Three-dimensional, single-molecule fluorescence
imaging beyond the diffraction limit by using
a double-helix point spread function
Sri Rama Prasanna Pavania,1, Michael A. Thompsonb,1, Julie S. Biteenb, Samuel J. Lordb, Na Liuc, Robert J. Twiegc,
Rafael Piestuna,2, and W. E. Moernerb,2
aDepartment of Electrical and Computer Engineering, University of Colorado, Boulder, CO 80309; bDepartment of Chemistry, Stanford University,
Stanford, CA 94305; and cDepartment of Chemistry, Kent State University, Kent, OH 44242
Contributed by W. E. Moerner, January 9, 2009 (sent for review December 21, 2008)
Wedemonstrate single-molecule fluorescence imaging beyond the
optical diffraction limit in 3 dimensions with a wide-field micro-
scope that exhibits a double-helix point spread function (DH-PSF).
The DH-PSF design features high and uniform Fisher information
and has 2 dominant lobes in the image plane whose angular
orientation rotates with the axial (z) position of the emitter. Single
fluorescent molecules in a thick polymer sample are localized in
single 500-ms acquisitions with 10- to 20-nm precision over a large
depth of field (2
m) by finding the center of the 2 DH-PSF lobes.
By using a photoactivatable fluorophore, repeated imaging of
sparse subsets with a DH-PSF microscope provides superresolution
imaging of high concentrations of molecules in all 3 dimensions.
The combination of optical PSF design and digital postprocessing
with photoactivatable fluorophores opens up avenues for improv-
ing 3D imaging resolution beyond the Rayleigh diffraction limit.
microscopy
photoactivation
superresolution
computational imaging

PSF engineering
F luorescence microscopy is ubiquitous in biological studiesbecause light can noninvasively probe the interior of a cell
with high signal-to-background and remarkable label specificity.
Unfortunately, optical diffraction limits the transverse (x–y)
resolution of a conventional f luorescence microscope to approx-
imately
/(2NA), where
is the optical wavelength and NA is the
numerical aperture of the objective lens (1). This limitation
requires that point sources need to be
200 nm apart in the
visible wavelength region to be distinguished with modern
high-quality f luorescence microscopes. Diffraction causes the
image of a single-point emitter to appear as a blob (i.e., the
point-spread function or PSF) with a width given by the diffrac-
tion limit. However, if the shape of the PSF is measured, then the
center position of the blob can be determined with a far greater
precision (termed superlocalization) that scales approximately
as the diffraction limit divided by the square root of the number
of photons collected, a fact noted as early as Heisenberg in the
context of electron localization with photons (2) and later
extended to point objects (3, 4) and single-molecule emitters
(5–8). Because single-molecule emitters are only a few nano-
meters in size, they represent particularly useful point sources for
imaging, and superlocalization of single molecules at room
temperature has been pushed to the 1-nm regime (9) in trans-
verse (2-dimensional) imaging. In the third (z) dimension, dif-
fraction also limits resolution to 2n
/NA2 with n the index of
refraction, corresponding to a depth of field of 500 nm in the
visible wavelength region with modern microscopes. Improve-
ments in 3D localization beyond this limit are also possible by
using astigmatism (10, 11), defocusing (12), or simultaneous
multiplane viewing (13).
Until recently, superlocalization of individual molecules was
unable to provide true resolution beyond the diffraction limit
(superresolution) because the concentration of emitters had to
be kept at a very low value, less than one molecule every (200
nm)2, to prevent overlap of the PSFs. In 2006, three groups
independently proposed localizing sparse ensembles of photo-
switchable or photoactivatable molecules as a solution to the
‘‘high concentration problem’’ to obtain superresolution fluo-
rescence images (14–16) (denoted PALM, STORM, and F-
PALM, respectively). A final image is formed by summing the
locations of all single molecules derived from imaging the
separate randomly generated sparse collections. Variations on
this idea have also appeared, for example, by using accumulated
binding of diffusible probes (17) or quantum dot blinking (18).
Importantly, several of these techniques have recently been
pushed to 3 dimensions by using astigmatism (19), multiplane
methods (20), and 2-photon activation by temporal focusing (21)
to quantify the z position of the emitters. In the astigmatic case,
the depth of field was only 600 nm, whereas in the extensively
analyzed (13) multiplane approach, the maximum depth of field
was 1 m, which has been recently extended to 2.5 m with
bright quantum dot emitters (22).
