A general lens design method, with a photographic lens example

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A general method of optical design is described with a detailed sequence of steps and using a photographic lens example

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  • Dave, fabulus presentation!
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  • Great Dave! Thanks for sharing. I just usually put in a bunch of plane parallel plates and let Hammer work it out. Your method takes much longer :-)
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A general lens design method, with a photographic lens example

  1. 1. A General Design Method, With Photographic Lens Examples Dave Shafer David Shafer Optical Design shaferlens@sbcglobal.net 203-259-1431
  2. 2. Where do we get our ideas about how to do optical design?
  3. 3. Without a good design method our chances for success are similar to those of this hitchhiker – quite limited.
  4. 4. With my general design method producing a high performance camera lens design can be a piece of cake
  5. 5. SESSION 1. . . . . . . . . . . . . . . . . . . . . . . . WED 8:30 AM TO 10:00 AM Lens Design Methodology I Session Chair: R. Barry Johnson, Alabama A&M Univ. (USA) A zoom lens from scratch: the case for number crunching (Invited Paper), Donald C. Dilworth, Optical Systems Design, Inc. (USA) . . . . . . . . . . . . . . . [9947-1] I strongly urge you to go to Don Dilworth’s talk tomorrow morning at 8:30. He has the complete opposite approach to design from me and I am quite unhappy that it works so well.
  6. 6. This evening we will look at a detailed plan for building up a high performance camera lens design from scratch, using a general design method applicable to many diverse situations.
  7. 7. A General Design Method 1) Always do a monochromatic design first, even if starting from an existing color- corrected design. See if color-correcting surfaces can be removed with no loss in monochromatic correction. Goal is simple starting design with single glass type. Find the simplest design that meets the required monochromatic performance 2) Use aspherics during the monochromatic design evolution but remove them later 3) Find locations to add color correcting surfaces that require the least change in the monochromatic design and the least change in the monochromatic performance 4) Minimize amount of color inside the design. Use no more than 3 glass types. 5) If run into problems, always go back to an earlier monochromatic design to solve them.
  8. 8. This whole slideshow is on the internet at www.slideshare.net/operacrazy/ camera-lens-talk There is no need to take notes I will give this link again on the last slide
  9. 9. Design method is shown with a photographic lens design example • Design a 50 mm focal length f/1.7 camera lens for a digital sensor with a +/- 15.7 mm diagonal field • Length to image < 170 mm, long back focus for flip mirror • Spectral weights quite small below .4861u, about equal from . 4861u to .6563u • Distortion < 1%, vignetting 50% at edge of field • Focus down to 500 mm object to image, with no performance loss • Very high MTF performance required
  10. 10. A General Design Method 1) Always do a monochromatic design first, even if starting from an existing color- corrected design. See if color-correcting surfaces can be removed with no loss in monochromatic correction. Goal is simple starting design with single glass type. Find the simplest design that meets the required monochromatic performance 2) Use aspherics during the monochromatic design evolution but remove them later 3) Find locations to add color correcting surfaces that require the least change in the monochromatic design and the least change in the monochromatic performance 4) Minimize amount of color inside the design. Use no more than 3 glass types. 5) If run into problems, always go back to an earlier monochromatic design to solve them. First step
  11. 11. You don’t want to weigh down the design effort by attempting too many tasks at once.
  12. 12. • Estimate, by means of some experiments with a perfect system , what wavefront error will give the required MTF values on axis and at the edge of the field • Further estimate how that wavefront error might be divided into a monochromatic part and a chromatic part. • This takes some time and experience but it then gives correction goals for the beginning stages of the design. • We now look at that for our camera lens example.
  13. 13. Need very high monochromatic performance in order to be able to reach desired polychromatic MTF, and then need very good color correction for this 50 mm f/1.7 lens. Monochromatic performance - Need about .14 waves r.m.s. or better at .55u on axis and .22 waves r.m.s. or better at .55u at edge of field, with 50% vignetting Typical monochromatic MTF that is needed Required polychromatic MTF Axis spec Edge of field spec Polychromatic MTF specs Monochromatic MTF
  14. 14. Design starting point – monochromatic, no aspheres, all BK7. Double-Gauss plus negative front lens, gives long BFL On-axis = .26 waves r.m.s., Edge of 50% vignetted field = .46 waves r.m.s. Goal = .14 waves r.m.s. .22 waves r.m.s. Design needs 2X improvement in monochromatic correction
  15. 15. Low index glass designs • In the beginning stages of a design it might not be clear how important secondary color will be. • I always start out with a low index monochromatic design. If secondary color is important, then reducing it is easiest in low-index designs – shown here later. • If it is not important then you can always raise the glass index later, which will almost always improve performance.
