Medical Photonics Lecture Optical Engineering

Transcription

1 Medical Photonics Lecture Optical Engineering Lecture 13: Metrology Herbert Gross Winter term

2 2 Photometric Properties Relations of the 4 main definitions Cassarly's diamond per area illuminance per projected solid angle times n 2 flux per etendue luminance per solid angle intensity per projected area times n 2 Ref.: J. Muschaweck

3 3 Schedule Optical Engineering 2017 No Subject Ref Date Detailed Content 1 Introduction Gross Materials, dispersion, ray picture, geometrical approach, paraxial approximation 2 Geometrical optics Gross Ray tracing, matrix approach, aberrations, imaging, Lagrange invariant 3 Diffraction Gross Basic phenomena, wave optics, interference, diffraction calculation, point spread function, transfer function 4 Components Kempe Lenses, micro-optics, mirrors, prisms, gratings 5 Optical systems Gross Field, aperture, pupil, magnification, infinity cases, lens makers formula, etendue, vignetting 6 Aberrations Gross Introduction, primary aberrations, miscellaneous 7 Image quality Gross Spot, ray aberration curves, PSF and MTF, criteria 8 Instruments I Kempe Human eye, loupe, eyepieces, photographic lenses, zoom lenses, telescopes 9 Instruments II Kempe Microscopic systems, micro objectives, illumination, scanning microscopes, contrasts 10 Instruments III Kempe Medical optical systems, endoscopes, ophthalmic devices, surgical microscopes 11 Optic design Gross Aberration correction, system layouts, optimization, realization aspects 12 Photometry Gross Notations, fundamental laws, Lambert source, radiative transfer, photometry of optical systems, color theory 13 Illumination systems Gross Light sources, basic systems, quality criteria, nonsequential raytrace 14 Metrology Gross Measurement of basic parameters, quality measurements

4 Measurement of Focal Length with Collimator Collimated incident light Calibrated collimator with focal length f c and test chart with size y Selection of sharp image plane Analysis of image size f ' f ' c y' y f' c f' y y' test chart collimator test optic image

5 Measurement of Focal Length According to Gauss Setup with distance object-image L > 4f Known location of the principal plane P of the system distance d P between principal planes Selection of two system locations with sharp image Relative axial shift D between the two setups f L d 4 H 4 2 D L d H d P P P' F F' position 1 s' s f f' D F F' position 2 L P P'

6 Measurement of Focal Length with Abbe-Focometer Telecentric movable measurement microscope with offset y Focusing of two different test charts with sizes y 1 and y 2 Determination of the focal length by tan y f y y e 2 1 u test lens y 1 y 2 u F e y measuring microscope test scale 1 test scale 2 f focusing movement

7 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

8 Measurement of Focal Length with Focimeter Afocal setup with sharp image plane Measurement of long focal lengths Insertion of test system in collimated light segment and refocussing Applying the lens makers formula 1 1 x 2 f f f 2 2 test target collimator lens lens under test focusing lens f 2 new image plane reference image plane re-focusing f 2 x f 2

9 Measurement of Focal Length by Moire Deflectometry Setup with collimator and two Ronchi rulings System under test is inserted Grating period d and azimuthal angle q between the gratings Moire pattern is rotated by angle a, if test lens acts as focussing element Radius of curvature R or focal length R d q tana test target collimator lens lens under test Ronchi gratings observation plane Moire pattern q a d

10 Measurement of Focal Length by Talbot Imaging Setup with Ronchi grating in collimated light gives a series of Talbot images The Talbot planes are imaged by the system under test Analysis of the imge plane by lens formula gives the desired focal length By use of several planes, the position of the principal plane can be eliminated A second Ronchi grating can be used to find the accurate image planes test target collimator lens Ronchi grating intermediate Talbot images lens under test Talbot images

11 Determination of Best Focus Criteria for best focus: 1. Paraxial centre of curvature for the paraxial spherical wave of an on axis object point. 2. Maximum of the Strehl ratio 3. Smallest rms-value of the wave aberration 4. Highest contrast of the modulation of an object feature of given spatial frequency 5. Highest value of the slope of an edge 6. Highest value of the entropy of the detected digital image Requirements for focus detection procedure 1. Steep curve dependency to get high accuracy 2. Robust definition to deliver a large dynamic range 3. Suppression of side lobe effects to guarantee an unambiguous solution 4. High frequency pre-filtering to be noise insensitive

12 Determination of Best Focus Blur of defocussed plane object plane optical system best focus plane actual plane defocus Dz D blur diameter Minimum of image entropy w j log w j E 2 j Maximum of image contrast

13 Determination of Best Focus Phase analysis by Zernike coefficient c 4 object plane optical system measuring plane sensor plane c 4 1 Dz NA 4n 2 Ronchi gratings Measurement with two Ronchi gratings defocus Dz c j c 4 0 c 9 0 z grating location

14 Determination of Best Focus Measurement by image abalysis: 1. Maximum gradient of edges 2. Power of gradients G I x y 2 (, ) dx dy I I g I( x, y) x y Laplacian L 2 I x y 2 (, ) dx dy rms ( I ) Dz [a.u.]

