Microscopy. Lecture 2: Optical System of the Microscopy II Herbert Gross. Winter term

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1 Microscopy Lecture 2: Optical System of the Microscopy II Herbert Gross Winter term 212

2 Preliminary time schedule 2 No Date Main subject Detailed topics Lecturer Optical system of a microscope I overview, general setup, binoculars, objective lenses, performance and types of lenses, tube optics Gross Optical system of a microscope II Physical optics of widefield microscopes Performance assessment Fourier optical description Etendue, pupil, telecentricity, confocal systems, illumination setups, Köhler principle, fluorescence systems and TIRF, adjustment of objective lenses Point spread function, high-na-effects, apodization, defocussing, index mismatch, coherence, partial coherent imaging Wave aberrations and Zernikes, Strehl ratio, point resolution, sine condition, optical transfer function, conoscopic observation, isoplantism, straylight and ghost images, thermal degradation, measuring of system quality basic concepts, 2-point-resolution (Rayleigh, Sparrow), Frequency-based resolution (Abbe), CTF and Born Approximation Gross Gross Gross Heintzmann Methods, DIC Rytov approximation, a comment on holography, Ptychography, DIC Heintzmann Multibeam illumination, Cofocal coherent, Incoherent processes (Fluorescence, Raman), Imaging of scatter OTF for incoherent light, Missing cone problem, imaging of a fluorescent plane, incoherent confocal OTF/PSF Heintzmann Incoherent emission to improve resolution Fluorescence, Structured illumination, Image based identification of experimental parameters, image reconstruction Heintzmann The quantum world in microscopy Photons, Poisson distribution, squeezed light, antibunching, Ghost imaging Wicker Deconvolution Building a forward model and inverting it based on statistics Wicker Nonlinear sample response STED, NLSIM, Rabi the information view Wicker Nonlinear microscopy two-photon cross sections, pulsed excitation, propagation of ultrashort pulses, (image formation in 3D), nonlinear scattering, SHG/THG - symmetry properties Heisterkamp Raman-CARS microscopy Tissue optics and imaging principle, origin of CARS signale, four wave mixing, phase matching conditions, epi/forward CARS, SRS. Tissue optics, scattering&aberrations, optical clearing,optical tomography, lightsheet/ultramicroscopy Heisterkamp Heisterkamp Optical coherence tomography principle, interferometry, time-domain, frequency domain. Heisterkamp

3 Contents of 2nd Lecture 3 1. Etendue 2. Pupil 3. Telecentricity 4. Confocal systems 5. Illumination setups 6. Köhler principle 7. Fluorescence systems and TIRF 8. Objective adjustment

4 Microscope Objective Lens No rigid relationship between magnification and aperture Product of field size and NA fixes the overall capacity NA immersion m 2 4 obj Variation of image-sided numerical aperture.3 NA' m obj

5 Etendue of Microscope Objective Lenses Information capacity, etendue, space-bandwidth product, number of PSF s resolved in the field Non-rigid correlation between magnification and etendue G [mm 2 ] 1 G 4 D NA 2 field Largest etendue for medium magnifications Immersion systems have larger etendue air oil water D field in [mm] m

6 Properties of the Pupil Relevance of the system pupil : Brightness of the image Transfer of energy Resolution of details, Information transfer, location of Fourier spectrum Image quality Aberrations due to aperture Image perspective Perception of depth Compound systems: matching of pupils is necessary, location and size

7 Entrance and Exit Pupil object point on axis lower marginal ray upper coma ray upper marginal ray U chief ray W U' field point of image on axis point of image outer field point of object exit pupil lower coma ray stop entrance pupil

8 Microscope Objective Lens: Pupil Object space telecentric Real rear stop is not object plane objective lens rear stop exit pupil defining the pupil marginal ray Collimated outgoing beam Exit pupil usually telecentric, entrance pupil infinity u y' p chief ray not accessible f' f' object plane pupil exit pupil rear stop chief ray