  16. 16. Splitting front or back meniscus lens does little to help performance. Use aspheres to find out where design needs new correction means. On-axis = .24 waves r.m.s., Edge of 50% vignetted field = .42 waves r.m.s. goal = .12 waves r.m.s. = .22 waves r.m.s. . Split lens
  17. 17. A General Design Method 1) Always do a monochromatic design first, even if starting from an existing color- corrected design. See if color-correcting surfaces can be removed with no loss in monochromatic correction. Goal is simple starting design with single glass type. Find the simplest design that meets the required monochromatic performance 2) Use aspherics during the monochromatic design evolution but remove them later 3) Find locations to add color correcting surfaces that require the least change in the monochromatic design and the least change in the monochromatic performance 4) Minimize amount of color inside the design. Use no more than 3 glass types. 5) If run into problems, always go back to an earlier monochromatic design to solve them. Next step
  18. 18. Use “temporary” aspherics to 1) Ease transition between one solution region and another nearby one. 2) Identify where in the design you need to split lenses or add elements to improve performance. 3) Predict what performance will be of design once lenses have been added and the aspherics have been removed
  19. 19. 1) Add an aspheric at front of design, at back of design, and one or two in the middle of the design 2) Use only 4th and 6th order terms 3) Optimize design for better performance 4) Remove aspherics, one at a time. 5) Some can be removed with little effect, others require replacing an aspheric lens with a doublet lens
  20. 20. On-axis = .11 waves r.m.s., Edge of 50% vignetted field = .16 waves r.m.s. goal = .14 waves r.m.s. .22 waves r.m.s. Four Aspheres Design This exceeds the monochromatic MTF goals Lens added so can have an aspheric near the stop Aspherics shown in red color
  21. 21. • Usually only one of the 3 or 4 aspheres has a big effect on performance • We will try removing them one by one until we find which is the “good” one • Why not just try adding one aspheric to different places in the design, instead of adding several and then removing all but one? • Glad you asked – because what if the aspheres do not give enough performance improvement, even with 3 or 4 of them? • Then you will know immediately that you need a different first-order configuration. So this is a quick way to find out.
  22. 22. On-axis = .08 waves r.m.s., edge of 50% vignetted field = .23 waves r.m.s. Two of the four aspherics were removed without much effect, since they were found to do very little to help the correction Has acceptable monochromatic correction 2 aspherics remain
  23. 23. Strong lens with aspheric was split in two, with no aspheric Only one aspheric left On axis = .13 waves r.m.s., edge of 50% vignetted field = .25 waves r.m.s. Almost meets monochromatic wavefront, MTF goals New shape
  24. 24. Sometimes an extra lens, here used to help replace an aspheric single lens, can also help the design move into a different solution region – just as aspherics can do that Once the design is in the new solution region, the extra lens might not be needed anymore, although it was needed to make the transition . Here this lens will be gone in the final design, just as we removed aspherics that were only temporarily in the design.
  25. 25. How to replace an aspheric surface with a doublet lens 1) Add zero-thickness flat lens next to aspheric 2) Write down system 3rd -order values 3) Remove aspheric terms Remove all system variables. Remove merit function 4) Vary only flat plate radii and aspheric surface radius 5) Correct spherical aberration, coma, and Petzval to values from step 2) (A systematic method)
  26. 26. Aspheric Zero power, zero thickness lens Simplest case, where there is no other lens right next to aspheric surface Case where there is already another lens surface next to aspheric Flat plate added between lenses
  27. 27. • 2 new surfaces plus aspheric surface radius = 3 radii variables • Correct 3rd -order spherical aberration, coma, and Petzval = 3 aberrations • Petzval correction makes power of these 3 surfaces be the same as original power of aspheric surface. Can be done by other means too. • Solutions are found the easiest, due to non-linearities, if aperture stop is temporarily shifted to be at the aspheric surface, unless it is very far from the stop • With stop at aspheric, aspheric has astigmatism and Petzval linked together, • So only need to correct for spherical aberration, coma, and Petzval • Then insert the new doublet without an aspheric in the original system in place of the aspheric lens, and reoptimize with all the system variables
  28. 28. 1) When a lens is right next to an aspheric lens, we can use the radius of that lens that is closest to the aspheric as another variable, in addition to the two new radii added in of the flat plate. You just have to keep the sum of the curvatures fixed. If aspheric element is thin than can use both of its radii as variables. But best results happen if all radii variables are in direct contact. 2) Multiple solutions are best found by starting out with radii made to have right net power and be +/- doublet, -/+ doublet, or with one lens being a negative meniscus. Try all of these. New solution region Aspheric replacement No aspherics Last aspheric Is now weaker
