction for solid immersion lens based fluorescence correlation...

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Optics Communications 271 (2007) 462–469

Field confinement with aberration correction for solid immersionlens based fluorescence correlation spectroscopy

Ramachandra Rao *, Jelena Mitic, Alexandre Serov, Rainer A. Leitgeb, Theo Lasser

Laboratoire d’Optique Biomedicale, Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

Received 28 August 2006; received in revised form 19 October 2006; accepted 23 October 2006

Abstract

The solid immersion lens (SIL) as a tool for increasing the field confinement as well as providing optimal performance by aberrationcompensation in a confocal fluorescence correlation spectroscopy (FCS) system is illustrated here. Using Zernike polynomials we showthat aberration compensation and the resultant pre-shaping of the incident wavefront enables near diffraction-limited performance. Thisis explained based on vectorial computations for high apertures in the Debye approximation. The obtained axial resolution parametersare compared with the obtained diffusion times in a SIL-FCS experiment for measurements in solutions done at the single molecule level.� 2006 Elsevier B.V. All rights reserved.

Keywords: Fluorescence correlation spectroscopy; Solid immersion lens; Aberration compensation

1. Introduction

The solid immersion lens (SIL) has proved itself to be auseful tool for providing improved spatial resolution inmicroscopic imaging [1]. Essentially extending the diffrac-tion limit by filling the object space with a high refractiveindex material [2], it has since found applications in datastorage [3], lithography [4], near-field optics [5] and thestudy of semiconductor nanostructures [6]. It turned outthat with the applications of SILs to photoluminescencemicroscopy one achieved not only high spatial resolutionbut also greater improvement in collection efficiency [7].This dual advantage of high spatial resolution with collec-tion efficiency was extended further to obtain a tightly con-fined observation volume of the order of femtoliters influorescence correlation spectroscopy experiments (FCS)[8].

In the Fig. 1 we see that there is a direct relation betweenthe size of the observation volume and the system numeri-cal aperture (NA) and also on the concentration of the

0030-4018/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.optcom.2006.10.044

* Corresponding author. Tel.: +41 0216937719; fax: +41 0216933701.E-mail address: [email protected] (R. Rao).

molecules. It highlights the role of increasing NA therebyconstraining the observation volume as required for a sin-gle molecule detection experiment. Many biological exper-iments require measurements in the lM (micro-molar)regime which is permitted by the SIL-FCS setup. Anotherimportant advantage from the SIL-FCS setup is the facilityto conduct temperature measurements due to the air-gapbetween the SIL for biological applications [9].

The previous experimental results showed that with suit-able aberration corrections it was possible to have a goodsignal to background with the SIL at a nominal focusingdepth of 15–20 lm. The experimental values obtained area direct consequence of the size of the confocal volumewhich is infact directly proportional to the illuminationpoint spread function (PSF) of the focused field after theSIL planar interface [10]. This showed that with the SILit is possible to improve on the focal geometry in solutionwith sufficient aberration compensation and obtain neardiffraction limited performance (see Fig. 2).

One can therefore relate the observation volume to thedimensions of the illumination PSF of the system NA [10].

We can compare with the diffusion times which isobtained by fitting the data in the Gaussian approximation

mailto:[email protected]

NA1.4 1.0 0.6 0.31.4 1.0 0.6 0.3

Air objective +SIL 1.2NA,Thermal decoupling.

1.45NA oilimmersion

objective

1al 10al 0.1f l 1fl 10fl 0.1p

Ve

10μM

1μM

0.1μM

10nM

1nM

0.1nM

Cf

1.4 1.0 0.6 0.3


1.4 1.0 0.6 0.3

0.9NA objective


1.45NA oilimmersion

objective

Fig. 1. Schematic (not to scale) showing the effect of increasing NA whichdecreases the size of the observation volume (Ve) of the confocal FCSsystem. The SIL-FCS system enables measurements in the lM (micro-molar) regime as required by many biological applications.

Fig. 2. (a) Schematic illustration of the SIL-FCS epi-illumination setup.(BS dichroic beamsplitter, SF spatial filter (pinhole), avalanche photodiode (APD)). Emitted fluorescence is detected by an APD and thenprocessed by a multiple tau correlator (Corr). (b) The correction collar ofthe air objective used with the SIL.

