■FEATURE:LENS DESIGNInduced aberrationscomplicate lens designDesign problem provides avehicle for exploration of in-duced aberrations.By David Shaferens-design programs that run onpersonal computers have recently al-lowed many people to experimentwith optical design.With all of theFIGURE 1.Design challenge is to improve the resolution of a lens design that otherwisenumerical calculations automated,onehas the same characteristics as this Cooke triplet,with all the elements contained in thecan quickly explore many ideas andbox sizedo basic research in this fascinatingfield.Although lens design has beendesigners came up with essentially the the same focal length,f3 speed,andaround for quite awhile,it is still pos-same solution.sible to propose simple design prob-15 total field?The box length turnslems for which the best answer is notout to be 47.5%of the focal length andThe problemknown.In the process of working onthe back-focus distance is 75%of theThis article describes a lens-designfocal length.such problems,one often gains newproblem that is somewhat contrivedinsight into image-aberration theoryAdditional constraints are that thebut that could arise in the real world.and learns lessons that can be appliedlenses are all BK-7 glass and no as-The Cooke triplet lens shown in Fig.1pherics,gradient index,or diffractiveto much more complicated and morehas been optimized for a speed of f3elements are used-in other words,challenging situations.and a total field of 15.Third-orderA recent example of this is myno cheating.[If these elements exist indistortion has been corrected,but col-the real world,then using them isn't'monochromatic quartet"problemor has not been corrected.It is amonochromatic design with all thesign Conference (Monterey,CA).Inlenses made of BK-7 glass or its equiv-must be corrected on the flat imagethat problem,it was necessary to findThis is an important constraint.Noalent.Such a design has a certainvignetting is allowed.the optimum four-element lens designperformance level across the field.Such a design problem could arise ifthat satisfied certain performanceand,for convenience,the rms spotspecifications,givena higher-resolution retrofit lens werecertain con-size at three field positions will beprovided that would fit in the samestraints.The size of the lens was not aused to characterize the performancepackage space and position as an ex-design constraint,and the optimumlevel.isting lens.solution found was fairly large,al-Now let us regard this lens as justthough not unreasonably so.It isfitting in a box that is slightly longerSolutionsprobably safe to say that we nowthan the triplet.There is a certainThis problem immediately weeds outknow the optimum design form thatback-focus distance from the end ofmany classical design types that seemsatisfies the problem,because manythe box to the image plane.The prob-like possibilities.The Cooke triplet inlem to be solved is this:what is theFig.1 is a rather compact lens formDAVID SHAFER runs David Shafer Opticalhighest-resolution design of any num-and has a long backfocus.Many otherDesign,56 Drake Lane,Fairfield,CTber of lenses that will just fit in thisdesign types are either too long to fit06430.same box,have the same back focus,in the box,such as the inside-out (orLASER FOCUS WORLD AUGUST 1991 103■LENS DESIGNinverse)triplet,or have too short aconstraints held,this design gives aa spot size over the field that is aboutback focus,such as the Sonnar form.spot half the size of the triplet spot15 times smaller than the Cooke tripletThe best bet seems to be to try modify-size over the field.This is good valueof Fig.1.It has a Sonnar-type fronting the triplet form,without signifi-for the additional element.As anend and a double-Gauss-type backcantly changing its first-order opticsaside,it turns out that there is a four-end.It fits in the same box,with theconfiguration.same back focus,and has almost iden-One quickly finds that splitting ei-tical first-order optics ray paths.Thether the front or rear positive lens ofmuch-higher performance is due tothe triplet does not give nearlybetter higher-order field curvatureenough improvement in performanceAlthough lens designthan the triplet and good correctionto justify the effort.The negative lenshas been around forfor oblique spherical aberration.How-in the middle is a much more produc-quite awhile,it is stillever,we are running out of room totive one to work on.By splitting it intoadd lenses.two equal weaker-power lenses,wepossible to propose veryAt this point,something quite inter-can then find bendings (the exterioresting is apparent.We can add twoshapes of lenses)for them that havesimple design problemslenses to the Fig.2 design to get aessentially the same third-order aber-for which the bestdifferent six-element system,by split-rations as the original negative lensanswer is not known.ting both of the outer positive lensesWhen optimized for rays,the resultinto two weaker positive lenses.Thislooks like a double-Gauss design with■might be expected to work well and isthin shells (more like a Topogon).a common configuration for more-Increasing the thickness of thecomplicated fast-speed camera lenses.shells leads directly to the design inlens Plasmat-type design that is just asHere,however,it does absolutelyFig.2,which is a classic double-Gaussgood as the Fig.2 design.nothing!When the box-size and backdesign.We can have a large perfor-Figure 3 shows a six-lens design,focus constraints were observed,thismance improvement if this gets muchthe next jump in complexity.No at-kind of lens splitting barely improvedlonger,but then it wouldn't fit in thetempt was made to find the best five-on the Fig.2 design performance.box.With the box-size and back-focuslens solution.This six-lens design hasTo investigate this,the lens length■LENS DESIGNFIGURE 2.Double-Gauss design is one of several four-lens designs that have smallerspot sizes than the Cooke Triplet in Fig.1.and back focus were allowed to wan-in some improvement,but less than ader.Then a design with four weakfactor of two on the spot sizes,hardlyouter positive lenses and two thickworth three aspherics.inner negative shells was found withabout the same performance as theInduced aberrationsFig.3 design,but it was more thanIt is hard to believe that this designtwice as long and had a shorter back-cannot be somehow significantly im-focus distance.This design cannot tol-proved by adding more lenses;thereerate the short lens length and longare some theoretical indications thatback focus being imposed here.Itsuch may be the case.Perhaps theseems,then,that splitting the inneroptical-design community would likeshells of the Fig.2 design is a muchto rise to the challenge.The prescrip-more worthwhile activity.tion of the Fig.4 design is given hereThe constraints have been statedFine-tuning the designearlier.Now the problem really gets interest-The reason that the Fig.4 designing.How do we add a lens or two toseems to be the end of the line,at leastthe design to make it better,but stillfor now,involves an important pointhave it fit in the box?Further splittingof aberration theory.Every opticalof the positive or negative lenses wassurface has image aberrations that cantried,and that did very little for per-be decomposed into two distinct com-formance.Figure 4 shows the bestponents:intrinsic and induced.Thedesign found so far,after a lot of workintrinsic components usually areon the problem.It has spot sizes aboutmuch larger than the induced ones60%of those of the Fig.3 design.and are caused by the first-order opti-Many attempts were made to add acal characteristics of the optical sur-lens or to split existing lenses,but tofaces and the ray paths entering andno avail.Adding more lenses madeleaving the surfaces.such a small improvement that it wasThe real ray paths are only approxi-not worth doing.Some other lens mately described by the first-order tra-configurations were tried as well.Fi-jectories,however,due to the aberra-nally,three higher-order asphericstions of all the optical surfaces preced-were added to the two outermost sur-ing the one being studied.Intrinsicfaces and one inner one.This resulted aberrations require higher-order corFIGURE 3.Six-lens solution is crowded but provides a spot size about 1/15th that ofthe Cooke Triplet in Fig.1.