  29. 29. Design with no aspherics meets monochromatic wavefront and MTF goals Removing last aspheric was quite difficult. Several doublets were tried before this one was found with good higher-order match to aspheric it replaced Monochromatic MTF
  30. 30. Summary Starting point = very optimized monochromatic design with no aspherics 3 or 4 aspherics added to get best performance One at a time, aspherics are removed or replaced with doublet. This can be tricky and take a lot of work. Result usually has same performance as aspheric design
  31. 31. A General Design Method 1) Always do a monochromatic design first, even if starting from an existing color- corrected design. See if color-correcting surfaces can be removed with no loss in monochromatic correction. Goal is simple starting design with single glass type. Find the simplest design that meets the required monochromatic performance 2) Use aspherics during the monochromatic design evolution but remove them later 3) Find locations to add color correcting surfaces that require the least change in the monochromatic design and the least change in the monochromatic performance 4) Minimize amount of color inside the design. Use no more than 3 glass types. 5) If run into problems, always go back to an earlier monochromatic design to solve them. Next steps
  32. 32. Color correction plan 1) Minimize the amount of color inside the design. Use low dispersion crown glass like FK51 for positive lenses. 2) Use glasses with good partial dispersion match. This requires strong curves, so have to compromise some in glass choice or design complexity. 4) Try to correct color with the smallest changes to the monochromatic design’s first-order values and lens shapes.
  33. 33. Correction of primary axial and lateral color • Achromatize with buried surfaces of glasses of about the same index, to minimize changes in the monochromatic design performance. • Minimize number of new lenses needed to achromatize the design. • Use stop shift theory to do this. • Use temporary stop shift to help in lateral color correction.
  34. 34. • If primary axial color is uncorrected (non-zero) then there is always an aperture stop position that corrects for primary lateral color (i.e. makes it zero) • If we achromatize at that stop position, the design is then corrected for both axial and lateral color • It stays that way then, regardless of stop position • In an ideal world we could then correct both axial and lateral color with a single cemented surface between two glasses, at the right position in the design. Temporary stop shift
  35. 35. 10X smaller scale Lateral color in all BK7 design Move aperture stop to find out what position corrects for lateral color, then achromatize at that location, then move stop back to original position. Original stop location Temporary stop location
  36. 36. = lateral color corrected stop position All same glass type Actual stop position More dispersive positive power to left of stop moves lateral color corrected stop position to the left. So does more dispersive negative power to right of stop.
  37. 37. 1) Achromatize at stop position that corrects for lateral color 2) May require thickening up a lens there to give enough room for a strong cemented surface Thicker lens Too thin for strong cemented surface 3) There might be a small monochromatic correction penalty
  38. 38. Another example – a more inverse front end shape. We will stay with this new other example for a few slides All same glass type – SK16 = stop position for no lateral color To achromatize at this stop location requires much too strong a cemented surface of F2 glass – not practical
  39. 39. F2 flint glass here Shifts lateral color corrected stop position to here Then achromatize here Stronger flint here All SK16 except Shifts achromatizing position further to left Then achromatize here +/- doublet -/+ doublet
  40. 40. In this design we could have corrected both axial and lateral color by making cemented lenses here and here. But that would require much stronger lens powers. My method gives weaker powers and has a systematic rational to it.
  41. 41. Chromatic variation in aberrations is mostly induced by color coming into certain surfaces, and is not mainly an intrinsic aberration. All lenses are FK51 glass Largest amount of spherical aberration in design Proof – 1) set index of that lens to be same for all wavelengths. Result is almost no change in chromatic variation of spherical aberration. It is not intrinsic to that surface 2)) set index of lenses before that surface to be same for all wavelengths, so no color coming into that surface. Result = almost zero chromatic variation in spherical aberration 3) This shows why we want to minimize the amount of color inside the design
  42. 42. • Now we are returning to our original design example and trying some glass choices for color correction. • First we see what happens if we don’t try to correct secondary color. How bad is the polychromatic MTF?
