Multi-Plane Tomographic Phase Retrieval for 4D Cell Microscopy. Emrah Bostan Computational Imaging Lab UC Berkeley

Transcription

1 Multi-Plane Tomographic Phase Retrieval for 4D Cell Microscopy Emrah Bostan Computational Imaging Lab UC Berkeley IMA Workshop Series: Phaseless Imaging in Theory and Practice University of Minnesota, August 18, 2017

2 Joint work with Laura Waller Michael Unser Theo Lasser

3 Joint work with Pascal Odermatt Benjamin Rappaz Theo Lasser

4 Bright-field image of a HeLa cell

5 3.55E+04 Intensity Profile 3.53E E E+04 Bright-field image of a HeLa cell

6 E. Bostan, Phase Retrieval in Bioimaging Low-contrast images under the conventional light microscope Phase Object

7 Bright-field image of a HeLa cell

8 Zernike phase contrast image [Zernike, 1942]

9 Di!erential interference contrast (DIC) image [Nomarski, 1955]

10 Looking at Unstained Cells Dedicated phase imaging modalities: Interferometry-based microscopes + Quantitative phase maps - Higher cost Courtesy of Phasics Courtesy of Lyncée tec Denis Gabor [Marquet et al., 2005] [Cotte et al., 2013] [Kim et al., 20016] Courtesy of TomoCube Courtesy of Nanolive E. Bostan, bostan@berkeley.edu

11 Defocus Microscopy

12 E. Bostan, Phase Retrieval in Bioimaging U(x,z) +z U(x,z)=U 0 (x,z)e jkz z R x =(x,y) R 2 y z x

13 E. Bostan, Phase Retrieval in Bioimaging U 0 z U 0(x,z) j 2k 2 U 0 (x,z)=0 k z I = I [Teague, 1983] 2kI 2 z = 1 2 I 2 I I 2 I ki 2 2

14 E. Bostan, Phase Retrieval in Bioimaging U 0 z U 0(x,z) j 2k 2 U 0 (x,z)=0 k z I = I [Teague, 1983] 2kI 2 z = 1 2 I 2 I I 2 I ki 2 2

15 E. Bostan, Transport-of-Intensity Approach x 1 defocus planes x 2 plane z infocus imaging system illumination source z z object plane image plane Phase Object

16 E. Bostan, Transport-of-Intensity Approach x 1 defocus planes x 2 plane z infocus imaging system illumination source z z object plane image plane Transport-of-Intensity Equation (TIE) k I(x,z) z I(x,z)= 2 (x,z) Phase Object z I(x,z) I(x,z + z) I(x,z z) 2 z

17 E. Bostan, Transport-of-Intensity Approach x 1 defocus planes x 2 plane z infocus imaging system illumination source z z object plane image plane ĥ 1 TIE TIE Forward Model (in Fourier domain) ˆb( )=4 2 2 z ˆ( ) ĥ TIE z =0.1 z = noise power spectrum = 632 1( 1 )

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19 E. Bostan, Contrast Transfer Function I(x,z)= U 0 (x) p F (x,z) 2

20 E. Bostan, Contrast Transfer Function I(x,z)= U 0 (x) p F (x,z) 2 First-order assumptions: Absorption is negligible, Weak-phase object, U 0 =e j e j 1+j measured image at distance z I(x,z)= (1 + j ) p F (x,z) 2 = ((1 j ) p F (x,z)) ((1 + j ) p F (x,z)) We ignore the ignore second-order terms as phase is small.

