Motivation in addition to Purpose What is Holography Design of the Microscope Flowchart as long as Procedure 1. Calculating the phase
Wrenn, Lisa, Features Editor has reference to this Academic Journal, PHwiki organized this Journal Digital Holographic Microscopy as long as Measurement of Cellular Refractive Indices Robert Thomen Creighton University Masters Thesis Defense 4-27-11 Motivation in addition to Purpose What we want: the refractive index of living cells, particularly bone cells! Why we want it: the refractive index is required to accurately determine pressure measurements in the optical stretcher. Records 3-D images by taking advantage of the wave nature of light Can also be used to record differences in optical path length through transparent objects What is Holography d
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Design of the Microscope so, how do we find y x If we find , we can find nc in addition to h. Flowchart as long as Procedure 1. Calculate phase using Hilbert Trans as long as m 2. Unwrap phase using Goldsteins Algorithm 3. Calculate cell height in addition to index as long as every pixel 4. Profit Cell Height Cell Index 1. Calculating the phase Any analytic signal can be written in the as long as m: where the imaginary part is the Hilbert Trans as long as m of the real part. So what does the Hilbert trans as long as m actually do The Hilbert Trans as long as m is defined The phase of our signal at every point is then
The Hilbert Trans as long as m has the effect of shifting each frequency component in a signal by /2 We can make this manipulation in frequency space! What exactly does the HT do Hilbert in addition to Fourier are close relatives The Hilbert Trans as long as m manipulates the phase of the signals frequency space Let =wt The Fourier Trans as long as m Two-Dimensional Phases The 2D Fourier Trans as long as m DC centered Fringe Frequencies We have now found ! or have we .
2. Unwrapping the Phase We must then unwrap the phase By nature of the arctan function, our phase map is wrapped The Effects of Noisy Data 2 4 6 2 4 Digital noise can cause miscalculation of the phase in The unwrapping algorithm. How can we deal with noisy data Filtering processes to Remove Noise Median Filtering For each pixel, a surrounding box of pixels is selected in addition to the median pixel intensity of these is substituted Several filtering techniques have been employed in our code Fourier Filtering By taking the Fourier trans as long as m of an image, we can selectively remove certain frequency in as long as mation. But filtering changes our data!
Residues in addition to Branch Cuts Problematic pixels can be recognized as residues Residues occur at singularities in otherwise entirely analytic functions Residues can be calculated as long as a contour around each pixel Residues can be connected by branch cuts which disallow unwrapping progression through certain parts of the phase map We have implemented Goldsteins Algorithm to make these branch cuts. This can be done in LabVIEW Capture image Take the Hilbert Trans as long as m of that image Inverse tangent to find phase What do we get when we do this Labview Program We now have the phase image!
3. Taking the Data We require 3 images 1. Background Move cell into the frame 2. Cell in media of index n Add media of higher index Must monitor phase shift 3. Cell in media of index n+ C0 N0 C+ This procedure was developed by Rappaz et al. Opt Express 13, 9361 (2005) Verifying the integrity of our results We have constructed a program to synthesize perfect data to test our algorithms Are the numbers accurate Do we take good data Does our program work Now we can address the effects of filters Examples of a Gaussian-shaped cell of index 1.38 in addition to peak height 10,000nm Effects of Filtering on Ideal Data So what are filters good as long as
Effects of Filters on Noisy Data n=1.38874+/-.002827 Even if filtering is necessary, the average index is preserved! Single Cell Results (EMT6) nm nm radians Frame Refractive Index Data as long as EMT6 cells What is the characteristic Index of EMT6 cells n633 = 1.384 ± 0.041 n735 = 1.387 ± 0.023 n812 = 1.375 ± 0.013 Average precision of .003
Conclusions DHM is operational in addition to taking data Image processing algorithm has been tested on synthesized data to verify the integrity of results There seems to be a great deal of index variation from cell to cell (EMT6 cell data at 735nm) Portable model has been developed Soon to take data at 1064nm Acknowledgments Dr. Mike Nichols Semere Woldemariam NIH grant P20 RR016475 from the INBRE Program of the National Center as long as Research Resources. Questions Extra slides follow
Holography in addition to Interferometry Holography can display 3D images because it records not only the lights intensity but also its phase Cell images from Tomographic Phase Microscopy, Michael S. Feld et al. September 2007 Nature Methods Vol. 4, No. 9. We use this principle of holography to detect optical path length variations in transparent media. This difference in OPL is measured as a phase difference Design in addition to Construction Mach-Zender Interferometer Frequency Analysis Simply get rid of negative frequencies using a Fourier trans as long as m! This process will follow this procedure Let in addition to Recall f(t) is two dimensional
What good is phase We have phase data, but who cares about phase In order to get n in addition to h, we have developed decoupling techniques Acknowledgments Dr. Mike Nichols Semere Woldemariam NIH grant P20 RR016475 from the INBRE Program of the National Center as long as Research Resources. Questions
Wrenn, Lisa Features Editor
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