Here, we present a uniquemethod for 3D superresolution with
single fluorescent molecules where the PSF of the microscope
has been engineered to have 2 lobes that have a different angle
of the line between them depending on the axial position of the
emitting molecule. In effect, the PSF appears as a double-helix
along the z axis of the microscope; thus, we term it the
double-helix PSF (DH-PSF) for convenience (see Fig. 1B Inset).
This method is based on earlier work that showed that rotating
intensity DH-PSF distributions could be formed by taking
superpositions of G-Laguerre (GL) modes that form a cloud
along a line in the GL modal plane (23–25). The DH-PSF has
been used to localize photon-unlimited point scatterers inside
the volume of a glass slide, and to track moving fluorescent
microspheres (26). In addition, an information theoretical anal-
ysis shows that the DH-PSF provides higher and more uniform
Fisher information for 3D position estimation than the PSFs of
conventional lenses. Here, we show that a particularly useful
photon-limited source, a single-molecule emission dipole, can be
imaged far beyond the diffraction limit by using a DH-PSF. In
thick samples, we demonstrate superlocalization of single fluo-
rescent molecules with precisions as low as 10 nm laterally and
20 nm axially over axial ranges
2 m. Further, we also show
that 3D superresolution imaging of high concentrations of single
molecules in a bulk polymer sample can be achieved by using a
Author contributions: S.R.P.P., M.A.T., R.P., and W.E.M. designed research; S.R.P.P., M.A.T.,
J.S.B., R.P., and W.E.M. performed research; S.R.P.P., M.A.T., S.J.L., N.L., and R.J.T. contrib-
uted new reagents/analytic tools; S.R.P.P. and M.A.T. analyzed data; and S.R.P.P., M.A.T.,
J.S.B., S.J.L., R.J.T., R.P., and W.E.M. wrote the paper.
The authors declare no conflict of interest.
1S.R.P.P. and M.A.T. contributed equally to this work.
2To whom correspondence may be addressed. E-mail: wmoerner@stanford.edu or
piestun@colorado.edu.
This article contains supporting information online at www.pnas.org/cgi/content/full/
0900245106/DCSupplemental.
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photoactivatable 2-dicyanomethylene-3-cyano-2,5-dihydrofuran
(DCDHF) fluorophore, a modification of the recently reported
azido-DCDHF (27). Two molecules as close as 14 nm (x), 26 nm
(y), and 21 nm (z) are resolved by this technique. The ideas
presented here should be broadly applicable to superresolution
imaging in various fields ranging from single emitters in solid
hosts for materials science applications to biological and bio-
medical imaging studies.
Fundamentals of Imaging by Using the DH-PSF
The 3D positions of multiple sparse molecules are estimated with
a single wide-field fluorescence image by using the DH-PSF
design as follows. The imaging system is composed of a sample
located at the objective focal plane of a conventional inverted
microscope and an optical signal-processing section as shown in
Fig. 1A. The signal-processing section is essentially a 4f imaging
system with a reflective phase-only spatial light modulator
(SLM) placed in the Fourier plane. Specifically, an achromatic
lens L1 placed at a distance f from the microscope’s image plane
produces the Fourier transform of the image at a distance f
behind the lens. The phase of the Fourier transform is modulated
by reflection from the liquid crystal of the SLM. Because the
SLM is sensitive only to vertically polarized light, a vertical
polarizer P is placed immediately after the SLM to block any
horizontally polarized light not modulated by the SLM. The final
image is produced by another achromatic lens L2 ( f  15 cm)
placed at a distance f after the SLM and recorded with an
electron-multiplying CCD (EMCCD) camera.
When the SLM is loaded with the DH-PSF phase-mask (26)
(see supporting information (SI) Appendix), the Fourier trans-
form of the sample image is multiplied by the DH-PSF transfer
function. Equivalently, every object point is convolved with 2
DH-PSF lobes, with the angular orientation of the lobes de-
pending on the axial location of the object above or below focus.
The lobes are horizontal when the emitter is in focus. As the
emitter is moved toward the objective, the DH-PSF lobes rotate
in the counterclockwise direction. However, if the emitter is
moved away from the objective the lobes rotate in the clockwise
direction. When a sample comprises multiple sparse molecules
at different 3D positions, the detected DH-PSF image will
exhibit 2 lobes (with different angular orientations) for each
molecule. The transverse (x–y) position of a molecule is esti-
mated from the midpoint of the line connecting the positions of
the 2 lobes, and the axial position is estimated from the angle of
the line connecting the 2 lobes by using a calibration plot that
maps angles to axial positions. An example calibration plot of
angle versus z position is shown in Fig. 1B. Fig. 1B Inset is a
simulation of the 3D shape of the DH-PSF. Fig. 1C also shows
actual DH-PSF images taken from a fluorescent bead at differ-
ent z positions illustrating the type of data used to extract the
calibration plot. The beads (pumped with 514 nm) have an
emission spectrum with a peak at 580 nm.
