Research Article
Vol. 2, No. 2 / February 2015 / Optica
177
Adaptive optics correction of
specimen-induced aberrations
in single-molecule switching microscopy
DANIEL BURKE,1 BRIAN PATTON,1 FANG HUANG,3 JOERG BEWERSDORF,3,4
MARTIN J. BOOTH1,2,*
1
Centre for Neural Circuits and Behaviour, University of Oxford, Mansfield Road, Oxford OX1 3SR, UK
2
Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK
3
Department of Cell Biology, Yale University School of Medicine, New Haven, Connecticut 06511, USA
4
Department of Biomedical Engineering, Yale University, New Haven, Connecticut 06511, USA
AND
*Corresponding author: [email protected]
Received 3 September 2014; revised 6 November 2014; accepted 19 January 2015 (Doc. ID 221760); published 19 February 2015
Single-molecule switching (SMS) microscopy is a super-resolution method capable of producing images
with resolutions far exceeding that of the classical diffraction limit. However, like all optical microscopes,
SMS microscopes are sensitive to, and often limited by, specimen-induced aberrations. Adaptive optics
(AO) has proven beneficial in a range of microscopes to overcome the limitations caused by aberrations.
We report here on new AO methods for SMS microscopy that enable the feedback correction of specimeninduced aberrations. The benefits are demonstrated through two-dimensional and three-dimensional
STORM imaging. We expect that this advance will broaden the scope of SMS microscopy by enabling
deep-cell and tissue-level imaging. © 2015 Optical Society of America
OCIS codes: (180.2520) Fluorescence microscopy; (180.6900) Three-dimensional microscopy; (350.5730) Resolution; (220.1080) Active
or adaptive optics.
http://dx.doi.org/10.1364/OPTICA.2.000177
1. INTRODUCTION
Single-molecule switching (SMS) microscopes provide superresolved images of fluorescence-labeled biological specimens,
enabling the visualization of structures many times smaller
than the classical diffraction limit of the microscope [1–3].
Super-resolution is obtained through the localization of isolated single molecules to a much higher precision than the diffraction limit of the microscope. This process is enabled by the
stochastic switching of fluorescent molecules such that only a
small proportion of them can emit at any one time and ensures
that emission from adjacent molecules does not overlap in the
image. With these means, an image with resolution up to 10
times smaller than the diffraction limit of the microscope [4]
can be reconstructed. In the ideal (background-free) case, the
obtainable resolution is limited physically by the number of
2334-2536/15/020177-09$15/0$15.00 © 2015 Optical Society of America
photons that can be detected from each emitter, as the localization precision improves with the square root of the number
of photons [5]. In practice, the precision and accuracy of any
given localization is also affected by optical aberrations, such as
those introduced by the refractive index structure of the specimen, which degrade the imaging properties of the microscope
[6]. In this paper, potential localization errors and subsequent
image artifacts arising from optical aberrations have been investigated and a novel adaptive optics (AO) scheme has been
developed to negate these effects. The implementation of AO
in SMS microscopes will broaden the range of possible applications of these microscopes by enabling deep-cell and tissuelevel super-resolution imaging.
In considering the effects of aberrations, we note that the
optics of a SMS microscope are equivalent to those of a conventional wide-field fluorescence microscope and the detector
Research Article
is usually a pixelated EMCCD or sCMOS camera [7]. In a
wide-field microscope, aberrations cause an enlargement of
the point-spread function (PSF), particularly along the optic
axis, coupled with a decrease in the peak value of the PSF.
These effects cause a blurring and loss of contrast in the resulting images. When the object is a single molecule, free to rotate
[8], the spatial probability distribution for photon detection is
proportional to the PSF and the probability at a particular pixel
is proportional to the integral of the PSF over the pixel area. An
essential step in SMS microscopy is the estimation of the emitter position based on the distribution of detected photons.
This localization process usually involves the fitting of a model
PSF (often approximated for mathematical convenience as a
two-dimensional Gaussian) to the measured pixel data [4].
If a particular fit meets certain quality criteria—such as having
an estimated precision better than a chosen threshold—the fit
will be accepted and will contribute to the final image.
