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1 Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 Supporting Information for Exitation polarization modulation in loalization mirosopy allows to resolve struture of individual non-blinking nano-objets D. Thomsson, G. Sforazzini, H. L. Anderson and I. G. Sheblykin * Chemial Physis, Lund University, Box 14, 100, Lund, Sweden ivan.sheblykin@hemphys.lu.se Chemistry Researh Laboratory, Department of Chemistry, University of Oxford, Mansfield Road, Oxford, OX1 3TA (UK) 1. The polymer and sample preparation. Centroid loalization 3. Chung-Kennedy (C-K) algorithm 4. Error estimation 5. Image drift 6. Experimental errors and hek of the drift ompensation 7. Notes on hain onformation reovery 8. Influene of the emission polarization on the loalization auray 9. Fluoresene brightness of a single moleule 10. Estimation of NA in exitation 11. Movie showing the entroid motion for the moleule m4 1. Sample preparation The polymer For the sample preparation the polystyrene (PS) was dissolved in toluene (10 mg/ml). PFBV-Rtx (Fig. S-1) was also dissolved in toluene at low onentrations and mixed with the PS/toluene solution. The weightto-weight ratio of PFBV-Rtx/PS was PFBV-Rtx/PS solutions were spin ast on leaned quartz substrates resulting in 00 nm thik PS films. DXP was also immobilized in PS films using the same tehnique. Figure S-1. Chemial struture of the polymer DXP dye To alibrate the setup we used N,N -bis(,6-dimethylphenyl)perylene-3,4,9,10-tetraarboxyli diimide (DXP). This dye is ommerially available from Aldrih. DXP moleules were dissolved in toluene. Mixing with a PS/toluene solution followed by spin asting on leaned quarts substrates resulted in 00 nm thik DXP/PS films with w/w ratio of 10-3 to Centroid funtion loalization Two-dimensional (D) Gaussian funtions f x, y x x y y 0 0 Aexp x y (S-1) 1

2 Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 were fitted to the fluoresene entroid using a weighted nonlinear least square fit: N k 1 1 u i f i (S-) i The weight fator σ i in eq. S- is a sum of the varianes of the photon ounting noise and the variane of the bakground. 1 So σ i = σ photon i + σ BG or σ i = f i + σ BG sine the expetation value is equal to the variane for the Poisson distribution. A nonlinear Levenberg-Marquardt algorithm was used to find the best fit. 3. Chung-Kennedy (C-K) algorithm The measured time-dependene of the entroid positions (x, y) of the D Gaussian funtions were filtered with an edge preserving filter (Chung-Kennedy (C-K) algorithm) -5 in order to derease the loalization error. The C-K filter is a nonlinear filter that statistially evaluates data in a window of length (w) before and after the sampled data point i. The idea is to alulate preditors based on the events before and after i. The preditors are then used to weight so-alled estimators, whih are alulated for the same historial and future events. The notations below follow those in referene. 5 The first step is to alulate the mean values (estimators) for the windows in front of (+) and behind (-) the data point i. w 1 X i x i (S-3) k w k1 The length of the window an be hosen arbitrarily. For the same windows as in equation (3) the varianes are alulated: w xi k Xi 1 i (S-4) w k 1 The varianes are used to alulate the preditors 4 or, in other words, swithing fators g: 5 g i g i p i p p i i p i p p i i (S-5) (S-6) The nonlinear parameter p an be hosen arbitrarily. A useful range is [1, 100]. 4 Using p = 0 onverts the nonlinear filter into a regular linear filter i.e. a nearest neighbor smoothing filter. The number of data points that are inluded in the smoothing is determined by the size of the window. The denominators are used for the normalization: g g 1 (S-7) i i The filtered output is given by X i g X g X (S-8) out i i i In the end the optimal hoie of the parameters p and w is determined by the experimental data inluding the features of the noise. We used p = 1 and w = 10 for our experiments. The nonlinearity was still high enough to onsider the filter to be signifiantly different from the linear filter. 4. Error Estimation Several fators ontribute to the errors in the loalization auray. First of all there are fundamental reasons like photon ounting noise, pixelation noise and bakground emission. i