R. Rao et al. / Optics Communications 271 (2007) 462–469 463

for the detection volume element given as V ¼ p3=2x2xyxz,

where xxy and xz are the transversal and axial extents,respectively [11]. Experimental data from a single moleculedetection technique like FCS depend not only on the opti-cal system parameters, as the signal detected is also essen-tially a function of the photophysical properties of thefluorescent molecules with an impact of the triplet-stateand photobleaching kinetics, excitation saturation andlaser-beam geometry. The shape of the measured correla-tion function due to diffusion is therefore accuratelydescribed by the molecule detection efficiency functionand by the diffusion coefficient of the molecules [12]. How-ever, when comparing the nature of the focused fields insolution most of these factors can be justifiably assumedto be constant.

In order to establish the viability of such an approach,it therefore becomes necessary to characterize the aberra-tions typically present and also ask how much correctionhas been done to produce the required focal field confine-

ment. Since the setup is essentially a confocal microscopethe basic formulations are analogous to that of a tradi-tional confocal imaging system with a fixed pinholediameter.

When the coverslip is replaced with the SIL, the treat-ment becomes even more important because of the highrefractive index of the SIL and the arising mismatch withwater. The unique geometry of the SIL needs to be takeninto consideration for studying the field confinement afterthe planar interface. The integral representations used hereare based on Torok’s formalism [13] which is essentiallybased on the diffraction integrals proposed by Wolf [14],valid for optical systems of high NA in the Debyeapproximation.

Motivated by the experimental data from our SIL-FCS experiments, this report seeks to characterize thefield after the SIL by presenting a detailed analysis ofthe SIL aberration function in the framework of the vec-torial Debye theory. Several accounts on the SIL withvectorial considerations have been undertaken before[15,16]. However, this is for the first time an exact formu-lation with a facility for generalized aberration compen-sation at increased nominal focusing depths is presentedwith an optimization of the pupil function for optimalnear diffraction limited performance for a SIL system.Taking into account the geometry of the SIL, we developthe exact phase function based on the wavefront coordi-nates of the SIL system which then is generalized interms of the Zernike circle polynomials. The role of aber-ration correction is highlighted by defining a ‘‘cost func-tion’’ which is optimized with a minimization algorithmto generate the amplitudes of the Zernike coefficients.This defines the pre-aberrated focusing field accordingto the Strehl ratio criterion for an optimal PSF in solu-tion after the SIL planar surface. The correspondingincrease in the amplitude of the intensity for the compen-sated PSF is also linked to the obtained experimentalresults.

2. Vectorial formulation

The origin O (as marked in caps in Fig. 3) of the(X,Y,Z) coordinate system is positioned at the Gaussianfocus. In formulating the mathematical expressions here,we use a relative coordinate system placed in the objectspace of the microscope system. We make the hypothesisthat a standard microscope based setup is used, with thesample consisting of the solution on the SIL planar sur-face (Fig. 2). We therefore have a moving coordinatesystem which corresponds to the axial variation of theair objective such that distances from the SIL planarsurface to the actual focusing point appear negative withrespect to the coordinate system. The focus distancefrom the SIL planar surface along the optical axis (z-axis) points from the sample to the objective. The SILplanar interface is therefore at a distance z = �d fromthe origin.

Fig. 3. Schematic of the SIL illumination geometry. The SIL is defocusedaxially at a distance z = �d from the Gaussian focus. The dark sphericalcurved line (W1) represents the unaberrated wavefront emerging from theobjective which is perfectly symmetrical with respect to the curved SILsurface while the dotted aspherical line (W2) represents the compensatedwavefront from the objective which balances the axial defocus intosolution.

464 R. Rao et al. / Optics Communications 271 (2007) 462–469

The system is illuminated by a linearly polarized E-field(x-direction) through the objective lens. W1 and W2 arerepresentations of the uncompensated (spherical) andcompensated (aspherical) wavefronts emerging from theobjective. The origin of the (X,Y,Z) coordinate systemis at the focus of the objective lens as if the SIL werenot present.

