Estimation of nonlinear
dynamics of S. Pombe cells
growth via Rényi Entropy
Msc. Tomáš Náhlík
nahlik@ufb.jcu.cz
Institute of physical biology
Zamek 136, Nove Hrady
S. Pombe – 1 day experiment
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S. Pombe – 1 day experiment
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S. Pombe – 1 day experiment
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S. Pombe – 1 day experiment
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S. Pombe – 1 day experiment
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S. Pombe – 1 day experiment
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Genealogical tree
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Problems
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S. Pombe cells are very small
Cells are not flat object
Cells are moving
Cells don’t stay in focal plane
Long interval between images – inner
object cannot be tract
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Point Spread Function
 What is PSF?
 PSF describes response of an imaging
system to point source (point object)
 System’s impulse response
 When we see PSF?
 Homogeneous objects in distance bigger
then resolution
 Why we talk about PSF?
 Because PSF blurs images
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Point Spread Function
 What caused PSF?
 Diffraction, interference, imperfection of
glasses, lenses even human eyes and
brain, but mainly by Heisenberg
uncertainty principle
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Point Spread Function
 Diffraction

sin k  (2k  1)
2
 Airy disc simulation
 2 J1 (ka sin  ) 
I ( )  I 0 

 ka sin  
2
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Point Spread Function
 Simulation of closing two particles
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Point Spread Function
 Airy Resolution
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Point Spread Function
 Distinctness by Eye
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Point Spread Function
 Distinctness by Computer
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Point Spread Function
 PSF can have many different shapes
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Point Spread Function
 Experimental PSF – Latex balls
(550nm) – Phase contrast - real PSF
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Different Focuses
 Eye Focus
 Airy Focus
 Information Focus
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Different Focuses
 Minimal difference between Phase
contrast and bright field
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Different focuses
 Minimal difference between phase
contrast and bright field
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Point Spread Function
 Experimental PSF – Latex balls
(550nm) – Phase contrast
 Focused by eyes
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Point Spread Function
 Experimental PSF – Latex balls
(550nm) – Phase contrast
 Focused by eyes
 Different color channels
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Point Spread Function
 Experimental PSF – Latex balls
(550nm) – Phase contrast
 Airy focus – 18 microns from eye focus
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Point Spread Function
 Experimental PSF – Latex balls
(550nm) – Phase contrast
 Airy Focus
 Different color channels
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Point Spread Function
 Experimental PSF – Cell spread
function caused by inhomogeneous
near objects
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Conclusion
 We are not able to reconstruct the
image without PSF
 Knowledge of PSF brings us
knowledge of real object
 Everyone who use microscope should
know about PSF and how PSF
influences images
 Knowledge about PSF can help us
with automatic image focusing
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Finance
 Set of Pipets – 14 400Kč
 Camera – 27 278Kč
 External HDD – 2 400Kč
 Total: 44 078Kč
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Acknowledgements
 To my supervisor
Doc. RNDr. Dalibor Štys, Csc
 To my co-workers
Ing. Petr Císař, PhD
Ing. Jan Urban
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Literature
1) Lipson S.,G. Why is super-resolution so
inefficient? – Micron 34 (2003) 309-312
2) Mizushima Y. Detectivity of very small objects
by video-enhanced microscopy – Applied
Optics vol. 27, No. 12, 15 June 1988
3) Airy, G. B. (1856) Philosophical Transactions
of the Royal Society
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Thank you for your attention
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