Phase Contrast Microscopy. Colin Sheppard Nano- Physics Department Italian Ins9tute of Technology (IIT) Genoa, Italy

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1 Phase Contrast Microscopy Colin Sheppard Nano- Physics Department Italian Ins9tute of Technology (IIT) Genoa, Italy

2 Phase contrast Dark field Zernike phase contrast Defocus Transport Of Intensity equa9on (TIE) Offset illumina9on (Schlieren) Hoffmann modula9on contrast Differen9al phase contrast (DPC) Differen9al Interference Contrast (DIC) Interference microscopy Digital holographic microscopy (DHM)

3 Imaging in a par9ally- coherent microscope Spatial frequency in the image is (m p, n q)

4 WOTF C(m;0) and PGTF C(m;m) for conven9onal microscope Constant phase gradient deflects light through an angle (prism effect) C(m;0) C (m) 0.6 S = 0 C(m;m) C (m) 0.6 S = S = S = m m Weak object transfer function Interference of scattered light with direct light p = 0 for direct light (uniform) Phase gradient transfer function Only one spatial frequency present: p = m C(m;m) varies as the phase gradient changes

5 Dark field microscope Direct light blocked Partially-coherent imaging Encyclopedia of Modern Optics, RD Guenther, DG Steel, L Bayvel, eds, Elsevier, Oxford, 3, pp

6 Dark field Weak phase object Spectrum Dark field, C(0, 0; 0, 0) = 0 T (m,n) = δ (m)+ i d 2 δ (m ν) + i d δ (m +ν) 2 δ (n) I(x, y) = 1 2 d 2 C(ν,ν;0,0) + C(ν, ν;0,0)cos 4πνx M Zero for annular dark field system Therefore no contrast for single spatial frequency component

7 Dark field Only difference frequencies imaged Sum frequencies not imaged

8 Zernike phase contrast F. Zernike, "Phase contrast, a new method for the microscopic observation of transparent object," Physica 9, (1942). Direct light changed in phase Partially-coherent imaging Direct light on an annular cone increases resolution Encyclopedia of Modern Optics, RD Guenther, DG Steel, L Bayvel, eds, Elsevier, Oxford, 3, pp

9 Zernike phase contrast Weak phase object Spectrum T (m,n) = δ (m)+ i d 2 δ (m ν) + i d δ (m +ν) 2 δ (n) Phase imaging from imaginary part of C: I(x, y) = 1± 2d c I(x, y) = 1 dc i (ν,0;0,0)cos 2πνx M If c is the amplitude transmittance of the phase ring: 2πνx C(ν,0;0,0)cos M Phase contrast is amplified

10 Weak phase object, φ small Brightfield Total almost unchanged Direct light iφ (x,y ) t(x, y) = a(x, y)e Weak phase object t = a + iaφ Darkfield Weak phase object No direct light to reduce contrast Zernike Change in total much larger Phase of phase object altered Direct light

11 Zernike phase contrast Superposed on dark field image Imaginary part (phase contrast)

12 Zernike phase contrast Phase contrast amplified by transmisance of phase ring Can make +ve or ve phase contrast from phase of phase ring Difficult to get quan9ta9ve informa9on Haloes around phase changes

13 Transport of intensity equa9on (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 the paraxial wave equation logarithmic derivative k I z = T I T φ ( ) k ln I z = 2 Tφ T ln I T φ often small Similar to eikonal equation Wavefront curvature sensing

14 Photo: Miguel Porras

15 Logarithmic deriva9ve image Testicle of rat, Streibl, Opt. Commun. 6, 49 (1984)

16 Barty, Nugent, Paganin, Roberts Opt. Le*, 23, 817 (1998) DIC TIE phase image

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

18 Quan9ta9ve phase imaging by TIE IATIA system: measure φ using TIE equation Can then simulate Zernike, DIC, etc. images

19 Features of TIE imaging Similar to the defocus method for a weak object, but not limited to weak phase Measures phase of the image not the object Not enough information to directly recover the object phase for a strong object Problem with 3D imaging: Measure so no information on zero axial spatial frequency Sheppard CJR (2002) Three-dimensional phase imaging with the intensity transport equation, Appl. Opt. 41,

20 Hoffmann modula9on contrast Encyclopedia of Modern Optics, RD Guenther, DG Steel, L Bayvel, eds, Elsevier, Oxford, 3, pp

21 Differen9al phase contrast (DPC) Can do simply in a confocal microscope Encyclopedia of Modern Optics, RD Guenther, DG Steel, L Bayvel, eds, Elsevier, Oxford, 3, pp

22 Differen9al phase contrast

23 Extrac9ng phase Two detectors, A and B Can also use quadrant detector to get dφ/dx, dφ/dy

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

25 DPC image of an integrated circuit Can also do in reflection DPC DIC

26 DPC image of a single monolayer Very sensitive to weak phase changes

27 Phase- gradient transfer func9on C(m;m) (PGTF) signal phase gradient (slope) Anti-symmetrical

28 DPC with an annular split detector Hamilton DK, Sheppard CJR, Wilson T, Journal of Microscopy 153, (1984) a = 1 a = 0.7 slow changes in slope high spatial frequency response Can adjust contrast/ resolution