Single-Molecule Localization by Using the DH-PSF
Although imaging of highly fluorescent beads with the DH-PSF
has been recently reported (26), it is critical to demonstrate
useful imaging of single molecules because the much lower
signal-to-background inherent in a typical single-f luorophore
experiment taxes any imaging system and highlights areas for
future development. Single-molecule imaging can be impeded by
the
75% loss associated with the SLM reflection arising from
nonidealities in the device. Nevertheless, we have achieved 3D
localization precision that compares well with previous ap-
proaches while more than doubling the available depth of field.
Fig. 2 shows the results from the localization of one single
molecule in a2-m-thick poly(methyl methacrylate) (PMMA)
film. The molecule is a derivative of the previously described
class of photoswitchable fluorogenic azido-DCDHF molecules,
specifically (E)-2-(4-(4-azido-2,3,5,6-tetrafluorostyryl)-3-cyano-
5,5-dimethylfuran-2(5H)-ylidene)malononitrile, abbreviated as
DCDHF-V-PF4-azide (see SI Appendix for structure). Although
a full photophysical characterization of this molecule is needed,
it was chosen for this study because (i) the azido-DCDHF class
Fig. 1. DH-PSF imaging system and z-calibration. (A) Collection path of the
single-molecule DH-PSF setup. IL is the imaging (tube) lens of the microscope,
L1 and L2 are focal-length-matched achromatic lenses, and SLM is a liquid
crystal spatial light modulator. (B) Typical calibration curve of angle between
2 lobes with respect to the horizontal versus axial position measured with a
piezo-controlled objective. (Inset) 3D plot of the DH-PSF intensity profile
(Scale bar: 400 nm.) (C) Images of a fluorescent bead used for the calibration
curve at different axial positions, with 0 being in focus.
Fig. 2. 3D localization of a singlemolecule. (A) Histogramof 44 localizations
of one single photoactivated DCDHF-V-PF4 molecule in x, y, and z in a layer of
PMMA. The standard deviations of the measurements in x, y, and z are 12.8,
12.1, and 19.5 nm, respectively. The smooth curve is a Gaussian fit in each case.
An average of 9,300 photons were detected per estimation on top of back-
ground noise fluctuations of 48 photons per pixel. (B) Representative single-
molecule image with DH-PSF acquired in one 500-ms frame. (C) Localizations
plotted in 3 dimensions.
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of fluorophores emit on the order of 106 photons before
photobleaching (27) (an order of magnitude more than photo-
switchable fluorescent proteins), (ii) the molecule has a suitable
emission wavelength for our SLM, and (iii) a relatively small
amount of blue light irradiance is necessary for photoactivation.
For the data shown, the fluorogenic azide functionalized mol-
ecule was previously irradiated with 407-nm light to generate the
amine functionalized emissive form (27). For imaging, the
molecule was pumped with 514 nm and the fluorescence peaking
at 580 nm was recorded for 500 ms per frame to yield images
similar to Fig. 2B. The synthesis and optical properties of the
molecule can be found in the SI Appendix.
In this work, the location of each single molecule was deter-
mined by using 2 different schemes (see SI Appendix). The first
method found the center of each DH-PSF lobe by using a
least-squares Gaussian fit, then determined the midpoint be-
tween the centroid positions to define the x,y position of the
bead, and finally obtained the angle between the centroid
positions, which gives the z position of the emitter. The second
method, which was considerably more computationally efficient
than the first, determined the positions of the lobes of the PSF
by using a simple centroid calculation. The first procedure gives
better precision measurements than the second, although it is
less robust in that it requires a fairly symmetric shape to obtain
a good fit. The data in Fig. 2 were analyzed by using the first
scheme, and data for the large number of molecules in Figs. 3 and
4 were analyzed by using the second scheme for computational
convenience.
