1 November 2009
Collecting data in the
lab is a learning experience. My goals for the three times I’ve collected data
include an analysis of the point spread function (PSF), a calibration data set
of axial scanning, and examining drift effects. In order to examine the images
of the PSF, I look for fluorescence with bright emission and low background. I
scan through several microns of depth, in order to capture images of the
fluorescent bead while out of focus and in focus. The analysis script in matlab
then examines the scan of images and determines the radius of the spot sizes at
100 and 50 nanometer intervals in the scan. The radius is determined by binning
the pixels in the image of the spot along both the vertical and horizontal
axes. The light intensity distribution is nearly Gaussian-distributed in the
2-dimensional image of the fluorescent beads, but by binning the pixels and
measuring a characteristic radius of two 1-dimensional Gaussian-approximated
distributions, not only is the speed of the quantification (fitting routines
and calculations to characterize the radius of the intensity distributions)
increased, but possible noise in the 2-dimensional spot becomes less of an
issue, meanwhile this method preserves the accuracy of the fit.
With 100 nanometer steps, the PSF may be measured with
acceptable resolution. An axial profile of the PSF is included. Recently, a
scan of the PSF with 50 nanometer steps has been imaged, and is being analyzed.
The hope is that with an accurate profile of the point spread function, a
fitting routine may be developed to examine the biplane images and determine
the axial position. There are variations in each of the different imaged
fluorescent beads’ point spread functions. These differences, although subtle,
prevent perfect localization. By averaging many spots together, a fitting
routine may be able to appropriately localize many of possible spots, and that
is the goal for developing the algorithm.
the scans provide a calibration set of data. Unsure of the mathematics behind
developing a fitting algorithm, I am able to quantify the two images and then
draw a regression to compare the axial position as a function of the
quantifier. I have compared the images in each focal plane each by a
characteristic spot radius. Then, I relate the radii in each plane (rA
and rB) as: (rA-rB)/(rA+rB).
This quantifier is used to relate the two spot sizes to an axial location.
Testing a subset of the calibration set against the developed calibration curve
is a preliminary test of accuracy. To quantify these results, I will find the
difference between fitted position and known position and examine the standard
deviation of the distribution. This standard distribution in the fitting
accuracy is the localization precision. Published research has achieved axial
localization precision to less than 100nm. Preliminary analysis has shown that
I am able to achieve a position-dependant localization precision which varies
from ~100nm to 150nm, and is not dependent upon focus. That is, a smaller
localization precision is expected for clear images near the focal plane, while
the blurred, out of focus spots should contribute to a poorer localization
precision. My analysis shows that localization precision is oscillatory and
shows no benefit to spots in focus. The oscillatory nature of this localization
precision suggests that the true relationship between the quantifier and the
axial position is not being utilized.
a spot was measured at the same focus for 15 minutes. Any variations in the
spot will more easily be identified with the matlab script, in order to gather
an understanding of microscope drift along the optical axis (axially). Recent
investigations by group members have shown lateral microscope drift to occur on
the order of tens of nanometers in just ten to fifteen minutes. This distance
proves a limiting factor in lateral localization precision; however, an
additional camera collecting transmitted light will help correct for stage
drift. Until the recent data is analyzed, we are unsure how much drift occurs
axially, and if it causes a problem in axial localization.