Supplementary Information

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1 Supplementary Information Interferometric scattering microscopy with polarization-selective dual detection scheme: Capturing the orientational information of anisotropic nanometric objects Il-Buem Lee #,,, Hyeon-Min Moon #,,, Jong-Hyeon Joo,, Kyoung-Hoon Kim,, Seok-Cheol Hong *,,, Minhaeng Cho *,, Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science, Seoul 0841, Korea Department of Physics, Korea University, Seoul 0841, Korea Department of Chemistry, Korea University, Seoul 0841, Korea 1

2 Supplementary Note 1. Signals in the psiscat technique and the effective scattering coefficients for lights directed to the cameras. Here we derive the light intensities measured in cameras H and V for a cylindrical nano-object (AuNR), the optical response of which is given as the following diagonal matrix (the first coordinate is along the long axis of AuNR and the second is perpendicular to the s e 0 symmetric axis): S 0 s. 0 We also consider the reflected field, the matrix for a half-wave plate, and the transformation matrix that links the lab coordinates and the particle coordinates, which are given as follows. re 1 i cos sin cos sin Er, HW 1 sin cos, TM sin cos Then the scattered field is given as re se s0 se s0 cos sin i Es se s0 se s0 cos sin Here we assume that asymmetric response for different polarizations only comes from scattering by anisotropic particles. r and r contain the effects of various optics and interfaces on the strength of electric fields of reference and scattered lights, respectively. Then, the electric fields of vertical and horizontal polarizations are given by rei se s0 r se s0 r Ev 1 cos sin r r E re s s r s s r r r i e 0 e 0 h 1 cos sin s s s s as s v (for -) and e 0 e 0 If we define r rcos cos s h (for +), we recover the expression in Eq. (). rs i For a cylindrical AuNR, we can make a further simplification. By assuming se s 0 and e e 1 r r and complex in general, we have i i Ei e e Iv Ev r cos sin Ei r r cos 1 cos sin Ei Ih r r cos 1 cos sin. and The signal usually appears dark against constant bright background and it corresponds to the -dependent cross term. The experimentally measured quantity is the one obtained by integrating the -dependent terms in I v and I h over ROI. Thus, we take the fitting functions S v and Sh for signals as follows. Sv Acos sin B, h cos sin the averaged and scaled differential signals are given by SiSCAT Acos B and Sdiff A sin B / C cos D S A B. Consequently,. Here A, B, C and D are fitting parameters. We recover the expressions in Eq. (9).

3 Supplementary Note. Focusing-dependent interferometric image. One interesting point in imaging a single AuNP (as well as AuNR) is that the contrast of the AuNP changed as the sample chamber was vertically translated with respect to the objective lens (Fig. S). We recognize this phase inversion as a result of the Gouy phase shift of light, varying sharply near the focal point of Gaussian beam. 4 The Gouy phase shift is defined as 1 z 1 z ( z) tan tan w0 zr where is the wavelength of light, w the beam waist of Gaussian beam, 0 z the axial position with the waist of the Gaussian beam at origin, and z, the characteristic length (named Rayleigh length) over which the Gouy phase shift becomes appreciable. r By translating the focus of the laser beam through a scatterer, the Gouy phase at the scatterer changes by at maximum. Upon scattering of light by scatterers, the scatterer serves as the origin of radiation. Thus, the evolution of the Gouy phase prior to scattering depends on the location of a scatterer relative to the focus while the evolution of the Gouy phase to the far-field detector after scattering would be the same / regardless of the relative position of the scatterer. On the other hand, the phase of the reflected light continuously evolves plus the constant shift. Thus, depending on the relative position of a focus to scatterers, we expect to see the phase difference up to, which can reverse the contrast (from bright to dark and vice versa) of the scattering center. Typically, z ~ / 0.6 f / D ~ f / D where is the wavelength of light in the medium of n ~1.4. Since the effective focal R length ( f ) is 1.8 mm (tube length/magnification) and size of aperture ( D ) is 5.4 mm (= NA f ), z ~ 3 nm, which can account for the observed phase change as we translate the sample over the indicated range. r 3

4 Figure S1. Schematics of the setup for the psiscat technique. The setup is largely similar to the setup reported for iscat technique except for several critical modifications. The linear polarizer (for 45 o polarization) followed by HWP1 enables us to turn the incident polarization at the sample. BS is a non-polarizing beam splitter while the original design for iscat utilizes a PBS followed by QWP to distinguish the output signal from the incident beam. HWP restores the polarization of the reflected light back to 45 o to split the output equally to the two CMOS cameras. In order to monitor the level of input intensity, we take out a small fraction of input beam at BS1 and direct it to a photodiode. 4

5 Figure S. iscat images of scattering particles (AuNP) for various vertical positions of the objective lens. Note the contrast inversion of the spot at -80 nm and +80 nm with respect to the reference position. 5

6 Figure S3. Background subtraction in iscat images. Subtraction is carried out separately for each polarization (left: h-pol, right: v-pol). 6

7 Figure S4. Image matching by the Affine transformation. Averaged images with and without the transformation are shown in (a) and (b), respectively. Differential image clearly indicates the effect of the Affine transformation (c): without the Affine transformation, artefactual ghost spots appear in the differential image (d). 7

