Metrology and Sensing

Transcription

1 Metrology and Sensing Lecture 13: Metrology of aspheres and freeforms 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 Aspheres Null lens tests CGH method Freeforms Metrology of freeforms

4 y x z y x c y x c z y x R R R R z x x y y Conic section Special case spherical Cone Toroidal surface with radii R x and R y in the two section planes Generalized onic section without circular symmetry Roof surface y c x c y c x c z y y x x y x z y tan 4 Aspherical Surface Types

5 5 Conic Sections Explicite surface equation, resolved to z Parameters: curvature c = 1 / R conic parameter Influence of on the surface shape cx y 1 c x z 1 1 y Parameter Surface shape = - 1 paraboloid < - 1 hyperboloid = 0 sphere > 0 oblate ellipsoid (disc) 0 > > - 1 prolate ellipsoid (cigar ) Relations with axis lengths a,b of conic sections a b 1 c b a b 1 c 1 a c 1 1

6 Simple Asphere Parabolic Mirror Equation Radius of curvature in vertex: R s Perfect imaging on axis for object at infinity Strong coma aberration for finite field angles Applications: 1. Astronomical telescopes. Collector in illumination systems z y R s axis w = 0 field w = field w = 4

7 Simple Asphere Elliptical Mirror Equation Radius of curvature r in vertex, curvature c eccentricity Two different shapes: oblate / prolate Perfect imaging on axis for finite object and image loaction Different magnifications depending on used part of the mirror Applications: Illumination systems s z cy 1 1 (1 ) y c s' F F'

8 Asphere: Perfect Imaging on Axis Perfect stigmatic imaging on axis: Hyperoloid rear surface r s z n 1 s n 1 s r n 1 n 1 1 n z s F Strong decrease of performance for finite field size : dominant coma Alternative: ellipsoidal surface on front surface and concentric rear surface D spot m] w in

9 Aspherical Single Lens Correction on axis and field point Field correction: two aspheres spherical axis field, tangential field, sagittal 50 m 50 m 50 m a one aspherical 50 m 50 m 50 m a a double aspherical 50 m 50 m 50 m

10 Reducing the Number of Lenses with Aspheres Example photographic zoom lens Equivalent performance 9 lenses reduced to 6 lenses Overall length reduced Photographic lens f = 53 mm, F# = 6.5 a) all spherical, 9 lenses Dy axis field Dx Dy Dx 436 nm 588 nm 656 nm y p x p y p x p b) 3 aspheres, 6 lenses, shorter, better performance Dy axis field Dx Dy Dx A 1 A 3 A y p x p y p x p Ref: H. Zügge

11 Lithographic Projection: Improvement by Aspheres Considerable reduction of length and diameter by aspherical surfaces Performance equivalent a) NA = 0.8 spherical 31 lenses lenses removable b) NA = 0.8, 8 aspherical surfaces -9% -13% 9 lenses Ref: W. Ulrich

12 Aspheres - Geometry Reference: deviation from sphere Deviation Dz along axis Better conditions: normal deviation Dr s y z(y) deviation Dz y height y tangente z(y) deviation Dz along axis z height y sphere perpendicular deviation Dr s aspherical shape spherical surface z aspherical contour

13 Aspherical Expansion Order Improvement by higher orders Generation of high gradients Dy(r) order 50 D rms [m] order 8. order 1. order 10. order r order k max

14 Aspheres: Correction of Higher Order Correction at discrete sampling Large deviations between sampling points Larger oscillations for higher orders Better description: slope, defines ray bending y residual spherical transverse aberrations y perfect correcting surface Corrected points with y' = 0 corrected points residual angle deviation points with maximal angle error paraxial range y' = c dz A /dy real asphere with oscillations z A

15 Polynomial Aspherical Surface Standard rotational-symmetric description Basic form of a conic section superimposed by a Taylor expansion of z z( h) 1 h 1 1 c h M m0 a m h m4 h... Radial distance to optical axis h x... Curvature c... Conic constant a m... Apherical coefficients y 1,5 1 0,5 h^4 h^6 h^8 h^10 h^1 h^14 h^ , 0,4 0,6 0,8 1 1, h Ref: K. Uhlendorf 15

