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Chapter 4 – MicroscopyGabriel PopescuUniversityy of Illinois at Urbana‐Champaignp gBeckman InstituteQuantitative Light Imaging Laboratoryhttp://light.ece.uiuc.eduPrinciples of Optical ImagingElectrical and Computer Engineering, UIUC

ECE 460 – Optical Imaging4.1 Resolution of Optical Microscopes The Microscopep can be approximatedppbyy 2 lenses F [ F [U [ x , y ]]]SampleTube lensObjectiveF2F2’F’’1U(x,y)F1[U [ x, y ]]F2 [ F1[U [ x, y ]]] U [ x y , ]M M “‐” sign means inverted image The objective is the most important part of the microscope Usually a third lens (ocular) images F2’ at , such that we canvisualize it with the relaxed eye.Chapter 4: Microscopy2

ECE 460 – Optical Imaging4.1 Resolution of Optical Microscopes The objectivejlens dictates the resolution or size of thesmallest object that the microscope can resolve. Contrast is generated by absorption, scattering, etc. Microscopes can be categorized by the methods that they useto produce contrast. LetLet’ss consider an infinitely small object (point):x1x2xMθfChapter 4: MicroscopyHow small can we see?f3

ECE 460 – Optical Imaging4.1 Resolution of Optical Microscopes Fourier ppropertiespof the lens;; the reconstructed field is: U [ x, y ] U[, ]e2 i ( x1ξ y1 )d d (4.1) xξ M fM and yM f We know that ξ and because We can access only a finite frequency range and therefore wecan only achieve finite resolution. We would need an infinite spectrum to reconstruct ad‐function (in this case a point)MChapter 4: Microscopy4

ECE 460 – Optical Imaging4.1 Resolution of Optical Microscopes Given the finite frequencyqy supportpp we can write:U [ , ] U [ , ] H [ , ] WhereH {1 if ξ ξ M , 0 o th e rw is e1ξ(4.2)Mξξξ So, eq. 4.1 becomesU [ x, y ] F [U [ , ] H [ , ]]Chapter 4: Microscopy(4.3)5

ECE 460 – Optical Imaging4.1 Resolution of Optical Microscopes Use the Convolution Theorem once more ((which states thatconvolution in one domain is multiplication in another) to get:U [ x, y ] U [ x, y ] V h[ x, y ] Where U [ x, y ] is the microscope imageU [ x, y ] is the ideal imageh[ x, y ] is the impulse responseeh[ x, y ] F [ H [ , ]] H[ fx , f y ] Chapter 4: Microscopy 1 if f x 2 f y 2 w20 otherwise i ( x ξ y )(4.4)(4.5)pL circ[ ] w(4.6)2w6

ECE 460 – Optical Imaging4.1 Resolution of Optical MicroscopesF [H ] A J 1[ 2 W ] h,2 W w h e re J is a B e sse l fu n c tio n o f th e 1 st k in d a n d o rd e r So,, So the image of a “point” becomes:h[ x , y ] Since WM xM f 2A2 1J 1[2 W ]2 W and 2W M 1 .2 2 .6161 fxM(eq. 4.8)(4.7)2xM2 1.22 f so,so2J1[ x] x The Airy Function‐1.221.22 A point will be imaged as a smeared spot of diameter .61Chapter 4: MicroscopyxH fxM7

ECE 460 – Optical Imaging4.1 Resolution of Optical Microscopes Imagineg that we have two such points.pThen the resolution isthe minimum distance between the points that are separated,ρwhich is ρ. resolution An objectivejlens that allows highergspatialpfrequenciesq((orangles) provides a higher resolution.Chapter 4: Microscopy8

ECE 460 – Optical Imaging4.1 Resolution of Optical MicroscopesxM 1 1Sx2Ob2x1Ob1xM 2 2Sf1f1xMsin tan Definition:11ff2f2sin 1 NA Numerical Aperture TheTh resolutionl i becomesbbbut .61NA Compare Ob1 and Ob2 above: 2NA(4.10)iis goodd enoughh 1 2 , xM 1 xM 2 NA1 NA2 1 2(4 11)(4.11) So Ob2 provides a better resolution.Chapter 4: Microscopy9

ECE 460 – Optical Imaging4.1 Resolution of Optical Microscopes In general, objectives are made out of several lenses complex systemsPP'FWfEntrance PupilObjectivejf focal distance measured from principal planeW working distance distance from F to physical surface of lensEntrance Pupil image of physical aperture f and entrance pupil determine numerical aperture i.e. resolutionChapter 4: Microscopy10

ECE 460 – Optical Imaging4.1 Resolution of Optical Microscopes Note: if the objectivejlens is immersed in a medium for whichn 1, thenNA n NA (4.12)n This means that it is possible for immersed objective lenses tohave a better resolution.Chapter 4: Microscopy11

