Lens Design Tips Richard Juergens Adjunct Fellow in Optical Design [email protected] Opti 517 Anatomy of a Lens Edge thickness (ET) Usually fine ground Edge blackening reduces stray light Outer diameter (OD) Clear aperture (which Clear may go to the annulus) aperture (CA) Annulus or sag flat Sag Center thickness (CT) Sharp corners (≤ 90°) usually chamfered to 0.5 mm face width 2 Used Optical Beams and Footprints Beam footprint(s) Outer diameter (OD) On-axis beam Coating aperture or clear aperture (CA) Lens diameter does not necessarily define the used footprint for a given field 3 Lens Geometry: Edge Thickness • Lenses are usually oversized 1-2 mm during fabrication – Chipping may occur at the edges, prompting the oversize margin – If too little margin, scratch/dig specifications may be compromised • On steep radii surfaces, allow for more oversize margin • In CODE V, the MNE general constraint (minimum edge thickness) in AUTO only constrains the ET over the clear apertures – To constrain ET over a larger physical diameter during AUTO, use ET Sk MEC [overage_factor [overage_constant]] > target ET > 1.0 mm Oversized for fabrication Margin for manufacturing Max ray heights Margin for mounting and coating tooling Final ET sized appropriately 4 Lens Geometry: Long Radius • Long radii are hard to test – During use of test plates in production – On a radius slide or on an interferometer • If a radius approaches 20x the outer diameter, make the surface flat • To constrain this in CODEV, use a user-defined constraint in AUTO @ratio_sj == 0.5*absf((rdy sj)/(sd sj)) DSP ratio_sj @ratio_sj < 20 < 20 Radius Outer Diameter (OD) 5 Lens Geometry: Aspect Ratio • High aspect ratios risk surface irregularities due to springing after deblocking • In CODE V, the aspect ratio can be constrained during AUTO with ATC Sk [MEC [overage_factor [overage_constant]]] >=< target ATE SK [MEC [overage_factor [overage_constant]]] >=< target For example, ATC S3 MEC 1.0 1.0 > 3 < 12.5 ET 3 < < 12.5 Outer Outer diameter CT diameter (OD) (OD) = = 6 Lens Geometry: Focal Length • Lens centering machines (e.g., from Trioptics) work off beam deviations • Long focal length singlets and doublets can lead to measurement errors • Simple optimization constraint can save fabrication difficulties with centering – |EFLcomponent| < 500 mm to avoid problems – In CODE V, use the constraint in AUTO EFY Sj..k < pos_target or EFY Sj..k > neg_target – You can also use @EFLjk == absf((efy sj..k)) DSP @EFLjk @EFLjk < target Trioptics top w/ headlens V-Chuck Spins about vertical axis Trioptics bottom 7 Spherical Aberration as an Assembly Metric • A well-designed optical system balances every surface’s spherical aberration to minimize the sum of the spherical aberration content at the image plane • Lateral shear of spherical wavefronts produces coma • Coma produces the largest MTF drop to MTF compared to other aberrations • Constraining the maximum surface spherical aberration reduces the sensitivity of the surface to decenter and reduces the costs of tolerances and assembly TS Diff. Limit TS 0.0000, 3.0000 (deg) TS 0.0000, 0.0000 (deg) 1.0000 TS 0.0000, 2.1213 (deg) 1.0 0.9000 0.9 0.8000 0.8 0.7000 0.7 0.6 0.6000 0.5 0.5000 Wavefront 0.4 0.4000 0.3 0.3000 λ/15 PTV Modulus of the OTF 0.2 0.2000 λ/50 RMS 0.1 0.1000 0.0 0 160 320 480 640 800 960 1120 1280 1440 1600 Spatial Frequency in cycles per mm 0.0000 Centered Polychromatic Diffraction MTF Interferogram between reference beam and Configuration 1 V1Enoch.len V1Enoch.len 5/24/2018 5/24/2018 Y Data for 0.4861 to 0.6563 µm. 0.5461 µm at 0.0000, 0.0000 (deg). Surface: Image Peak to Valley = 0.0656 waves, Fringes/Wave = 1.0000. X Z Surface: Image V1Enoch.zmx Exit Pupil Diameter: 4.1908E+000 Millimeters V1Enoch.zmx Configuration 1 of 1 Xtilt = 0.00, Ytilt = 0.00. TS Diff. Limit TS 0.0000, 3.0000 (deg) TS 0.0000, 0.0000 (deg) 1.0000 TS 0.0000, 2.1213 (deg) 1.0 0.9000 0.9 0.8000 0.8 0.7000 0.7 0.6 0.6000 0.5 0.5000 Wavefront 0.4 0.4000 0.3 3λ PTV 0.3000 Modulus of the OTF 0.2 0.2000 λ/2 RMS 0.1 0.1000 0.0 0 160 320 480 640 800 960 1120 1280 1440 1600 Spatial Frequency in cycles per mm 0.0000 Polychromatic Diffraction MTF Interferogram between reference beam and Configuration 1 V1Enoch.len V1Enoch.len +100µm Decenter 5/24/2018 5/24/2018 Y Data for 0.4861 to 0.6563 µm. 0.5461 µm at 0.0000, 0.0000 (deg). 