The vectorial electric field in the focal region of the SILfor an incident polarization in the x-direction is given by[17,18]

E3x

E3y

E3z

264

375 ¼ pi

k

I0 þ I2 cosð2wÞI2 sinð2wÞ2I1 cosðwÞ

264

375 ð1Þ

in the x-, y- and z-direction and I0, I1, I2 are the followingintegrals:

I0 ¼Z a

0

ffiffiffiffiffiffiffiffiffiffiffifficos h1

psin h1J 0ðk2r sin h2ÞðT s þ T p cos h3Þ

� exp½ik0Uðh1Þ� expðik3z cos h3Þdh1; ð2aÞ

I1 ¼Z a

0


psin h1J 1ðk2r sin h2ÞðT p sin h3Þ

� exp½ik0Uðh1Þ� expðik3z cos h3Þdh1; ð2bÞ

I2 ¼Z a

0


psin h1J 2ðk2r sin h2ÞðT s � T p cos h3Þ

� exp½ik0Uðh1Þ� expðik3z cos h3Þdh1: ð2cÞ

In the above expressions, a is the convergence semi-angle ofthe illumination and Jn(x) are the Bessel function of ordern. k1, k2 and k3 are the wave numbers in air, SIL and waterrespectively. h1 is the incident angle made by the lens withthe focal point which ranges from 0 to the maximum valuea and is used as the integration variable. w(x,y) is the anglecoordinate in the focal plane. The transmission coefficientsTs, p(h1) for the air-SIL-water media are computed as in[19]. The angles h2(h1) and h3(h1) are both a function ofthe incident angle as will also be seen in the followingsection.

The novelty in our treatment of the aberration functionlies in accounting for the particular wavefront coordinategeometry through the SIL for both the uncompensatedand compensated wave fronts that can further be general-ized for higher aberrations [20].

3. SIL aberration function

The incoming spherical wavefront from the micro-scope objective, which illustrates the plane of constantphase, is a sphere with a radius corresponding to the dis-tance with respect to the origin O. The curved sphericalwavefront represents the ideal wavefront when focusedon the SIL planar surface, corresponding to the aplanaticcondition. The wavefront due to the variation by the cor-rection collar is represented by the aspherical dotted linein Fig. 3.

The overall wavefront aberration of the SIL system isnow given by

U ¼ Usph þ Uplanar; ð3Þwherein, Usph denotes the contribution from the sphericalinterface of the SIL and Uplanar is the contribution fromthe planar interface.

Since, d� rSIL (Fig. 3), the difference in the curvaturesof the incident wavefront and the SIL spherical surface issmall. The contribution from the spherical interface Usph

is essentially a longitudinal defocus term which can beneglected in the overall analysis when compared to thedominant contribution due to the planar interface termUplanar [21].

Therefore the geometric aberration function for the SILwith good approximation is given as [22]:

Uðh1Þ � d½n3 cos h3 � n2 cos h2�: ð4ÞThe aberration function is independent of the azimuthalangle of the system and therefore, for a simple evaluationof the angles that go into the SIL aberration function weconsider the Z–X plane corresponding to the plane of thepaper. The following analysis takes into account the systemgeometry and provides the angles required for every mi-cron of axial displacement in solution. These angles are fur-ther incorporated in the overall computation of the Fresnelcoefficients.

In order to visualize the interdependence of the angleswith respect to the SIL coordinate system, we consider

Table 1Functional forms of Zernike circle polynomials of order n and zero kind,together with the aberrations that they describe

n Z0nðqÞ Description

2ffiffiffi3pð2q2 � 1Þ Defocus

4ffiffiffi5pð6q4 � 6q2 þ 1Þ First-order spherical

aberration6

ffiffiffi7pð20q6 � 30q4 þ 12q2 � 1Þ Second-order spherical

aberration8

ffiffiffi9pð70q8 � 140q6 þ 90q4 � 12q2 þ 1Þ Third-order spherical

aberration


the propagation of an arbitrary ray traversing across theentire air–SIL–water optical system.

The spherical SIL surface can be represented as

ðz1 þ dÞ2 þ x21 ¼ r2

SIL; ð5Þand the equation of the incident wavefront from the objec-tive is given by

z21 þ x2

1 ¼ ðrSIL þ dÞ2; ð6Þwhere the nominal axial defocus parameter d has alsobeen included. From Eqs. (5) and (6) we see that the wave-front intersects the SIL spherical surface at (z,x) =(�(rSIL + d),0).