ECE 460 – Optical Imaging4.2 Contrast The final imageg consists of a distribution I [ x, y ] which is theresult of absorption, scattering/diffraction, etc. Contrast a measure of the intensity fluctuations across theiimage.I general,l thInthe more contrastt t theth bbetter.ttLow ContrastHigh ContrastIIxChapter 4: Microscopyxdemo available12

ECE 460 – Optical Imaging4.2 Contrast Microscopep imageg2 regions of interest: A, BN is the background noise (in sample)Contrast :(4.13)C AB S A S B ; S A, B signal A, B Contrast to noise ratio:CNR AB C AB N S A SB N N standard deviation of noise. ( S i S ) ; S i signal in pixels22NiChapter 4: Microscopy13

ECE 460 – Optical Imaging4.2 Contrast While resolution is ggiven byy the instrument,, the contrast isgiven by the instrument/sample combination. Most biological structures (i.e. cells) are very transparent soI [ x, y ]is flat, which means there is low contrastThey can be assumed “phase objects”Wave frontI [ x, y ]Example of a phase object:100 nmkImagingsystemN 1.5‐Glass Profile‐Phase GratingChapter 4: Microscopy14

ECE 460 – Optical Imaging4.2 Contrast No absorptionpso I [ x, y ] constant contrast 0 BUT: the wave front carries information about the sampleE[ x, y ] E0 ei [ x , y ]((4.14)) This is the expression for the field in the vicinity of a phaseobjectobject. Bright Field microscopy produces low contrast images ofphase objectspjChapter 4: Microscopy15

ECE 460 – Optical Imaging4.2 Contrast There are several ways to enhance contrast: EndogeneousgContrast Dark fieldPhase contrastSchlereinQuantitative phase microscopyConfocalgflorescenceEndogeneous Exogeneous Contrast Agents StainingFull field Florescent taggingConfocal More recently Beads (dielectric and metallic) Nano Quantum DotsChapter 4: Microscopy16

ECE 460 – Optical Imaging4.3 Dark Field Microscopy Consider the low contrast imageI( )I(x)I(x,y)x Typical low pass filtering remove CI(x)FourierI(fx)xRemove lowFrequencyfx Then take the inverse Fourier TransformationInverseFourierChapter 4: MicroscopyI(x)HighContrastx17

ECE 460 – Optical Imaging4.3 Dark Field Microscopy Actual MicroscopeObjectfLensBlocks lowfrequencyEnhanced Contrast High frequency components areenhanced ((eg.g edges)g ) Without the sampleDark FieldChapter 4: Microscopy18

ECE 460 – Optical Imaging4.4 Schlerein Method Not used very often nowadaysBlocks ½spectrumFourier Image PlaneInverse FourierEnhances ContrastPhase objects can be rendered visibleEdges are enhancedRelates to Hilbert Transform.Chapter 4: Microscopy19

ECE 460 – Optical Imaging4.4 Schlieren Method Exercise: Show the following for a real signal f(x)f(x)FourierCut ½InverseF(g) spectrum Ft(g) Fourier f(x)f (x) and f (x) 1 f (x) i P f (x') dx'22 x x'HilbertTo the left:David Hilbert aGermanMathematician,recognized asone of the mostinfluential anduniversalmathematiciansof the 19th andearly 20thcenturies.Chapter 4: Microscopy20

ECE 460 – Optical Imaging4.5 Phase Contrast Microscopy Developed by Frits Zernike (1935) yielding Noble prize in1953(Physics) Very powerful, commonly used today. Consider a phase object:U ( x, y ) ei ( x , y )(4.15) Intensity distribution:I ( x, y ) U2 1 No Contrast Assume: The microscope has a magnification M 1(x,y)SChapter 4: Microscopy(x’,y’)Fourier PlaneImageplane21

ECE 460 – Optical Imaging4.5 Phase Contrast Microscopy i 2 ( f x f y )U ( f x , f y ) U ( x, y )edxdy(4.16) fx xy; fx f f(4.17) Note: U (0, 0) U ( x, y )dxdy Central Ordinate Theorem Zero Frequency component corresponds to a plane wave inPlane Wavethe image plane(constant of (x,y)) U(x, y)dxdyChapter 4: MicroscopyU0 1U(x, y)dxdy A22

ECE 460 – Optical Imaging4.5 Phase Contrast Microscopy Note: U hash no informationi fi aboutbtheh structure off theh sample.l0U0 1U(x, y )dxdy Average field AImage formation is an interference between the average fieldand high frequency components.U( x, y ) U0 [U( x, y ) U0 ]High FrequencyCComponenttChapter 4: Microscopy(4.18)U1(x, y )23

