Chapter 4 Microscopy

Transcription

1 Chapter 4 Microscopy Gabriel Popescu University of Illinois at Urbana Champaign Beckman Institute Quantitative Light Imaging Laboratory Principles of Optical Imaging Electrical and Computer Engineering, UIUC

2 4.1 Resolution of Optical Microscopes The Microscope can be approximated by 2 lenses F [ F [ U [ x, y ]]] Sample U(x,y) Objective F 2 F 1 Tube lens FUxy [ [, ]] x y 1 F2 [ F1 [ U [ xy, ]]] U [, ] M M sign means inverted image The objective isthe mostimportantpart part of the microscope Usually a third lens (ocular) images F 2 at, such that we can visualize it with the relaxed eye. F 2 2

3 4.1 Resolution of Optical Microscopes The objective lens dictates the resolution or size of the smallest object that the microscope can resolve. Contrast is generated by absorption, scattering, etc. Microscopes can be categorized by the methods that they use to produce contrast. Let s consider an infinitely smallobject (point): x 1 x 2 x M θ M How small can we see? f f 3

4 4.1 Resolution of Optical Microscopes Fourier properties p of the lens; the reconstructed field is: 2 i ( x1ξ y1) U[ x, y] U[, ] e d d M M We know that ξ and because ξ and x f (4.1) We can access only a finite frequency range and therefore we can only achieve finite resolution. We would need an infinite spectrum to reconstruct a d function (in this case a point) M y M f 4

5 4.1 Resolution of Optical Microscopes Given the finite frequency support we can write: U [, ] U [, ] H [, ] Where H M 1 if ξ ξ, { 0 otherwise M (4.2) 1 ξ ξ ξ ξ So, eq. 4.1 becomes Uxy [, ] FU [ [, ] H [, ]] (4.3) 5

6 4.1 Resolution of Optical Microscopes Use the Convolution Theorem once more (which states that convolution in one domain is multiplication in another) to get: Uxy [, ] Uxy [, ] V hxy [, ] Uxy [, ] Where is the microscope image Uxy [, ] is the ideal image hxy [, ] isthe impulse response e i ( x ξ y ) (4.4) (4.5) hxy [, ] FH [ [, ]] L x y [, ] [ ] 1 if f f w H fx f y 0 otherwise circ w 2w p (4.6) 6

7 4.1 Resolution of Optical Microscopes J [2 W ] 2 W 1 So, F[ H ] A h, J 1 So the image of a point becomes: where is a Bessel function of the 1st kind and order 2 2 J [2 ] 1 W h [ x, y ] A 2 W (4.7) M Since W and so, M x M x 2W M 1.22 f f.61 f x M (eq. 4.8) [ ] 1 2 J x x A point will be imaged as a smeared spot of diameter 1.22 x H The Airy Function.61 f x M 7

8 4.1 Resolution of Optical Microscopes Imagine that we have two such points. Then the resolution is the minimum distance between the points that are separated, which is ρ. ρ = resolution An objective lens that allows higher spatial frequencies (or angles) provides a higher resolution. 8

9 4.1 Resolution of Optical Microscopes Ob x 1 Ob x x M 1 2 x M 2 S S f1 1 M Definition: sin1 tan x 1 f 1 f f2 f2 sin NA Numerical Aperture (4.10).61 NA 2NA The resolution becomes but is good enough Compare Ob 1 and Ob 2 above:, x x NA NA (4.11) 1 2 M 1 M So Ob 2 provides a better resolution. 9

10 4.1 Resolution of Optical Microscopes In general, objectives are made out of several lenses => complex systems P P ' F f W f Entrance Pupil Objective focal distance measured from principal plane W working distance = distance from F to physical surface of lens Entrance Pupil = image of physical aperture f and entrance pupil determine numerical aperture i.e. resolution 10

11 4.1 Resolution of Optical Microscopes Note: if the objective lens is immersed in a medium for which n 1, then NA nna (4.12) n This means that it is possible for immersed objective lenses to have a better resolution. 11

12 4.2 Contrast Ixy [, ] The final image consists of a distribution which is the result of absorption, scattering/diffraction, etc. Contrast = a measure of the intensity fluctuations across the image. In general, the more contrast tthe better. Low Contrast High Contrast I I x x demo available 12

13 4.2 Contrast Microscope image 2 regions of interest: A, B N is the background noise (in sample) (4.13) Contrast : C S S ; S = signal A, B AB A B A, B Contrast to noise ratio: CNR N AB C AB N S A = standard deviation of noise. 2 2 N i i i N S B ( S S) ; S = signal in pixels 13

