Zemax光學與光學設計課件

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1、(C)R G Bingham 2005.All rights reserved.光學與光學設計Richard G.Bingham Session 1IntroductionCoordinatesRays that may appear oddImage rotation and parity and an image slicerSpherical Trigonometry advanced option(C)R G Bingham 2005.All rights reserved.The beginningSix pages of introductory notes(C)R G Bingh

2、am 2005.All rights reserved.AimsRay-tracing software is amazingly accurate and comprehensive,but practising with the buttons on the toolbar is not enough.Our aims are:to understand optical systems;to understand what the program is doing;to gain a feeling for what problems are tractable and what opti

3、cal capabilities are provided by existing designs;to assess the performance of optical designs constructively;to see how complex optics may be comprised of sub-systems exploiting local aberration correction or special cases;to express our ideas with the program;to handle the tools that are available

4、 for designing new systems;to see what factors may stop optical aberrations from being made smaller;to be aware of cost and weight;to avoid redundant complexity in a design or its manufacturing specification;and to be practical and economic as regards the optics that we design and the use of our tim

5、e.We hope to achieve all this by properly understanding the designers methods,so that we can learn and keep up to date in our own new designs or others that we may evaluate.(C)R G Bingham 2005.All rights reserved.Format of this textThis material,although created in PowerPoint,was not intended for,an

6、d is not suitable for,projection as slides.PowerPoint was used to encapsulated successive ideas and topics in a format that ultimately will be neatly separate screens.A slide is referred to here as a“page”.The material is arranged separate“sessions”of about 25 pages each.A few sessions may include o

7、ne or two.doc files as well.As mentioned above,the material could be viewed as successive screens by an individual user,but initially,it will be printed(quite large),again to be read individually.The suggested procedure is to first to read a session individually and to follow that by discussing it w

8、ith others in a group,or if possible,to arrange some kind of tutorial following the individual reading.(C)R G Bingham 2005.All rights reserved.How to handle thisI think that it is impossible fully to practise each topic before moving on.Perhaps material can be skimmed over if it does not seem helpfu

9、l.Or perhaps the concepts and terminology from complex areas may be acquired in an effortless osmosis,later.Most equations are given here without derivations;the aims of this particular course are such that we need to press on to the work of the designer.The fundamentals,however,may be useful for a

10、physicist or engineer to understand.They are written up by Welford in“Aberrations of Optical Systems”,Hilger 1986.It may be worth considering whether to work systematically through the whole book,as indeed I did with the previous edition,for a comprehensive foundation.I refer to the book as Welford

11、throughout.Examples are given in Zemax.If both the.zmx and the.ses files are in the same folder,graphics windows should open when the Lens Data Editor opens.Also explore any of the other Zemax features,their local help files and the main manual(.pdf).Within the ZEMAX examples,there is a window calle

12、d Title/Notes that appears on a tab after the Gen button is pressed.As you view one of the examples,it is vital to read those notes that are within the Zemax data,as I have often put critical information there.I recommend that you do not personalise the default toolbar buttons in your own copy of Ze

13、max.If you do,you may find that a different computer is slower to use,and it will become markedly more difficult to demonstrate things to other users.(C)R G Bingham 2005.All rights reserved.How can I get to practise on some real designs?If you are already working with any optics,a way to practice on

14、 real optics without spending money is to create a ray-tracing model of your experiment as soon as there is even a minor modification to explore.So for example,if some existing instrument needs merely to be differently focused or to have a thicker colour filter,or some as-made data becomes available

15、,use that as a reason to set up a ZEMAX lens data file,however simple,and then use your ZEMAX file to check the modification.Once you have a few ZEMAX models,you will also be better placed to solve any further problems arising with your experiment,and will be able to create realistic graphics for pu

16、blication.However,I would say that whilst setting up and using ZEMAX yourself for even simple purposes is very instructive,collecting complex data files from other people would be a waste of time.(C)R G Bingham 2005.All rights reserved.ZEMAX ZEMAX was created by Ken Moore from 1990 to date.It is for

17、 PCs only.We shall use Zemax in this course.The hard key allows only one person to access it at once.It is worth the whole value of the software.You can open Zemax twice on the same machine(except with Remote Desktop).The second instance of Zemax is useful for running long computations whilst gettin

18、g on with something else,or for cutting and pasting between systems.You need individual,unrestricted,continuous access to the program,along with technical support and updates,to do much productive work in optical design,if that is your task.Sharing a system is frustrating and hinders the design of r

19、eal lenses.(C)R G Bingham 2005.All rights reserved.Example setting up a ball lensThe example is a glass ball,as available from Melles Griot.It is used as a lens(e.g.for fibre-optics work).It can be set up by following the details in Ball_lens_data.doc.This is the main example with such instructions