Inevitably, the precision of the fitting process is affected by
the compatibility of the model and the data. In an imaging
configuration where aberrations are negligible—for example,
when using a well-aligned microscope to image just beyond a
coverslip—the Gaussian PSF model is realistic [6]. However,
when imaging deeper into the specimen through varying
refractive indices, the actual PSF deviates significantly from
the Gaussian model [6,9].
There are two possible approaches to solve this problem. If
the aberrations can be determined, then this information may
be incorporated into the PSF model, so that it more accurately
represents the recorded data [10–12]. However, this can add
significant complexity to the fitting calculations, which then
has to accommodate the uncertainty in aberration measurement and include more degrees of freedom. Conversely,
AO can return the operation of the system to near the diffraction limit [13], hence permitting the use of the Gaussian PSF
model. AO aims to correct wavefront aberrations by deforming
an optical element by an equal and opposite amount to that of
the aberrations present in the system [14].
Following the AO approach, we have implemented a SMS
microscope incorporating a deformable mirror (DM) for aberration correction. DMs have previously been applied to SMS
microscopy to correct for instrumental aberrations, depthdependent spherical aberration from a known refractive index
mismatch, and to enable astigmatic three-dimensional (3D)
SMS imaging [15]. Here, we demonstrate a new feedback
AO scheme that enables for the first time the correction of
complex specimen-dependent aberrations. This is achieved by
a DM in a sensorless AO feedback correction loop using a
novel image-based metric, which is computed directly from
raw images of blinking emitters. This AO approach does not
rely on the presence of artificial guide stars, as is the case in
several other AO microscopes, but can be used with regular
specimen labeling. We show that the correction of specimen
aberrations significantly improves the performance of the microscope over correcting only for instrumental aberrations.
Furthermore, it is shown that additional spherical aberration
is present, which would not be corrected if assuming a
depth-dependent spherical aberration model.
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In this study, we show that AO extends the imaging capability of SMS microscopy down to several micrometers in cells.
Specifically, the AO scheme is applied to two-dimensional and
3D SMS microscopy.
2. MICROSCOPE LAYOUT AND DATA
ACQUISITION
The adaptive microscope layout is shown in Fig. 1. Wide-field
illumination was provided by a 500 mW, 655 nm wavelength
laser (MLL-III-655-500, Changchun New Industries), which
was brought to focus in the back aperture of a 1.4 NA oil
immersion lens (Olympus UPLSAPO 100XO). A second,
100 mW laser of wavelength 405 nm (Cobolt MLD 040506-01-0100-100) was coupled into the system as an activation
laser. Fluorescence emission was separated from laser excitation
using a dichroic filter (Chroma T660LPXR) and an emission
filter (Chroma ET690/50M). Images were acquired at up to
100 frames per second using an electron-multiplied CCD camera (Andor iXon DV887). This provided an effective field of
view of approximately 30 μm using 2 × 2 binning pixels,
each of unbinned effective projected size of 61.7 nm. A
140-actuator micromachined DM (Boston Micromachines
Corporation, multi-DM) was placed in the imaging path at
a plane conjugate to the objective lens pupil. A 4f lens system,
with magnification of 0.86, imaged the 5.04 mm diameter pupil of the objective lens onto a region of 4.28 mm diameter on
the DM. The DM was set up using the method explained in
the next section, to ensure that any instrumental aberrations
were removed before the imaging experiments were begun.
Sample and stage drift were negated by generating a superresolution optical fluctuation imaging [16] image from every
200 frames, then estimating and removing the relative image
shifts via their cross correlation [17].
Single-molecule emitters were identified in each frame using the maximum likelihood estimation (MLE) procedure described in [6,18]. Each frame was split into many small
subregions, each containing a single-emitter signal. An iterative
routine calculated the MLE for the x and y (and, where relevant, z) positions of each emitter along with the estimated
localization precision, photon count, and the background
Fig. 1. Simplified schematic of our custom-built microscope. Illumination from a 405 and a 655 nm laser were combined and focused into a
1.4 NA objective lens to create wide-field illumination. The light emitted
was separated from the excitation light by a dichroic filter and an
emission filter before being relayed onto a 140-actuator DM and finally
focused onto an EMCCD camera.
Research Article
fluorescence level. Out-of-focus single-molecule emission
events and unconverged fits were rejected using a rejection algorithm based on a log-likelihood ratio [18].