14 4.2 Contrast While resolution is given by the instrument, the contrast is given by the instrument/sample combination. Most biological structures (i.e. cells) are very transparent so I[ xy, ] is flat, which means there is low contrast They can be assumed phase objects Example of a phase object: Wave front I[ xy, ] N= nm k Imaging system Glass Profile Phase Grating 14

15 4.2 Contrast No absorption so I [ x, y ] constant contrast = 0 BUT: the wave front carries information about the sample Exy [, ] E e i [ x, y] (4.14) This is the expression for the field in the vicinity of a phase object. Bright Field microscopy produces low contrast images of phase objects 0 15

16 4.2 Contrast There are several ways to enhance contrast: Endogeneous Contrast Dark field Phase contrast Schlerein Quantitative phase microscopy Confocal Endogeneous florescence Exogeneous Contrast Agents Staining Florescent tagging Full field Confocal More recently Beads (dielectric and metallic) Nano Quantum Dots 16

17 4.3 Dark Field Microscopy Consider the low contrast image I(x) I(x,y) x Typical low pass filtering = remove C I(x) I(fx) x Fourier Remove low Frequency fx Then take the inverse Fourier Transformation Inverse Fourier I(x) x High Contrast 17

18 4.3 Dark Field Microscopy Actual Microscope Object f Lens Blocks low frequency High frequency components are enhanced (eg. (gedges) Without the sample Dark Field Enhanced Contrast 18

19 4.4 Schlerein Method Not used very often nowadays Blocks ½ spectrum Image Plane Fourier Inverse Fourier Enhances Contrast Phase objects can be rendered visible Edges are enhanced Relates to Hilbert Transform. 19

20 4.4 Schlieren Method Exercise: Show the following for a real signal f(x) Cut ½ spectrum Inverse Fourier f(x) Fourier F(g) Ft(g) f(x) ~ fx () and 1 P f( x') f () x f() x i dx' 2 2 xx' Hilbert To the left: David Hilbert a German Mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. 20

21 4.5 PhaseContrast Microscopy Developed by Frits Zernike (1935) yielding Noble prize in 1953(Physics) Very powerful, commonly used today. Consider a phase object: U( x, y) i ( x, y) e (4.15) Intensity distribution: I( x, y) U 2 1 No Contrast Assume: The microscope has a magnification M=1 (x,y) (x,y ) S Fourier Plane Image plane 21

22 4.5 PhaseContrast Microscopy x y i2 ( f f ) U ( fx, fy) U( x, y) e dxdy (4.16) f x x f ; f x y f U U x y dxdy (4.17) Note: (0,0) (, ) Central Ordinate Theorem Zero Frequency component corresponds to a plane wave in Plane Wave the image plane(constant of (x,y)) Uxydxdy (, ) U0 1 A U( x, y) dxdy 22

23 Note: 4.5 PhaseContrast Microscopy has no information i about the structure of the sample. U 0 1 U0 U ( x, y ) dxdy A = Average field Imageformation is an interference between the average field and high frequency components. Uxy (, ) U [ Uxy (, ) U ] 0 0 High Frequency Component U ( x, y ) 1 (4.18) 23

24 4.5 PhaseContrast Microscopy Phase contrast relies on shifting the phase of U 0 by U i U ae 0 0 i Assume ; U U ae becomes: U The intensity distribution in the imageplane becomes: 2 I( x, y) U( x, y) i i( x, y) 2 ae e 1 2 i( ) i i a ae ae e 1 1 Re[2 2 2 ] i U( x, y) ae [ U( x, y) 1] (4.19) 2 a 2[1 acos cosacos( )] (4.20) 24

25 4.5 PhaseContrast Microscopy Note: For a = 0 recover Dark Field Microscopy Assume small phase shift cos 1; 2 2 I( x, y) a 2a sin sin 2 a a x y 2 (, ) sin 2 I( x, y) a 2 a ( x, y) (4.21) PC couples into intensity a<1 enhances contrast (best modulationfor U U )

26 4.6 Nomarski/Differential Interference Contrast Microscopy DIC= Differential Interference Contrast P 1 1 Condenser x 1 1 Movable Wollaston S Obj. Wollaston Prism #1 Wollaston Prism #2 Use polarization discrimination to create 2 interfering beams Illuminate sample(s) with 2 drifted beams 26

27 4.6 Nomarski/Differential Interference Contrast Microscopy Shift amount Airy disk 2NA Wollaston prism #2 brings the 2 beams together through interference. E E E A e A e Total i 1 i (4.22) l l d. d. l d 1 0 n1 k n0 d k cos 27

