Supplemental Material for:
A bisected pupil for studying single-molecule
orientational dynamics and its application to 3D
super-resolution microscopy
Adam S. Backer1,2, Mikael P. Backlund2, Alexander R. von Diezmann2, Steffen J. Sahl2 and W. E.
Moerner2
1
2
Institute for Computational and Mathematical Engineering, Stanford University, 475 Via
Ortega, Stanford, California, 94305, USA
Department of Chemistry, Stanford University, 375 North-South Axis, Stanford, California,
94305, USA
Contents:
A: Localization shift tables………………………………………………………………….
2
B:
Orientation affects lobe separation……………………………………………………….
6
C:
Calibration notes…………………………………………………………………………
7
D: Overview of single-molecule fitting algorithms…………………………………………
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Lobe asymmetry and linear dichroism indicate rotational mobility……………………..
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E:
1
A. Localization shift tables
Figure S1: Plots show the orientation-induced localization shifts (Δx, Δy) and lobe asymmetries
(LA) in each polarization channel (T and R) for the BSP method based on simulations in
matched media. Each plot is a projection of the unit sphere into the plane in which the center
corresponds to θ = 0° and the outer edge corresponds to θ = 90° (see axis labels in bottom left
plot for exact transformation). Each row of plots corresponds to a different z position of the
emitter relative to the coverslip. The discontinuities present in the top row of results, when the
molecule is placed at the coverslip (distance from the focal plane Δz≪ 0), occur due to the two
lobes of the PSF nearly overlapping, leading to erratic behavior of our double-Gaussian fitting
algorithm and unreliable LA values; this regime is avoided in actual experiments.
2
Figure S2. Same as Figure S4 but for simulations carried out with the molecules embedded in
water, above a water/glass interface.
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Figure S3. Determination of LA threshold for rotationally fixed molecules. (a) Increasing the
LA threshold leads to (i) a decrease in 𝜒, and (ii) an increase in number of localizations retained.
(b) Representative histograms generated using LA thresholds of (i) 0.3 and (ii) 0.9.
To inform our choice of LA threshold for our simulations and experiments we generated
a library of simulated single-molecule images over the full range of orientation space (with ~1.6°
sampling in both θ and φ) and throughout a 1-μm z range. Images were calculated according to a
previously described vectorial method1, 2. We took the objective to be oil-immersion (n = 1.518)
and the sample to be in either a matched medium (Figure S1; corresponding to the simulated
experiments described in the main text) or water (n = 1.33; Figure S2; corresponding to
experimental imaging described in main text). We simulated molecules emitting light at λ = 600
nm. The focal plane of the objective was placed ~650 nm above the interface such that molecules
placed 500 nm above the interface would appear in focus due to the mismatch-induced focal
shift. Molecule z positions were varied between z = 0 (at the interface) and z = 1 μm above the
interface. We then fitted each image to a double-Gaussian function using nonlinear least squares
and estimated the position and LA. The plots in Figure S4 show the resulting orientation-induced
localization shifts and LAs. From inspection of these plots, we observe that the greatest
magnitude shifts occur when 𝜃 ≈ 45° with respect to the microscope coverslip. In comparing
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Figures S1 and S2 we note similar overall behavior, but with slightly lower-magnitude shifts in
the matched media case. We also note that the dipole orientations that cause severe
mislocalizations also induce LA values of large magnitude. Hence, by discarding detected
molecules with pronounced LAs, we can effectively filter out inaccurate localizations. In
practice, our choice of an LA magnitude threshold of 0.5 was based on the following
consideration: On one hand, a lower threshold would lead to a more accurate final image, but it
would also lead to fewer localizations overall, necessitating a higher labeling density, which may
be a challenge for some specimens of interest. In figure S3, we demonstrate the effects of more
aggressive LA thresholding applied to one of our simulated datasets (maximum signal: 1000
photons, background: 0 photons/pixel, separation distance: 60 nm): Indeed, a lower LA threshold
sacrifices labeling density, but achieves a superior resolution ratio, 𝜒. In the case of rotationally
fixed molecules, we found that a threshold of 0.5 served as a good compromise between
accuracy and number of localizations. On average, we found that ~50% of detected molecules
were discarded due to their LA being greater than 0.5. While rotationally mobile molecules will
be adequately pumped by an excitation source polarized perpendicular to the optical axis, we
found that at moderate signal levels, fixed molecules oriented near the optical axis could not be
effectively detected, due to their low pumping/collection efficiency. In this worst-case scenario,
we found that ~50% of the initial 90000 molecules in a given simulation were discarded, since
there was not enough signal for our template matching algorithm to identify them. We do not
expect such a low detection rate under more conventional imaging conditions, since rotational
mobility will be sufficient to ensure that the majority of molecules assume favorable orientations
for a significant fraction of the camera’s integration time.
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B. Orientation affects lobe-separation
Figure S4: a.) A plot of the lobe separation in the two polarization channels, inferred from fitting
Gaussians to simulated images of a dipole at different  orientations. Even though Δz is held
constant for all simulated images, the distance between lobes changes by over 250 nm. This
would cause Δz estimates to incur errors on the order of ~300nm, if one were to use the simple
calibration-curve method described in the text. Hence, our method requires rotationally mobile
molecules to accurately estimate Δz. b.) Sample simulated images of a molecule at different
orientations (Δz = 0nm, =0o, λ=609nm). Simulation resolution: 160nm/pixel.
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C: Calibration notes
Figure S5:(a) Calibration curve used to assign depth from lobe separation. (b) Precision
benchmarking data.