Image representations were generated by placing a twodimensional Gaussian profile at the estimated position of each
located emitter. The standard deviation (σ) of the Gaussian
was set to the estimated localization uncertainty [6]. For each
reconstructed image, the resolution was estimated using the
Fourier ring correlation (FRC) method [19].
3. ADAPTIVE OPTICS SCHEME
The microscope employed an image-based wavefront-sensorless adaptive optical scheme for aberration correction, whereby
the necessary aberration correction is inferred from a sequence
of images acquired with different bias aberrations applied to
the DM [20]. Such a scheme requires an appropriate choice
of aberration modes, an image quality metric, and an optimization scheme. The various specifications for the implementation are outlined below.
A. Aberration Modes
The AO scheme used Zernike polynomials as the aberration
modes. The DM was controlled using a matrix that encoded
the actuator signals required to generate Zernike modes. For an
initial set of input basis functions, the DM control matrix was
obtained by estimating the wavefront produced by the DM via
phase retrieval on images of a 40 nm red fluorescent bead
[21,22]. A combination of defocused bead images permitted
the recovery of the phase introduced by the DM when particular amounts of each basis function were applied [23]. Rather
than determining each actuator influence function separately,
we took the more robust method of using numerically derived
orthogonal mirror modes as the initial basis functions [24].
These modes provided a better-conditioned starting point
for the determination of the Zernike modes.
For each modeled basis function, a combination of the first
21 Zernike polynomials, N 21, ignoring the piston mode,
were fitted to the retrieved phase functions and the resulting
coefficients were placed in a matrix. Repeating this decomposition for the first 21 modeled mirror modes, M 21, resulted in an M × N matrix of Zernike mode coefficients.
Multiplying the pseudo-inversion of this matrix with the original DM control matrix provided a DM control matrix capable
of generating Zernike aberration modes. It is important to ensure that image shifts are not introduced by the DM. For this
reason, the lowest-order Zernike modes—tip, tilt, and defocus,
which correspond to shifts in x, y, and z, respectively—were
removed from the control loop. This ensured that the use of
the remaining aberration modes would not cause translation of
the images [25].
B. Image Quality Metric
One of the challenges in the specification of an image-based
AO scheme is finding an image quality metric that allows aberration estimation that is independent of the specimen. By the
nature of microscopy, the specimen structure is always to some
degree unknown. However, in SMS methods, there is an
Vol. 2, No. 2 / February 2015 / Optica
179
important property of the raw images that provides useful a
priori information about the images. The blinking images consist of a pseudorandom combination of point-like emitters,
even when the underlying specimen contains extended objects.
The way in which aberrations affect each of the blinking images is therefore very closely related to the effect of the aberrations on the PSF of the microscope. Even though each image
acquisition will see a different combination of emitters—and
so could be considered an image of a different specimen—
there are strong spatial correlations between the properties of
subsequent images. In practice, there are differences in numbers of emitters and their individual intensities between
frames. Therefore, an image sharpness metric was chosen as
being insensitive to the intensity and number of emitters; it
was therefore ideal for optimization in this microscope. The
sharpness metric, S, was defined in terms of the second moment of the image Fourier transform (FT) as [26]
S
X
X
μn;m Î n;m n 02 m 02 ∕ Î n;m ;
n;m
(1)
n;m
where Î n;m is the discrete FT of the image, n 0 n − N2−1 ,
m 0 m − M2−1 , and n and m are coordinates ranging from
0 to N − 1 or M − 1, respectively, where N and M are the
number of pixels along each dimension of the image. The
function μn;m is a circular mask, given by
μn;m 1;
0;
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
n 02 m 02 ≤ w
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
;
n 02 m 02 > w
(2)
where w was a radius defined as the size of the field of view of
the image divided by the expected resolution of the wide-field
imaging system, assumed to be approximately the Abbe diffraction limit of λ∕2 NA 240 nm [27]. This mask ensures
that high-frequency noise does not adversely affect the calculation of S. Qualitatively, sharp images lead to a broad image
Fourier spectrum. Therefore a large S value relates to a sharp
image arising from a narrow PSF.
