Part 1 - Basic Interferometers for Optical Testing

Transcription

1 Part 1 - Basic Interferometers for Optical Testing Two Beam Interference Fizeau and Twyman-Green interferometers Basic techniques for testing flat and spherical surfaces Mach-Zehnder Zehnder,, Scatterplate and Smartt Interferometers Shearing Interferometers Typical Interferograms James C. Wyant Part 1 Page 1 of 43 Two-Beam Interference Fringes I = I 1 + I I 1 I 2 cos(α 1 α 2 ) α 1 α 2 is the phase difference between the two interfering beams α 1 α 2 = ( 2 π )(optical path difference) λ James C. Wyant Part 1 Page 2 of 43

2 Sinusoidal Interference Fringes I = I 1 + I I 1 I 2 cos(α 1 α 2 ) James C. Wyant Part 1 Page 3 of 43 Pioneer Fizeau Interferometer 1862 Light Source Beamsplitter Eye Test Surface Lens Reference Surface James C. Wyant Part 1 Page 4 of 43

3 Typical Interferogram Obtained using Fizeau Interferometer James C. Wyant Part 1 Page 5 of 43 Relationship between Surface Height Error and Fringe Deviation S (x,y) λ Surface height error = ( )( ) 2 S James C. Wyant Part 1 Page 6 of 43

4 Fizeau Fringes Hole Bump 1 Top View Reference Test For a given fringe the separation between the two surfaces is a constant. 1 Top View Reference Test Height error = (λ/2)( /S) S Interferogram S Interferogram James C. Wyant Part 1 Page 7 of 43 Fizeau Fringes for Concave and Convex Surfaces CONCAVE SPHERE CONVEX SPHERE Thick Part of Wedge Thin Part of Wedge Reference Flat Test Sample Reference Flat Test Sample James C. Wyant Part 1 Page 8 of 43

5 Twyman-Green Interferometer (Flat Surfaces) Reference Mirror Laser Beamsplitter Test Mirror Imaging Lens Interferogram James C. Wyant Part 1 Page 9 of 43 Twyman-Green Interferometer (Spherical Surfaces) Laser Beamsplitter Reference Mirror Diverger Lens Imaging Lens Test Mirror Interferogram Incorrect Spacing Correct Spacing James C. Wyant Part 1 Page 10 of 43

6 Typical Interferogram James C. Wyant Part 1 Page 11 of 43 Fizeau Interferometer-Laser Source (Flat Surfaces) Beam Expander Reference Surface Laser Imaging Lens Test Surface Interferogram James C. Wyant Part 1 Page 12 of 43

7 Fizeau Interferometer-Laser Source (Spherical Surfaces) Beam Expander Reference Surface Laser Imaging Lens Interferogram Diverger Lens Test Mirror James C. Wyant Part 1 Page 13 of 43 Testing High Reflectivity Surfaces Beam Expander Reference Surface Laser Imaging Lens Diverger Lens Attenuator Interferogram Test Mirror James C. Wyant Part 1 Page 14 of 43

8 Mach-Zehnder Interferometer Sample Imaging Lens Interferogram Laser Beamsplitter Testing samples in transmission James C. Wyant Part 1 Page 15 of 43 Laser Beam Wavefront Measurement Reference Arm Input Source Pinhole PZT Test Arm Detector Array James C. Wyant Part 1 Page 16 of 43

9 Scatterplate Interferometer Four Terms: Scattered-Scattered Scattered-Direct Direct-Scattered Direct-Direct Source High magnification image. of a scatterplate Interferogram Scatterplate (Near center of curvature of mirror being tested) Scatterplate has inversion symmetry Scatterplate is located at center of curvature of test mirror Direct-scattered and scattered-direct beams produce fringes Mirror Being Tested James C. Wyant Part 1 Page 17 of 43 Microscopic Image of Scatterplate James C. Wyant Part 1 Page 18 of 43

10 Scatterplate Interferometer James C. Wyant Part 1 Page 19 of 43 Scatterplate Interferograms James C. Wyant Part 1 Page 20 of 43

