Presentation on theme: "Image Quality Degradation due to Lens Surface Polishing Irregularity"— Presentation transcript:
1 Image Quality Degradation due to Lens Surface Polishing Irregularity Dave StephensonMadison, CTJune 1, 2009
2 Outline Motivation Spatial frequency regimes Performance measures BackgroundProblem statementSpatial frequency regimesPerformance measuresEmpirical study: MTF degradationSummary & References
3 Applications & Benefits of Lenses with Aspheric Surfaces Consumer, medical, industrial applicationsFewer elementsReduced cost & weightImproved light transmissionImproved imaging performanceMultiple spheres combine to act aspheric
4 Polishing Techniques Aspheric lens surfaces Spherical lens surfaces Computer controlled dwell via “hit” mapPolishing pads are smaller than the surface and can cause localized slope errorsSpherical lens surfacesTraditionally the pad or lap is larger than the surface, so small-pad polishing errors don’t normally occurBut small-pad techniques are now being employed for spherical surfaces, not just aspheric
5 Full-Contact Polishing Errors (Figure) CylindricalNon-rotationally symmetric irregularityPattern may clock arbitrarilyTypically all that is toleranced“B” in ISO /A(B/C)Hole & rollRotationally symmetric irregularityHole typical in center; bump possibleEdge typically rolled down; a rolled up edge is also possible“C” in ISO /A(B/C)
6 Small-Pad Polishing Errors (Mid-Spatial Frequency) Radial spoke-like defectControl with slope or PSD specNon-rotationally symmetric irregularityPattern may clock arbitrarilyAdds to “B” in ISO /A(B/C)Concentric ring-like defectRotationally symmetric irregularityAdds to “C” in ISO /A(B/C)
7 Questions & IssuesHow do these polishing errors degrade imaging performance?What simulation tools are available to explore design sensitivity for tolerancing?
9 Spatial Frequency Regimes Mid-Spatial Frequency (MSF)Typically 0.2 – 3.0 c/mm for ø25 mmLow-to-Mid boundaryZernike polynomial limit for figure5 – 10 cycles per diameterMeasured with laser Fizeau interferometerMid-to-High boundaryThe roughness definition sets it (RMS roughness is the square root of area under PSD curve)Measured with white light Mirau interferometer or AFMJ.E. Harvey and A. Kotha, “Scattering effects from residual optical fabrication errors”, Proc. SPIE 2576, pp
10 Control MSF with a PSD spec Peak in the PSD corresponds to the ripple freqCan define a limit line & stay below it during polishingPSDlimit = 5x104 * freq-1.55 in units of A2µm shown herePeak is above the limit at 0.3 c/mm (3.3 mm period)
12 Modulation Transfer Function (MTF) Linear system frequency domain analysisReflectivity alters amplitude of complex object fieldHeight modifies phase of complex object fieldOptics low-pass filter as function of spatial frequencyComplex image field is linear superposition of filtered complex-valued components, frequency-by-frequencyImage-to-object ratio is the Optical Transfer FunctionMTF is modulus of the complex-valued OTFMTF(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 contentP. de Groot, “Instrument transfer function in interferometry”, FRINGE /12/2005.
16 Cylindrical irregularity First surface perturbed .048λ (30 nm) RMS Nearly all figure error; little MSF errorLens design software toolsAll model irregularity as a cylinderOther shapes require extra modelingLittle impact on DoF or peak MTF
17 Cylindrical irregularity Every surface perturbed .048λ (30 nm) RMS 6 of 12 perturbations shown aboveRandom clockingsDoF: reduced from 0.32 to 0.25 mmPeak: drops from 0.75 to 0.70 MTF
18 Hole & roll irregularity First surface perturbed .048λ (30 nm) RMS Nearly all figure error; little MSF errorLens design software toolsModel as Zernike terms or with aspheric perturbation termsLittle impact on DoF or peak MTF
19 Hole & roll irregularity Every surface perturbed .048λ (30 nm) RMS 6 of 12 perturbations shown aboveRandom clockingsDoF: reduced from 0.32 to 0.17 mmPeak: drops from 0.75 to 0.52 MTF
20 Spoke-like MSF irregularity First surface perturbed .048λ (30 nm) RMS Nearly all MSF error; little figure errorLens design software toolsNot practical to model with Zernike termsNo tools have a native perturbation like thisLittle impact on peak MTF or DoF
21 Spoke-like MSF irregularity Every surface perturbed .048λ (30 nm) RMS 6 of 12 perturbations shown aboveRandom clockingsDoF: reduced from 0.32 to 0.17 mmPeak: drops from 0.75 to 0.48 MTF
22 Ring-like MSF irregularity First surface perturbed .048λ (30 nm) RMS Nearly all MSF error; little figure errorLens design software toolsNot practical to model with Zernike termsCodeV has native perturbation to modelSignificant impact on peak MTF & DoF
23 Ring-like MSF irregularity Every surface perturbed .048λ (30 nm) RMS 6 of 12 perturbations shown aboveRandom clockingsBad: When on inner elements (0.45 peak)Worse: When on outer elements (0.30 peak)Worst: When on all elements (DoF zero)
25 Summary Figure errors from traditional full-contact polishing Significant mid-spatial frequency (MSF) content is unlikelyCylinder, and hole & roll, typically resultHole & roll is the worst (similar impact to spoke-like MSF)If using small pad polishing techniques, MSF is importantConsider for both spherical and aspheric surfacesSpoke-like MSF is less troublesome for the Double Gauss lensRing-like concentric MSF is the worst for the Double Gauss lensCommercial “¼ wave P-V, λ/20 RMS” may not be adequateTolerance slope or PSD using ISO to limit MSF contentTolerance analyses done with lens design software commonly only explore sensitivity to cylindrical irregularityCodeV is now able to tolerance ring-like MSF
26 ReferencesD. 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 /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 (2000).