We now consider an arbitrary ray from this incidentwavefront from the objective to the origin of the coordinatesystem that is given by

x1 ¼ �m1z1; ð7Þwhere m1 = tanh1 is the slope of the ray with respect to thehorizontal.

Solving for (5) and (7) gives the intersection point on thespherical surface of the SIL for the incoming ray given by

Aðz1; x1Þ ¼�2d �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4d2 � 4ð1þ m2

1Þðd2 � r2Þq

2ð1þ m21Þ

;�m1z1

0@

1A:ð8Þ

The angle u which corresponds to the normal for the SILspherical surface can be computed from the slope of thetwo points A(z1,x1) and C(�d, 0) as

u ¼ tan�1 x1

d þ z1

� �: ð9Þ

On the SIL’s spherical interface, we have: n1 sin(u � h1)= n2 sin(u � h2), from which the refracted angle into theSIL is then given by

h2 ¼ u� sin�1 n1

n2

sinðu� h1Þ� �

: ð10Þ

The refracted angle in water due to the refractive index mis-match at the interface is then given by

h3 ¼ sin�1 n2 sin h2

n3

� �: ð11Þ

The above coordinate transformations through the SIL arevalid for an aberrated wavefront propagating through theSIL system. The Eqs. (7)–(11) provide the variation inthe angles for the SIL geometry.

Following Torok [23], we next use a general aberrationfunction that can be expanded in terms of Zernike polyno-mials that eliminates the explicit dependence on h.

4. Optimization of the SIL aberration function

When analyzing wavefront aberrations of a circularpupil, Zernike polynomials are convenient to use becausethey have some useful properties: they form a complete

set, they can be separated into radial and angular func-tions, the individual polynomials are orthogonal and nor-malized over the unit circle and that they balanceaberrations. We now seek to correct the defocus term byintroducing a pre-aberration that is opposite to the amountof each Zernike aberration contained within U(d,q). To dothat we represent the SIL phase aberration function as aninfinite sum of Zernike aberration terms with An0 beingthe strength of the Zernike mode.

Assuming that the objective obeys the sine condition, weintroduce the normalized radius, q = sinh1/sina, where a isthe maximum angle determined by the numerical apertureof the objective lens. We can therefore rewrite Eq. (4) as [24]:

Uðd; qÞ ¼ d � f ðqÞn1 sin a: ð12ÞSince there is no azimuthal variation we can consider onlyZernike circle polynomials of order n and zero kind, Z0

nðqÞ(see Table 1). We therefore have

f ðqÞ ¼ A00 þX1n¼2

An0Z0nðqÞ: ð13Þ

Ignoring the coefficient A00 as a constant piston term andwhich has no effect on the aberrated PSF, we can thereforewrite the SIL aberration function as

Uðd; qÞ ¼ d �X1n¼2

An0Z0nðqÞ

( )n1 sin a: ð14Þ

We now seek the various strengths of the Zernike modesfor increasing aberration orders for correction at increasingfocusing depths. This is specified by the compensated phaseaberration function where we consider the influence ofaberrations corresponding to n P 2. We denote the corre-sponding coefficients for the correction terms by Bn0.

U0ðd; qÞ ¼ Uðd; qÞ � d �X2Nþ2

n¼2

Bn0Z0nðqÞ

( )n1 sin a: ð15Þ

To obtain the improved performance in solution we nowoptimize the SIL compensated aberration function U 0(q)in conjunction with the Strehl ratio definition till N = 2.

Based on the definition of the Strehl ratio for a systemwith the above input aberration function the variance ofthe phase aberration across the pupil is given by [25]

r2U ¼ hU02i � hU0i

2 ð16Þ

Table 2Look-up table for the aberration coefficients obtained for Eq. (11) afterthe minimization routine

d (lm) B20 B40 B60

1 �0.1 0 02.5 �0.3 0 05 �0.5 �0.1 07.5 �0.8 �0.1 0

10 �1 �0.2 012.5 �1.3 �0.2 �0.115 �1.6 �0.3 �0.117.5 �1.8 �0.4 �0.120 �2.1 �0.4 �0.1


with

hU0ni ¼ 1

p

Z 1

0

Z 2p

0

U0nðq;wÞqdqdw; ð17Þ

where the angular brackets indicate an average across thepupil given by the integral in Eq. (17). The pupil functionoptimization is done by minimizing the variance of thephase function in Eq. (16) over the exit plane of the micro-scope objective for the SIL system. The phase function de-fined by Eq. (15) is given as an input to the ‘‘fmins’’function which is defined for multivariate functions inMATLAB. Eq. (15) therefore acts as a ‘‘cost function’’and generates unique solutions of (B20,B40,B60) in its mul-ti-dimensional parameter space (Fig. 4).