11 Smartt Point Diffraction Interferometer Lens under Test Reference & Aberrated Wavefronts Source PDI Interferogram James C. Wyant Part 1 Page 21 of 43 Lateral Shear Interferometry Measures wavefront slope Shear Plate Source Collimator Lens Interferogram Shear = x James C. Wyant Part 1 Page 22 of 43

12 Lateral Shear Fringes W( x,y)is wavefront being measured Bright fringe obtained when W(x + x,y) W(x, y) = mλ W( x,y) x Average over shear distance ( x) = mλ Measures average value of slope over shear distance James C. Wyant Part 1 Page 23 of 43 Collimation Measurement No wedge in shear plate Not collimated Collimated (one fringe) Vertical wedge in shear plate Not collimated Collimated James C. Wyant Part 1 Page 24 of 43

13 Typical Lateral Shear Interferograms James C. Wyant Part 1 Page 25 of 43 Lateral Shear Interferometer Source Two-frequency grating placed near focus Two sheared images of exit pupil of system under test Lens under test Two diffracted cones of rays at slightly different angles Measures slope of wavefront, not wavefront shape James C. Wyant Part 1 Page 26 of 43

14 Interferogram Obtained using Grating Lateral Shear Interferometer James C. Wyant Part 1 Page 27 of 43 Rotating Grating LSI (Variable Shear) James C. Wyant Part 1 Page 28 of 43

15 Rotating Grating LSI James C. Wyant Part 1 Page 29 of 43 Shearing Interferograms (Different Shear) James C. Wyant Part 1 Page 30 of 43

16 Radial Shear Interferometry Wavefront is interfered with expanded version of itself 2S 1 2S 2 Laser S 1 Radial Shear = R = S 1 S 2 S James C. Wyant Part 1 Page 31 of 43 Analysis of Radial Shear Interferograms Wavefront being measured W ρ,θ ( )= W 020 ρ 2 + W 040 ρ 4 + W 131 ρ 3 cosθ + W 222 ρ 2 cos 2 θ Expanded beam can be written W( Rρ,θ)= W 020 (Rρ) 2 + W 040 (Rρ) 4 + W 131 (Rρ) 3 cosθ +W 222 (Rρ) 2 cos 2 θ Hence, a bright fringe is obtained whenever W( ρ,θ) W( Rρ,θ)= W 020 ρ 2 (1 R 2 ) + W 040 ρ 4 (1 R 4 ) +W 131 ρ 3 (1 R 3 )cosθ + W 222 ρ 2 (1 R 2 )cos 2 θ Same as Twyman- Green if divide each coefficient by (1- R n ) James C. Wyant Part 1 Page 32 of 43

17 Radial Shear Interferogram Variable Sensitivity Test Large shear - results same as for Twyman-Green Small shear - Low sensitivity test James C. Wyant Part 1 Page 33 of 43 Interferograms, Spherical Aberration Paraxial Focus Mid Focus Marginal Focus No Aberration Focal Shift Small Spherical Aberration Larger Spherical Aberration James C. Wyant Part 1 Page 34 of 43

18 Interferograms Small Astigmatism, Sagittal Focus Tilt James C. Wyant Part 1 Page 35 of 43 Interferograms Small Astigmatism, Medial Focus Tilt James C. Wyant Part 1 Page 36 of 43

19 Interferograms, Large Astigmatism, Sagittal Focus, Small Tilt Tilt James C. Wyant Part 1 Page 37 of 43 Interferograms, Large Astigmatism, Medial Focus, Small Tilt Tilt James C. Wyant Part 1 Page 38 of 43

20 Interferograms Small Coma, Large Tilt Tilt James C. Wyant Part 1 Page 39 of 43 Interferograms Large Coma, Small Tilt Tilt James C. Wyant Part 1 Page 40 of 43

21 Interferograms Large Coma, Large Tilt Tilt James C. Wyant Part 1 Page 41 of 43 Interferograms Small Focal Shift Focus Coma Sagittal Astigmatism Medial Astigmatism James C. Wyant Part 1 Page 42 of 43

22 Interferograms Combined Aberrations Spherical Coma Sph + Coma Sph + Astig Sph + Coma + Astig All wavefronts have 1 λ rms departure from bestfitting reference sphere. Astig Coma + Astig James C. Wyant Part 1 Page 43 of 43