C. Aberration Correction Procedure
Each Zernike aberration mode was corrected independently by
sequential optimization of the image quality metric. For a
chosen mode, a sequence of blinking images was acquired,
each with a different amount of the chosen Zernike mode
applied to the DM. A Gaussian function was fitted to this sequence of metric evaluations. The position of the maximum of
the fitted function was taken as the estimate for the required
correction amplitude for that particular mode. The principle of
this modal correction is shown in Fig. 2. This procedure was
repeated for each mode of interest. For the corrections in this
paper, we used a total of typically 11 evaluations per mode for
Zernike modes 5–17, following the numbering convention
adopted by Noll [28]. A typical correction cycle therefore used
a total of approximately 200 captured image frames. However,
the number of evaluations per aberration mode was varied empirically from sample to sample depending on the complexity
of the measured aberration.
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Vol. 2, No. 2 / February 2015 / Optica
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Fig. 2. Principle of aberration measurement. For each aberration mode
Z i , a number of images are acquired, each with different amplitude of the
mode applied to the DM (red dots). The image metric S is plotted as a
function of the total aberration amplitude a. The metric value is then
calculated for each image and the peak of the metric curve is estimated
via a Gaussian fit to the values (green dot). A coma aberration mode is
used for illustration purposes.
Fig. 3. (a) Maximum projection of a captured SMS data set, equivalent
to a diffraction-limited image. (b) A reconstructed super-resolution SMS
image, with an FRC resolution of 42 nm and localization precisions of
σ x 9 nm and σ y 9 nm. The scale bar is 1 μm in both images.
D. Correction of Instrumental Aberrations
5. CORRECTION OF SPECIMEN-INDUCED
ABERRATIONS
Before any imaging experiments were performed, static instrumental aberrations (including any introduced by the DM)
were compensated. The instrumental correction was performed as described in the previous section by imaging 40 nm
diameter fluorescent beads adhered to a coverslip in conventional wide-field mode. For this particular correction cycle,
an alternative image quality metric—the maximum pixel
intensity—was used because the maximum intensity of a point
source can be related to the amplitude of aberrations in an
imaging system [29].
Before correction, phase retrieval was utilized to estimate
the uncorrected phase, which was found to have amplitude
of 1.03 rad RMS, corresponding to a Strehl ratio of 0.34.
These instrumental aberrations were dominated by astigmatism, although other modes were also present. After correction,
phase retrieval estimation showed a residual phase of 0.47 rad
RMS, corresponding to a Strehl ratio of 0.81. All aberrations
mentioned in this paper are expressed as the additional correction relative to this instrumental correction.
A similar specimen was used to demonstrate the correction of
specimen-induced aberrations. The microtubules were imaged
through the cells at a depth of approximately 6 μm. Initial images were obtained using only compensation for instrumental
aberrations, corresponding to the aberrations experienced
when focusing just beyond the coverslip. We acquired
10,000 frames with an exposure time of 20 ms per frame, using
4. LOW-ABERRATION IMAGING
In order to demonstrate the capabilities of the microscope in
low-aberration conditions, i.e., conventional SMS imaging, we
carried out SMS imaging of microtubules in COS-7 cells immunolabeled with Alexa-647 (Invitrogen A-21236) mounted
in an oxygen-scavenging imaging buffer (Fig. 3). For details of
the sample and buffer preparation, see Huang et al. [7]. The
observed region of the cells was immediately behind the coverslip, where any specimen-induced aberrations should be negligible. The sample was excited with 655 nm laser light, with a
measured excitation intensity of 1 kW∕cm2 . Fifty thousand
frames were acquired with an exposure time of 20 ms per
frame. Figure 3(a) shows the conventional long-exposure image for these data. The reconstructed super-resolution image
is shown in Fig. 3(b). The FRC resolution of the superresolution image was estimated at 42 1 nm with localization
precisions of σ x 9 nm and σ y 9 nm. These figures are
comparable to others reported in the literature [7].
Fig. 4. Correction of specimen-induced aberrations. An SMS image
was reconstructed [(a1) and (b1)] with the AO set to correct for instrumental aberrations only and [(a2) and (b2)] with modes Z 4 –Z 15 corrected using sensorless AO. Spherical aberration dominated the
correction of the specimen-induced aberrations (insets). The insets show
the specimen-only component of the applied correction. The scale bar is
1 μm and the units of phase are radians.