16 16 Forbes Aspheres Strong asphere Q con sag along z-axis slope orthogonal true polynom type Q 1 in Zemax cr z r r a Q r cr kmax 4 ( ) ( ) k k k direct tolerancing of coefficients Mild asphere Q bfs difference to best fit sphere sag along local surface normal not slope orthogonal not a polynomial type Q 0 in Zemax cr z(r) 1 1 cr r 1 r c 1 cr M m0 a B no direct relation of coefficients to slope m m r 0,5 1,5 1 0, , 0,4 0,6 0,8 1 1, h^4*q0 h^4*q1 h^4*q h^4*q3 h^4*q4 h^4*q , 0,4 0,6 0,8 1 1, u(1-u)b0 u(1-u)b1 u(1-u)b u(1-u)b3 u(1-u)b4 u(1-u)b5-0,5-1 h -0,5 h

17 17 Forbes Aspheres New representation of aspherical expansions according to Forbes (007) z( r) 1 c r 1 1 c r k max k Special polynomials Q k (r ): 1. Contributions are orthogonal slope. tolerancing is easily measurable 3. optimization has better performance 4. usually fewer coefficients are necessary 5. use of normalized radial coordinate makes coefficients independent on diameter a k Q k ( r ) Two different versions possible: a) strong aspheres: deviation defined along z b) mild aspheres: deviation defined perpendicular to the surface

18 Aspheres Correcting Residual Wave Aberrations Special correcting free shaped aspheres: Inversion of incoming wave front Application: final correction of lithographic systems conventional lens lens with correcting surface

19 19 Asphere Testing Creating a spherical wave for autocollimation Ref: F. Hoeller

20 0 Asphere Testing Ref: F. Hoeller

21 Test of Aspheres with Null Lenses K-system (null lens) generates aspherical replica of the wavefront for autokollimation Samll residual perturbations of the autocollimation are resolved by the interferometer Alignment of the K-lens is critical due to large spherical contributions test beam negative lens increases beam diameter positive lens generates desired spherical aberration wave front aspherical surface under test

22 Test of Aspheres with Null Lenses System configurations for compensating null lenses a) test surface convex null optical lens asphere under test here convex b) test surface convex asphere steeper outside null lens asphere under test here steeper outside c) test surface concave asphere less steep outside null lens asphere under test, here outside less steep

23 Test of Aspheres with Null Lenses c) concave test surface no intermediate focus asphere steep outside null lens asphere concave d) concave test surface with intermediate focus asphere less steep outside null lens with intermediate focus concave asphere less steep in outer range e) concave test surface with intermediate focus and field lens for diameter adaptation null lens with intermediate focus field lens asphere concave less steep outside

24 Test of Aspheres with CGH Measuring of an asphere with (cheap) spherical reference mirror Formation of the desired wavefront in front of the asphgere by computer generated hologram Measurement in transmission and reflection possible Critical alignment of CGH spherical mirror asphere CGH light source

25 5 CGH Null Test 1. CGH. Interferogram without CGH (asphere) 3. Interferogram with CGH Ref: R. Kowarschik

26 6 CGH Null Test 1. CGH in reflection. CGH in transmission Ref: R. Kowarschik

27 Test of Aspheres In interferometer gradients are measured Absolute error differences are of no meaning Residual gradinet differences are essential for the performance of a null system Example: system 1 (red) is more benefitial, because the gradients are smaller h h System System 1 System System 1 W in dw/dh in / mm

28 8 Optical Components Asphere Cylindrical lens Freeform lens Axicon Prisms

29 9 Freeform Systems: Motivation and Definition General purpose: - freeform surfaces are useful for compact systems with small size - due to high performance requirements in imaging systems and limited technological accuracy most of the applications are in illumination systems - mirror systems are developed first in astronomical systems with complicated symmetry-free geometry to avoid central obscuration Definition: - surfaces without symmetry - reduced definition: plane symmetric or double plkane symmetric surfaces are freeforms - special case: off-axis subaperture of circular symmetric aspheres - segmented surfaces included?

30 Optical System with Freeform Surfaces 30 Lens Design Design of optical systems Aberration theory Performance evaluation of optical systems Metrology of system quality Layout of laser beam delivery systems Optimization methods in optical design Tolerancing of optical systems free formed surface image total internal reflection eye pupil field angle 14 free formed surface

31 31 Spectacle Freeform Lenses Ref: W. Ulrich

32 3 Free Shaped Eye-Glasses Simultaneous correction of : 1. far, upper zone. near, lower zone Continuous transition with reduced horizonthal field of view, zone of progression Approach in 1980: 800x800 patches, cubic spline despription, optimization with 10 7 parameters Relaxed requirements on accuracy far zone no vision progression zone no vision near zone

33 33 Lithographic Lens Projection lenses in micro-lithography today uses freeform surfaces: 1. at 13.5 nm only mirrors are possible. at 193 nm the mirrors are helpful in correcting the field flatness

