Image Quality Degradation due to Lens Surface Polishing Irregularity

1. Image Quality Degradation due to Lens Surface Polishing Irregularity Dave Stephenson Madison, CT June 1, 2009

2. Outline • Motivation • Background • Problem statement • Spatial frequency regimes • Performance measures • Empirical study: MTF degradation • Summary & References

3. Applications & Benefits ofLenses with Aspheric Surfaces • Consumer, medical, industrial applications • Fewer elements • Reduced cost & weight • Improved light transmission • Improved imaging performance • Multiple spheres combine to act aspheric

4. Polishing Techniques • Aspheric lens surfaces • Computer controlled dwell via “hit” map • Polishing pads are smaller than the surface and can cause localized slope errors • Spherical lens surfaces • Traditionally the pad or lap is larger than the surface, so small-pad polishing errors don’t normally occur • But small-pad techniques are now being employed for spherical surfaces, not just aspheric

5. Full-Contact Polishing Errors(Figure) • Cylindrical • Non-rotationally symmetric irregularity • Pattern may clock arbitrarily • Typically all that is toleranced • “B” in ISO 10110 3/A(B/C) • Hole & roll • Rotationally symmetric irregularity • Hole typical in center; bump possible • Edge typically rolled down; a rolled up edge is also possible • “C” in ISO 10110 3/A(B/C)

6. Small-Pad Polishing Errors(Mid-Spatial Frequency) • Radial spoke-like defect • Control with slope or PSD spec • Non-rotationally symmetric irregularity • Pattern may clock arbitrarily • Adds to “B” in ISO 10110 3/A(B/C) • Concentric ring-like defect • Control with slope or PSD spec • Rotationally symmetric irregularity • Adds to “C” in ISO 10110 3/A(B/C)

7. Questions & Issues • How do these polishing errors degrade imaging performance? • What simulation tools are available to explore design sensitivity for tolerancing?

8. Outline • Motivation • Spatial frequency regimes • Performance measures • Empirical study: MTF degradation • Summary & References

9. Spatial Frequency Regimes • Mid-Spatial Frequency (MSF) • Typically 0.2 – 3.0 c/mm for ø25 mm • Low-to-Mid boundary • Zernike polynomial limit for figure • 5 – 10 cycles per diameter • Measured with laser Fizeau interferometer • Mid-to-High boundary • The roughness definition sets it (RMS roughness is the square root of area under PSD curve) • Measured with white light Mirau interferometer or AFM J.E. Harvey and A. Kotha, “Scattering effects from residual optical fabrication errors”, Proc. SPIE 2576, pp. 155-174.

10. Control MSF with a PSD spec • Peak in the PSD corresponds to the ripple freq • Can define a limit line & stay below it during polishing • PSDlimit = 5x104 * freq-1.55 in units of A2µm shown here • Peak is above the limit at 0.3 c/mm (3.3 mm period)

11. Outline • Motivation • Spatial frequency regimes • Performance measure: MTF • Empirical study: MTF degradation • Summary & References

12. Modulation Transfer Function (MTF) • Linear system frequency domain analysis • Reflectivity alters amplitude of complex object field • Height modifies phase of complex object field • Optics low-pass filter as function of spatial frequency • Complex image field is linear superposition of filtered complex-valued components, frequency-by-frequency • Image-to-object ratio is the Optical Transfer Function • MTF is modulus of the complex-valued OTF MTF(f) = | OTF(f) | = | ImageField(f) / ObjectField(f) |

13. MTF Example • Image MTF decreases with increasing frequency • Even perfect optics will low-pass filter the high frequency content P. de Groot, “Instrument transfer function in interferometry”, FRINGE 2005 9/12/2005.

14. Outline • Motivation • Spatial frequency regimes • Performance measure: MTF • Empirical study: MTF degradation • Summary & References

15. Example Double Gauss Lens • 6-elements, 12 polished surfaces • Well balanced nominal MTF • Through-focus @ 0.5 Nyquist • Through-frequency @ best focus ~0.32 mm depth-of-focus (DoF) for 40% MTF at 0.5 Nyquist ~0.75 MTF at 0.5 Nyquist

16. Cylindrical irregularityFirst surface perturbed .048λ (30 nm) RMS • Nearly all figure error; little MSF error • Lens design software tools • All model irregularity as a cylinder • Other shapes require extra modeling • Little impact on DoF or peak MTF

17. Cylindrical irregularityEvery surface perturbed .048λ (30 nm) RMS • 6 of 12 perturbations shown above • Random clockings • DoF: reduced from 0.32 to 0.25 mm • Peak: drops from 0.75 to 0.70 MTF

18. Hole & roll irregularityFirst surface perturbed .048λ (30 nm) RMS • Nearly all figure error; little MSF error • Lens design software tools • Model as Zernike terms or with aspheric perturbation terms • Little impact on DoF or peak MTF

19. Hole & roll irregularityEvery surface perturbed .048λ (30 nm) RMS • 6 of 12 perturbations shown above • Random clockings • DoF: reduced from 0.32 to 0.17 mm • Peak: drops from 0.75 to 0.52 MTF

20. Spoke-like MSF irregularityFirst surface perturbed .048λ (30 nm) RMS • Nearly all MSF error; little figure error • Lens design software tools • Not practical to model with Zernike terms • No tools have a native perturbation like this • Little impact on peak MTF or DoF

21. Spoke-like MSF irregularityEvery surface perturbed .048λ (30 nm) RMS • 6 of 12 perturbations shown above • Random clockings • DoF: reduced from 0.32 to 0.17 mm • Peak: drops from 0.75 to 0.48 MTF

22. Ring-like MSF irregularityFirst surface perturbed .048λ (30 nm) RMS • Nearly all MSF error; little figure error • Lens design software tools • Not practical to model with Zernike terms • CodeV has native perturbation to model • Significant impact on peak MTF & DoF

23. Ring-like MSF irregularityEvery surface perturbed .048λ (30 nm) RMS • 6 of 12 perturbations shown above • Random clockings • Bad: When on inner elements (0.45 peak) • Worse: When on outer elements (0.30 peak) • Worst: When on all elements (DoF  zero)

24. Outline • Motivation • Spatial frequency regimes • Performance measure: MTF • Empirical study: MTF degradation • Summary & References

25. Summary • Figure errors from traditional full-contact polishing • Significant mid-spatial frequency (MSF) content is unlikely • Cylinder, and hole & roll, typically result • Hole & roll is the worst (similar impact to spoke-like MSF) • If using small pad polishing techniques, MSF is important • Consider for both spherical and aspheric surfaces • Spoke-like MSF is less troublesome for the Double Gauss lens • Ring-like concentric MSF is the worst for the Double Gauss lens • Commercial “¼ wave P-V, λ/20 RMS” may not be adequate • Tolerance slope or PSD using ISO 10110 to limit MSF content • Tolerance analyses done with lens design software commonly only explore sensitivity to cylindrical irregularity • CodeV is now able to tolerance ring-like MSF

26. References • D. Aikens, J. E. DeGroote, and R. N. Youngworth, "Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems," in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuA1. • J. Rogers, “Slope error tolerances for optical surfaces”, SPIE Technical Digest TD0404, (invited paper), SPIE Optifab Conference, Rochester NY May 2007. • P. de Groot, “Instrument transfer function in interferometry”, FRINGE 2005 9/12/2005. • R. N. Youngworth & B. D. Stone, “Simple estimates for the effects of mid-spatial frequency surface errors on image quality”, Applied Optics 39(13), pp. 2198-2209 (2000).