November Update


 

        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.

            Furthermore, 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.

Additionally, recently 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.



 
Figure 1.


Each 2d imaged spot is resolved into 2x1d approximately-Gaussian intensity distributions. These 1d images are quicker to analyze and are less affected by noise in the image.
 
Figure 2.


The PSF radius as measured by each channel. The local minima is shifted in each channel which represents the focal separation in the sample. The data was collected with 100 frames taken at 100nm scanning intervals axially.
 
Figure3.


The PSF radius of a spot was determined by combining the images captured in each focal plane. This profile is interesting because it elucidates an axial asymmetry in the PSF.
  Figure4.

A central region of 2x2pixels was summed at the center of a spot. The sample was imaged for 100frames at each 100nm scan interval. This shows the central peak intensity of one spot in two focal planes. The framenumber offset of the maxima of each of these intensity profiles represents the focal separation in the sample. The maximum intensity in each channel is also different, representing the additional mirror in the beam path.












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