Metrology and Sensing

Transcription

1 Metrology and Sensing Lecture 5: Confocal sensors Herbert Gross Winter term 06

2 Preliminary Schedule No Date Subject Detailed Content 8.0. Introduction Introduction, optical measurements, shape measurements, errors, definition of the meter, sampling theorem 9.0. Wave optics (ACP) Basics, polarization, wave aberrations, PSF, OTF Sensors Introduction, basic properties, CCDs, filtering, noise Fringe projection Moire principle, illumination coding, fringe projection, deflectometry Interferometry I (ACP) Introduction, interference, types of interferometers, miscellaneous 6.. Interferometry II Examples, interferogram interpretation, fringe evaluation methods Wavefront sensors Hartmann-Shack WFS, Hartmann method, miscellaneous methods Geometrical methods Tactile measurement, photogrammetry, triangulation, time of flight, Scheimpflug setup Speckle methods Spatial and temporal coherence, speckle, properties, speckle metrology Holography Introduction, holographic interferometry, applications, miscellaneous Measurement of basic system properties Bssic properties, knife edge, slit scan, MTF measurement 0.0. Phase retrieval Introduction, algorithms, practical aspects, accuracy Metrology of aspheres and freeforms Aspheres, null lens tests, CGH method, freeforms, metrology of freeforms OCT Principle of OCT, tissue optics, Fourier domain OCT, miscellaneous Confocal sensors Principle, resolution and PSF, microscopy, chromatical confocal method

3 3 Content Principle of confocal imaging Resolution and PSF Pinhole size Impact of aberrations Scanning Examples / applications Chromatical confocal method

4 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 '

5 Confocal Microscope General Aspects Laser scan microscope produces only images in combination with software for the image processing Realtime image gathering is possible today Usually the illumination is a scanning laser beam Usually the detection/observation uses the same lens The confocal pinhole detection guarantees: - a z-sectioning capability - a good suppression of straylight out of other planes in the sample In scanning systems: - the field is generated by transverse scanning with a mirror in a pupil-conjugated plane - in case of volume imaging, the z-scan is performed by moving the stage - the signal beam is descanned after a beam splitter - primary image gathering is monochromatic in a plane-by-plane z-scan Due to the very small pinhole, the sensitivity of the microscope is high: - strong impact on residual aberrations - large environmental sensitivity

6 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

7 Confocal Laser Scan -Microscope Fourier optical model: - illumination with point spread function h ill - object function plane, t obj, scanned - detection with point spread function h det - detector function by pinhole size D ph General transform of amplitudes U U U U ' U U h ill t obj 3 U' hdet ' 3 U 3 D ph source object t obj scan pinhole detector D ph U illumination U U detection U 3 U 3 h ill h det

8 Image in Confocal Laser Scan Microscope Amplitude of PSF: h Illumination and observation with same lens: identical PSF Confocal intensity in image Real conditions: - thick sample, straylight from other z-planes - apodization of source due to laser illumination - residual aberrations of lenses - finite size of the pinhole - special shapes of detectors (circle, square, slit,..) - Partial coherence of illumination - high-na, vectorial PSF - wavelength shift for fluorescence Other/different imaging modes: - -photon - 4p - interference - structured illumination -... H H H I psf ill obs conf H psf 4 Ref: M. Wald

9 Image Formation Confocal LSM Special cases: Brightfield, perfectly small pinhole D=d(x)d(y), imaging coherent I ima h ill h det t obj Fluorescence, coherence destroyed perfectly small pinhole I ima hill hdet tobj ill det Point like object t obj = d(x) d(y) I ima h ill h det D ph Point object and perfectly small pinhole I ima h ill h det Plane mirror object t obj = const. perfectly small pinhole I ima h det ( x, y,z) ill det dx dy h ill hdet Ref: M.Wald

10 Confocal Microscopy Imaging Simple model of confocal imaging: - illumination with coherent PSF H ill - object function T obj - observation with coherent PSF H obs I H H T conf obs ill object Rearrangement spatial domain transfer in frequency domain p i x x y y I ( x, y) T (, ) H (, ) e d d conf obj x y conf x y x y H (, ) H (, ) H (, ) conf x y ill x y obs x y laser source object scan pinhole detector objective lens illumination objective lens observation

11 Confocal Resolution Confocal microscope: - lateral resolution is complicated function - not only optical influence functions digitization pixels noise sensor object ideal theory lateral resolution image residual aberrations lenses noise optic pinhole size apodisation