15 Measurement of Principal Planes Measurement for systems in air via the nodal planes Imaging of a test pattern with a collimator onto a detector Invariant lateral image location for rotated system around the nodal point Critical: vignetting effects for large angles test pattern collimator test system P P' detector tilt angle j movable along z invariant image position turning point

16 Measurement of Principal Planes Setup of the test lens with different object locations: axial shift D Analysis of the lens imaging formula a j 1 1 D a' D j 1 f Minimazing the error of several measurements j f 2 a a' Da a' a a' D j j j j j j test pattern test system P P' detector reference plane a j s j D a' j s' j

17 Measurement of Pupil Size Setup with collimating auxiliary lens pinhole illumination lens under test tan u image plane D 2 f movable for collimation auxiliary lens with f glass plate with scale u D collimated Determination with measuring microscope (dynameter) f light source collimator test system exit pupil movable dynameter lens

18 Measurement of Pupil Size Setup with Ronchi grating Measurement of the lateral shift of higher diffraction orders at distance z test system image plane x Dx D ExP q f Ronchi grating z a Dx D +1st order 0th order -1st order Fluorescence intensity pupil illumination High-NA in microscopy: NA>1 Measurement of total internal reflection of fluorescence light r max r TIR TIR NA

19 Measurement of Telecentricity Measurement of object sided telecentricity errors by lateral shift of image location during defocussing telecentricity error image plane j T exact telecentric object space Dx' 2Dz F High accuracy measurement by interferometry and measurement of Zernike coefficients c 2/3.

20 Measurement of Lens Position Measurement of reflexes at lens vertex points Analysis of confocal signal in autocollimation Avoiding spherical aberration induced errors by ring illumination laser source ring stop beam splitter lens under test vertex S j confocal pinhole -M movable for focusing on one surface vertex DI confocal difference signal channel 2 confocal pinhole +M channel 1 lens z sensor S 1 S 2 S 3 S 4 d 1

21 Autocollimation Measurement of tilt errors (plane or spherical surface) in autocollimation Projection of the cross Observation of lateral shift in Fourier plane x f 2j illumination objectiv measurement scale reticle collimator focal length f centered test object j x eyepiece beam splitter f' tilt angle j

22 Test of Prism Angles Measurement og 90 angle in air Wedge interferogram Kink of fringes gives angle error a m 2D test piece test angle 90a auxiliary glass plate in contact test range D P d distance of fringes / 2 a measuring angle 90a s deviation of the fringes 2a basis D / 2 incident collimated beam D a emerging wavefront

23 Measurement of Centering Errors by Reflected Light Projection of test marker Autocollimation of sharp image, focal point coincides with center of curvature of surface with radius r Rotation of test system: tilt of surface induces a lateral shift of the image v vm 2 r Problems with inner surfaces light source illumination zoom system test surface r rotating C tilt q detector deviation circle adjustment of the image location

24 Measurement of Centering Errors in Transmission Thin collimated beam through lens Focussing of the beam onto detector Measurement of wedge angle by lateral shift v Tilt angle of lens not detectable Not feasible for very short focal lengths j ( n 1) q ( n 1) a1 a2 v f laser light source lens under test focal length f objective rotated q wedge error inclination of the axis j detector circle of deviation

25 Measurement of Transmission Reasons for reduced system transmission: 1. Absorption in the bulk material of the components 2. Scattering in the bulk materials by inclusions or finite scattering parameters 3. Absorption in the coatings of the surfaces 4. Partial reflection or transmission at the coatings at transmissive or reflective surfaces 5. Blocking of light via mechanical or diaphragm parts of the system due to vignetting 6. Scattering of light by local surface imperfections or non-perfect polished surfaces 7. Deflection of light by diffraction of the light at edges 8. Deflection of light in unwanted higher orders of diffractive elements Usually strong dependency on: 1. field position 2. wavelength of light 3. used pupil location 4. polarization Critical: 1. absolute values for test lens 2. influence of auxiliary components 3. change of vignetting and incidence angles

26 Measurement of Transmission Measurement of transmission: a) Calibration setup b) Measurement setup P T P in out source collimator mirror collimator P in P source in P out Ulbricht sphere Ulbricht sphere system under test Reasons for measurement errors: 1. Absorption in the component materials 2. Absorption in the coatings 3. Finite reflectivity of the coatings 4. Vignetting of the aperture bundle for oblique chief rays 5. Natural vignetting according for oblique chief rays and projection of tilted planes 6. False light from surrounding light sources, which reach the image plane 7. Scattering of light at components of the system mechanical design 8. False light due to ghost images or narcissus in infrared systems

