Metrology and Sensing

Transcription

1 Metrology and Sensing Lecture 5: Interferometry I 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 Introduction Interference Types of interferometers

4 4 Interferometry Basic idea: - separation of a wave into two beams (test and reference arm) -every beam surpasses different paths - superposition and interference of both beams - analysis of the pattern Different setups for: - the beam splitting - the superposition - the referencing Different path lengths Difference equivalent of one fringe nt nt N tw t w n Measurement of plates: Haidinger fringes of equal inclination Newton fringes of equal thickness Ref: W. Osten

5 5 Classification of Interferometers Division of amplitude: - Michelson interferometer - Mach-Zehnder interferometer - Sagnac interferometer - Nomarski interferometer - Talbot interferometer - Point diffraction interferometer Division of wavefront: - Young interferometer - Rayleigh interferometer Division of source: - Lloyds mirror - Fresnel biprism Ref: R. Kowarschik

6 6 Classification of Interferometers Two-beam interferometers: - Michelson - Twyman Green - Sagnac - Young - Mach-Zehnder - Rayleigh - Fizeau - Shearing - Mireau - Linnik Multi-beam interferometers: - Fabry-Perot - Lummer-Gehrke Ref: R. Kowarschik

7 7 Localization of Fringes Interference volume for a plate incident light front side reflected back side reflected volume of interference fringes Interference volume for a wedge front side reflected incident light back side reflected volume of interference fringes Ref: R. Kowarschik

8 8 Interference of Two Waves Superposition of two plane waves:. Intensity. Phase difference Spacing of fringes Interference of two spherical waves More complicated geometry ),, ( cos ² ² ),, ( z y x A A A A z y x I r k k z y x z y x z y x ) ( ),, ( ),, ( ),, ( Ref.: B. Dörband sin n s

9 9 Two Beam Interference Interference of two point source spherical waves with perturbations

10 0 Two Beam Interference Interference of two point source spherical waves

11 Two Beam Interference Interference of two plane waves under different directions Fringe distance s s k k n e e

12 Two Beam Interference Interference of two plane waves with finite spectral width w 0 ))),,, ( )cos( ( ) ( ) ²( ) ²( ( ),, ( 0 d z y x A A A A z y x I

13 3 Two Beam Interference Interference of two spherical waves with finite bandwidth in x/z Delay rotated cone of maximum contrast bandwidth 0 nm bandwidth 60 nm bandwidth 00 nm no delay delay 5 ms

14 4 Haidinger Fringes Fringes of equal inclination: Haidinger Every inclination creates an individual delay in the plate

15 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 E I I I cos Difference of phase / path difference Number of fringes location of same phase Conrast s s N K I I max I min max I min I I I I

16 Interference Fringes at a Plane Plate Two beam interference at a plane plate - Fresnel fringes of equal thickness - Haidinger fringes of equal inclination Path difference s nd cos d n sin detector n : source transparent plane plate d

17 7 Interference at a Plane-Parralle Plate Multiple reflection superposition Airy formulas T: tranmittance R: Reflectance I ( r) ( R) 4Rsin 4Rsin I ( i) I ( t) ( R) T 4Rsin I ( i) Plane monochr. wave n r, t Reflection, Transmission Coeff. n n r, t Reflection, Transmission Coeff. n n n h n Ref: R. Kowarschik

18 Interference at a Plane Plate Multi beam interference Intensity of pattern I T ( R) R R cos Finesse determines the contrast F / R R n d I( ) R = 0. R = 0.6 m R = 0.9 (m+) (m+)

19 More complex Setup of an Interferometer Spectral filtering Straylight suppression Diameter adaptation stop B lens L distance L stop B lens L spectral filtering D :.5 mm D : straylight suppression and 3.8 mm diameter adaptation prism group lens L4 distance L stop B3 lens L3 D : 3.8 x 9.49 mm D : 0.0 mm distance D : L3 7.7 mm disrance s beam splitter M lens L5 Linse L6 distance s CCDcamera detection test surface M reference arm