9 Microscope Objective Lens: Pupil Diameter of pupil only weak correlated with magnification Pupil distorsion: D distexp y' p 1 f ' sin u D ExP D dist ExP a) Lister D dist ExP b) 1x.93 oil y p y p 6 5 D dist ExP 5 x 1-3 c) Laikin D x 1-3 dist ExP 1 d) Schwarzschild m Pupil distortion small (sine condition corrected) y p y p

10 Microscope Objective Lens: Pupil Imaging of the pupil is important Residual aberrations: sharp edge of aperture is desired Real systems : smoothed illumination profile lens v pupil stop 1 I(r) ideal edge r [mm]

11 Microscope Objective Lens: Pupil Example of larger residual aberrations of pupil image : 1. axial shift of pupil with field size 2. no sharp imaging of aperture stop 3. coloured edge of stop boundary nm 546 nm 644 nm 3 D spot [m] diffraction limit 11.6 axis z [mm] 23.1

12 Microscope Objective Lens: Pupil Vignetting of the pupil : 1. truncation of the bundle for finite field sizes 2. chief ray not identical with centroid 3. perturbation of telecentricity 4. in microscopic systems mostly at the front lens centre of gravity shifted full aperture vignetted aperture chief ray telecentric chief ray not telecentric

13 Vignetting Truncation at front lens Pupil vignetting: cover glass front lens oil truncating edge pupil shape crescent shape of light cone Illumination fall-off towards field boundary axis zone field I(r)/I o 1.5 y/y.5 1 max

Vignetting D S Truncation of regions with large

$5 diffraction limit axis field zone field edge$

14 Vignetting D S Truncation of regions with large aberrations as correction method Improved performance Psf elliptical, anisotropiuc resolution Energy reduced diffraction limit axis field zone field edge solid line : vignetted dashed line : without vignetting 48 nm 546 nm 644 nm.5 1 y'/y max x x y x y

15 Telecentricity Special stop positions: 1. stop in back focal plane: object sided telecentricity 2. stop in front focal plane: image sided telecentricity 3. stop in intermediate focal plane: both-sided telecentricity Telecentricity: 1. pupil in infinity 2. chief ray parallel to the optical axis a) image sided telecentric b) object sided telecentric object telecentric stop image object telecentric stop image f chief rays parallel to axis in image space chief rays parallel to axis in object space f'

16 Telecentricity Design problems with telecentricity: Usual telecentricity only fulfilled for one wavelength w tele [ ] Telecentricity is related to the centroid ray. Therefore the telecentricity is disturbed by vignetting effects nm 587 nm 656 nm w tele [ ] y'/y' max 1.8 centre ray with vignetting chief ray centre ray with coma y'/y' max

17 Confocal Microscope Laser scan microscope Depth resolution (sectioning) with confocal pinhole Transverse scan on field of view Digital image Only light comming out of the conjugate plane is detected Perfect system: scan mirrors conjugate to pupil location System needs a good correction of the objective lens, symmetric 3D distribution of intensity laser illumination objective lens in focus out of focus pinhole lens pinhole CCD '

18 Confocal Images Depth resolved images Ref.: M. Kempe

19 Confocal Laser Scan Microscope Complete setup: objective / tube lens / scan lens / pinhole lens Scanning of illumination / descanning of signal Scan mirror conjugate to system pupil plane Digital image processing necessary object plane objective lens pupil plane tube lens intermediate image scan lens scan mirror pinhole lens field point axis point pupil imaging beam forming laser source

20 Confocal Laser Scan Microscope Scan lens Diffraction limited Change in pupil location of objective lenses is critical perturbation of telecentricity scan mirror intermediate image w [ ] pupil location: + 3 mm paraxial exact.2.1 W rms 48 nm 546 nm 644 nm diffraction limit mm y/y max 5 1 in