20、for creating it from absolute scratch,which will provide a useful exercise if you have not previously set up lenses in ZEMAX.In any case,please find the further notes that I wrote within that.zmx file.They can be found on the General/Title/Notes tab(on the Gen button).Such further notes are held wit

21、hin all my ZEMAX examples in these lectures,so it will be useful to be able to find them.To check your results,the intended data is in file:Ex00-Ball_Lens.zmx.If the Ex00-Ball_Lens.SES file is also present,it will bring up relevant graphics as below.(C)R G Bingham 2005.All rights reserved.Coordinate

22、 systems13 pages(C)R G Bingham 2005.All rights reserved.+z In Zemax,light must leave the object surface in the+z direction.The thickness of the object surface must be positive.x,y,z+y+z+x inwardsRight-handed axesPositive sag zPositive radius of curvatureSurface of a lens+yNegative sag,negative radiu

23、s of curvature(C)R G Bingham 2005.All rights reserved.Lens.Sequential ray tracing1.The thickness or axial thickness is measured positive in the+z direction2.The curvature of the front surface is positive hereExample file:Ex01-Lens.ZMX+z+y5.This is an optical system4.Lens drawings in most diagrams ar

24、e cross-sections that are not shaded3.The front of a lens is the face that the light hits first(C)R G Bingham 2005.All rights reserved.Local coordinates.A surface S1 has an origin(O1 here)that serves to locate this surface within the optical system.The figure of surface S1 is defined by its sag z(x,

25、y)that is thus measured orthogonal to the x,y plane.Each surface also has a following thickness.For sequential ray tracing,the origin O2 of the next optical surface S2 is positioned by this thickness of S1 along the z axis.Each surface can be positioned in this way with reference to the previous sur

26、face.Defining surfaces for ray tracing+y+z+x is inwardsz(x,y)Some weird lensO1O2S1S2thickness(C)R G Bingham 2005.All rights reserved.Thickness after a mirrorThe thickness of glass or an air space entered into ZEMAXs Lens Data Editor changes sign at a mirror.(C)R G Bingham 2005.All rights reserved.Se

27、quential ray tracing-a Mangin mirrorThis one piece of glass has to appear in the data twice for sequential ray tracing.It has positive thickness before the mirror but negative thickness after the mirror;in the second pass,the thickness is measured in the minus z direction from the preceding surface,

28、the mirror.+y+zExample file:Ex02-Mangin.ZMX1234The three rays in this 2D layout are drawn optionally from a flat surface numbered 1 that is in the data file.This surface 1 is a dummy surface here.A dummy surface is one that has the same refractive index on both sides.The signs of these curvatures ar

29、e all negativeGlassA back-surface MirrorThe three rays started from an object at infinity at surface number 0.5(C)R G Bingham 2005.All rights reserved.The manufacturing specification is differentrzzGlass removal might correspond to positive z in the ray-tracing data but negative z on a machine.Lens

30、on machineLens in the ray-tracing dataWrongly made convex because a positive sign was quoted?A curvature with a positive sign is not necessarily convex in Zemax!There is a necessary intermediate stage where we supply an engineering drawing or at least a sketch.Zemax will output a good starting point

31、 for a proper drawing.LensAspheric lens(C)R G Bingham 2005.All rights reserved.Local Tilts and DecentresThe program provides for surfaces that are tilted or moved(decentred).The local frame of reference can be tilted or moved,leaving the function z(x,y)unchanged.+z+x is inwardsO2+yFor example,the we

32、ird lens can have a right-hand surface that is tilted around its local x axis.The tilt shown is positive around the local+x axis.Combinations of two or three tilts can be used.The origin O2 can also be locally shifted in x and y,but not z we have already chosen a z position,based on the previous sur

33、face.(C)R G Bingham 2005.All rights reserved.Rotations that are consistent with the above:1.In the x,y Argand diagram a positive angle is drawn anticlockwise,but it is clockwise looking along a+z axis emerging from the paper.A sign like that of the Argand diagram is also used for the angle of a ray

34、in some optical diagrams,and for position angle on the sky,e.g.for the plane of sky polarisation measured anticlockwise(from north).2.International standards for machine tools such as milling machines also use this sign.x,y,z rotations signs+y+zWe rotate the axes in which subsequent surfaces are the

35、n defined,so the subsequent surfaces move with the rotation.A positive rotation in ZEMAX is clockwise as viewed in a positive axis direction.A positive rotation around the x axis.The relevant matrix expression is in the ZEMAX manual.(C)R G Bingham 2005.All rights reserved.x,y,z rotations that are di