ECE 460 – Optical Imaging4.5 Phase Contrast Microscopy Phase contrast relies on shifting the phase of U 0 byU 0 U 0 aei Assume U 0 1 ; U 0 U 0 aei becomes: U ( x, y ) aei [U ( x, y ) 1] The intensity distribution in the image plane(4 19)(4.19)becomes:2I ( x, y ) U ( x, y ) i ae ei ( x , y )2 1 a 2 1 1 Re[2[ aei ( ) 2aei 2ei ] a 2 2[1 a cos cos a cos( )]Chapter 4: Microscopy(4.20)24

ECE 460 – Optical Imaging4.5 Phase Contrast Microscopy Note: For a 0 recover Dark Field Microscopy Assume “small”small phase shift cos 1; 2I ( x , y ) a 2 2 a sin sin a 2 2 a ( x , y ) sin I ( x, y ) a 2 2a ( x, y )(4.21) PC couples into intensity a 1 enhances contrast (best modulation for U 0 U1 )Chapter 4: Microscopy25

ECE 460 – Optical Imaging4.6 Nomarski/Differential Interference ContrastMicroscopyi DIC Differential Interference n Prism #110Obj.Wollaston Prism #2 Use polarization discrimination to create 2 interferingbeamsp ( ) with 2 drifted beams Illuminate sample(s)Chapter 4: Microscopy26

ECE 460 – Optical Imaging4.6 Nomarski/Differential Interference ContrastMicroscopyi “Shift” amount Airy disk 2NA Wollaston prism #2 brings the 2 beams together throughi t finterference.ETotal E1 E0 A1 ei 1 A0 ei 0(4.22)l. lddl.d 1 0 n1k n0 d kcos Chapter 4: Microscopy27

ECE 460 – Optical Imaging4.6 Nomarski/Differential Interference ContrastMicroscopyi By varying the position of Wollaston prismone can adjust 1 0 Phase Shift through the sample:ldxxei ( x dx ).ze i ( x )S becomes:ETotal An ei ( n ) A0 ei 0 A0 ei 0 [[1 ei ( 11 0 ) ]Chapter 4: Microscopy(4.23)28

ECE 460 – Optical Imaging4.6 Nomarski/Differential Interference ContrastMicroscopyi The Intensity in the image plane (as a function ofdisplacement x).I ( x) 2I0 (1 cos[ ( x dx) ( x) ]) Note: For small , best results obtained forf (4.24) 2I ( x) 2 I 0 (1 sin[ ( x dx) ( x)]) 2 I 0 [1 dx ( x dx) ( x)](4.25)dx SoS theh finalfi l iintensityi distributiondi ib i isi relatedl d to theh gradientdiof the phase: (x) xChapter 4: Microscopy29

ECE 460 – Optical Imaging4.6 Nomarski/Differential Interference ContrastMicroscopyi DIC is a very sensitive to edges, even though the actualphase shifts are “small”. Example:samplexIIntensityt it nocontrastxx PhasePhcontrastt t andd DIC heavilyh il usedd today,t d especiallyi ll forfinvestigating live biological structures (cells) noninvasively.Chapter 4: Microscopy30

ECE 460 – Optical Imaging4.7 Quantitative Phase Microscopy PC &DIC are great, but qualitative in terms of phase ( x, y ) quantitatively KnowingKii i l offersff some advantages,di.e.igives a map of structure density; for homogeneous structures,gives molecular information. QPM is a “rather new” domain; several methods so far. Main obstacle is noiseChapter 4: Microscopy31

ECE 460 – Optical Imaging4.8 Confocal Microscopy So far, we discussed full‐ field imaging, i.e obtaining theentire image at once(great feature: imaging as a parallelprocess). The image can be recorded point by point also(like TV),sometimes with some advantages. Confocal same focal point for illumination and collectionPinholeChapter 4: Microscopy32

ECE 460 – Optical Imaging4.8 Confocal Microscopy Due to pinhole, light out of focus is rejected, which cancreate stacks of slicesslices, 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 resolutionBS ! It works in reflection usuallyPinholeChapter 4: Microscopy33

ECE 460 – Optical Imaging4.8 Confocal Microscopy/ NSOM Recent development: Multi Foci ImprovesIacquisitioni i i timei Need more power Trade‐offMultipleFocused beam Confocal can provide many frames/seconds(video rate) Leading to 4D imaging(x,y,z,t)Chapter 4: Microscopy34

ECE 460 – Optical Imaging4.8 Confocal Microscopy/ NSOM Near Field Scanning Optical Microscope(NSOM) ContinuationC ii off confocalf l & AFM Tappered fiber as cantilever :FiberAperture down to 50 nmEvanescent waves(no transmission in air)Chapter 4: Microscopy35