Advances in Phase Contrast Microscopy

Transcription

1 Advances in Phase Contrast Microscopy Colin Sheppard, SS Kou & S Mehta Division of Bioengineering National University of Singapore colin@nus.edu.sg

2 Perfect imaging Object amplitude transmission a(x, y) (x, y) Perfect image i (x,y) t(x, y) a(x, y)e is modulus (amplitude), real is phase, real I (x, y) a(x, y)e i (x,y) 2 a 2 (x, y) No phase information in perfect image! Weak phase object, small Total almost unchanged Weak phase object Direct light t = a + ia

3 Methods of phase contrast Dark field Zernike phase contrast Defocus Transport of intensity equation (TIE) Offset illumination (Schlieren) - (Hoffmann modulation contrast) - Differential phase contrast (DPC) - Wavefront sensing (Shack-Hartmann) Interference microscopy Differential Interference Contrast (DIC) Digital holographic microscopy (DHM)

4 Divide into to two approaches 1 Coherent methods (Digital holographic microscopy) Spatial frequencies only on Ewald sphere Limited 3D imaging performance But can improve by holographic tomography Limited spatial resolution 2 Partially coherent methods Improved imaging (improved bandwidth) No speckle More difficult to extract quantitative information

5 Coherent imaging I(x,y) c(m,n)t(m,n)exp 2j(mx nydmdn c(m,n)c *(p,q)t(m,n)t *(p,q)exp 2j (m p)x (n q)y For partially coherent, C(m, n; p, q) does not separate 2 dmdndpdq

6 Imaging depends on coherence Fluorescence behaves as incoherent imaging Brightfield etc. S = 0, coherent illumination S = 1, full or complete illumination S ->, incoherent illumination Resolution depends on coherence Coherence parameter S = n c sin c n o sin o

7 Imaging in a partially-coherent microscope Spatial frequency in the image is (m - p, n - q) Original theory by Hopkins Proc. Royal Soc. London 217, 408 (1953)

8 WOTF C(m;0) and PGTF C(m;m) for conventional microscope Partially coherent imaging is complicated, but becomes simpler for 2 cases: Weak object Slowly varying phase gradient C(m;0) S = 0 C(m;m) S = 0 S = 1 S = 1 Weak object transfer function Phase gradient transfer function

9 Defocus WOTF, S = 0.01 (nearly coherent) Like cos or sin (ul 2 /2) Phase imaged by imaginary part l is radial spatial frequency, l = (m 2 +n 2 ) 1/2 Sheppard CJR Defocused transfer function for a partially coherent microscope, J. Opt. Soc. Am. A, 21, (2004)

10 WOTF, S = 0.5 Real Imaginary Sheppard CJR Defocused transfer function for a partially coherent microscope, J. Opt. Soc. Am. A, 21, (2004)

11 WOTF, S = 0.99 Real Imaginary (very weak) Sheppard CJR Defocused transfer function for a partially coherent microscope, J. Opt. Soc. Am. A, 21, (2004)

12 Small defocus: analytic expression Sheppard CJR Defocused transfer function for a partially coherent microscope, J. Opt. Soc. Am. A, 21, (2004)

13 I(Δu) I( Δu) gives phase contrast image (amplitude image cancels) Parabolic for small l Sheppard CJR Defocused transfer function for a partially coherent microscope, J. Opt. Soc. Am. A, 21, (2004)

14 Small defocus, after inverse Laplacian Phase restored up to l = 1 S Sheppard CJR Defocused transfer function for a partially coherent microscope, J. Opt. Soc. Am. A, 21, (2004)

15 WOTF Kou & Sheppard, Opt. Lett.

16 Transport of Intensity Equation (TIE) Teague, JOSA A 1434, 73 (1983) Streibl, Opt. Commun. 6, 49 (1985) Barty, Nugent, Paganin, Roberts, Opt. Lett. 817, 23 (1998) Amplitude in image space satisfies paraxial wave equation I z I T T ln I z T2 T ln I T

17 Logarithmic derivative image Testicle of rat, Streibl, Opt. Commun. 6, 49 (1984)

18 Barty, Nugent, Paganin, Roberts Opt. Lett, 23, 817 (1998) DIC TIE phase image

19 Quantitative phase imaging IATIA system: measure using TIE equation Can then simulate Zernike, DIC, etc. images

20 Problems with TIE imaging Measures phase of image not object Similar to defocus method for weak object, but not limited to weak phase Not enough information to directly recover object phase for strong object Problem with 3D imaging: Measure I /z so no information on zero axial spatial frequency

21 Differential phase contrast (DPC)

22 Differential phase contrast

23 Extracting phase Two detectors, A and B

24 DPC image of a cheek cell Hamilton DK, Sheppard CJR (1984), J. Microsc. 133, (1984)

25 DPC image of an integrated circuit DPC DIC

26 DPC image of a single monolayer

27 DPC with an annular split detector Hamilton DK, Sheppard CJR, Wilson T, Journal of Microscopy 153, (1984) a = 1 a = 0.7

28 Asymmetric Illumination DPC (AI-DPC) Arrows reversed, source from each semicircle

29 Asymmetric illumination DPC (AI-DPC) Condenser pupil structures (top row), partially coherent transfer function in direction of differentiation (middle row), and experimental images (bottom row) obtained with AIDPC. The sample is skin H&E stained section courtesy Graham Wright, TLL and Declan Lunny, IMB.

30 Phase measurement using DPC Integrate phase gradient to get phase (but still constant of integration) dx const. x Measure (x, y) F 1 / x, / y F x i y 2isin2m isin2n Arnison, Larkin, Sheppard, Smith, Cogswell, J. Microsc. 214, 7-12 (2004)

31 Phase reconstruction from AI-DPC S Mehta, Thesis (2010)

32 Nomarski Differential interference contrast (DIC)

33 Nomarski DIC Uses polarization so depends on birefringence of sample Can use in conventional or confocal mode

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35 Phase-stepping DIC Slowly-varying phase gradient 2πm I 2a 2 C(m;m) 2a 2 C(m;m)cos(2m 0 ) Same form as normal interference pattern Measure I for different values of bias retardation f 0 Using phase-stepping algorithm, can recover phase gradient 2πm Integrate phase gradient to get phase (but still constant of integration) dx const. x Cogswell, Smith, Larkin, Hariharan, Proc. SPIE 72, 2984 (1997)

36 Phase gradient from phase stepping DIC

37 Phase measurement using phasestepping DIC Measure / x, / y (x, y) F 1 F x i y 2isin2m isin2n Arnison, Larkin, Sheppard, Smith, Cogswell, J. Microsc. 214, 7-12 (2004)

38 Phase reconstruction from DIC S Mehta, Thesis (2010)

39 Three different DIC configurations

40 Transfer function C(m;p)

41 Mouse intestine Become more similar

42 Optical fibre, S = 0.4

43 Optical fibre, S = 1

44 Phase gradient from phase stepping DIC and TIE-DIC

45 Phase reconstruction from TIE-DIC, π/4 and 3π/4 bias

46 TIE from colour (single shot) HMVEC cells HeLa cells

47 Summary TIE can reconstruct phase from 2 sections TIE does not recover 3D information DIC can reconstruct phase from 2 directions of shear DIC has problems with birefringent objects DPC has inferior depth imaging performance (may be an advantage) Possibility to use combinations of DIC/TIE etc

48 Optical Bioimaging Group, October 2006