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Fig. 5. Zernike decompositions of the specimen-induced aberrations
presented in Figs. 4(a2) and 4(b2). The correction is dominated in these
cases by spherical aberration (mode 11), although there is also a significant specimen-dependent component that varies between specimens.
The amplitude units correspond to the RMS phase in radians.
an illumination intensity of 1 kW∕cm2 . Figures 4(a1) and
4(b1) present two examples of reconstructed SMS images.
Aberration correction was performed using the method
described in the previous section and new SMS data were
acquired. Figures 4(a2) and 4(b2) show the reconstructed
SMS images following specimen aberration correction. The
specimen aberrations introduced by the DM in each case
are represented by the inset figures. It can be noted that the
aberrations were different in each case, as the light emitted had
to pass through different specimen structures on the way to the
objective lens. A spherical aberration component is present—
as should be expected when focusing through a refractive index
mismatch [30]—but other modes are also seen.
The Zernike coefficients of individual specimen corrections
are shown in Fig. 5. At a depth of ∼6 μm, the depthdependent spherical aberration model [30] predicts
−0.61 rad of spherical aberration. In both cases presented
here, −0.7 rad of spherical aberration was measured, which indicates an additional amount of spherical aberration present
beyond that predicted from the refractive index mismatch
between the mounting and immersion media. The specimen
aberration also changed between samples. The nonspherical
components of the specimen correction accounted for
0.23 rad RMS of applied phase out of a total of 0.72 rad
RMS, for the results in Fig. 4(a2), and 0.26 out of
0.78 rad RMS for those in Fig. 4(b2).
Significant differences can be seen between the uncorrected
and corrected SMS images. The compensation of specimeninduced aberrations led to more microtubule structures being
reconstructed in some image areas, such as the top left of the
specimen [Fig. 4(a2)]. In other regions, e.g., [Fig. 4(b2)],
the compensation of specimen-induced aberrations resulted
in double the number of emitter localizations.
6. ADAPTIVE OPTICS CORRECTION APPLIED TO
3D LOCALIZATION VIA ASTIGMATISM
Previous work has shown that an astigmatic PSF can be used to
enable 3D localization microscopy, as the shape of an emitter
image changes dependent upon its position above or below the
nominal focus [31–33]. Astigmatism can be introduced by a
Vol. 2, No. 2 / February 2015 / Optica
181
Fig. 6. 3D SMS image was reconstructed (a) with the AO set to correct
for instrumental aberrations only and (b) with the AO set to correct for
instrumental and specimen-induced aberrations. The inset shows the
specimen-only component of the applied phase correction. The scale
bar is 1 μm and the units of phase are radians.
cylindrical lens or, more controllably, using a DM [15]. We
combined the use of the DM as the astigmatic element with
image-based aberration correction to show the effects of aberrations and the benefit of their correction on the 3D localization microscope.
The DM provides the ability to tune the amount of astigmatism used to encode axial information. A larger degree of
astigmatism will increase the change in the PSF shape relative
to the distance to the focal plane. However, a large amount of
astigmatism will also distort the PSF shape such that it will
become highly asymmetric. This PSF asymmetry will decrease
the x and y localization precisions [34] and possibly cause
borderline fits to fall beneath acceptability thresholds. In order
to find the optimum setting, we varied the amount of astigmatism (Z 5 ) between 1 rad while imaging a 40 nm red bead
mounted in immersion oil on a coverslip. Empirically, we
chose −0.4 rad as providing a suitable balance between PSF
asymmetry and the determination of the PSF centers [15].
Aberration correction was performed using the same procedure
as described previously, without the addition of astigmatism to
the DM. Following the aberration correction routine, 3D SMS
data were acquired with and, for comparison, without the
aberration correction applied.
Fig. 7. 3D SMS image was reconstructed (a) with the AO set to correct
for instrumental aberrations only and (b) with the AO set to correct for
instrumental and specimen-induced aberrations. The inset shows the
specimen-only component of the applied correction. The scale bar is
1 μm and the units of phase are radians.
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Vol. 2, No. 2 / February 2015 / Optica
Fig. 8. Zernike decompositions of the specimen-induced aberrations
presented in Figs. 6 and 7. The aberrations contained significant nonspherical components, including [in (a)] trefoil (mode 9) and [in (b)]
astigmatism (modes 5 and 6).
