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\subsection{Data acquisition}
This investigation Single photon data was
performed using acquired with a dual mode cooled Hamamatsu C1790-13
EBCCD comprised of EBCCD, with 512$\times$512 pixels
where each pixel is and 24$\times$24~$\mu$m
in pixel size. The photocathode in the EBCCD is a GaAsP plate with an approximate quantum efficiency of 50\% at 520~nm.
Upon liberation Photoelectrons liberated from the
photocathode, the photoelectrons photocathode are accelerated across a potential difference into a back-thinned CCD. The
vacuum chamber has an aluminium sheet 1.3~mm from the cathode to protect the back-thinned CCD from back-scattered photoelectrons. During data acquisition, the EBCCD was cooled to an operation temperature of
-15$^\circ$C and the EBCCD read-out was operated using the -15$^\circ$C. HiPic 7.1.0 software
package from Hamamatsu, which acquired data using an was used for image acquisition, with exposure time of 10$\mu$s and
a super-high amplifier gain.
The EBCCD was attached to the output port of an inverted Nikon Eclipse TE2000-E microscope, see Fig~\ref{fig1}a. For the
biological cell sample imaging, the microscope was used with a 100$\times$ 1.4NA air objective (Nikon) and for the 1951 USAF resolution test chart (Fig~\ref{fig1}b), the microscope was used with a 4$\times$ 0.13NA air objective (Nikon).
2,000 frames were collected for the biological A fluorescent cell sample
and 30,000 frames were collected for the USAF test pattern. The exposure time (FluoCells Prepared Slide \#1, Molecular Probes) was
set to 10$\mu$s, and the imaged with a 100$\times$ 1.4NA oil objective (Nikon). The illumination intensity
was adjusted such that single photon event could be observed (Fig~\ref{fig1}c,d).
\begin{figure}[tbp]
\centerline{\includegraphics[width=1\columnwidth]{fig1}}
\caption{\label{fig1} (a) Schematic diagram of the data acquisition setup. (b) Total imaged area of USAF test pattern. (c) A frame of raw data with single-photon events. (d) 3D representation of (c).}
\end{figure}
\subsection{Data processing}
The frames containing single photon events were processed with the ThunderSTORM \cite{Ovesny2014} superresolution imaging plug-in for
ImageJ, whose settings are explored in this paper. ImageJ. Due to computational memory restraints, the USAF test pattern data was processed in six 5,000 image stacks. The data is first processed to detect the photon events from the noise background, before
implementing a localization algorithm
to detect locates the
approximate centre of the photon event. Subsequently, a sub-pixel localization algorithm is used
on the data to fragment the pixels into 13$\times$13 grids to
allow calculate the centre of photon events
to be located with greater resolution.
For all the data, the parameters used for the The software camera
settings include a parameters were set to 80.0~nm pixel size
of 80.0~nm and 36 photoelectrons per A/D count. The base level varied between image stacks due to fluctuations in the
apparatus EBCCD temperature, and was set to the average minimum grey value for the image stack
which ranged between 100 A/D counts and 140 in the range of 100-140 A/D counts.
For all the data, a A wavelet (b-spline) image filter was applied with a b-spline order of 3 and a b-spline scale of 2.0. For the approximate localization algorithms, centroid of connected components (CoCC) was used with a peak intensity threshold (PIT) of 2*std(Wave.F1)
and the watershed algorithm enabled for the USAF
test pattern data, and a PIT of 1.5*std(Wave.F1)
for cell data, with
the watershed algorithm enabled for
the cells all data.
Local maximum (LM) was applied using a PIT of 2.5*std(Wave.F1) with a 4-neighbourhood connectivity and non-maximum suppression (NMS) was used with a PIT of 2*std(Wave.F1) and 1 pixel dilation radius. ***in the end only CoCC was used for the data in this paper, is it necessary to mention LM and NMS?***
For the sub-pixel localization algorithms, integrated Gaussian (IG) PSF was set to a 3 pixel fitting radius, a 1.6 pixel standard deviation
(SD) and the least squares (LS) fitting method and radial symmetry was applied with a 2 pixel estimation radius. To achieve good photon detection with adequate FPN in a very short period of time, the data can be processed with the Rapid Estimation (RE) settings described below. To achieve optimal photon detection, the resolution of overlapping events and a lower FPN, the Maximum Resolution (MR) settings can be applied to the data, however this produces a substantial increase in processing time. For the RE processing approximate localization algorithms, Gaussian PSF was set to a 2 pixel fitting radius with a 1.0 pixel
standard deviation SD and the Maximum Likelihood (ML) fitting method, and for the MR processing, Gaussian PSF was set to a 7 pixel fitting radius with a 1.0 pixel
standard deviation SD with the Maximum Likelihood (ML) fitting method.
When the multiple-emitter fitting analysis (MFA) was applied in conjunction to the PSF gaussian or IG algorithms, it was used with a maximum of 1 molecule per fitting region and a model selection threshold (p-value) of 10$^{-6}$ for the RE processing, or a maximum of 2 molecules per fitting region and a model selection threshold (p-value) of 10$^{-6}$ for the MR processing. For USAF test pattern data processed using the MR settings with MFA enabled,
thunderSTORM's remove duplicates ThunderSTORM's ``remove duplicates'' post-processing tool was applied with a distance threshold of 160~nm and an
"intensity>4000" ``intensity$>$4000'' filter was used. For cells data, the remove duplicates tool was also applied with a distance threshold of 160~nm but with an
"intensity>3000" ``intensity$>$3000'' filter. No post-processing was required for data processed using RE settings.