3 Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 The detetor (CCD amera) introdues an additional dark noise and a readout noise. Seondly there are errors whih originate from the mehanial parts of the experimental setup. These ould be due to hanges in the pressure of the gas flow (if a gas hamber with a ontinuous flow is used) or mehanial vibrations or stress in the optial elements. Moving parts an introdue a systemati drift whih is idential for all imaged objets in the experiment. An expression for the fundamental errors without the drift was derived by Thompson et.al. 1. In their paper a disrepany of 30 % between their analytial and numerial alulations was reported whih has been reently explained by Mortensen et.al. 6 4 p 8 b N 1N p N (S-9) Here σ is the standard deviation of the entroid, p is the effetive pixel size and b is the standard deviation of the bakground intensity (in number of photons). In our work the numerial simulations and the ontrol experiments on single dyes onstituted the basis for the error estimations. Numerially and experimentally obtained values were ompared with the expeted errors (aording to equation (9)) for the partiular experimental settings. 5. Image drift The image drift is different in eah experiment and must be ompensated for. One way to do that is by using a referene objet like a fluoresent bead 3 whih moves together with the sample. Another way is to do the ompensation by using the information from several objets whih experiened the same drift and to alulate their average positions. The latter proedure was the one hosen in this work. Examples of the loalization drift are shown in figure S-. By hoosing arefully a set of moleules for the average alulation the drift an be ompensated for with a reasonable auray. Only the most stable moleules were hosen for this purpose. One the average positions i.e. the drift were alulated the positions for all moleules in the same experiment ould be orreted. If the orretion is not suessful all moleules will show a systemati error in the x, y position plots. Typially the data are elongated in some diretion whih is the same for all moleules in the given experiment. a) b) Figure S-. Examples of the image drift. (a) Six single PFBV-Rtx hains were used to alulate the average positions for the drift ompensation. (b) Drift in the loalization data for a sample with DXP dyes. Five dye moleules were used to onstrut the average drift. The drift ould suessfully be ompensated for in both ases. The image exposure time in these two experiments was different: polymer - t exp = 0.5 s, dyes - t exp =.5 s. 3

Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 6.

arried out experiments on DXP moleules. In order to have a omparable signal to noise for single dyes and single polymer hains an exitation density of 60 W m - together with an exposure time of.

The DXP sample was irradiated for about 0 minutes in order to bleah most of the moleules.

4 Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry Experimental errors and hek of the drift ompensation In order to test the entire data handling from the aquiring to plotting and to get an estimation of the errors where all soures were inluded we arried out experiments on DXP moleules. In order to have a omparable signal to noise for single dyes and single polymer hains an exitation density of 60 W m - together with an exposure time of.5 s was used. These numbers an be ompared with those for the PFBV-Rtx polymer where the exitation density and exposure time was 60 W m - and 0.5 s respetively. The DXP sample was irradiated for about 0 minutes in order to bleah most of the moleules. Only few (the most stable ones) moleules remained strongly emissive after the irradiation treatment and were stable during the experimental time 50 s. The effetive onentration of the useful emissive moleules was omparable to that for a typial polymer sample used (see figure S-3). t = 0 min t = 0 min t = 0 min a) b) ) 8.0 μm 8.0 μm Figure S-3. Test of error estimations by loalization experiments on DXP dyes. (a) Dyes were mixed with PMMA at a relatively high onentration. The exposure time for the image (a) was 0. s. (b) After 0 minutes of laser irradiation with an exitation density of 60 Wm - only few stable dyes remained (exposure time 0. s). () A seond DXP/PMMA sample after 0 minutes of irradiation. The exposure time was.5 s for the image (). Loalization data for nine moleules obtained from the sample in () is shown in Figure S-4. Figure S-4 shows the loalization data for nine single moleules from Figure S-3(). Together with the loalization data irles are drawn. The radius of eah irle is.5 nm giving the sale to the piture. For eah moleule the average signal to noise ratio (SN) is reported. The spread in loalization an be ompared to the expeted errors shown in figure S-5. 4

5 Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 Figure S-4. Experimental tests of the loalization errors. Single DXP moleules were used to test the ability to remove the image drift and to get the theoretially estimated total loalization error. Data for nine stable single moleules is shown (Fig. S-3()). The signal to noise level is reported for eah dye. The irles are shown as a referene and have a radius whih orresponds to.5 nm. All nine moleules ame from the same experiment. In order to test further the data analysis addition simulations were arried out. Twodimensional Gaussian funtions (eq. S-3) were generated. Different levels of normally distributed noise (N) were added to the generated funtions. The signal to noise was haraterized by the signal amplitude B, whih was kept onstant, and the gradually inreasing noise N. x x y y f x y B 0 0, exp N (S-10) x y 5