8 Figure S5. The accuracy and precision of the Affine transformation in mapping nano-objects in the two polarization channels. Using three objects (circled in blue in (a)), we construct one Affine transformation. Applying the transformation to the location (x, y) of a nano-object shown in one polarization channel (Horizontal), we get the transformed location (x, y ) of the nano-object in the other channel (Vertical), which is not necessarily the same as the measured location (x", y") of the nano-object in the second channel. Here we define the accuracy of the transformation as the mean of the position difference (discrepancy) and the precision of the transformation as its standard deviation. (a) Identification of nano-object candidates (marked by circle) in the two channels. Nano-objects which the Affine transformation is applied for are circled in red. (b) Statistical analysis for x and y coordinates of the nano-objects. (Δx x" x : position difference in x, x : mean position difference, σ x : standard deviation of Δx; Δy ( y" y ), y, σ y are defined similarly.) The accuracy and precision of the transformation are less than one pixel. 8

9 Figure S6. iscat signals of single AuNPs as a function of incident polarization. 9

10 Figure S7. The response of AuNP to two orthogonal polarizations (θ = 45 and 135 ) is nearly identical as expected from the isotropy of AuNP. Histograms of the intensity ratio of iscat θ=45 to iscat θ=135 for (a) AuNP and (b) AuNR. As indicated by the kurtosis of the signal ratio, the ratio for AuNP is sharply populated near 1 (the mean of the ratio is 0.1 and its kurtosis is large (8.6), which indicates that the distribution is sharper than Gaussian (kurtosis ~ 3)). However, the ratio of AuNR has a very broad distribution as indicated by a small kurtosis value (-0.69). 10

11 Figure S8. (a-i) Scattering signals and epsf images from individual AuNRs, not shown in Fig. 4. Anisotropic scattering signals as a function of incident polarization. (inset) epsf image overlaid by a marker that represents the orientation acquired by the polarization-based method. Fair correlation of the orientations determined by the polarization-based method (orientation of polarization along which the iscat signal exhibits its maximum) and determined by the epsf shape of AuNRs (from (a) to (i), χ = 145.5, 80.8, 98.7, 186.5, 8.7, 5.8, 177.1, 146.9, and 55.4 ). 11

12 Figure S9. Requirement for the number of (independent) polarization angles in orientation determination via the polarization-based method. In Fig. 4, we acquired data points differing by 1 o in the polarization angle. In order to acquire data sets with less data points (hence with bigger steps in polarization angle), we utilized the same data shown in Fig. 4 but skipping a varying number of data points. For example, one complete set of data in Fig. 4 is composed of 180 data points (from 0 to 180 o by one degree step). To get a data set of 90 data points, we skip every second data point and for a set of 60 data points, we skip every two out of three data points, etc. To get a data set of 3 data points, we choose values at 0 o, 60 o, and 10 o. Figure shows how the orientation of AuNR determined experimentally changes as a function of data points used in the analysis. The four panels from top to bottom indicate the angle of AuNR orientation acquired from images from cameras H and V, their average, and their difference, respectively, with respect to various number of data points. Interestingly, the values of angle remain unchanged (lines are the best fits by constant for the entire data points from 5 to 180). Below 9 data points, we can estimate the orientation of AuNR within the accuracy of a few degrees. Such a high accuracy in with just a few data points suggests that the orientation information can be acquired with high temporal resolution. When we tried less than 5 data points (3 and 4 data points tested, shown in gray), we failed to get reliable fitting results. We can carry out a certain number of raster scans with one polarization angle and then we switch to another polarization angle and perform the same number of raster scans. We repeat the raster-scan to obtain a set of data with several polarization angles (say, 5 up to 9). In this way, we are still able to collect images with high spatial and temporal resolutions (as in iscat) while collecting the orientation information at the rate better than 1 sec -1. 1

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14 Figure S10. (a) Effect of SNR on the orientation determination of AuNRs. Images (at = 0) and signals (as a function of ) from individual AuNRs for various levels of laser output power ((i) 150 mw, (ii) 90 mw, (iii) 30 mw, (iv) 9 mw, (v) 5 mw) or SNR (characterized by signal/noise = μ t μ b where μ σ t 1 X N ROI t, μ b 1 X N ROI b, and σ 1 (X N ROI b μ b ) : μ t is the average total signal over ROI, μ b is the average background over ROI, σ is taken as the standard deviation of the background fluctuation, N is the number of pixels in ROI, and X t and X b are the total signal and background on each pixel in ROI, respectively). For the laser output power indicated above, the corresponding SNR values are 10.86, 8.05, 5.59, 5.47, and 5.7, respectively. While we got reasonable fits for orientation determination down to P = 30 mw (1/5 of the typical power used (150 mw)), we failed to acquire fair fits at power below 30 mw. Thus, we can say that the SNR below ~5.6 is not sufficient for reliable orientation determination. For 5 and 9 mw, only images are shown due to failed analysis. (b) Effect of (de)focusing on the orientation determination of AuNRs. Signals (as a function of ) from individual AuNRs for various defocusing distances. Within those defocusing distances, we could get reasonable fits for orientation determination. The scaled differential signals are expressed in normalized Strength (here, N. Strength ) meaning that differential signal in Strength is divided by sum signal in Strength. 14