12 Lateral and Axial Resolution Intensity distributions lateral axial Ref: U. Kubitschek

13 3 Confocal PSF Change of intensity distributions by confocal mode. lateral. axial Ref: A. Szameit

14 Confocal Microscopy: PSF and Lateral Resolution Normalized transverse coordinate v Usual PSF: Airy Confocal imaging: Identical PSF for illumination and observation assumed p v x' sin J I( v) v I(v) ( v) J I( v) v ( v) Resolution improvement be factor.4 for FWhM 4 0,9 0,8 0,7 0,6 0,5 0,4 incoherent coherent 0,3 0, 0,

15 Confocal Microscopy: Axial Sectioning Normalized axial coordinate Conventional wide field imaging: Intensity on axis sin( u / ) I( u) u / Axial resolution Confocal imaging: Intensity on axis ( ) z approx wide sin( u / ) I( u) u / Axial resolution improved by factor.4 for FWhM z confo 0.45 n' cos 0.39 n' cos 4 8 p u z sin ( / ), 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0, 0, I(u) incoherent coherent 0, u

16 6 Microscopic Resolution Signal, lateral and axial resolution depends on imaging mode Imaging mode signal lateral resolution axial resolution classical wide field S I ill 0.6 x 0. 5 nsin D airy z nsin R E confocal photon S I I ill S I ill obs 0.40 x 0.33 D airy nsin 0.70 x 0.43 D airy nsin.4 z n sin.3 z n sin photon confocal S I I ill obs Approximation in these formulas: wavelength shift by fluorescence Lateral resolution and coherence general formula: x k nsin u factors coherent incoherent Rayleigh Sparrow Abbe Rayleigh Sparrow Abbe Classical confocal

17 7 Lateral and Axial Resolution Tradeoff between:. lateral resolution. axial resolution 3. signal to noise ratio (detection yield) axial detection yield lateral Ref: U. Kubitschek

18 Confocal Microscopy: Laterale Transfer Function Ideal coherent transfer function: complex pupil function H coh ( v) xp P f Confocal transfer function: product in spatial domain, convolution in frequency domain identical to incoherent OTF H conf ( v) v arccos p v v H Confocal system has higher spatial resolution coherent confocal 0

19 9 CTF in Microscopy x x Brightfield P* xmax zmax PxP* P z z Incoherent laser scan microscope s x s x s zmax ( PxP* ) x ( QxQ* ) Coherent laser scan microscope PxP* QxQ* s xmax x x s z s z zmax Q P xmax z z PxQ

20 Lateral Resolution in Confocal Imaging Comparison of PSF in wide field and confocal imaging Improved -point resolution in confocal mode conventional wide field confocal

21 Generalized Depth Criterion H CTF : coherent transfer function/psf Integration over spatial frequencies function of the defocussing z Depth discrimination: FWhM of function J(z) decrease with z J(z) J (z) H (,z) d z 0 CTF x x p n sin o J (z) / 0.5 pinhole large z FWhM z FWhM pinhole small z

22 OCT - Microscope Large NA: confocal, depth discrimination by NA Small NA: OCT, depth discrimination by axial coherence I(z) z -3 x OCT, coherence limited NA = exact aperture limited, confocal NA = z NA

23 3 Confocal Depth Signal Measurement of the axial confocal signal by using a lateral shifted tilted mirror Detection of spherical aberration degradation tilted mirror objective lens field y z defocussing

24 4 Confocal Pinhole Size Change of pinhole size: Observation PSF changed Changing relative sizes of illumination and observation PSFs decreasing pinhole, detection PSF shrinking geometrical optical confocality illumination PSF quite smaller transition range wave optical confocality PSF of observation and illumination of nearly same size z obs z ill x ill x obs

25 Size of Pinhole and Confocality 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 S( u) U( u, v) p v dv NA = 0.30 NA = 0.60 NA = 0.75 NA = S(u) a = 3 a = a = a = u.5.5 geometrical D PH / D Airy

26 Confocal Signal for Different Pinhole Sizes Numerical result for different sizes a of the fiber radius The width increases with the fiber diameter The diffraction fine structure disappears with growing a S() a = 0 a = 5 mm a = 0 mm a = 0 mm

27 Confocal Signal and Pinhole Size Confocal signal S(z) without aberrations as a function of the pinhole size a Smaller pinhole: - low signal (bad SNR) - better z-resolution (sectioning) - centroid remains constant in case of perfect imaging S(z,a) a/d airy S(z,a) z / R u a/d airy z / R u