21 Confocal Laser Scan Microscope Pinhole lens Only axial colour is essential Usage on axis only due to descanning Variable pinhole size not too small: small aperture, retrofocus lens y p nm 546 nm 644 nm z in [mm] pinhole

22 Confocal Microscopy: PSF and Lateral Resolution Normalized transverse coordinate v Usual PSF: Airy Confocal imaging: Identical PSF for illumination and observation assumed 2 v x' sin 2J1 ( v) I( v) v I(v) 2 2J1 ( v) I( v) v Resolution improvement be factor 1.4 for FWhM 4 1,9,8,7,6,5,4 incoherent coherent,3,2,

23 Confocal Microscopy: Axial Sectioning Normalized axial coordinate Conventional wide field imaging: Intensity on axis Axial resolution Confocal imaging: Intensity on axis sin( u / 2) I( u) u / 2 ( ) z approx wide sin( u / 2) I( u) / 2 u Axial resolution improved by factor 1.41 for FWhM z confo 2.45 n' 1 cos.319 n' 1 cos 4 8 u z sin 2 ( / 2) 1,,9,8,7,6,5,4,3,2,1 I(u) incoherent coherent, u

24 Size of Pinhole and Cnfocality Large pinhole: geometrical optic Small pinhole: - Diffraction dominates - Scaling by Airy diameter a = D/D Airy - diffraction relevant for pinholes D < D airy Confocal signal: Integral over pinhole size x / D Airy a 2 S( u) U( u, v) 2 v dv NA =.3 NA =.6 NA =.75 NA = S(u) a = 3 a = 2 a = 1 a = u geometrical D PH / D Airy

25 Confocal Signal with Spherical Aberration Spherical aberration: - PSF broadened - PSF no longer symmetrical around image plane during defocus Confocal signal: - loss in contrast - decreased resolution S(u) spherical aberration relative pinhole size: a = 3 a = 2 a = 1 a = u

26 Confocal Laser Scan Microscope Depth signal as a function of wavelength Disturbance by axial colour aberration 3 z/r u z estim image plane -2 D ph = D airy

27 Illumination Optics: Overview Four possibilities for practical needs axis Epi vs. trans-illumination observation Bright vs. dark field illumination epi-bright field Comparison of light cones for imaging and illumination parts epi-dark field object plane trans-dark field trans-bright field

28 Illumination Optics: Overview Instrumental realizations a) incident illumination bright field b) incident illumination dark field c) transmitted illumination bright field d) transmitted illumination dark field observation observation ring mirror observation observation illumination illumination objective lens object plane object plane ring mirror object plane condenser object plane ring condenser illumination illumination

29 Illumination Optics: Overview Typical images for different illuminations epi trans bright dark

30 Köhler Illumination Principle Principle of Köhler illumination: collector condenser objective lens Alternating beam paths of field and pupil No source structure in image Light source conjugated to system pupil source field stop aperture stop object plane back focal plane - pupil image plane Differences between ideal and real ray paths field stop filter aperture stop condenser collector source object plane

31 Illumination Optics: Overview Types of settings : 1. Köhler : source into pupil, mostly used 2. Critical : source into field of view, source structure disturbs image 3. Projection : source into condenser 4. Arbitrary condenser a) Köhler = 1 f con fcon source b) =.5 collector c) Projection = d) = -.5 auxiliary lens object plane e) Critical = -1

32 Illumination Optics: Collector Requirements and aspects: 1. Large collecting solid angle 2. Correction not critical 3. Thermal loading large 4. Mostly shell-structure for high NA a) axis W(y p ) b) field 2 48 nm 546 nm 644 nm y p W(y p ) 2 y p a) axis W(y p ) b) field 2 W(y p ) 2 y p y p 48 nm 546 nm 644 nm