  43. 43. Design is not good enough – too much secondary color. Need different glasses. But keep the very good monochromatic correction All BK7 except F5 BK7 and F5 design, no aspherics Extra lenses for color correction have allowed this to revert to a single lens
  44. 44. 1) Minimize the amount of color inside the design. Use very low dispersion glass like FK51 for positive lenses. 2) Use glasses with good partial dispersion match. Demonstration of the color correction design principles Ultra low dispersion glass Relative partial dispersion
  45. 45. Herzberger secondary color correction method Connect 3 glasses to give a triangle with largest possible area, to minimize lens powers Extreme example = FK51, SF57, and KZFS1 - all three are anomalous dispersion glasses Relative partial dispersion
  46. 46. Three anomalous glasses gives very small residual color. Very dense flint in front has very little power. Herzberger method gives good results but requires 3 glasses. If you avoid extreme crowns and flints then result is very high lens powers. SF57-FK51-KZFS1 100 mm focal length
  47. 47. Herzberger secondary color correction method Connect 3 glasses to give a triangle with largest possible area, to minimize lens powers As base of triangle becomes more horizontal , the power of the 3rd glass gets weaker and weaker. That 3rd glass, at top right, disappears when triangle base is horizontal.
  48. 48. Want two glasses to be on horizontal line for super-achromat. FK51 and BK7 are a good pair. Glass pairs on “normal” glass line give BK7 and F2 fall on “normal’ glass line
  49. 49. Glass pairs with the same partial dispersion have relatively small dispersion difference, so strong lens powers are needed for a given focal length, or multiple doublets stacked up in a row. BK7-F2 achromat FK51-BK7 superachromat 10X smaller scale than other graph on left Quadratic color Cubic color Crown/flint glass pair Crown/crown glass pair
  50. 50. • When partial dispersions match, want largest possible dispersion difference to reduce required lens powers for achromatism. FK51 and the BK glasses are therefore the optimum glass pair by this criterion. • SSKN8 and KZFSN4, for example, have good match for partial dispersion but very small dispersion difference - so requires very strong lens curves in a doublet. • There are significant differences within the BK glasses, when matched to FK51. BK1 is better than BK7 for residual secondary color.
  51. 51. Calcium Fluoride and Silica FK51 and BK1 Has small reverse secondary color Very flat over most of spectrum
  52. 52. High index of LAK8 makes for weaker curves, better aberrations and chromatic variation of aberrations, but it also increases the Petzval of the doublet. FK51- LAK8 doublet
  53. 53. • Result of all this is good secondary color correction with just two glasses • These two glasses, FK51 and a BK glass have very high transmission in the blue region • The resulting design is a very low index design. • If the blue wavelengths are not too important than can use a more dispersive flint than BK glasses. Result is reduced (but not corrected) secondary color and weaker lens curves.
  54. 54. A glass pair of FK51 and a BK glass like BK7 requires only one anomalous dispersion glass type – FK51, which is quite expensive. A different choice, with two anomalous glass types, both expensive, is FK51 and KZFS2. Their partial dispersions are not quite on a horizontal line and their dispersion difference is considerably larger than that of FK51 and BK7. That gives much weaker powers of the lenses for color correction. Not quite horizontal line
  55. 55. FK51 and BK7 FK51 and KZFS2 Weaker powers = better aberrations But very expensive and more residual color 2.5X larger scale Different scales
  56. 56. • All of these results are for thin lenses in contact. In a real design with substantial lens separations, like a Double-Gauss or Distagon, the optimum glass pairs may shift some on the glass chart. • But this is a relatively small effect. Try some glasses near the thin-lens optimum choice to see what gives the best result. • The importance of all this depends on the spectral weighting. If deep blue wavelengths are important then secondary color can be very important.
  57. 57. In this design example we will only use one anomalous dispersion glass, FK51, in order to keep the lens cost down. An interesting exercise would be to use KZFSN2 instead of BK7, giving greater cost and not as good secondary color, but weaker powers and see how the performance is affected. Chromatic variations of aberrations would be less due to the weaker powers.
  58. 58. Paraxial focus shift from .4000u to .7000u For a 100 mm focal length lens Glasses focus shift strongest lens BK7, F2 +/- 100u 45 mm focal length FK51, BK7 +/- 7.5u 23.5 mm focal length FK51, KZFSN2 +/- 15u 35.7 mm focal length FK51, F2, KZFSN4 +/- 5u 32.4 mm focal length FK51, SF6, KZFSN4 +/- 2u 35.9 mm focal length FK51, LAK8, SF6 +/-1u 31.1 mm focal length FK51, LAK8, KZFSN4, SF6 +/- 0.3u 27.0 mm focal length FK51, BAFN11, SF1, SF6 +/.03u 16.4 mm focal length these are not the absolute optimum combinations but are close to it This goes outside the scope of this talk, where our design will only use one anomalous dispersion glass, but if several different anomalous glasses are used then amazing broad spectral band color correction is possible. 3000 X better
  59. 59. Color Correction Summary • Goal is to correct color with smallest change to the good monochromatic correction • Temporary stop shift shows where to add color correcting surfaces • Glass choice can minimize color inside the design, giving good chromatic variation in aberrations and low secondary color • Result has few flint lenses and very few glass types
  60. 60. Almost meets polychromatic MTF spec, but is slightly low All FK51 except LF5 50 mm f/1.7, no aspheres, just two glass types
  61. 61. Doesn’t quite meet the on-axis MTF goal. Very constant over the whole field 50 mm, f/1.7 design with no aspherics and just two glasses All FK51 except LLF6 Extra lens added A low index design – highest index is n = 1.53!