36、fferent1.OPTICA(Mathematica)is the opposite.It applies a positive rotation looking towards the origin,that is,in the negative axis direction.The difference arises from rotating an object the other way in global axes.The global axes in ZEMAX can also be unaffected,and often one need not be aware of t

37、hem anyway.Check how they are defined.In ZEMAX,with a coordinate break,fresh local axes are obtained for following parts of the system.2.In the Code V optical design code(current),a rotation around either the local x or the local y axis is negative as compared to the right-hand convention used in ZE

38、MAX,whilst rotation around z is not affected.3.In the GRT optical design code(obsolescent university FORTRAN),the x rotation is reversed as in Code V.However,the y rotation is not reversed.The z rotation appeared to be reversed when I rotated the lines on a diffraction grating.4.Other codes may be d

39、ifferent again.5.Doubts can be resolved by inspecting 3D graphics that the program will draw!(C)R G Bingham 2005.All rights reserved.Sequential ray tracing a prismThe Lens Data Editor contains a sequence of optical surfaces.The path of any ray is calculated to intercept the next optical surface,in t

40、he order in which they are listed in the Lens Data Editor.See next slide for an example in ZEMAX.(C)R G Bingham 2005.All rights reserved.-35+40Coordinate breaks-a prism1.The prism angles are defined by coordinate breaks.A coordinate break is placed at a dummy optical surface,taking up one line of da

41、ta in the Lens Data Editor.That line has boxes for x&y shifts and for x,y&z tilts in degrees.Other boxes on the same line hold the thickness to the next surface and a flag for reversing the order of the tilts.Axes-252.The coordinate breaks are:2 the tilt of the front surface;4 the tilt of the z axis

42、 leading to the required centre of the exit surface;5 the tilt of the exit surface;and 7 the tilt of the z axis leading to the required centre of the image surface.+60Example file:Ex03-Seq_Prism.ZMX3.The rays refract passively according to Snells law.The rays do not affect the tilts of the axes in t

43、hese data.RaysThickness 42457(C)R G Bingham 2005.All rights reserved.Coordinate breaks again1.If we place a coordinate break immediately before an optical surface,it is sometimes useful to put in another one with the opposite sign immediately after that surface,undoing the tilt etc.Then we can conti

44、nue with the previous axis direction.2.Reversing multiple tilt angles needs be done in the reverse sequence.Read the manual!(C)R G Bingham 2005.All rights reserved.Tilts and shifts again1.SEQUENTIAL RAY TRACING uses local coordinates:Coordinate breaks are inserted in the Lens Data Editor ahead of op

45、tical surfaces that need moving.The values of the angles and shifts can be varied in optimisation.Again for sequential ray tracing,individual optical surfaces can be given an intrinsic tilt or shift on a Surface Properties tab.The effect is the same as with with coordinate breaks but the data are no

46、t currently optimisable.2.For NON-SEQUENTIAL RAY TRACING,a whole object can have its own tilt and position set up in a line of data for that object within the Non-Sequential Components Editor.This is essentially a global reference system,although alternatively,one component can be referred to anothe

47、r.(C)R G Bingham 2005.All rights reserved.Rays that may appear oddTwo pages about geometrical rays in a ray-tracing program(C)R G Bingham 2005.All rights reserved.A geometrical ray is a line to the next surface,but AEFADBAA is a normal ray pathIn sequential ray tracing,ray B is a valid extrapolation

48、 to a virtual image in a negative space.It has to end the ray trace or to be reversed.But in a sequential ray trace,rays can fail or“crash”:Ray C misses a defined surface apertureRay D,if reflected by TIR,terminates unless the surface is defined as a mirrorRay E misses the sphere altogetherRay F may

49、 intersect the sphere at the wrong point.CLens(C)R G Bingham 2005.All rights reserved.Non-sequential ray tracing a prismExample:Ex04-NSC_Prism.ZMXThis Rectangular Volume object is defined on a single line of the Non-Sequential Components Editor.The faces of this object would form a cuboid by default

50、,but they can be angled as they are here,and the whole thing is tilted 30 around x.Rays shown here intercept 0,2 or 3 surfaces.There are many types of NSC objects.They can be positioned with respect to a single origin,or individually with respect to other defined objects.NSC rays can split,scatter,e

51、tc.,but dont crash.Two sorts of rays appear that go through this prism but are not dispersed in angle.(C)R G Bingham 2005.All rights reserved.Image Rotation and Parity and an image slicerTen Pages(C)R G Bingham 2005.All rights reserved.Inverting the image means rotating it 180 degrees around the axi