6 Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 In figure S-5 the loalization error is plotted against signal to noise. The standard deviation of the loalization error was alulated for different SN intervals as well. The first interval was alulated as ΔSN 1 = SN HIGH, 1 SN LOW, 1 = = 50. The proedure was repeated for twelve equally sized intervals. The alulated standard deviations are shown as blak squares in figure S-5. / nm Loalization Error () Standard Deviation ( ) SN Figure S-5. The loalization error (ε) as a funtion of signal to noise (SN). Gray squares; loalization errors obtained from simulations. Blak squares; standard deviations (σ ε ) of the loalization error alulated in intervals of ΔSN = 50, starting at SN = 75. The standard deviations σ ε in figure S-5 and the experimental data in figure S-4 show only moderate differenes. It is therefore possible to onlude that the drift (shown in figure S-(b)) does not ontribute signifiantly to the loalization error one it has been aounted for. 7. Notes on the hain onformation reovery y y i+1 y i (a) d i d i+1 i i+1 Figure S-6. Parameters of a multihromophore hain x i xi+1 x When N hromophores of the same length are onneted to eah other (Fig. S-6) the number of parameters fully determining the hain geometry is redued from 3N (for eah hromophore we need to know two oordinates and one angle) to oordinates of the first hromophore and N angles (N+). 6

7 Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 Notes to Fig. S-7 and Fig. 3. We want to stress that the fits for N = 6 are better than those for N = 4 even though it is not easily seen in the Fig. S-7. It should also be mentioned that a poor math between the original and the regenerated hain never oinides with a good fit of the entroid position and the oordinate derivatives. In onnetion to Fig. S-7 we would also like to mention that a suessful fit of N = 6 or 5 dipoles to a system onsisting of ten is quite unusual with the presented method. A possible improvement whih has not been tried yet is to start with even lower number of dipoles initially e.g. N = or 3. Fitted parameters for the model with N = 3 ould then be used to alulate the starting parameters for the system with N = 4. This proedure ould be repeated few times inreasing the hane for the suessful fit. Figure S-7. Reovery of onformation of a 10-hromophore hain. 4,5, and 6 hromophores per hain were used. 8. Influene of the emission polarization on the loalization auray In general the fluoresene intensity entroid of an infinitely small objet (point spread funtion (PSF)) is not ompletely symmetri unless the polarization anisotropy 7,8 of the objet is lose to zero. If the transition dipole moment of a single dye moleule (emission is fully polarized) is oriented in the sample plane the PSF is not rotationally symmetri relative to the optial axis, however, the middle point still oinides with the objet loation. However, if the transition dipole moment is oriented out of the plane with an angle < 90 the intensity 7

Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 maximum of the PSF will be shifted relative to the atual physial position of the objet.

8 Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 maximum of the PSF will be shifted relative to the atual physial position of the objet. This type of asymmetry affets the loalization auray 9, the larger the objetive lens NA the larger the effet. Aording to the alulations 9 if NA<1.1 for the extreme ase of a single dipole in the sample plane the maximum loalization error is smaller than.5 nm. However, sine in our ase the fluoresene of PFBV-Rtx hains is only partially polarized with an average polarization degree of the loalization error must be signifiantly smaller. Therefore, the loalization error due to the fluoresene light polarization an be negleted in omparison with the entroid shifts orrelated with the exitation light polarization (Fig. 5 of the main artile). The asymmetry of the entroid shape an be measured by the ratio of the widths σ x /σ y of the fitted Gaussian funtions. In figure S-8 the ratios σ x /σ y are shown for the four moleules. Figure S-8. Fluoresene intensity transients for moleules m1 to m4 (the same moleules as in figure 3 of the artile). Moleules m1 and m have a lear exitation polarization modulation. Ratios (σ x /σ y ) are reported for eah moleule. A weak osillation orrelated with the polarization orientation an be seen. Average photon ounts for m1 to m4 were 9500, 5700, 4800 and 000 photons per image respetively (exposure time 0.5 s). Some osillations in σ x /σ y an be indeed seen for m, m3 and m4. We believe that this is beause for an anisotropi system without omplete energy transfer the fluoresene polarization degree is dependent on the exitation polarization angle. 8,11 Basially the photoseletion determines whih subset of the hromophores within the single hain that emits the most. Upon rotation of the exitation polarization the subset of hromophores hanges leading to fluoresene polarization hange and, as a onsequene, a hange of the PSF asymmetry ratio σ x /σ y. The effet of light polarization on the entroid loalization, if signifiant, should be orrelated with the polarization anisotropy of the moleules. Therefore for PFBV-Rtx we plot the average polarization degree (or modulation depth 8 ) in exitation, M x, or in emission, M m, against the average loalization amplitude A defined by eq. S- in the main text. Data for 37 moleules are shown in figure S-9 and S-10. No orrelation ould be seen. Polarization 8

