Metrology and Sensing

Transcription

1 Metrology and Sensing Lecture 11: Measurement of basic system properties Herbert Gross Winter term 016

2 Preliminary Schedule No Date Subject Detailed Content Introduction Introduction, optical measurements, shape measurements, errors, definition of the meter, sampling theorem 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 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 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 Basic system properties Knife edge method Slit scan method MTF measurement

4 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 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 D L d H d P P P' F F' position 1 s' s f f' D F F' position L P P'

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

7 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 f f f test target collimator lens lens under test focusing lens f new image plane reference image plane re-focusing f x f

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.. 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. 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 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 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. Power of gradients G I x y (, ) dx dy I I g I( x, y) x y 3. Laplacian L I x y (, ) 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 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 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' Dz F High accuracy measurement by interferometry and measurement of Zernike coefficients c /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 confocal pinhole +M channel 1 lens z sensor S 1 S 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 j illumination objectiv measurement scale reticle collimator focal length f centered test object j x eyepiece beam splitter f' tilt angle j

22 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 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

23 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 a 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

24 Wedge Angle of a Thin Lens Thin lens with wedeg error v ( n 1) f optical axis C 1 C v v shape axis (edge cylinder) v r1 1 r v 1

25 Tolerances: Centering Methods Axially fixed Chuck Pressing Chuck Mechanical Ray in transmission Chuck Direction of lens motion Red surface centered Deflected laser beam Incoming laser beam Green surface after lens rotation by Rays in reflection Chuck Red surface centered Green surface after lens rotation by Reflected laser beam Incoming laser beam Incoming laser beam Reflected laser beam Ref.: M. Peschka

26 Centering of a Lens with Interferogram Measurement of the centering of lens by inspection of the interferogram of front and rear surface r 1 r source point Z Z 1 D

27 Centering of a Cemented Dublet Two equivalent forms of description: 1. Three single surface tilt angles. Decenter v, overall tilt angle K, tilt of cemented inner surface c, better correspondance to manufacturing steps c C 3 optical axis 1 / 3 K v C 1 mechanical axis

28 Centering in Bonding Process Centering carrier lens Light source Cross-hair Rotating chuck Surface being centered Collimator Eyepiece Eye / detector Adjustable test optics Beam splitter Reading scale Image of Cross-hair Adjusting second lens Centering motion of lens Light source Rotating chuck Centering motion of lens Surface being centered Cross-hair Collimator Eyepiece Adjustable test optics Beam splitter Reading scale Image of Cross-hair Eye / detector Ref.: M. Peschka

29 Tolerances and Mechanical Interface Coupling optics mechanics Interface glass metal clearance Dr Mechanical design of mountings and housing Typical options: 1. Filling cylinder with fixating screw. Cementing, later centering 3. Lace / bordering Critical: - Centering tolerances - reference surfaces - analysis of complete geometry (kinematic) D s fixating screw tilt angle a axis of mounting axis of lens mounting

30 Mechanicl Mounting Geometry Filling of lenses into mounting cylinder with spacers Accumulation of centering errors by transportation of reference Definition of lens positions by: 1. mechanical play inside mounting. fixating ring screw 3. planarity of spacers fixating screw mounting cylinder spacer

31 Measurement of Transmission Reasons for reduced system transmission: 1. Absorption in the bulk material of the components. 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. wavelength of light 3. used pupil location 4. polarization Critical: 1. absolute values for test lens. influence of auxiliary components 3. change of vignetting and incidence angles

32 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. 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

33 Measurement of Ghost Images and Veiling Glare Measurement of unwanted light: 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. intensive isolated point light source in the object plane at different locations detection of artificial distributions in the image area: glare spread function

34 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

35 Definition of Striae Standard not sufficient Appearance: like wood in transmission shadow image 60 mm 50 mm

36 Measurement with Shadowgraphy Advantages: 1. Fast, cheap. Simple setup 3. Small requirements on sample surface quality shadow image Disadvantage: 1. no quantitatve calibration until now observation camera screen quasi point-like Hg light source sample rotatable desk desk

37 Rotation of Sample Change of contrast for rotation in experiment shadow image Simulation of shadow image with data of interferograms interferogram shadow image calculated out of interferogram data

38 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 linear polarization variabel a 1 z y receiver variabel x light source

39 Physical Image Quality Criteria Wavefront PV-, rms-value, fractional pupil area Rayleigh-, Marechal criteria for diffraction limit Point spread function Strehl ratio, width, second moment, area equivalent, correlation, power in the bucket a) Strehl ratio b) Standard deviation c) Light in the bucket d) Equivalent width SR / D s STDEV LIB EW e) Second moment f) Threshold width g) Correlation width h) Width enclosed area SM FWHM Ref P=50% WEA CW