52、s.Notice that ZEMAX views the image in the+z direction.If there is an intermediate real image,the final image is erect.The same applies to mirrors as to lenses.Thus a Cassegrain telescope gives an inverted image but a Gregorian telescope,which has one intermediate image,gives an erect final image.In

53、verted real image in an axially symmetrical system FFz(C)R G Bingham 2005.All rights reserved.Image ParityReversal of parity is a three-dimensional effect.If the total number of mirrors is odd,the image parity is reversed.With an odd number of mirrors in an axially symmetrical system,the three-dimen

54、sional image must be reversed in depth,because neither lateral direction is special.Thus in a 3-mirror camera,if the object moves one way,the image moves in the opposite direction to the object,just as in a single plane mirror.Using these ideas,in a Cassegrain telescope,which way does the focus move

55、 between infinity and a laser guide star?(C)R G Bingham 2005.All rights reserved.Image rotatorsField of viewWe have a few objects around a field of view that is fixed in space.Image 1The image rotator flips their images across a diameter A.That is what it does.AImage 2Then if the flipping diameter r

56、otates by an angle to line B,the field of view rotates by 2 as compared with Image 1.AB(C)R G Bingham 2005.All rights reserved.Three-mirror image rotator(K-mirror)+Directions of the z axis and the signs of the thicknesses.The unusual,reversed final thickness affects the sign of the final z rotation

57、in the data file.Ex08-Rotator.ZMXAnimate with Tools,Slider(C)R G Bingham 2005.All rights reserved.Two other devices with flat mirrorsThree pages(C)R G Bingham 2005.All rights reserved.Dihedral mirrorsEx06-Dihedral.ZMXThe direction of the emergent rays is unchanged when tilting a pair of plane mirror

58、s together.Furthermore,if the tilt is around the line of intersection of the mirrors,the directions,positions and total path lengths of the emergent rays are all unchanged.So for example,mounting a pair of flat mirrors on the same base can provide stability.The example uses both coordinate breaks an

59、d a tilt on a Surface Properties tab.(C)R G Bingham 2005.All rights reserved.Image slicer/assemblerSide viewView into emerging beamEnlarged View into beamThe slit formedThis modified Walraven-type image slicer cuts a patch of light into 5 slices to fit the slit of a spectrometer.Ex07-5-Slicer.ZMXTwo

60、 mirrors simulating TIR(C)R G Bingham 2005.All rights reserved.Two image slicers assembled in one unit,comprising four pieces of glass.Image slicers(illustration)Silica base plate 55 mm diameterThe bHROS 5-slicers.(C)R G Bingham 2005.All rights reserved.Spherical Trigonometry-Advanced optionNote.I j

61、oined a project that had been running six months,only to find that no one had been using the correct 3D geometry in ZEMAX.As a result,nothing was quite right and no correct 3D layouts could be drawn.Spherical Trigonometry may seem a forbidding subject area to step into,but personally,I dont expect t

62、o solve these problems in an hour or a morning.Even if it takes a few days to puzzle out the Spherical Trigonometry,it may be well worth the effort.Ten pages.(C)R G Bingham 2005.All rights reserved.Great and small circles and spherical trianglesSeveral great circlesOne small circleSpherical Triangle

63、s.Their angles add to more than 180 degrees.The sides of the triangles are great circles.They are also angles.Notice the spherical triangles in which at least one of the angles is a right angle.These triangles are often needed and can be solved by Napiers rules.(C)R G Bingham 2005.All rights reserve

64、d.Sketching for calculations in 3DNorth PoleSouth PoleStereographic projection onto the equatorial plane from the South Pole.PP as projectedMapping a sphere onto a planeSide view through a sphere,showing a plane and its pole P North Pole90-9090-(C)R G Bingham 2005.All rights reserved.Good News about

65、 the Stereographic Projection1.We never need to calculate the actual projection.It serves as a way of sketching diagrams of 3D objects.2.Angles measured locally on the surface of the sphere are the same angle in the projection.3.A circle drawn on the sphere appears as a circle in the projection.(C)R

66、 G Bingham 2005.All rights reserved.Napiers rules for a right-angled triangle(C=90)(C)90-c90-B90-A baC=90 bAc B aArrange the symbols in five“parts”as shown on the right.Thensin(middle part)=prod tan adjacent parts =prod cos opposite partse.g.sin(90-c)=cos a cos b =tan(90-A)tan(90-B)This is the one that we shall use for the example(C)R G Bingham 2005.All rights reserved.Napiers rules for a quadrantal triangle(c=90)C bAc=90 B a(c)C-9090-b90-a BAsin(middle part)=prod tan adjacent parts =prod cos op