The optimal Bn0 values were obtained for various axialdisplacements as seen in Table 2. We see that for everymicron of axial displacement there is a unique set of(Bn0) values. The normalized aberration functions for

Fig. 4. The 2D convex cross-sections of the multidimensional minimization rpresence of a unique solution space for every d value.

U(d,q) and U 0(d,q) for Eqs. (14) and (15), as a functionof q are given in Fig. 5a and b, respectively.

From Table. 2 we see that there the impact of higherorder terms (N = 2) starts after several microns of nominalfocusing depth.

outine for every micron of axial variation in solution. This indicates the

Fig. 5. (a) The form of the SIL aberration functions U(q) representing the uncompensated condition (W1) and (b) U 0(q) representing the compensatedconditions (W2). Note the vertical axes (in radians) are different in both cases.

Fig. 6. The x-component of the illumination PSFs (plotted in log scale) of(a) SIL + 0.6NA objective at d = 1 lm, (b) Diffraction limited 1.15NAreference system.


Generally, aberration compensation with increasingfocusing depth would do the following:

(a) Increase the peak intensity for increasing d.(b) Decrease the axial and lateral full width at half max-

imum (FWHM) of the compensated PSF when com-pared to the aberrated PSF.

From the viewpoint of a SIL-FCS experiment all theabove three considerations would imply an increase inthe signal to background translating into higher count ratesper molecule (CPM) [8].

We now present the numerical results of these consider-ations in the following section.

5. Distribution of point spread functions

The system parameters for modeling are based on theexperimental setups in [8]. For the low NA microscopeobjective with a correction collar we chose a Zeiss objective0.6NA LD Achroplan 40·/0.60 Korr, with a working dis-tance of 1.8 mm, which is sufficient to position the SIL lens(0.7 mm radius, LASF35, RI = 2.02). The resultant NA forthe above system is 1.2. This is compared with a waterimmersion objective of NA 1.15 [40·/1.15 Olympus,Uapo/340, (cover slip corrected)]. This is considered asour standard reference system in all the calculations. Dueto their similar NAs the EM field distributions for bothof them are compared. All computations were performedusing MATLAB and it showed narrower PSFs in the direc-tion perpendicular to that of the incident polarization.

Fig. 6a shows the PSF in the x–z plane for the SIL basedsystem. We denote it as the limiting experimental diffrac-tion limited PSF, obtained with a nominal focusing depth(d = 1 lm). This axial displacement is considered as wefocused in solution to prevent surface effects on the overallexperimental FCS curve [26]. The axial FWHM obtainedfor the SIL is 0.5725 lm.

Fig. 6b shows the PSF for a numerical aperture of 1.15.We consider a simple coverglass (ncg = 1.518) and water(nwater = 1.33) interface here and calculate the best near dif-fraction limited PSF here. The PSFs have therefore beenestimated for the best possible performance (cover glasscorrected) for the case of the reference system here. Theaxial FWHM obtained for the 1.15NA water immersionobjective system is 0.66 lm.

In Figs. 7 and 8a, it is clearly seen that for the nominalfocusing depth of 15 lm the focal spot is severely aber-rated. The strong oscillations on one side of the maximumagree qualitatively with other results for axial responses inliterature. We incorporate Eq. (14) as the SIL aberrationfunction in obtaining this PSF here. We note that the valueof the defocus term z/d = �0.4 is close to the value pre-dicted by the low angle theory, z/d = (1 � n1/n2) = �0.51.The distribution consists of a central aberrated spot thatis displaced from the origin of coordinates and a fringe

Fig. 7. The x-component of the illumination PSFs (plotted in log scale) of(a) SIL + 0.6NA objective at d = 15 lm, (b) SIL + 0.6NA objective(aberration compensation setting) at d = 15 lm.