21 E. Bostan, Contrast Transfer Function measured image at distance z (in Fourier domain) Î(w,z)=I (w) + 2 sin( z w 2 2 ˆ(w)) [Joachim, 1996] 0 z1 z2 -z2 -z1 300 µm 50 µm 0 50 µm 300 µm z

22 E. Bostan, Contrast Transfer Function CTF gives us a TIE-like equation: ˆb( ) = 4 sin( 2 z 2) ˆ( ) ĥ CTF 0 z1 z2 -z2 -z1 300 µm 50 µm 0 50 µm 300 µm z Finite Differences

23 E. Bostan, Analysis of Spatial Frequencies CTF Forward Model (in Fourier domain) ˆb( ) = 4 sin( 2 z 2) ˆ( ) ĥ CTF Large defocus Small defocus region 1 region ( 1 ) 0 max 1 2 1( 1 ) 0 max ĥ 1 TIE ĥ 1 CTF

24 E. Bostan, Regularized Phase Imaging [Bostan et al., 2016] = arg min 1 2 H 1 b H 2 b k [L ] k 2 TV regularization spectral weighting filters highly-modular building-blocks We can recover existing methods [Paganin et al., 2004] [Chou et al., 2007] [Tian et al., 2012] [Zuo et al., 2013] [Bostan et al., 2014] [Carranza et al., 2015] 0

25 E. Bostan, Regularized Phase Imaging 300 µm 50 µm 0 50 µm 300 µm z 300 µm 50 µm 0 50 µm 300 µm (a) z Tikhonov regularization (b) (c) (d) TV regularization (e) (f) (g) Small defocus measurements Large defocus measurements Small and large defocus measurements

26 Experimental Results

27 E. Bostan, Experiment Settings

28 E. Bostan, Experiment Results TIE-Tik Reconstruction (using 3 images) TIE-Tik Reconstruction (using 5 images) Bright-field image (infocus) TIE-TV Reconstruction (using 3 images) Proposed method

29 E. Bostan, Validation Results DHM image Bright-field image (infocus) DIC image (infocus) DHM (detail) TIE reconstruction TIE reconstruction [Bostan et al., 2015]

30 Segmentation Results Bright-field image (infocus) TIE Reconstruction Delineation Result (b)

31 Towards Multi-Modal Cell Imaging

32 E. Bostan, Multi-Modal Cell Imaging Super-resolution fluorescence microscopy: + High specificity + Unprecedented insight into subcellular structures - Complete morphology is harder to observe Phase (label-free) microscopy: + Complete morphology is observable - No specificity! [Hell and Wichmann, 1994] [Betzig et al., 2006] [Rust et al., 2006]

33 E. Bostan, Multi-Modal Cell Imaging SLOW DATA ACQUISITION! Super-resolution fluorescence microscopy: + High specificity + Unprecedented insight into subcellular structures - Complete morphology is harder to observe Phase (label-free) microscopy: + Complete morphology is observable - No specificity! FAST DATA ACQUISITION!

34 Multi-Modal Cell Imaging + Super-resolution optical fluctuation imaging (SOFI) already uses multi-plane system. [Dertinger et al., 2009] [Geissbuehler et al., 2014] Multi-plane Imaging for Phase + Fluorescence - Sample stability! - Partial coherence for 3D objects!

35 Multi-Modal Cell Imaging PRISM (Phase Retrieval Instrument with Super- resolution Microscopy)

36 Multi-Modal Cell Imaging Defocus Phase Imaging Super-Resolution Optical Fluctuation Imaging + Simultaneous 8 defocus measurements are acquired + The image acquisition up to 200 Hz + Quantification of membrane fluctuations

37 Phase Image Fluorescence Image Courtesy of P. Odermatt

38 3D Forward Model Cross-spectral density between the scattered and the incident field (,t = 0) = 0 U s (,v),u i (,v) dv ( )=jf( )H( ) U s (,v)=j F ( ) A (, z n) n(v/c) 2 2 Monochromatic scattering (under Born approximation) I(x) =I DC + (x)+ (x) Single-scattering object assumption [Born and Wolf, 1996] [Sheppard et al., 1994] [McCutchen, 2002]

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43 Conclusion 4D cell imaging is feasible via multi-plane model. Linearized models can be valid for single cell imaging.

44 Acknowledgements

45 Thanks!