28 4.6 Nomarski/Differential Interference Contrast Microscopy By varying the position of Wollaston prism one can adjust 1 0 Phase Shift through the sample: dx l. x i ( x dx) e i ( x) z e S becomes: E A e A e Total Ae i( n ) i0 n i0 i( 110) 0 e [1 e ] 0 (4.23) 28

29 4.6 Nomarski/Differential Interference Contrast Microscopy The Intensity in the image plane (as a function of displacement x). Ix () 2 I(1cos[( xdx) () x]) 0 Note: For small, best results obtained for I( x) 2 I (1 sin[ ( xdx) ( x)]) 0 (4.24) 2 (4.25) ( xdx) ( x) 2 I0[1 dx ] dx So the final intensity i distribution ib i is related to the gradient of the phase: ( x) x 29

30 4.6 Nomarski/Differential Interference Contrast Microscopy DIC is a very sensitive to edges, even though the actual phase shifts are small. Example: sample x x Intensity no contrast Phase contrast tand DIC heavily used today, especially ill for investigating live biological structures (cells) noninvasively. x 30

31 4.7 QuantitativePhaseMicroscopy PC &DIC are great, but qualitative in terms of phase Knowing ( xy, ) quantitatively i offers some advantages, i.e. gives a map of structure density; for homogeneous structures, gives molecular information. QPM is a rather new domain; several methods so far. Main obstacle is noise 31

32 4.8 Confocal Microscopy So far, we discussed full field imaging, i.e obtaining the entire image at once(great feature: imaging as a parallel process). The image can be recorded point by point also(like TV), sometimes with some advantages. Confocal = same focal point for illumination and collection Pinhole 32

33 4.8 Confocal Microscopy Due to pinhole, light out of focus is rejected, which can create stacks of slices, hence 3D rendering Scanning: either by scanning the sample or the beam Note: 3D Info large field of view (limited by aperture) up to 2 better resolution! It works in reflection usually BS Pinhole 33

34 4.8 Confocal Microscopy/ NSOM Recent development: Multi Foci Improves acquisition iii time Need more power Trade off Multiple Focused beam Confocal can provide many frames/seconds(video rate) Leading to 4D imaging(x,y,z,t) 34

35 4.8 Confocal Microscopy/ NSOM Near Field Scanning Optical Microscope(NSOM) Continuation i of confocal l& AFM Tappered fiber as cantilever : Fiber Aperture down to 50 nm Evanescent waves (no transmission in air) 35

36 4.8 Confocal Microscopy/ NSOM Sample nm D Evanescent waves couple into sample Became propagating Not limited dby dff diffraction Drawback: scanning time; difficult in liquids 36

37 4.9 Fluorescence Microscopy Illumination and emission have different wavelengths Endogenous Fluorophoress eg. NADH Most commonly exogenous Recently: GFP technology (given fluorescent protein) geneticallyencoded encoded, fused with DNA GFP live cell imaging allowsfor multiple fluorophores dynamic monitoring of processes(cell signaling) 37

38 4.9 Fluorescence Microscopy Fluorescence adds specificity to the measurement. (organelledynamics dynamics, process specific) Typically epi fluorescence( reflection geometry) Obj. S < BS Filter Filter blocks the excitation light 38

39 4.9 Fluorescence Microscopy Full Field is limited to thin samples Combine fluorescence & confocal leads to deeper penetration Issues when imaging live cells: acquisition time, sensitivity, damage. Photo bleaching can produce cell damage: limit duration of illumination need efficiency sensitivity use intensified ifi CCD Acquisition speed: improve with multi foci &Nipkow disk scanning 39

40 4.9 Fluorescence Microscopy Other Fluorescence Techniques: Total linternal reflection FCS Fluorescence correlation spectroscopy FRAP Fluorescence recovery after photobleaching FRET Fluorescence resonance energy transfer. FLIM fluorescence lifetime imaging. g STED Stimulated emission depletion 100nm spot STED+ 4Pi confocal microscopy 33nm diffraction spot single molecule imaging. PALM, fpalm Fiona, etc 40

41 4.10 Multiphoton Imaging 2 Photon laser scanning microscopy Nonlinear process Deep Penetration Requires high power density 1 I f I 2 x Improves Resolution 2 Illumination spot is reduce by z 0 Fluorescence = 41

42 4.10 Multiphoton Imaging 2nd harmonic Imaging recent: Endogenous SHG molecules(e.g l collagen) ( L) 2 P E coherent process (phase matching) Same advantage of smaller illumination spot Let s take a look at examples! 42

43 Microscopy images Nikon

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45 1. Cell imaging

46 Fluorescence microscopy Nikon

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55 2. Tissue slice imaging

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64 Confocal fluorescence