8 Surface: Image Peak to Valley = 3.2451 waves, Fringes/Wave = 1.0000. X Z Surface: Image V1Enoch.zmx Exit Pupil Diameter: 4.1903E+000 Millimeters V1Enoch.zmx Configuration 1 of 1 Xtilt = 0.00, Ytilt = 0.00. Surface Spherical Aberration Theory Figures from “Optical Shop Testing”, Malacara Reduce Reduce Tolerance? surface SA! Reduced surface SA reduces axial coma induced by tilted and decentered elements 9 SA Desensitization in Optical Design Optical Design iteration #1 without Surface SA constraints Optical Design iteration #2 With Surface SA constraints Minimizing the maximum surface SA "spreads the pain" among all the elements 10 Surface SA Goal Based on F/# and MTF Drop These are empirically based on measured data for many lens assemblies fabricated at Edmund Optics Target the maximum surface SA based on the allowable MTF drop and the system f/number 11 Constraining the Maximum Surface SA • To constrain the surface spherical aberration in waves for surface Sk in AUTO, use the following (for dimensions in mm) AUTO ... ^sa_target == 2 ^ref == (ref) ^sa_sk == absf((sa sk)/8/((wl w^ref)/1e6)/2) dsp ^sa_sk ^sa_sk < ^sa_target ... 12 Optical System Color Correction Regimes • Refractive optical systems have to color correct for the defocus due to glass dispersion • There are many solutions available, primary, achromatic, apochromatic, etc. • The level of correction and first order optical properties can impose heavy requirements on glass tolerances 13 Achromatic Lens Design • Correcting secondary color requires consideration of a parameter called the partial dispersion • Partial dispersion is defined for four wavelengths across the spectral band P = (nl1 - nl2) / (nl3 - nl4) • Correcting secondary color takes special glasses whose partial dispersions are different from "normal" glasses – These glasses cost significantly more than "normal" glasses – Most glasses follow a "normal" line • The technique is to find two glasses that have reasonably similar partial dispersions, but have different V values – Use these glasses with the standard achromatic equations to solve for the lens powers • If the V values are too close together, the lens powers will be strong, and the lenses will be "fat" – This will introduce significant spherochromatism (change in spherical aberration with wavelength) due to the higher angles of incidence 14 Partial Dispersion Map Normal line PSK53 10 X Cost of BK7 15 Reduction of Secondary Color PSK53 – KZFSN4 BK7 – SF2 PSK53 is10x cost of BK7 SF2 is 1x cost of BK7 KZFSN4 is 6x cost of BK7 0.0060 0.0040 0.0030 0.0040 0.0020 0.0010 0.0020 0.0000 480. 520. 560. 600. 640. 680. 0.0000 480. 520. 560. 600. 640. 680. -0.0010 FOCUS SHIFT (in) FOCUS SHIFT (in) -0.0020 -0.0020 -0.0030 -0.0040 -0.0040 WAVELENGTH (nm) WAVELENGTH (nm) 16 Apochromatic Design • Apochromatic lenses (significantly reduced secondary color) can be designed using three different glasses Tij is the slope of the line between glasses i and j All three lenses will be as weak as possible if glasses are selected with large E1, E2, E3 17 Apochromatic Design Example 0.345 0.340 0.335 S-TIL27 0.330 0.325 S-FPL51 0.320 0.315 0.310 0.305 Partial Value 0.300 0.295 S-NPH2 0 20 40 60 80 V Value 18 Apochromatic Example Performance Compare with standard N-BK7 – F2 doublet 19 Surface Axial Color • Optical design tools for material selection have become very adept at locating new solutions for color correction – Glass substitution and Hammer in Zemax – Glass Expert in Code V • Unfortunately, solutions can be found which are very sensitive to material dispersion tolerances – Commercial dispersion tolerances typically range between 0.8% and 0.5% • Surface axial color is proportional to glass tolerances 20 Sensitivity to Glass Dispersion 21 Controlling Surface Axial Color • In CODE V, use a user-defined constraint for each sensitive lens – For example, AUTO ... ^LCA_Target == 0.01 @LCA_E2 == absf((ax s3)+(ax s4)) @LCA_E2 < ^LCA_TARGET ... • Use third-order coefficients (THO output) to identify sensitive lenses 22 Sample Design • Linescan lens requirement: – Polychromatic focus, high resolution – Red, green, or blue monochromatic high resolution without refocus – Apochromatic solution too costly (elements with short EFL and sensitive to mount) • Solution: Achromat with secondary color ~1/2 diffraction-limited DoF Reducing surface axial color in half allowed the use of standard grade catalog glasses vs. requiring melt fitting 23 Passive Athermalization • Due to lenses' CTEs and dn/dTs and the housing's CTE, optical systems often go out of focus with changes in temperature – This is OK if you have a focus adjustment (man-in-the-loop) • For stand-alone systems (no man-in-the-loop), it may be necessary to design the optical system to be passively athermal • A lens can be represented by its plano-convex equivalent – F = r/(n-1) • The thermal derivative of this is dF 1 dr r dn ræ 1 dr 1 dn ö æ 1 dn ö = -2 =ç - ÷ =F ç a - ÷ dT n----- 1 dT (n 1) dT n 1è r dT n 1 dT ø è n 1 dT ø • The change in focal length is then DF = n FDT where 1 dn n = a - n- 1 dT – n is often referred to as the thermo-optic coefficient 24 n Values of Optical Materials (x106/°C) • Visible glasses N-BK7 -1.5