28 Wilsons Formula T. Wilson, Jour. of Microsc. 44 (0) p3, Resolution and optical sectioning in the confocal microscope Empirical formula for the width of the confocal signal in the case of a finite size pinhole and a fluorescence object ( self luminous, phase information lost ) 0.67 D ph 3 First factor: diffraction D.47 FWHM n n NA Second factor: finite size object Dairy 3 z Fwhm = 675 nm geometrical regime diffraction regime = 450 nm D ph /D airy

29 Wilsons Formula: Critical Review Formula is valid for:. one wavelength. self luminous object (fluorescence molecule) 3. perfect corrected spherical aberration A different object interaction changes the pre-factor: mirror: S confocal D FWHM n 0.45 n NA 3 D.47 D ph airy numerical point reflector: D FWHM n 0.6 n NA 3 D.47 D ph airy 3 3 Wilson at l peak D pinhole /D airy This causes errors of the first factor in the range of 30% Incorporation of spherical aberration: t.b.d., PCA analysis as approach seems to be promising

30 Variable Pinhole Diaphragm Real shape of pinhole: quadratic or circular signal depends on shape Variable pinhole easy to realy quadratic Typical size: D pinhole = D airy y y y Kreis x Quadrat senkrecht x Quadrat 45 gekippt x Easy to fabricate: approx. 30 mm very small numerical aperture in pinhole objective lens helps moving part D D

31 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 = a = a = u

32 Confocal Signal with Spherical Aberration Spherical aberration with Zernike coefficient W 40 Integration over finite size pinhole with radius a Asymmetry and width depends on a and W 40 Large pinhole: - depth discrimination decreased - fine structure disappears Sphärische Aberration mit Koeffizient W 40 S(z) Pinhole : a = D Airy / 4 W 40 = 0.0 W 40 = 0. W 40 = 0. W 40 = 0.5 W 40 = S(z) Pinhole : a = D Airy / W 40 = 0.0 W 40 = 0. W 40 = 0. W 40 = 0.5 W 40 = z z S(z) Pinhole : a = D Airy W 40 = 0.0 W 40 = 0. W 40 = 0. W 40 = 0.5 W 40 = z

33 Confocal Signal with Spherical Aberration. c 9 = 0.3 re-normalized c9 =. c 9 =.0 re-normalized S(z,a) a/aairy z c 9 =.0 not normalized

34 Signal Errors due to Spherical Aberration In the case of spherical aberration the confocal signal curve S(z) is degraded:. in position measurement error possible criteria: a) centroid b) midpoint of 50% threshold c 9 = c 9 = 0.7 gauss correlation centroid 50% threshold a. in width loss of accuracy possible criteria: a) nd moment b) 50% threshold (FWHM) c 9 = c 9 = % threshold nd moment a

35 Numerical Results Width of the confocal signal in the spectral domain width 0 8 Fwhm 6 4 nd moment Location of the sample z position position D ph [mm] centroid peak D ph [mm]

36 Confocal Distance Sensor Principle of the confocal distance sensor Illumination beam splitter pinhole detector pinhole objective in focus out of focus objective lens S [a.u.] 0.8 a) ds/dz [a.u.] linearity b) D PH = 0.3 D airy D PH =.0 D airy D PH =.8 D airy z [R u ] z [R u ]

37 Confocal Depth Measuring System The system is described by - Zernike c 4, gives the defocus - Zernikes c 9, c 6,... describe the correction of the system The point spread function is calculated with the help of the Zernike coefficients as h psf ( a, z) ra A o e p i c4z4 ( x, y) c9z9 ( x, y) c6z6 ( x, y)... dx dy Approximations of the model:. psf considered as shift invariant. perfectly incoherent fiber source 3. perfectly homogeneous fiber source 4. in reality, the sample is not a perfect mirror but introduces scattering contributions I(x) total profile finite size PSF finite object size pinhole diameter

38 Change Over Measuring Range Polychromatic illumination Airy diameter changes of measuring range Measuring accuracy varies over range Larger relative influence for small pinholes z/z x D ph = 0. D airy D ph =.0 D airy D ph = 5.0 D airy [mm]

39 Surface Smoothness Smooth / polished surface: - only reflected light is measured - maximum acceptable slope of the sampe surface max arcsin( NA) NA maximum angle max max sample max max Diffuse surface: - larger slopes can be measured - quantitatively the BRDF determines the limit sample

40 Ghost Foci If parts of a polished sample are spherical in shape: - ghost foci with high intensity - wrong interpretation of the depth out of the signal wrong distance right distance sample