27 Measurement of Ghost Images and Veiling Glare Measurement of unwanted light: 2 different approaches: 1. object area black, surrounded by bright source detection of irradiance in image region bright illumination field system under test image plane not perfectly black black screen irradiance 2. intensive isolated point light source in the object plane at different locations detection of artificial distributions in the image area: glare spread function

28 Tactile Measurement 28 Scanning method - Sapphire sphere probes shape - slow - only some traces are measured Universal coordinate measuring machine (CMM) as basic engine Contact can damage the surface Accuracy 0.2 mm in best case Ref: H. Hage / R.Börret

29 Tactile Measurement Influence of the tast sphere: filtering of higher spatial frequencies due to finite size Gradient of skew touching geometry can be calibrated and corrected Periods of same size as the sphere: error in amplitude High frequencies: not detected A calibration according to contact slope v high accuracy gradient correction amplitude reduced period not resolved

30 30 Measurement by Fringe Projection Projection of a light sheet onto a deformed surface Corresponds to one fringe in more complicated pattern projection

31 31 Example Fringe projection Monochromatic illuminated technical surface

32 32 3D Shape Measurement for Biometry Colored biometric fringe projection Projection of a 2D triangular pattern

33 Shape Measurement by Fringe Projection Shape measurement of a surface Projection of a fringe pattern onto the surface Observation of the fringe deformation by a camera A shift corresponds to a change in depth Non-trivial image processing light source amplitude grating condenser collector surface under test sensor objective for detection

34 Fringe Projection d x u P 1 x z d P 2 test surface q1 q 2 Data evaluation Fringe period d d x cosq 1 Lateral shift projected fringes z u z cosq1 cosq 2 Corresponding depth value z f ( x) u d x z cosq cosq z sinq q 1 d cosq 1 2 d 1 cosq 2 2

35 Triangulation Projection of a narrow beam onto a surface Backscattering of light Observation un der an oblique angle: Lateral shift of image point corresponds to depth Dz Scattered light amplitude depends strongly on material properties Problems with polished surfaces Dz C 2 sinq sin u laser illumination test piece q Dz u sensor observation Dx

36 Abbe Refractometer Measurement of the refractive index of a liquid Thin film of test liquid between prisms, adjustment of total internal reflection Special setup with direct sight prisms, no color fringes direction of the telescope axis test liquid a j n measuring prism compensators Amici prism without deviation objective telescope eyepiece image

37 Ellipsometry for Polarization Measurement Measurement of material data by polarization Incident linear polarized light Reflected light elliptical polarized Compensation of ellipticity, quantitative determination of null-test parameter test piece compensator elliptical polarization j linear polarization analyzer a 2 linear polarization variabel a 1 z y receiver variabel x light source

38 Two Beam Interference Two beam interference of two waves: - propagation in the same direction - same polarization - phase difference smaller than axial length of coherence Coherent superposition of waves I I E 1 1 E I I I cos Dj Difference of phase / path difference Number of fringes location of same phase Conrast Ds D j12 2 Dj 12 Ds N 2 K I I max I 2 min max I min I 1 I 1 I I 2 2

39 Testing with Fizeau Interferometer Long common path, quite insensitive setup Autocollimating Fizeau surface quite near to test surface, short cavity length Imaging of test surface on detector Straylight stop to bloc unwanted light Curved test surface: auxiliary objective lens (aplanatic, double path) Highest accuracy collimator auxiliary lens convex surface under test beam splitter light source stop detector Fizeau surface

40 Testing with Twyman-Green Interferometer Short common path, sensible setup reference mirror Two different operation modes for reflection or transmission collimated laser beam Always factor of 2 between detected wave and component under test beam splitter objective lens stop 1. mode: lens tested in transmission auxiliary mirror for autocollimation 2. mode: surface tested in reflection auxiliary lens to generate convergent beam detector

41 41 Test by Newton Fringes Reference surface and test surface with nearly the same radii Interference in the air gap Reference flat or curved possible Corresponds to Fizeau setup with contact to detector Broad application in simple optical shop test Radii of fringes beamsplitter r m mr illumination test surface path difference reference surface here: flat Ref: W. Osten

42 42 Interferograms of Primary Aberrations Spherical aberration 1 Astigmatism 1 Coma Defocussing in

43 43 Real Measured Interferogram Problems in real world measurement: Edge effects Definition of boundary Perturbation by coherent stray light Local surface error are not well described by Zernike expansion Convolution with motion blur Ref: B. Dörband