In order to calibrate the 3D imaging capability of our bisected phase mask imaging
system, we imaged a fluorescent bead (FluoSpheres, 200nm, 625/645, Invitrogen) immobilized
in polyvinyl alcohol on a microscope coverslip, while applying different amounts of defocus Δz.
Addition of a droplet of water above the bead was used to approximate the refractive index of a
cell. Once a suitable series of images had been acquired using known amounts of defocus, a
double-Gaussian was fit to the image of the fluorescent bead, and the lobe separation distance
was computed. Δz was then plotted as a function of the lobe separation distance, and a cubic
polynomial was fit to our calibration data (see figure S5.a). Δz values were then assigned to the
Alexa 647 molecules detected in our imaging experiment, simply by plugging their lobe
separation distances into the polynomial determined from our calibration data.
In figure S5.b, we benchmark localization precision of the BSP with respect to photons detected,
by imaging fluorescent beads under various laser intensities. Multiple localizations of the same
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beads were acquired, and the mean background-subtracted photons per frame for each bead were
calculated using an appropriate conversion factor from ADC counts. Localization precision as a
function of signal photons was estimated as the standard deviation in the extracted positions from
100 localizations of the same bead. Our precision (~15-30 nm x/y, ~30-50 nm z at typical singlemolecule intensity levels) is comparable to similar techniques that use wavefront modulation to
encode depth 3. Fits to the precision data demonstrate the expected 𝑁 −1/2 scaling, where 𝑁 is the
number of detected photons.For this plot, only molecules in the T-channel were used, causing the
x-precision to be slightly worse than the y-precision, due to the asymmetric shape of the PSF.
This behavior is reversed in the R-channel.
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D. Overview of single-molecule fitting algorithms
Due to the fact that the PSFs induced by the BSP phase mask appear as two
approximately Gaussian lobes, the 3D positions of molecules within a given polarization channel
may be determined by leveraging previously described methods 4. Briefly, we first identify the
double-lobed image from candidate molecules using a template matching algorithm, making use
of a template library composed of simulated images of fixed dipoles and isotropic emitters. Then,
using the MATLAB command lsqnonlin, a function composed of two Gaussians and a
constant offset is fit to each candidate single-molecule image—the means, amplitudes and
covariance matrices of each Gaussian, as well as the constant offset are treated as variable
parameters. The x-y position of the single molecule is estimated as the midpoint between the two
Gaussians. The depth of the molecule is inferred from the separation distance between the
Gaussians and the calibration data as in figure S5(a). Once molecules have been found in a given
polarization channel, their LDs must be determined by pairing the localizations between the two
channels. For our simulations involving fixed molecules, this task is trivial, since only one
molecule appears in each frame of data. Furthermore, for our experiments with fixed DCDHF-N6 molecules at low concentration, only a few individual molecules were analyzed, so it was
possible to locate their images in both polarization channels by hand. However, for our
experiments involving Alexa-647 labeled microtubules in a blinking buffer, it was necessary to
automate the pairing of localizations between channels. To accomplish this task, we employed
the Munkres assignment algorithm 5, 6. Given a list of molecules in the T- and R-polarization
channels, as well as a user-provided coordinate transformation that maps the position of a
molecule in the T-channel to where it ought to appear in the R-channel, the Munkres algorithm
computes the ‘cost’ of a pairing of a T- and R-channel localization as the square of the Euclidean
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distance between its R-channel coordinates and transformed T-channel coordinates. The
algorithm attempts to pair all localizations in the T-channel to appropriate localizations in the Rchannel, while minimizing the sum of the associated costs. If a suitable match for a molecule in
the T-channel could not be found within 1m of an R-channel localization (after coordinate
transformation), that molecule was discarded. In order to construct an appropriate coordinate
transformation, relating positions on our EMCCD detector in the T-channel to those in the Rchannel we imaged a microscope coverslip spincoated with fluorescent beads (FluoSpheres,
200nm, 625/645, Invitrogen) immobilized in polyvinyl alcohol. Individual beads were manually
identified in both polarization channels, and used as ‘control points’ for determining a linear
coordinate transformation between channels. With just ~10-20 control points, a sub-micron
accurate coordinate transformation can be established using the MATLAB function cp2tform.
This transformation is sufficiently accurate for the purpose of pairing localizations and thus
computing LDs. However, if one wished to precisely overlay localizations from the two different
polarization channels, a far more sophisticated image-mapping, such as that developed in 7,
would be required. Since the labeling of our microtubule sample was quite dense, we used the Rchannel localizations only for the purpose of computing LDs, and did not use the localization
data for super-resolution purposes. On the other hand, for our simulated experiments with
immobilized molecules, the coordinate transformation between polarization channels was known
exactly (i.e. the identity matrix). Hence, for these simulations we used localization data from
whichever channel provided more photons for a given molecule. Table ST1 provides a flowchart
of our data-processing protocols for both simulated and experimental data.
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Table ST1. Image processing pipelines for simulated and experimental data.
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E. Lobe asymmetry and linear dichroism data indicate rotational mobility
Figure S6: The region of interest used for compiling the LD and LA histograms of Figure 4.b,
main text, is depicted above, color-coded with respect to Δz, LA and LD. Throughout the field of
view, the LA and LD have low magnitude, implying that the Alexa-647 molecules labeling the
antibodies attached to the microtubules must be freely rotating on a timescale much faster than
the integration time of the detector, causing their PSFs to closely resemble isotropic emitters.
Red box shows region analyzed in Figure 4.a.iii, main text.
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