Chapter 4 –Microscopy

1 Chapter 4 Microscopy Gabriel PopescuUniversity of Illinois at Urbana ChampaignypgBeckman InstituteQuantitativeLightImagingLaborat oryElectrical and Computer Engineering, UIUCP rinciples of Optical ImagingQuantitative Light Imaging 460 Optical Imaging The Microscope can be approximated by 2 lenses [ [ [ , ]]] Resolution of Optical MicroscopespppyTube lensSampleF2 F2 Objective[ [ [ , ]]]yU(x,y)F 1[[ ]]FUxy[[[ ]]] []xyFFUU sign means inverted image Theobjectiveisthemostimportantpartofthem icroscope1[[,]]FUxy21[[[,]]][,]yFFUxyUMM The objective is the most important part of the microscope Usually a third lens (ocular) images F2 at , such that we can visualize it with the relaxed 4: Microscopy 460 Optical Imaging The objective lens dictates the resolution or size of the Resolution of Optical Microscopesjsmallest object that the microscope can resolve.

2 Contrast is generated by absorption, scattering, etc. Microscopes can be categorized by the methods that they use to produce contrast. Let sconsideraninfinitelysmallobject(point): Let s consider an infinitely small object (point):x1x2xM M How small can we see?ff3 Chapter 4: Microscopy 460 Optical Imaging Fourier properties of the lens; the reconstructed field Resolution of Optical Microscopespp;( )112()[, ][, ]ix yUxyUedd We know that and because and MMxf MMyf We can access only a finite frequency range and therefore we can only achieve finite resolution. Wewouldneedaninfinitespectrumtoreconstru ctafWe would need an infinite spectrum to reconstruct a d function (in this case a point)4 Chapter 4: Microscopy 460 Optical Imaging Given the finite frequency support we can Resolution of Optical Microscopesqypp Where ( )[, ][,] [,]UUH 1 if , 0th i{MMH 10 otherwise{H So, eq.}}

3 Becomes( )[] [[][]]Uxy FUH ( )[,][[,][,]]Uxy FUH 5 Chapter 4: Microscopy 460 Optical Imaging Use the Convolution Theorem once more (which states that Resolution of Optical Microscopes(convolution in one domain is multiplication in another) to get: ( )[, ][, ] [, ]Uxy Uxy hxy V()ix y Where is the microscope imageis the ideal imageistheimpulseresponse[, ]Uxy[, ]Uxy[]hx y()ix ye is the impulse response [,]hx y[, ][ [, ]]hx y FH ( ) 2221 if 0 otherwise[, ][]xyffwxyLHf fcircw p( ) w2w6 Chapter 4: Microscopy 460 Optical Imaging So,11where is a Bessel function of the 1st kind and order[2][], 2 JJWFHAhW Resolution of Optical Microscopes, So the image of a point becomes:2W 2221[2][, ]2 JWhx yAW ( ) Since and2W 1[]2Jx MMxWf Hx so2x fThe Airy 61f so.)

4 61f (eq. )A point will be imaged as a smeared spot of diameter Mx 7 Chapter 4: Microscopy 460 Optical Imaging Imagine that we have two such points. Then the resolution is Resolution of Optical Microscopesgpthe minimum distance between the points that are separated, which is . = resolution An objective lens that allows higher spatial frequencies (or jgpq(angles) provides a higher 4: Microscopy 460 Optical Resolution of Optical Microscopes1 S1 MxS2Mx2 Definition:11sintanMxf 1f1f2f2fThlibbidhf1sinNumerical ApertureNA ( ) The resolution becomes but is good enough Compare Ob1and Ob2above:.61NA 2NA 12 12121 2 MMxxNANA (4 11) So Ob2 provides a better 12121 2, MMxxNANA ( )9 Chapter 4: Microscopy 460 Optical Imaging In general, objectives are made out of several lenses => Resolution of Optical Microscopescomplex systems 'PPFfWObjectiveEntrance Pupiljfocal distance measured from principal planeworking distance = distance from F to physical surface of lensEntrance Pupilimage of physical aperturefW Entrance Pupil = image of physical aperture and entrance pupil determine numerical aperf ture resolution 10 Chapter 4: Microscopy 460 Optical Imaging Note.)

5 If the objective lens is immersed in a medium for which Resolution of Optical Microscopesjn 1, then NAn NAn ( ) This means that it is possible for immersed objective lenses to have a better 4: Microscopy 460 Optical Imaging The final image consists of a distribution which is the [, ] Contrastgresult of absorption, scattering/diffraction, etc. Contrast = a measure of the intensity fluctuations across the iIlthttthbtt[, ]yimage. In general, the more contrast the ContrastHigh ContrastIIxx12 Chapter 4: Microscopy demo 460 Optical Imaging Microscope Contrastpg 2 regions of interest: A, B N is the background noise (in sample)( ) Contrast :,; = signal A, BABABA BCSSS Contrast to noise ratio:ABABABSSCCNR 2 = standard deviation of 22() ; = signal in pixelsNi iiSS S 13 Chapter 4: Microscopy 460 Optical Imaging While resolution is given by the instrument, the contrast is Contrastgy,given by the instrument/sample combination.