Fig. 8. The y-component of the illumination PSFs (plotted in log scale) of(a) SIL + 0.6NA objective at d = 15 lm, (b) SIL + 0.6NA objective(aberration compensation setting) at d = 15 lm.

Table 3Comparison of experimental diffusion times with the axial and lateralFWHMs

Experiments[8]

Simulations

0.6NA + SIL sD (ls) Axial FWHM(lm)

Lateral FWHM(lm)

Uncompensatedd = 1 lm

29 0.5725 x: 0.2835,y: 0.1890

Compensatedd = 15 lm

29 0.5636 x: 0.3150,y: 0.2520

The PSFs are of comparable axial and lateral extents when close to theSIL planar surface and when focused in solution after optimal aberrationcompensation.

Fig. 9. The variation in the axial dimensions and the relative peakintensities of the illumination PSF when focusing at a nominal depthd = 15 lm. The uncompensated (dash–dot) PSF and the compensatedPSF (dot) with spherical aberration correction. The d = 1 lm (dark line)case for the SIL is considered as the reference.


pattern situated on the interface side of the diffractionfocus. The PSF is focused 8.8 lm away from the SIL planarsurface. The axial FWHM obtained here is 1.38 lm.

Figs. 7b and 8b show the extent to which the aberra-tion compensation has taken place with a resultantincrease in the peak intensity of the primary lobe andalso the FWHM optimized to 0.56 lm. We see that thefocus position is close to the nominal value here. Thisis obtained for the case of aberration compensation(Eq. (15)) which mainly takes into account the first andsecond order (N = 1 and 2) here. We note that our sim-ulations require the best possible wavefront to obtain theleast aberrated PSF at the desired z = �d value. No addi-tional assumptions regarding the axial defocus terms havebeen made here.

Table 3 summarizes the experimental details and links itto the computed PSF values. There is also an increase in therelative peak intensity for the case of compensated aberra-tions here. This also accounts for the high count-rates permolecule in the FCS experiments from a dye molecule dif-fusing far away from the SIL planar surface in the solution.

We clearly see that aberration compensation hasresulted in a decrease in the axial FWHM from 1.38 to0.56 lm comparable to the case when the focusing is closeto the SIL surface. The lateral extents exhibit the vectorialasymmetry confirming the non-Gaussian nature of the illu-mination PSF profiles. Fig. 9 shows the plots on a z varia-tion scaled to a common offset indicating the axial extentsand peak intensities relative to the 1 lm focusing case forthe SIL. Infact, the effect of compensation affects the PSFsmore strongly in the axial direction than that in the trans-verse direction. Also, a greater improvement in the PSFquality for the SIL is seen with a slight amount of aberra-tion correction. Infact, the residual aberration in the caseof N = 2 case is very small and it starts to play a role onlyfor larger d values in solution.

The reduction in the axial dimensions for the compen-sated case therefore highlights the confinement of the con-focal volume in the SIL-FCS experiments.


6. Discussion and conclusion

We have presented a detailed vectorial theory frame-work with a generalized aberration compensation for thefocusing with the SIL. In particular, the analysis proposedwith the SIL-aberration phase function enables us to justifyoptimal performance characteristics according to the Strehlratio and can be applied to any general SIL based applica-tion. From the dimensions obtained from the primary max-ima of the PSFs we see that the PSF is optimally focusedfor the SIL after suitable spherical aberration compensa-tion by the collar variation of the microscope objective.The FWHMs in both the cases are comparable to the dif-fraction limited PSF of a conventional high NA waterimmersion objective case. The effect of tighter field confine-ment is clearly seen for the SIL systems. We are thereforeable to justify the comparable performances for the SILbased system in solution aided by appropriate aberrationcompensation. Simple aberration correction upto secondorder restores near diffraction limited performance in solu-tion for an axial focusing of 15–20 lm. These results alsoagree well with the obtained parameters of the confocalvolumes in SIL-FCS experiments. The present model canbe further used for characterizing any SIL based systemwith improved resolution and contrast for conventionaland confocal microscopy.

Acknowledgement

This research is partly funded by the Swiss National Sci-ence Foundation.

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