41 4 Measurement of Focal Length by Confocal Setup Setup with fiber and plane mirror for autocollimation Change of distance between test lens and fiber Analysis of the recoupled power into the fiber (confocal) gives the focal point lens under test plane mirror recoupled energy autocollimation case z lens position z

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

43 Confocal Microscopy 3-D volume imaging with reconstruction in confocal Laser scan microscope a) Classical microscopy depth of object : 300 mm b) Confocal microscopy with 3-D reconstruction Ref: M. Kempe

44 Examples Microelectronic circuit Abbrasive paper Smooth paper Ref.: R. Leach

45 Examples Silicon surface with stitching Microlens array

46 Chromatical Confocal Sensor Spectral sensitive sensor white light source Objective lens with large axial chromatical aberration grating pinhole measuring range confocale pinhole focussing objective chromatical objective E detector nm 546 nm 656 nm nm nm nm z [mm] z [mm]

47 Confocal Imaging with Hyper Chromate Wide field 0x0.5 Confocal with chromate at low aperture 0x0.5 Confocal with chromate at high aperture 50x0.9 Ref: R. Semmler

48 Principle Goal:. large chromatical spreading (large CHL) z. large numerical aperture 3. corrected spherochromatism In the case of a large ratio z / f, the numerical aperture shows a considerable change in the measuring interval Design approach:. Achromate with positive flint and negative crown. Achromates cascaded 3. Improved spherochromatism by asphere 4. monochromatic lens with buried surface adapter = 644 nm = 546 nm = 480 nm z

49 Comparison Confocal signal as a function of distance and wavelength Cases:. single lens / gauss-aberration corrected. pinhole size Airy 3. no quadrature of confocal psf z + z z. single lens, D ph = D airy +. corrected, colors inverted +.5 D ph = D airy 3. corrected, D ph = D airy

50 on 3=z 3.0=AN 50 XMZ.telbuod noitarugifnoc g i f n o C A M I ) g e d ( : e c a f r u S fo mm tuoyal :htgnel latot laixa etamorhc repyh XMZ.telbuod noitarugifnoc xmz.telbuod noitarugifnoc noitarreba 7/3/30 :htgnelevaw noitarreba sretemillim lanidutignol etamorhc ledies M XMZ.telbuod :noitarugifnoc tops noitarugifnoc e t a m o r h c fo lla 5 3 on 4 on g i f n o C 3=z 3=z 3.0=AN 3 3.0=AN sretemillim margaid m µ y a R g i f n o C f e i h C : s u i d a R xirtam : :suidar e c n e r e f e R y r i A lipup m µ e r a :shtgnelevaw 4 s t i n U : 5 - r a b repyh e l a c S r e p y H 3 roloc fo laretal U S on 3=z roloc laixa 3.0=AN O T S noitrotsid margaid erutavruc.sretemillim.sretemillim dleif msitamgitsa si elacs.mµ decaps a m o C era etamorhc dirg senil mumixam lacirehps repyh Optical Design Case - NA image = 0.3, NA object = 0. Δz = 3 mm, f = 3 mm z free = 6.3 mm st surface: aspherical

51 5 Specifications lenses with asphere Only spherical lenses Extension in Δz NA=0.3, Δz=3mm z free = 6 mm Δz=3.9mm NA=0.4, Δz=0.4mm z free = 0 mm XMZ.telbuod noitarugifnoc 3 fo on 3=z 3.0=AN mm tuoyal :htgnel latot laixa etamorhc repyh OVERVIEW NA=0.4, Δz=mm z free = 0 mm xmz.4.0=z fo lacirehps noitarugifnoc xmz.serehps X M Z. s e r e h p s noitarugifnoc noitarugifnoc repyh repyh snel fo fo 4---6v f 40 AN eerht r u o f =z tamorhc 3 = z repyh 3.0=AN 3. 0 = A N mm tuoyal mm tuoyal mm tuoyal :htgnel :htgnel :htgnel latot laixa etamorhc latot laixa etamorhc latot laixa etamorhc repyh Optical Design Δz=.5mm NA=0.7, Δz=0.mm z free = 3 mm Δz=0.5mm

52 Confocal Depth Measuring System Fourier optical model: - object/sample to be assumed as a plane mirror - fiber source incoherent, diameter D fib, uniformly radiating - optical system with point spread function h psf - confocal detection by fiber (pinhole) size D fib Incoherent imaging model to get the intensity of at the fiber Calculation of the confocal signal by integration over the pinhole I ima ( a, z) I ( a) h ( z) fib ra psf S ( a, z) I ( a, z) dx dy conf ima hyperchromatic system sample surface fiber D recoupling into fiber confocal selection focal plane for selected z