9 Optial axis Amplitude Amplitude Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 parameters were measured before the super-resolution imaging was arried out therefore only moleules with minor photobleahing were inluded M m M x Figure S-9. Loalization amplitude A as a funtion of the polarization modulation depth in emission (M m ). No lear orrelation between M m and the amplitude an be seen. Figure S-10. Loalization amplitude A as a funtion of the polarization modulation depth in exitaion (M x ). No lear orrelation between M x and the amplitude an be seen. 9. Fluoresene brightness of a single moleule z Figure S-11 d vetor of the transition dipole moment E d Sample plane ex y E vetor of the exitation light eletri field Fluoresene is olleted by the same objetive lens. x Objetive lens Aording setion 3. of the paper, in the ase of low NA in exitation, intensity of the fluoresene olleted by the objetive lens with numerial aperture NA is: 9

10 Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 I B fl.oll Iex A, NA sin os ( e ) IexB, NA 1, NA A, NA os ( e ) (S-11) where A is the fluoresene olletion effiieny, is fluoresene quantum yield of the hromophore, I ex exitation power density, - absorption ross setion of the hromophore at the exitation wavelength, B fluoresene brightness.{lin, /id} Sine the emission of the hromophore an be represented as the sum of the emissions of two hromophores with the absorption ross setions os and sin oriented along Z-axis and within the XY plane respetively we an re-write the olletion effiieny A as follows: NA A A ana A, NA A, os sin (S-1) Z omponent XY omponent where a does not depend on the orientation of the dipole. Then the Eq.4 an be re-rewritten as follows: I fl.oll ex NA A, NA z os sin sin os ( ) I a (S-13) And fluoresene brightness then is B NA ana A, NA z os sin, 1 sin z The dependene of brightness on retains even for small NA. If NA 0, then A z =0, and the overall -dependene of the fluoresene intensity is sin 4 : e B I if 1 ana I a fl.oll ex NA 0 NA sin 4 4 sin os ( ) e (S-14) 10

11 Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry Estimation of NA in exitation Exitation spot, 30 Sample plane 17 mm n=1 100 mm Front lens of the objetive n=1.5 Figure S-1 Sample exitation sheme Figure S-13 To the alulation of the NA in exitation. =9.6 o ; 1.5*sin = sin ; = 6.4 o NA ex = n sin= 0.17 Before reahing the objetive lens, the exitation laser beam was de-ollimated by a lens with 300 mm foal distane. That is why the laser is foused slightly above the sample plane reating exitation spot of 0 in diameter (see fig. S-1). The diameter of the laser beam at the bak lens of the objetive lens was a 0.7 mm, while the diameter of the bak lens of the objetive was 7 mm. That is why the NA in exitation was muh less than the maximum ahievable with the urrent objetive lens (1.5). We estimated the maximum inlination angle of the laser light to the optial axis at the sample plane () by measuring the laser beam radius at a ertain distane from the objetive lens (Fig. S-13). The results of the measurements and alulations are given in the Fig.S-13 aption. Inlination angle of 6.4 degrees is very small, NA ex = So, the exitation was done in the regime lose to the paraxial limit. [1] R.E. Thompson, D.R. Larson, and W.W. Webb, Biophysial Journal, 00, 8, [] S. Habuhi, S. Onda, and M. Vaha, Physial Chemistry Chemial Physis, 011, 13, [3] S. Habuhi, S. Onda, and M. Vaha, Chemial Communiations, 009, [4] S.H. Chung and R.A. Kennedy, Journal of Neurosiene Methods, 1991, 40,

12 Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 [5] D.A. Smith, Philosophial Transations of the Royal Soiety of London Series B-Biologial Sienes, 1998, 353, [6] K.I. Mortensen, L.S. Churhman, J.A. Spudih, and H. Flyvbjerg, Nature Methods, 010, 7, 377-U59. [7] D.H. Hu, J. Yu, K. Wong, B. Baghi, P.J. Rossky, and P.F. Barbara, Nature, 000, 405, [8] O. Mirzov, R. Bloem, P.R. Hania, D. Thomsson, H.Z. Lin, and I.G. Sheblykin, Small, 009, 5, [9] J. Enderlein, E. Toprak, and P.R. Selvin, Opt. Express, 006, 14, [10] R. Camaho, D. Thomsson, G. Sforazzini, H.L. Anderson, and I.G. Sheblykin. Inhomogeneous quenhing as a limit of the orrelation between fluoresene polarization and onformation of single moleules Submitted to JPC Letters [11] R. Camaho, D. Thomsson, D. Yadav, and I.G. Sheblykin, Chem. Phys., 01, 406,

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