20 0 Real Interferometers Ref: R. Kowarschik

21 Interferometers Accuracy of interferometers Ref: F. Hoeller

22 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

23 Example Interferograms spherical aberration coma tilt astigmatism

24 Fizeau Interferometer Fizeau surface as part of the system work as reference Fizeau surface near to test surface: - large common path, insensitiv setup - small cavity length The test surface is imaged onto the detector collimator light source beam splitter stop detector Fizeau surface plane test surface

25 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

26 Mach-Zehnder Interferometer no common path setup, sensitive long distances, measurement of samples with small effects mirror sample beam combiner test arm detector source reference arm beam splitter mirror

27 Michelson Interferometer Test and reference arm separated: setup sensitive Both arms aligned: fringes of equal inclination Tilt in reference arm: fringes of equal thickness Setup corresponds to Twyman-Greeninterferometer reference beam reference mirror compensator plate laser source test beam beam splitter surface under test screen

28 8 Michelson Interferometer Visibility of fringes S S S S M M M M S S B M B M Ref: R. Kowarschik Haidinger Fringes Fizeau Fringes

29 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 between detected wave and component under test beam splitter objective lens stop. mode: lens tested in transmission auxiliary mirror for autocollimation. mode: surface tested in reflection auxiliary lens to generate convergent beam detector

30 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

31 Shearing Interferometer Schematic drawing of sheared wavefronts wavefront W x Typical interferogram shear distance

32 Radial Shearing Interferometer Compact setup wavefront under test beam splitter lens Modified Mach-Zehnder setup with telescope wavefront with radial shear mirror test arm beam splitter detector telescope for change of diameter source beamsplitter reference arm mirror

33 Nomarski Interferometer Separation of both arms by polarization Shear principle Used in microscopy for differential interference contrast (DIC) pahse imaging analyzer Wollaston prism adjustment phase objective shear distance x object condenser -R R splitting ratio Wollaston prism compensator polarizer

34 34 Point Diffraction Interferometer Full setup according to Smartt

35 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

36 36 Fabry-Perot Interferometer Setup of an etalon Point source Fabry-Perot Etalon n B Applications: - spectral line resolution - laser mode selection h Ref: R. Kowarschik

37 37 Fabry-Perot Interferometer Intensity Finesse Transmission Contrast Ref: R. Kowarschik ) ( ) ( sin R R R A I I i t R R F max ) ( ) ( R A I I i t p min ) ( ) ( max ) ( ) ( 4 F R R I I I I C i t i t

38 38 Fabry-Perot Interferometer Intrumental functions Properties W( ) RP F Perfectly planeparallel plate R m0 ( ), m m m d 0 Absorption R T R 4R ( R) sin ( d A d A F A Surface imperfections R, h H( ) f ( h) h H h F H Finite range of incidence R, (cos ) F( ) f ( cos( ) (cos) F (cos ) F F Ref: R. Kowarschik

39 39 Young Interferometer Division of the light from a source by two pinholes or two slits screen with slits distance D light source detector z D x x x z S P s Q y D s z P a Ref: R. Kowarschik A B

40 Double Slit Experiment of Young Young interference experiment: Ideal case: point source with distance z, ideal small pinholes with distance D Interference on a screen in the distance z, intensity Width of fringes z D x I Dx ( x ) 4 I cos 0 z x detector source D region of interference z screen with pinholes z

41 Coherence Measurement with Young Experiment Typical result of a double-slit experiment according to Young for an Excimer laser to characterize the coherence Decay of the contrast with slit distance: direct determination of the transverse coherence length L c

42 Young Experiment with broad Band Source Realization with movable triple mirror reference mirror movable triple mirror contrast 0,9 0,8 0,7 contrast curve laser 0,6 0,5 0,4 beam splitter scan x 0,3 0, 0, x I(x,y) detector interferogram x y