March Update

 

            Work on my senior project is progressing well this semester. Last semester ended with work on a regression function to relate a ratio of spot sizes in two focal planes to the axial position of the emitting bead between the focal planes. A preliminary fit proved insufficient inasmuch to accurately predict the axial positions at all distances within the focal planes. Due to artifacts in the fit, axial drift was questioned; to combat drift by reducing acquisition time, a labview interface was developed to communicate with the camera and piezoelectronic microscope stage. With a new interface, scanning the same regions as last semester (100 frames/step, 100nm/step, 2microns depth) takes as little as 2 minutes, compared to a 20 minute manual scan. To further ensure accuracy, glass cover slides and cover slips were imaged with an atomic force microscope (AFM) in order to reference the planar nature of the cover slides. Figure 1 shows that the glass slide which we imaged shows deviations on the order of nanometers or tens of nanometers. This deviation in the plane is less than the localization precision of the biplane technique and thus should not be a problem in introducing errors in fitting fluorescent beads on a slide to a plane.

            Another point of progress is within the fitting algorithm. Biplane FPALM relies on a comparison of the degree of un-focus in each of two spatially separated focal planes in the sample. To do this previously required binning each spot image across its rows and columns of pixels. Using the two 1D Gaussian-approximated distributions to fit Gaussian functions, characteristic widths were related in each frame (named A and B) by the ratio R=(ra-rb)/(ra+rb). A new technique has been employed which finds characteristic widths more robustly and much more quickly. Termed the ‘Brenner gradient’, the algorithm for an n x n image, “s” is: ALGORITHM. The spots in each focal plane are characterized by this figure of merit (FOM), and the ratio of the two Brenner gradients in each focal plane composes the same relationship used previously. The advantage of using the Brenner gradient over a fitting routine is that the Brenner gradient changes by orders of magnitude from a sharply focused spot to an unfocused spot. Figure 2 shows the Brenner gradients for each focal plane through the calibration scan.

            Now knowing that cover slides are sufficiently planar, and with a new tool to acquire image scans, data has been collected of fluorescent beads dried on a cover slip and actuated over several microns in 50nm steps. The labview scanning algorithm allows ease in scanning the smaller step sizes.

            First results show that the Brenner gradient indeed returns large numbers near focus, and the FOM drops away quickly with defocus. The ratio used to relate the two frames produces a position-ratio relationship which is sharp and distinct for regions between the focal planes and asymptotically approaches limits of -/+1 for distant focus. Figure 3 shows the ratio of the Brenner gradients.

            The distinct curve and ease of determining focus with the Brenner gradient and ratio seems promising, however the sharp decline in the Brenner gradient for defocused spots may prove to be too sharp a decline, perhaps zoning in too narrowly on sharply focused regions, thus leaving visible but blurry spots absent in the analysis. Preliminary results show that accurate and precise localization is possible but limited to the central 500nm with a focal plane separation of 1 micron. Previous results and published papers report that accurate and precise localization should be possible for the entire 1 micron with the same focal plane separation in the sample.

            With the scanning algorithm in a workable form, my next plans are to image a cell membrane with fluorophores tagged to the membrane protein hemagluttinin (HA). HA plays an important role in the infection of viruses and the arrangement of HA in the cell membrane is not clear.



Figure 1. AFM Image of a glass coverslide reveals surface defects which are less than 10nm, very acceptable for Biplane FPALM.
 

Figure 2. Brenner gradient for a single spot imaged 100 times at each 50nm step. Red and blue identify each focal plane with one standard deviation error bars. For areas near focus in each plane, the brenner gradient is clear and distinct.





Figure 3. Brenner gradient ratio of a single spot in each focal plane. Imaged 100 times at each 50nm step, the error bard represent 1 standard deviation at each step. Because the Brenner gradient is so distinct, the ratio is easily resolvable at regions near 'focus'. 'Focus' here is considered to be the position at which the ratio (vertical axis) is equal to zero.

 
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