The 3D position of one single molecule was estimated 44 times
and the histograms of the 3 spatial coordinates of the molecule
are presented in Fig. 2A. The molecule was found to have a mean
z position of 644 nm above the standard focal plane. Each
estimation used an average of 9,300 photons with an average rms
background fluctuation of 48 photons per pixel. The histograms
in Fig. 2A must be regarded as a population of successive
position determinations that have a population standard devi-
ation, or localization precision, of 12.8, 12.1, and 19.5 nm in x, y,
and z, respectively. The x direction is defined as the orientation
of the line between the 2 DH-PSF lobes for a molecule at z 
0 in Fig. 1. These values should be regarded as the expected
localization precision for a single measurement (7). As is well
known, if all of the 44 position measurements in Fig. 1A are
combined, the result will have a far smaller localization precision
as would be expected from the scaling of the standard error of
the mean (i.e., the inverse of the square root of the number of
measurements or 6.6 times smaller), but in many studies, mul-
tiple localizations of the same single molecule may not be
possible. The localization precision of our method is within the
same range as both the astigmatic (19) and multiplane tech-
niques (20), while simultaneously more than doubling the depth
of field. It is worth noting that the simple estimators reported
here are not statistically efficient because they do not reach the
Cramer–Rao bound for the DH-PSF (26). This indicates that the
simple estimators are not currently using all of the possible
information contained in the images, and that there is room for
significant improvement through the choice of a better estima-
tor. Also, the system can be made more photon-efficient by using
a custom DH-PSF phase mask, which would take away the need
for a polarizer and would avoid the SLM losses. These and other
improvements in background minimization and drift correction
should allow for improved localization precision in the future.
DH-PSF Imaging of Single Molecules in a Thick Sample
The DH-PSF imaging system can be used to identify the 3D
position of many molecules in a single image as long as the PSFs
from the different emitters do not appreciably overlap. Fig. 3
demonstrates this capability by using a sample containing a low
concentration of the fluorophore DCDHF-P (28) (see SI Ap-
pendix for structure) embedded in a 2-m-thick PMMA film.
Fig. 3A compares the standard and the DH-PSF images of 2
molecules at different 3D positions selected to be fairly close to
Fig. 3. 3D superlocalizations of a low concentration of DCDHF-P molecules
in a thick PMMA sample. (A) Comparison of the standard PSF (i.e.,Upper, SLM
off) to the DH-PSF image of 2molecules (Lower, SLMon). (Scale bar: 1m.) (B)
Representative image of many single molecules at different x, y, and z posi-
tions. (Scale bar: 2 m.) (C) 4D (x, y, and z, time) representation of single-
moleculepositiondeterminationsduringa sequenceof97 frames,witha color
map showing the time of acquisition.
Fig. 4. 3D superresolution imaging. (A) High concentrations of single mol-
ecules of DCDHF-V-PF4-azide in a thick PMMA sample image using the PALM/
STORM/F-PALM method with the DH-PSF as described in the text. Color
indicates total number of photons used for estimation after background
correction. (B) Zoom-in of position estimations formolecules 1 and2 (blue and
red, respectively) separated by 14 nm (x), 26 nm (y), and 21 nm (z); Euclidean
distance (green): 36 nm. (Scale bar: 20 nm.) (C) Image from activation cycle 1
showing molecule 1. (D) Image from later in cycle 1 confirming that molecule
1 bleached. (E) Image from activation cycle 2 showing molecule 2. (Scale bar:
C–E, 1 m.)
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the focal plane for purposes of illustration only. Notable in the
DH-PSF image is a slightly increased background compared with
the standard PSF, a property that arises from the distribution of
photons between the DH-PSF lobes over a long axial range. In
general, molecules away from the focal plane appear quite blurry
in the standard PSF image. In contrast, the DH-PSF image
encodes the axial position of the molecules in the angular
orientation of the molecules’ DH-PSF lobes, which are distinctly
above the background with approximately the same intensity
through the entire z range of interest. This increased depth-of-
field is illustrated directly in Fig. 3B, which shows a represen-
tative DH-PSF image of multiple molecules in a volume. Each
molecule is seen to exhibit 2 lobes oriented at an angle that is
uniquely related to its axial position. This image is obtained by
averaging 97 successive frames recorded with a 500-ms exposure
time. Fig. 3C shows the 3D positions of molecules extracted from
each of these 97 frames as a function of time in the imaging
sequence (encoded in the color map). Molecules were localized
below the diffraction limit over an axial range of 2m.Molecules
that were localized more than once are shown as a spread of
points, each representing a single localization event. This ap-
parent spread is not due to drift, but is rather an ensemble of
multiple position determinations as in Fig. 2A.