182
accounted for 0.51 of 0.71 rad RMS and 0.88 of 1.15 rad
RMS for the phase corrections in Figs. 6 and 7, respectively.
In addition to the larger number of acceptable emitter fits
following aberration correction, there are regions where the
aberrations had caused erroneous estimation of the z position.
This is further illustrated in Fig. 9, which shows the z profile
retrieved from three regions of the specimen. For each location,
a section through the microtubule is extracted, as indicated
by the superimposed box in Fig. 6. The points corresponding
to the emitter locations within this box were then projected
along the y direction to provide a projected x–z distribution.
It is clear from these results that the presence of specimen-induced aberrations can have a significant effect on the apparent
position of the microtubules, particularly in the z coordinate.
The number of localizations; the FRC resolution estimate; and
the x, y, and z precision estimates for the reconstructed data
shown in Figs. 6 and 7 are presented in Table 1. From Table 1
it is clear that correcting specimen-induced aberrations, at a
depth of ∼6 μm, dramatically increases the number of single-emitter localizations. Even though the x, y, and z precision
estimates do not vary significantly with AO correction, as the
emitter density increases with AO correction, the FRC resolution estimate improves considerably.
7. EFFECT OF ACCEPTANCE CRITERIA ON
IMAGE QUALITY
Fig. 9. x–z projections of the three locations marked in Fig. 6. The
top row are the instrumental correction projections and the bottom row
are the specimen-corrected projections. AO correction of specimeninduced aberrations resulted in denser and more localizations than
without AO correction. The scale bar is 100 nm.
Figure 6 shows the resulting images of microtubules, imaged in Vectashield buffer [35], with the z coordinate encoded
by color over a range of approximately 400 nm. Again, the
microtubules were imaged through the cells at a depth of
approximately 6 μm. After aberration correction, more of the
specimen was visible as more of the emitter fits satisfied the
acceptance criteria (particularly in the region at the center of
the image). A further example, imaged in oxygen-scavenging
buffer, is shown in Fig. 7. The Zernike coefficients of
the specimen corrections are shown in Fig. 8. Significant
specimen-dependent nonspherical components were present
in the applied DM correction. The nonspherical components
As aberrations distort the PSF of the microscope, they also affect whether an emitter is accepted as a “good” fit during the
analysis of the images of the blinking emitters. The first selection criterion in the estimation process was based on the
brightness (total number of detected photons) attributed to
each emitter. If the brightness was above a chosen threshold,
then the emitter data were passed through to the localization
routine, or were otherwise discarded. In the ideal case, the
localization precision is inversely proportional to the square
root of the total number of photons detected. If the acceptance
threshold for emitter brightness were increased, it should
therefore be expected that the average localization precision
would improve. Similarly, precision should also be enhanced
after aberration correction, as the average number of photons
in the emitter images above the brightness threshold will increase. Moreover, the fidelity of the PSF would increase and
with it the precision of the fit. The shape of the PSF also plays a
role in the emitter acceptance criteria, if a further filtering stage
based on estimated localization precision is used. A full understanding of the relationship between the final reconstructed
image quality and the PSF distortion due to aberrations could
Table 1. Summary of Fitting Results for the 3D Microtubule Imaginga
Data
Figure
Figure
Figure
Figure
a
6(a)
6(b)
7(a)
7(b)
AO
Setting
Number of
Localizations
FRC
(nm)
σx
(nm)
σy
(nm)
σz
(nm)
Instrum.
Specimen
Instrum.
Specimen
5783
11,842
5161
17,215
94.9
69.0
88.1
76.2
22.6
20.3
35.6
31.9
26.6
26.2
35.5
33.4
57.4
51.1
66.6
57.8
Instrum., instrument correction only; specimen, specimen and instrument correction.
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be obtained through detailed modeling, which is outside the
scope of this work. We can however illustrate the effects of
the brightness threshold and the quality of fit criterion on the
experimentally acquired data.