33 Illumination Optics: Condenser 2. Abbe type, achromatic, NA =.9, aplanatic, residual spherical a) axis b) field y' 1m tangential y' 1m sagittal x' 1m y p y p x p 48 nm 546 nm 644 nm 3. Aplanatic achromatic, NA =.85 a) axis b) field y' 1m tangential y' 1m sagittal x' 1m y p y p x p 48 nm 546 nm 644 nm

34 Illumination Optics: Condenser Dark-field illumination systems 1. Trans-illumination Cardioid-mirror cardiode object plane R/2 C P R R/2 circle 2R cardioide illumination cone cover slide object carrier immersion Realizations: approximation of Cardioid curve condenser

35 Illumination Optics: Condenser 2. Epi-illumination Complicated ring-shaped components around objective lens observation illumination ring lens circle 1 observation illumination object ring lens object circle 2

36 Illumination Optics: TIRF-Illumination Epi- and trans illumination for TIRF substrate illumination prism cover glass total internal reflexion carrier illumination probe cover glass objective lens observation signal

37 Fluorescence Microscopy Fluorescence microscopy is the most frequently employed mode of light microscopy used in biomedical reserach today Setup: dicroitic beam splitter UV bloc filter fluorescence red or infrared object objective lens excitation filter image plane illumination at 365 nm 1 Fluorescein Iso Thio Cyanate UV source absorption.5 emission Necessary components: Dicroitic beam splitter, excitation filter with sharp edge [nm]

TIRF Microscopy Total internal reflection microscopy: Excitation

better SNR, no fluorescence background Problem in optical design:

observation light cone illumination ring channel observation cover

38 TIRF Microscopy Total internal reflection microscopy: Excitation with evanescent field Advantages: 1. better axial resolution 2. better SNR, no fluorescence background Problem in optical design: Extremly small illumination ring-shaped channel around the observation light cone illumination ring channel observation cover glass probe total internal reflexion Epi-Fluorescence TIRF Objective lens TIRF 1x1.45

39 Adjustment of Objective Lenses Adjustment of air gaps to t 2 t 4 t 6 t 8 optimize spherical aberration Reduced optimization setup c j c jo k1,4 c j c t k j, j 2,4,6,8 Compensates residual aberrations due to tolerances (radii, thicknesses, refractive indices) d 2 d 4 d 6 d 8 c 2 c 4 c 6 c 8 W rms nominal d 2 varied d 4 varied d 6 varied d 8 varied optimized

40 Adjustment of Objective Lenses Significant improvement for one wavelength on axis Possible decreased performance in the field W rms in.3 48 nm 546 nm 644 nm solid lines : nominal dashed lines : adjusted.15 improvement.5 1 y/y max

Object plane Defocus compensator On compensator axis astigmatism Nr. 1 2 Optical System of the Microscope II Adjustment and Compensation Example microscopic lens Adjusting: 1.

41 Object plane Defocus compensator On compensator axis astigmatism Nr. 1 2 Optical System of the Microscope II Adjustment and Compensation Example microscopic lens Adjusting: 1. Axial shifting lens : focus 2. Clocking: astigmatism 3. Lateral shifting lens: coma Onaxiscoma compensator Spherical aberrati compensator Ideal : Strehl D S = % With tolerances : D S =.1 % After adjusting : D S = 99.3 % PSF (energynormalized) Systemwithtolerances Strehl:,2% Onaxisastig compensator N Ref.: M. Peschka

Strehl ratio [%] 2 Optical System of the Microscope II Adjustment and Compensation Sucessive steps of improvements PSF (intensity PSF normalized) (energy

42 Strehl ratio [%] 2 Optical System of the Microscope II Adjustment and Compensation Sucessive steps of improvements PSF (intensity PSF normalized) (energy normalized) % Not adjusted 21.77% 25.48% 97.2% Step 1 Step 2 Step 3 Z, 4 Z 9 Z, 7 Z 8 Z, 5 Z 6 WithTolerances Step1(Z, Z) 4 9 Ref.: M. Peschka Step2(Z, Z) 7 8

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