  62. 62. 50 mm, f/1.7 design with no aspheric and just two glasses All FK51 except LLF6 As the flint glass choice is changed from F5 to LF5 to LLF6 the secondary color keeps getting better. The line connecting FK51 to the flint glass gets more horizontal as partial dispersions become more equal. But the powers become stronger as the dispersion difference gets smaller. FK51 and F5 pair and FK51 and LLF6 pair
  63. 63. Once get a good design, look for other versions with same number of lenses Very slightly short of MTF specs Meets MTF specs -/+ +/- +/- -/+
  64. 64. This alternate solution has a stronger negative lens, so making it a flint glass shifts the lateral color corrected stop position further to the left = a good thing This doublet replacement for the last aspheric lens has very little negative power, so making that lens a flint glass has little effect on lateral color Try to correct axial and lateral color with the smallest change to a good monochromatic design, and adding the least number of new lenses
  65. 65. This is very unusual – we now have a very high performance camera lens design with only two glass types and with n<1.53!
  66. 66. That is as rare as catching Volkswagons going at it, which they usually only do at night.
  67. 67. • If blue spectrum is more important than in this example, then secondary color must be better corrected • Then flint glasses must be better partial dispersion match to FK51 crowns, such as BK glasses • This requires more lenses to keep the negative lens powers from being too strong. • Or can use both FK51 and KZFS2 to get good color correction but at increased glass expense
  68. 68. Now we have a good design. What’s next? There are only two glass types, both very low index. Now we can consider looking at some higher index glasses, maybe de- cementing one or both of the doublets to get more design variables, optimizing for tolerances, etc. My design method gives a good design that can then be fed into optimizers like a glass expert program to get even better performance. The good design here can be the end of the road or the start of a new path to an even better one.
  69. 69. Moves as a pair Focusing from infinity down to 500 mm object to image distance. stop stop Correction should not change, throughout focusing range - very hard to do I could not find a good solution with this design. What to do next? Back end of design Focusing Requirement
  70. 70. And you thought that you were all done! Best plan is to go back to monochromatic design and temporary aspherics and build in good focusing correction at an early stage of the design evolution. Be willing to start over ! Difficult tasks should not be left to the end of the design process, but should be solved much earlier.
  71. 71. When an almost mature design gets stuck on a difficult requirement it is almost always best to try to solve that problem at an early stage of the design evolution. In other words, start over again!
  72. 72. A General Design Method 1) Always do a monochromatic design first, even if starting from an existing color- corrected design. See if color-correcting surfaces can be removed with no loss in monochromatic correction. Goal is simple starting design with single glass type. Find the simplest design that meets the required monochromatic performance 2) Use aspherics during the monochromatic design evolution but remove them later 3) Find locations to add color correcting surfaces that require the least change in the monochromatic design and the least change in the monochromatic performance 4) Minimize amount of color inside the design. Use no more than 3 glass types. 5) If run into problems, always go back to an earlier monochromatic design to solve them. Be willing to start over!
  73. 73. A General Design Method - Review 1) Always do a monochromatic design first, even if starting from an existing color- corrected design. See if color-correcting surfaces can be removed with no loss in monochromatic correction. Goal is simple starting design with single glass type. 1) Find the simplest design that meets the required monochromatic performance 2) Use aspherics during the monochromatic design evolution but remove them later 3) Find locations to add color correcting surfaces that require the least change in the monochromatic design and the least change in the monochromatic performance 4) Minimize amount of color inside the design. Use no more than 3 glass types. 5) If run into problems, always go back to an earlier monochromatic design to solve them
  74. 74. In addition to being intellectually stimulating this design method is also more fun than sitting around waiting for some global optimizer to slowly grind away at the design task.
  75. 75. This camera lens would be great for nude photography
  76. 76. My time is finished - any questions? This whole slideshow is on the internet at www.slideshare.net/operacrazy/camera-lens-talk

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