6 Most biological structures ( cells) are very transparent so is flat, which means there is low contrast They can be assumed phase objects [, ]Ixy Example of a phase object:100 nm[, ]IxyImaging systemWave frontN= Glass Profile Phase Grating14 Chapter 4: Microscopy ECE 460 Optical No absorption so[, ]constant contrast = 0 Ixy Contrastp BUT:the wave front carries information about the sample[, ]y( )[,][]ixyExy E e This is the expression for the field in the vicinity of a phase object()0[,]Exy E e object. Bright Fieldmicroscopy produces low contrast images of phase objectspj15 Chapter 4: Microscopy ECE 460 Optical There are several ways to enhance contrast: Endogeneous Contrastg Dark field Phase contrast Schlerein Quantitative phase microscopy Confocal Endogeneous florescenceg Exogeneous Contrast Agents Staining FlorescenttaggingFull fieldFlorescent tagging More recently Beads (dielectric and metallic) NanoConfocalNano Quantum Dots16 Chapter 4: Microscopy 460 Optical Imaging Consider the low contrast imageI( ) Dark Field MicroscopyI(x)xI(x,y) Typical low pass filtering = remove CI(x)I(f)Remove low I(x)xFourierI(fx)fxFrequency Then take the inverse Fourier TransformationInverseI(x)Inverse FourierI(x)xHigh Contrast17 Chapter 4.

7 Microscopy 460 Optical Imaging Actual Dark Field MicroscopyfObjectLensBlocks low Enhanced Contrastfrequency High frequency components are enhanced (eg. edges)(gg) Without the sample Dark Field18 Chapter 4: Microscopy 460 Optical Imaging Not used very often nowadaysBlocks SchlereinMethodspectrumImage PlaneFourierInverse Fourier Enhances Contrast Phase objects can be rendered visible Edgesareenhanced Edges are enhanced Relates to Hilbert 4: Microscopy 460 Optical Imaging Exercise: Show the following for a real signal f(x)Cut SchlierenMethodf(x) F(g) Ft(g) f(x)FourierCut spectrumInverse Fourier~() andfx Hilbert1(')()()'22'Pfxfxfxidxxx To the left: David Hilbert a German Mathematician, recognized as one of the most influential and universal mathematicians ofthe19thandof the 19th and early 20th 4.

8 Microscopy 460 Optical Imaging Developed by Frits Zernike (1935) yielding Noble prize in 1953(Physics) Phase Contrast Microscopy1953(Physics) Very powerful, commonly used today. Consideraphaseobject:Consider a phase object: Intensity distribution: (,)(, )ixyUxy e ( )2(, )1 No Contrast Ixy U Assume: The microscope has a magnification M=1(x,y)(x ,y )Fourier PlaneSImage plane21 Chapter 4: Microscopy 460 Optical Imaging2()(, )(,) xyiffxyUffUxyedxdy( ) Phase Contrast Microscopy; xxxyffff Note: Central Ordinate Theorem(0, 0)( , ) UUxydxdy( ) Zero Frequency component corresponds to a plane wave in the image plane(constant of (x,y))Plane Wave1(,)Uxydxdy 01(,)UU x y dxdyA 22 Chapter 4: Microscopy 460 Optical Imaging Note: hif Phase Contrast Microscopy has no information about the structure of the ()UU x y dxdy 0U= Average fieldImageformationisaninterferencebetwe entheaveragefield0(,)UU x y dxdyA Image formationis an interferencebetween the average field and high frequency components.

9 () [() ]UxyUUxy UHigh Frequency Ct00(,)[(,)]UxyUUxy U 1(,)Uxy( )Component1(,)y23 Chapter 4: Microscopy 460 Optical Imaging Phase contrast relies on shifting the phase of by Phase Contrast Microscopy00iUUae Assume ; becomes: Theintensitydistributionintheimageplane0 1U 00iUUae 00(, )[ (, ) 1]iUxy aeUxy (4 19) The intensity distribution in the image plane becomes:2(, )(, )Ixy Uxy ( )2(,)2()111 Re[222]iixyiiiaeeaaeaee 2[]2[1coscoscos()]aaa ( )24 Chapter 4: Microscopy 460 Optical Imaging Note: For a = 0 recover Dark Field Microscopy Assume small Phase Contrast Microscopy Assume small phase shift cos1;2 222(, )2 sin sin2(,)sinIxy aaaaxy PC couples into intensity a<1enhancescontrast(bestmodulationfor) 2(, )2(, )Ixy aaxy ( )UU a<1 enhances contrast (best modulation for ) 01UU 25 Chapter 4: Microscopy Nomarski/Differential Interference Contrast iECE 460 Optical Imaging DIC= Differential Interference ContrastMicroscopy11 CondenserxMovable WollastonP1111000 SSWollaston Prism #1 Wollaston Prism #2 Obj.

10 Usepolarizationdiscriminationtocreate2in terfering Use polarization discrimination to create 2 interfering beams Illuminate sample(s) with 2 drifted beamsp()26 Chapter 4: Microscopy Nomarski/Differential Interference Contrast iECE 460 Optical Imaging Shift amount Airy disk2NA Microscopy Wollaston prism #2 brings the 2 beams together through it 10iiTotalEEE Ae Ae ( ) 10 10cosdnkndk 27 Chapter 4: Microscopy Nomarski/Differential Interference Contrast iECE 460 Optical Imaging By varying the position of Wollaston prism Microscopyone can adjust Phase Shift through the sample:10 ()ixdxe ()ixe S becomes:00110()0()0[1]niiTotalniiEAe AeAee ( )0[]ee28 Chapter 4: Microscopy Nomarski/Differential Interference Contrast iECE 460 Optical Imaging The Intensity in the image plane (as a function of Microscopydisplacement x).