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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.05614 |
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| _version_ | 1866913230076510208 |
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| author | Li, Wenchao Li, Shuo Brown, Timothy C. Sun, Qiang Wang, Xuezhi Yakovlev, Vladislav V. Kealy, Allison Moran, Bill Greentree, Andrew D. |
| author_facet | Li, Wenchao Li, Shuo Brown, Timothy C. Sun, Qiang Wang, Xuezhi Yakovlev, Vladislav V. Kealy, Allison Moran, Bill Greentree, Andrew D. |
| contents | Fluorescence microscopy is of vital importance for understanding biological function. However most fluorescence experiments are only qualitative inasmuch as the absolute number of fluorescent particles can often not be determined. Additionally, conventional approaches to measuring fluorescence intensity cannot distinguish between two or more fluorophores that are excited and emit in the same spectral window, as only the total intensity in a spectral window can be obtained. Here we show that, by using photon number resolving experiments, we are able to determine the number of emitters and their probability of emission for a number of different species, all with the same measured spectral signature. We illustrate our ideas by showing the determination of the number of emitters per species and the probability of photon collection from that species, for one, two, and three otherwise unresolvable fluorophores. The convolution Binomial model is presented to model the counted photons emitted by multiple species. And then the Expectation-Maximization (EM) algorithm is used to match the measured photon counts to the expected convolution Binomial distribution function. In applying the EM algorithm, to leverage the problem of being trapped in a sub-optimal solution, the moment method is introduced in finding the initial guess of the EM algorithm. Additionally, the associated Cramér-Rao lower bound is derived and compared with the simulation results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_05614 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Estimation of the number of single-photon emitters for multiple fluorophores with the same spectral signature Li, Wenchao Li, Shuo Brown, Timothy C. Sun, Qiang Wang, Xuezhi Yakovlev, Vladislav V. Kealy, Allison Moran, Bill Greentree, Andrew D. Quantum Physics Mathematical Physics Biological Physics Optics Fluorescence microscopy is of vital importance for understanding biological function. However most fluorescence experiments are only qualitative inasmuch as the absolute number of fluorescent particles can often not be determined. Additionally, conventional approaches to measuring fluorescence intensity cannot distinguish between two or more fluorophores that are excited and emit in the same spectral window, as only the total intensity in a spectral window can be obtained. Here we show that, by using photon number resolving experiments, we are able to determine the number of emitters and their probability of emission for a number of different species, all with the same measured spectral signature. We illustrate our ideas by showing the determination of the number of emitters per species and the probability of photon collection from that species, for one, two, and three otherwise unresolvable fluorophores. The convolution Binomial model is presented to model the counted photons emitted by multiple species. And then the Expectation-Maximization (EM) algorithm is used to match the measured photon counts to the expected convolution Binomial distribution function. In applying the EM algorithm, to leverage the problem of being trapped in a sub-optimal solution, the moment method is introduced in finding the initial guess of the EM algorithm. Additionally, the associated Cramér-Rao lower bound is derived and compared with the simulation results. |
| title | Estimation of the number of single-photon emitters for multiple fluorophores with the same spectral signature |
| topic | Quantum Physics Mathematical Physics Biological Physics Optics |
| url | https://arxiv.org/abs/2306.05614 |