44 44 Interferogram - Definition of Boundary Critical definition of the interferogram boundary and the Zernike normalization radius in reality

45 Interferometry Color fringes of a broadband interfergram Ref: B. Dörband

46 Shearing Interferometer Separation of wavefront: self reference Interferograms are looking completly different Aperture reduced due to shear Splitting and shift of wavefront: - by thin plate - by grating d shear distance source

47 Point Diffraction Interferometer Focussing onto a transparent plagte with pinhole Pinhole creates a reference spherical wave Optimization of contrast: - size of pinhole - numericalaperture - transparency of the plate Very stable setup transparent plate with pinhole wavefront under test reference wavefront

48 48 Temporal Coherence Radiation of a single atom: Finite time Dt, wave train of finite length, No periodic function, representation as Fourier integral with spectral amplitude A() Example rectangular spectral distribution E( t) A( ) A( ) e 2 i t sin Dt Dt d Finite time of duration: spectral broadening D, schematic drawing of spectral width Corresponding axial coherence time c 1 D Axial coherence length I() D 1 / Dt l c c c

49 49 Lateral and Axial Resolution Intensity distributions Aberration-free Airy pattern: lateral resolution D Airy NA axial resolution n R E 2 NA lateral axial Ref: U. Kubitschek

50 50 OCT Setup 1,0 Basic principle of OCT Michelson interferometer Time domain signal 0,8 0,6 0,4 filtered signal second mirror 0,2 0 primary signal t moving z signal beam wave trains with finite length relative moving z reference beam overlap I(z) first mirror from source beam splitter l c receiver

51 51 Optical Coherence Tomography Example: sample with two reflecting surfaces 1. Spatial domain 2. Complete signal 3. Filtered signal high-frequency content removed Ref: M. Kaschke

52 52 Example of OCT Imaging Example: Fundus of the human eye

53 53 Optical Coherence Tomography Dimensions of OCT imaging: a) only depth (A-scan), one-dimensional b) depth and one lateral coordinate B-scan), two-dimensional c) all three coordinates, volume imaging Ref: M. Kaschke

54 54 White Light Interferometry Examples Ref: R. Kowarschik

55 55 Knife Edge Method Moving a knife edge perpendicular through the beam cross section knife edge x movement Relationship between power transmission and intensity: Abel transform for circular symmetry beam x y P( x) 2 x I( r) r dr r 2 2 d Example: geometrical spot with spherical aberration before caustic zone rays below near paraxial focus z

56 56 MTF-Measurement by Edge Spread Function Measurement of an edge image Evaluating the derivative: Line spread function Fourier transform: optical transfer function I H LSF OTF d ( x') I ESF ( x') d x' ( s) Fˆ I ( x') LSF incoherent illumination I in (x) x edge object diffracted light x' detector plane I(x') geometrical image of the edge d I(x') dx'

57 MTF-Measurement by Imaging Gratings Setup: Imaging of a grating diffusor grating object lens under test slit sensor lamp Possible realizations: 1. Density type grating, the sine wave is modelled by gray levels 2. Area type gratings, the sine wave is modelled by geometrical sine-shaped structures Area coded sine grating:

58 58 Hartmann Shack Wavefront Sensor Lenslet array divides the wavefront into subapertures Every lenslet generates a simgle spot in the focal plane The averaged local tilt produces a transverse offset of the spot center Integration of the derivative matrix delivers the wave front W(x,y) array detector wavefront D array h f D meas u x spot offset D sub refractive index n

59 Hartmann Shack Wavefront Sensor Typical setup for component testing detector test surface lenslet array fiber illumination Lenslet array collimator beamsplitter telescope for adjustment of the diameter a) b) subaperture point spread function 2-dimensional lenslet array

60 Spot Pattern of a HS - WFS Aberrations produce a distorted spot pattern Calibration of the setup for intrinsic residual errors Problem: correspondence of the spots to the subapertures a) spherical aberration b) coma c) trefoil aberration

61 Real Measurement of a HS-WFS Problem in practice: definition of the boundary

62 Hartmann Method Separated spots in case of diffraction d d obj d d d d ( gesamt) 2 ' s ds d1 f D 2.44 d s object plane Hartmann diaphragm ideal image plane 2. camera plane d s d 2 D obj h finite site source field of view spot intensity f d 1 broadening due to diffraction geometrical projected size of pinhole D Airy /2 d' s D' Feld /2 total pinhole defocus and diffraction convolution with field of view

63 Hartmann Method a) b) c) peak b threshold minimum L d a D Real pinhole pattern with signal Problems with cross talk and threshold

64 Time is Over

65 Optics Many mysterious things and new notations Ref: T. Kaiser

66 Feedback nothing clear? to much stuff? to complicated? Ref: D. Shafer

67 67 Thank you Thank you for your attending the lecture