40 PSF Measurement by Edge Spread Function In principle, the complete information on the optical systems performance can be recovered form measurements of 1. Point spread function. Line spread function 3. Edge spread function The ESF and the LSF covers the spatial frequencies in the pupil only in one direction. The complete information requires the measurements of ESF / LSF in several angle orientations (azimuth) Between the ESF and the LSF, a simple relationship allows a conversion d I ESF ( xi ) I LSF( xi ) dx i There are three symmetry classes, which can be distinguished: 1. Circular symmetry The Abel transform allows a non-iterative calculation of the PSF from the LSF/ESF. Mirror symmetry with decoupling of x and y The calculation can be performed in two separated 1D-sections 3. General case without symmetry A complete tomographic reconstruction is necessary

41 Knife Edge Measurement Characteristic s-shaped curve for the ernegy transmission Definition of centroid by corresponding threshold values E diameter 0.5 P centroid x 85% % % x

42 4 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) x I( r) r dr r d Example: geometrical spot with spherical aberration before caustic zone rays below near paraxial focus z

43 43 Slit-Scan-Method Method very similar to moving knife edge Integration of slit length must be inverted: - inverse Radon transform - corresponds to tomographic methods x moving slit d beam x y

44 Slit-Scan-Method Examples: Gaussian profile signaö Variation of the ratio between beam width W and slit width v: - w / v large: width of the slit can be neglected - w / v small: strongly changed profile P I( x, y) w w T x y e x w y x w y 1 x v I SSC( x) Io erf erf wx x v wx w = 0.3 w = 1.0 w =.0 w = 4.0 w = x

45 45 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'

46 46 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. Area type gratings, the sine wave is modelled by geometrical sine-shaped structures Area coded sine grating:

47 MTF Measurement Definitions: 1. Fourier transform of PSF H OTF (, ) x y I PSF x', y' e i x x' y y' dx' dy'. Autocorrelation of pupil function Overview: classification H OTF (, ) x 1. Imaging of special test structures and analyzing the corresponding image contrast behavior 1.1 If the structures are sine grating structures, a single frequency response is determined 1. If the structures have a large frequency content like points, lines, edges or bar patterns, a careful analysis of the higher frequency components and calculation the OTF from the measurement data must be performed. Direct measuring of the autocorrelation function of the optical system pupil corresponding to the Duffieux-integral formulation of the transfer function y 3. Measurement of the point spread function and digital calculation of the transfer function by performing the Fourier transform. P( x p f ' x, y p f ' y * ) P ( xp P( x, y ) p p f ' x, y dx p dy p p f ' y ) dxpdy p

48 MTF Measurement Conditions for measuring the incoherent transfer function: 1. An object is illuminated by incoherent light.. The object acquires, through its structures, all relevant spatial frequencies that have to be measured. 3. The object is imaged by the test system. 4. Spatial resolution is provided for the detection of the image intensity. As a rule this is achieved by an adjustable slit located in front of the detector. Alternatively, the slit can be fixed and scanning is accomplished by the imaged grating or object structure. 5. The contrast is derived from the intensity distribution and analysed as a function of the spatial frequency Possible test structures of the object: 1. Point object. Edge object 3. Line object or slits 4. Bar pattern 5. Random transparencies 6. Sine gratings with one or several periods 7. Special test charts like the Siemens star

49 MTF-Measurement by Edge Image Analysis mathematical relationships Direct analysis of the frequency content H MTF ( ) A'( ) A( ) Problem: zero crossing points solution: filtering, windowed calculation

50 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. Area type gratings, the sine wave is modelled by geometrical sine-shaped structures Area coded sine grating:

51 MTF-Measurement by Imaging Gratings Realization by a rotating radial grating Spatial frequency depends on azimuthal angle q slit effective grating period 1/s rotation for spatial scanning rotation for the angle of the slit / grating : spatial frequency q a slit grating g

52 MTF Measurement by Pupil Autocorrelation Basis : Duffieux integral H OTF (, ) x y P( x p f ' x, y p f ' y * ) P ( xp P( x, y ) p p f ' x, y dx p dy p p f ' y ) dxpdy p roof mirror variable phase variable shear laser source focusing lens stop lens under test roof mirror beam splitter lens diffuser sensor

53 Sources of Errors in MTF Measurements Typical shortcomings of MTF measurements: 1. Mechanical tolerances of the movable parts of the setup like line scan, rotatable edges and alignment errors. Application of precise correction factors for finite size slits 3. Truncation errors of the finite lengths structures of the object 4. Calibration of the spatial frequency variable, in particular for finite fields of view with projection changes of lengths and pattern widths 5. Poorly known residual aberrations of auxiliary optical components 6. Use of incorrect spectral and coherence constraints of the illumination 7. Shortcomings of sensor performance 8. Perturbing glare and stray light