Imaging of Molecules Spaced Closer than the Diffraction Limit
When a large concentration of fluorophores is present, repeated
photoactivation, image acquisition, localization, and photo-
bleaching of nonoverlapping subsets of fluorescent molecules
provides resolutions beyond the classical diffraction limit (su-
perresolution). Fig. 4 shows that 3D superresolution can be
achieved with a DH-PSF system. We used the fluorogenic
DCDHF-V-PF4-azide (see SI Appendix) as our photoactivatable
molecule, again in a thick film of PMMA. Subsets of the
molecules were photoactivated with 407-nm light, and then
excited with 514-nm light to image the fluorescent emission
centered at 578 nm. Accordingly, a DH-PSF mask designed for
578 nm was loaded into the SLM. The power and the duration
of the purple 407-nm beam were chosen so that only a sparse
subset of molecules activate in each cycle.
Fig. 4A shows the 3D average position of each molecule
extracted from 30 activation cycles, with 30 (500 ms) frames per
activation. The color map encodes the total number of photons
available for position localization. Fig. 4B shows a zoom-in of 2
molecules establishing the superresolving capability of the
method: these 2 molecules are separated by 14 nm (x), 26 nm (y),
and 21 nm (z), for a Euclidean distance of 36 nm. Fig. 4 C–E
shows the corresponding images for these 2 molecules during 2
consecutive activation cycles. The initially emissive first mole-
cule (Fig. 4C) bleaches near the beginning of an activation/
imaging cycle (Fig. 4D), and the second molecule starts emitting
precisely after the second activation, 9.5 s after the first
molecule bleached. Because the dark time gap is far larger than
the blinking timescale for these molecules (100’s of millisec-
onds), and because these molecules are photoactivatable, but not
photoswitchable, the molecules that appear in different imaging
cycles (Fig. 4 C and E) must be different molecules. In future
work, where photoactivatable or photoswitchable molecules are
labeling a particular structure, superresolution information can
be extracted as long as the labeling density is sufficiently high to
satisfy the Nyquist criterion (29).
Conclusion
The DH-PSF provides a powerful new tool for 3D superlocal-
ization and superresolution imaging of single molecules. By
encoding the z-position in the angular orientation of 2 lobes in
the image, the x, y, and z positions of each single emitter can be
determined well beyond the optical diffraction limit. Moreover,
the DH-PSF enables 3D imaging with greater depth of field than
is available from other imaging methods. Despite losses from the
insertion of an SLM into the imaging system, single small
molecules can in fact be localized with precision in the 10- to
20-nm range in 3 dimensions with single images. It is expected
that future improvements in the phase mask design, the use of
a custom phase mask, optimized estimators, background mini-
mization, and a closed-loop drift correction will lead to even
further improvements in resolution. With the proofs-of-principle
reported here, the path is open to implementation of these ideas
in a range of areas of science, including the study of materials for
defect characterization, the quantum optical generation of op-
tical fields by using subwavelength localization of properly
coupled single emitters, the use of single molecules to charac-
terize nanostructures, and 3D biophysical and biomedical imag-
ing of labeled biomolecules inside and outside of cells.
Methods
Sample Preparation.Axial position calibration datawere obtained at 2 different
emissionwavelengths, 515nmand580nm,usingfluorescentbeads (Fluospheres
505/515, 200 nm, biotin labeled, and Fluospheres 565/580, 100 nm, carboxylated,
both fromMolecular Probes) immobilized in a spin-coated layer of 1%poly(vinyl
alcohol) (72,000 g/mol, Carl Roth Chemicals) in water; the polymer solution was
cleaned with activated charcoal and filtered before being doped with beads.
Single-molecule sampleswerepreparedbydopingananomolarconcentrationof
DCDHF-P (28) into a 10% solution of poly(methyl methacrylate) (Tg  105 °C,
molecular mass  75,000 g/mol atactic, polydispersity 7.8, Polysciences) in
distilled toluene that was spun (at 2,000 rpm for 30 s with an acceleration of
10,000 rpm/s) onto a plasma-etched glass coverslip to form a2-m-thick layer.
Thethicknesswasestimatedbyfindingtheaxial in-focuspositionofvarioussingle
molecules by scanning the zpositionof theobjective. The thick photoactivatable
sample was made similarly by using the molecule DCDHF-V-PF4-azide (for syn-
thesis, see SI Appendix), except that a layer of PVA containing 565/580-nm
fluorescent beads was spun on top of the PMMA layer to incorporate fiduciary
markers in the images.