Figure 10 shows these phenomena for the x, y, and z precisions estimated from the 3D reconstructed data presented in
Fig. 6. In each case, aberration correction provides improved
localization precision across the whole range of emitter
Fig. 11. Number of “good” fits versus the single-molecule photon
detection threshold, expressed as effective photon count. A good fit
was defined as having σ x and σ y less than 20 nm and σ z less than
40 nm. Correction of the specimen-induced aberrations resulted in a significant increase in the number of good localizations at all detection
thresholds tested here.
brightness thresholds. One can also see that apparently equivalent localization precisions could be obtained by adjusting the
threshold instead of compensating for the aberrations. This
apparent improvement is only brought about by excluding
poor-quality fits, thus reducing the number of localizations
and leading to inferior quality of the final reconstructed image.
In order to illustrate this, the localization data, which generated
Fig. 6, were then analyzed again, whereby fits were only
accepted if the precisions σ x and σ y were less than 20 nm
and σ z was less than 40 nm. As it is more likely that emitter
images above the brightness threshold have better-defined
peaks after aberration correction, we expect that the total
number of acceptable fits for the AO corrected data should
be significantly higher than that for the uncorrected data. This
is illustrated in Fig. 11.
Due to the strict nature of this acceptance criterion, many
more emitters are accepted after the correction of specimeninduced aberrations. For this reason, many specimen features
may not appear in the reconstructed uncorrected localization
image. Relaxation of the acceptance criteria could lead to more
emitters being included without aberration correction, but this
would be at the expense of worse effective resolution of the
final image.
8. CONCLUSION
Fig. 10. Localization precisions in x, y, and z versus the singlemolecule photon detection threshold, expressed as effective photon
count. The detection threshold was varied between 200 and 900 photons
and the x, y, and z localization precisions were estimated at each threshold. Correction of the specimen aberrations resulted in better localizations along each spatial axis for all detection thresholds tested here.
We have shown that the presence of specimen-induced aberrations detrimentally affects the images obtained in our SMS
microscope. Correction of the aberrations using AO improved
the quality of the raw images and ensured that the microscope
PSF was closer to the model used in the estimation routine.
This in turn had a significant effect on the final image representation, particularly in the 3D SMS mode, where aberrations
caused the corruption of the estimated z coordinate of the
emitters. These effects were observed even at modest depths
of less than 10 μm into the specimen.
Correction of the specimen aberrations required a new AO
method that used raw blinking images as the source for the
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image-based sensorless adaptive scheme. It is a useful feature of
localization microscopes that these images arise essentially
from pseudorandom arrays of point emitters. The sharpness
metric we employed was therefore independent of the overall
specimen structure as it was derived purely from images of
point sources. The image-based feedback scheme allowed the
correction of aberrations, which would not have been predicted by simpler models based on refractive index mismatch.
The magnitude of the additional corrections constituted a considerable fraction of the total applied correction, and nonspherical aberration modes played an important role.
As the images consist of random arrays of PSFs, one might
also consider using methods of phase retrieval to determine
aberrations in future implementations [21]. Furthermore, it
should be noted that the correction of sample-induced aberrations only used a tiny fraction of the total sample exposure
time. In general, less than 200 blinking frames were used
to achieve AO correction, compared with 20,000–50,000
blinking frames acquired to reconstruct the final data.
The effects of aberrations on the reconstructed localization
microscope images were quite different from those in conventional forms of microscopy, where a gradual reduction in resolution and contrast is observed as aberrations increase in
magnitude. In localization microscopy, the use of acceptance
criteria to separate high-quality emitter fits from poor fits
means that emitters are more likely to be excluded from the
final image representation when aberrations are present. The
resulting images can therefore still appear sharp, as only good
fits are ever included. As aberrations increase in magnitude,
fewer regions of the specimen will contain acceptable fits,
so parts of the specimen will appear dark in the final representation. It is clear that adaptive correction of these aberrations is
desirable. However, there are important caveats to be considered when imaging without AO; for example, it is possible that
objects that would be visible in an aberration-free image could
disappear were aberrations present. This would not be obvious
from the final image representation considered alone. It follows
that care must be taken in the interpretation of localization
images in the presence of aberrations.
FUNDING INFORMATION
Wellcome Trust (095927/A/11/Z, 095927/B/11/Z).
ACKNOWLEDGMENT
We thank L. Schermelleh and J. Demmerle for providing test
samples for the development of the AO scheme, and L.
Schroeder for providing the COS-7 samples and for helpful
discussions about the buffer and sample preparation.
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