34 34 PSD Ranges Typical impact of spatial frequency ranges on PSF Low frequencies: loss of resolution classical Zernike range High frequencies: Loss of contrast statistical log A Four larger deviations in K- correlation approach oscillation of the polishing machine, turning ripple Large angle scattering Mif spatial frequencies: complicated, often structured fals light distributions low spatial frequency figure error mid frequency range 1/D loss of 10/D 50/D resolution special effects often regular micro roughness loss of contrast large angle scattering 1/ ideal PSF

35 35 Regular Ripple Errors Diamond turning or milling creates regular ripple in nearly any case - reason: point-like tooling and tool vs workpiece oscillations - in case of final polishing effect is strongly reduced Depending on the ratio of tool size and surface diameter this structure can not be described by figure representations a) b) c) d) original low frequency fit residual errors

36 Metrology of Freeform Surfaces 36 Tactil / profilometer Confocal microscopy Optical coherence tomography Hartmann sensor Hartmann-Shack sensor Deflectometry Fringe projection Interferometer with stitching Interferometer with CGH for Null compensation Tilted Wave Interferometer

37 Measurement Approaches for Freeforms 37 volume 1000mm³ Laser scanner tactile UA3P mm³ Interferometer 10mm³ Fringe projection Hartmann 1mm³ white light, AFM, 10µm 1µm 0,1µm 0,01µm 0,001µm accuracy Ref.: J. Heise

38 Measurement Approaches for Freeforms 38 Properties Method Benefit Disadvantage Tactile coordinate measuring maschine Special maschines ISARA, UA3P Interferometer with CGH universal universal accurate fast, accurate slow, damage, expensive tactile, slow expensive expensive, small dynamic range Fringe projection fast not accurate, poor lateral resolution Shack-Hartmann-Sensor fast small dynamic range -38- Ref.: J. Heise

39 Tactile Measurement 39 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. m in best case Ref: H. Hage / R.Börret

40 Tilted Wave Interferometer 40 Basic setup: Twyman-Green interferometer Several points sources: at least one is in autocollimation to a sample point Calibration complicated Unusual interferogramms by superposition Ref: H. Hage

41 Tilted Wave Interferometer 41 Interferometer with array of points sources (ITO / W. Osten, Mahr) At least one source points generates a subaperture nearly perpendicular Complicated data evaluation Ref: H. Hage

42 Measurement by Nulltest with CGH 4 Measurement of an freeform in transmission Shaping a spherical wavefront by computer generated hologram Preshaping the wavefront for autocollimation Method can be used in transmission or reflection Without CGH: dynamic range too small Expensive method Calibration of CGH necessary spherical reference mirror freeform under test CGH light source wavefront aspherical wavefront spherical

43 CGH Metrology - Example Fraunhofer IOF 43 9 CGH for primary mirror of the GAIA-satellite telescope 9 CGH for secondary mirror of the METi-satellite telescope Critical Parameters: size up to 30mm x 30mm positioning accuracy data preparation! homogeneity of etching depth and shape of grooves wave-front accuracy < 3nm (rms) demonstrated Ref: U. Zeitner

44 Compensating Null Systems 44 Null compensation: improved accuracy by subtracting the main effect Null optic: refractive or CGH Different schemes for null compensation Ref: B. Dörband

45 Low Accuracy Measurement: Hartmann Sensor 45 Measurement of eyeglasses with low accuracy: Hartmann sensor (hole mask) Hartmann-Shack sensor also possible Low spatial resolution Measurement in transmission preferred Illumination Hartmann sample mask under test CCD -45- Ref.: J. Heise

46 Contributions of Surface Shape 46 Decomposition of surface shape: 1. separation of circular symmetric part. separation of spherical part Ref: B. Dörband

47 Measurement by Subaperture Stitching 47 Stitching of complete surface by subapertures: dynamic range increased Overlapping subapertures: minimizing stitching errors due to movement Large computational effort Ref: B. Dörband

48 PSD measurement over manufacture flow 48 shape deviation after grinding: PV 6,µm grinding Micro roughness 40x (0,15x0,15mm) polishing shape deviation after correction and polishing: PV,5 µm Micro roughness,5x (,5x,5mm ) Ref: G. Günther 48

49 Positioning and Orientation of Freeforms 49 Fixation of a surface by spheres Optical positioning of spheres by CGH with stitching subapertures in catseye setup polished spheres surface Higher accuracy in comparison to tactile measurement Ref.: M. Brunelle, Proc SPIE (015)