Imaging. All epifluorescence images of both fluorescent beads and single
molecules were collected with an Olympus IX71 inverted microscope
equipped with a 1.4 NA 100 oil-immersion objective, where the setup has
been fully described in ref. 30 with the exception of the collection path. The
filters used were a dichroic mirror (Chroma Z514RDC or z488RDC) and a
longpass filter (Omega XF3082 or Chroma HQ545LP). The objective was fitted
witha z-piezoadjustablemount (PIFOCp-721.CDQstagewithE625.COanalog
controller, Physik Instrumente) that allowed for control of the zpositionof the
objective. The samples were imaged with either 488 nm (DCDHF-P) or 514 nm
(DCDHF-V-PF4-azide) circularly polarized excitation light (Coherent Innova 90
Ar laser)with an irradiance of 1–10 kW/cm2. Because someof thefluorogenic
DCDHF-V-PF4-azide molecules were already activated, the molecules were
first exposed to the 514-nm beam until most of them were bleached, leaving
only a sparse subset of them in the fluorescent state. For further superreso-
lution imaging, molecules were photoactivated by using circularly polarized
407-nm(Coherent Innova300Kr laser) lightwithan irradianceof1kW/cm2,
which was chosen such that only a few molecules were turned on at a time.
Images were then continuously acquired with 514-nm pumping with 500-ms
exposure time. After all of the molecules were bleached, the green beam was
blocked and the purple beam was unblocked for 100 ms to photoactivate
additional molecules. The green beam was then unblocked for the next 15 s,
until all of the activated molecules were bleached again. Each round of one
100-ms activation period and one 15-s imaging period constitutes one acti-
vation cycle. Thirty such cycles were required to obtain the data in Fig. 4.
Mechanical shutters under computer control were used to define the timing
of the imaging and activation beams.
In the collection path, a standard 4f imaging setup was used with a
phase-only spatial light modulator (Boulder Nonlinear Systems XY Phase
Series) programmed to generate the DH-PSF placed at the Fourier plane. The
light exiting the side port of the microscope was collected by a 15-cm focal
lengthachromat lens (EdmundNT32–886)placed15 cmfromthemicroscope’s
image plane (25.5 cm from the exit port). The SLM was placed 15 cm from this
lens at a slight angle such that the phase-modulated reflected beamwould be
diverted from the incoming beamby30°. The phase pattern on the SLMwas
made by using an optimization procedure described in ref. 25 (see SI Appen-
dix). The reflected light passed through a polarizer and was then collected by
another achromat lens 15 cm from the SLM. The real image was then focused
onto an EMCCD (Andor Ixon). Bead samples were imaged with no electron
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multiplication gain, whereas single-molecule samples were imaged with a
software gain setting of 250 yielding a calibrated gain of 224.5. The imaging
acquisition rate for all single-molecule imaging was 2 Hz.
Analysis.Movies from the camerawere exported by theAndor software as tiff
stacks. The imageswere thenanalyzedwithMATLAB. Twomethodswereused
to determine the center position of each lobe of theDH-PSF (see SI Appendix).
In brief, a threshold was applied to remove background, and then the center
position of each lobe of the DH-PSF was determined by using either a least-
squares Gaussian fit or a simple centroid calculation. The midpoint of the 2
centroids gave the x and y positions of the emitter and the angle of the line
connecting the 2 centroids with respect to the horizontal gave the axial
positionafter conversion fromdegrees tonanometers byusing the calibration
curve in Fig. 1.
The average number of photons detected in each case was obtained by
summing the fluorescence counts in a background corrected image coming
from a molecule and then converting the A/D counts into photons. The
conversion gain of our camera, 24.7 e per count, was calibrated by a method
described in the SI Appendix and the electron multiplication gain was cali-
brated to be 224.5 by measuring the increase in detected signal with gain
versus that for no gain.
ACKNOWLEDGMENTS. This work was supported in part by National Institute
of General Medical Sciences Grant R01GM085437 (to W.E.M.), by National
Science Foundation Award NIRT-0304650 (to R.P.), and by the Technology
Transfer Office of the University of Colorado (R.P.). S.R.P.P. was supported by
a CDM Optics PhD fellowship and M.A.T. was supported by a National Science
Foundation Graduate Fellowship and a Stanford Graduate Fellowship.
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