29 PGTF for DPC Often advantageous to have linear behaviour Hamilton DK, Sheppard CJR, Wilson T, Journal of Microscopy 153, (1984)

30 Asymmetric Illumination DPC (AI-DPC) Can also do in a conventional microscope Arrows reversed, source from each semicircle Need to take two images Or 4 to get dφ/dx, dφ/dy

Asymmetric illumina9on DPC (AI- DPC) Condenser pupil structures (top row), partially coherent transfer function in direction of differentiation (middle

31 Asymmetric illumina9on 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.

32 Phase measurement using DPC Integrate phase gradient to get phase (but still constant of integration) Measure φ / x, φ / y φ F x + i φ y φ(x, y) = F 1 2i sin 2πmΔ + isin2πnδ ( ) Arnison, Larkin, Sheppard, Smith, Cogswell, J. Microsc. 214, 7-12 (2004) Similar to Frankot-Chellappa algorithm IEEE Trans. Pattern Analysis 10, 439 (1988) (Shape from shading)

33 Phase reconstruc9on from AI- DPC S Mehta, Thesis (2010)

34 History N. H. Dekkers and H. de Lang, "Differential phase contrast in a STEM," Optik 41, (1974). N. H. Dekkers and H. De Lang, "A detection method for producing phase and amplitude images simultaneously in a STEM," Philips Tech. Review 37, 1 (1977) Hamilton DK, Sheppard CJR (1984), J. Microsc. 133, (1984)

35 Nomarski Differen9al interference contrast (DIC) Phase difference (bias) between two images altered using compensator: Translate Wollaston prism Rotate polarizing elements G. Nomarski, "Microinterferometrie differential a ondes polarisés," J. Phys. Radium 16, (1955) Encyclopedia of Modern Optics, RD Guenther, DG Steel, L Bayvel, eds, Elsevier, Oxford, 3, pp

36 Nomarski DIC Bias changed using shih of Wollaston prism or rota9on of polariza9on (Sénarmont compensator) Uses polariza9on, so depends on birefringence of the sample Can use in conven9onal or confocal mode

used for CCD detection, large signal, linear, weaker

37 Effect of bias zero bias (dark field) small bias: used for visual observation, high contrast 45 o bias: used for CCD detection, large signal, linear, weaker contrast, but enhance digitally 90 o bias (bright field)

38 Birefringent

39 Confocal DIC

40 Transfer func9on for DIC 2Δ is the shear 2φ 0 is the bias compensation Weak object transfer function p = 0 (WOTF) Odd part: DPC term Strength depends on φ 0 Phase-gradient transfer function, p = m (PGTF)

41 Weak object transfer func9on for DIC m 0 Δ too big Even part (amplitude contrast) Odd part (DPC) m 0 is spatial frequency cut-off

42 Phase- gradient transfer func9on for DIC Not anti-symmetrical highlighting (Small bias)

43 PGTF for DIC depends on m 0 Δ confocal confocal small bias bias = π/4 Non-linear behaviour

Phase- stepping DIC Slowly-varying phase gradient φ / x = 2πm(x,y) Constant phase gradient deflects light through an angle (prism effect) I = A + Bcos[2π m(x, y)δ φ 0 ] Same form as normal

44 Phase- stepping DIC Slowly-varying phase gradient φ / x = 2πm(x,y) Constant phase gradient deflects light through an angle (prism effect) I = A + Bcos[2π m(x, y)δ φ 0 ] Same form as normal interference pattern Measure I for different values of bias retardation φ 0 φ 0 is bias retardation Using phase-stepping algorithm, can recover phase gradient 2πm(x,y) Integrate phase gradient to get phase (but still constant of integration) Streaking artifact

45 Phase- stepping DIC Phase gradient reconstructed from phase-stepping DIC

46 Phase measurement using phase- stepping DIC Measure φ / x, φ / y Arnison, Larkin, Sheppard, Smith, Cogswell, J. Microsc. 214, 7-12 (2004) Similar to Frankot-Chellappa algorithm IEEE Trans. Pattern Analysis 10, 439 (1988) (Shape from shading)

47 Phase reconstruc9on from DIC

48 Phase reconstruc9on from DIC S Mehta, Thesis (2010)

49 Can use TIE on DIC (TI- DIC) Bias π/4 Bias 3π/4 DIC Phase reconstructed from DIC by TIE

50 PS- DIC and TI- DIC Phase gradient reconstructed from phase-shifting DIC Phase gradient reconstructed from DIC by TIE

51 Quan9ta9ve phase from TIE- DIC

52 Conclusions Par9ally coherent imaging gives beser resolu9on than coherent illumina9on (holographic microscope) Zernike phase contrast not used so much now (qualita9ve) DIC gives good 3D imaging, but problem with birefringence (e.g. plas9c substrate for stem cells) DIC can be linearized using phase stepping DPC not so good for 3D TIE not sensi9ve for weak phase gradients (improved by using more images)

Par$ally Coherent Imaging & Phase Contrast Microscopy

Par$ally Coherent Imaging & Phase Contrast Microscopy Colin Sheppard Nano-Physics Department Italian Ins$tute of Technology (IIT) Genoa, Italy colinjrsheppard@gmail.com Perfect imaging Object amplitude