1 NTITIES . . . . . E Technical Guide Technical ENS L
Breault Research Organization, Inc.
...... ASAP
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ASAP Technical Guide
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Contents ......
Lens Entities in ASAP 7 Lens Type Description 9 Explicit Lens Types 9 SEQUENCE 9 MIRROR 11 COMPOSITE and REPEAT (lens modifier) 12 DOME 14 PERFECT 15 Predefined Lens Types 17 IDEAL 17 SINGLET 19 Bending Factor 21 Lens Designer 21 RIGHT, PENTA and WEDGE 22 DOUBLET 22 MANGIN 24 AFOCAL 24 TELESCOPE 26 Entity Modifiers 33 EXPLODE 33 IMAGE 36 Optimization 38 ABERRATIONS 39 VARIABLES 39 MINIMIZE 40 Tolerancing in ASAP 43 Tolerancing in the ASAP Builder 43
ASAP Technical Guide 5 Tolerancing in ASAP scripts 45 Step 1: Creating a tolerance data file 45 Step 2: Performing Monte Carlo Analysis 47 Special Syntax Rules for Tolerancing in ASAP Scripts 49 Brute Force Tolerancing Using $ITER 51
6 ASAP Technical Guide LENS ENTITIES IN ASAP ......
In this technical guide, you will learn how about lens entities in Advanced Systems Analysis Program (ASAP®) from Breault Research Organization, Inc. (BRO®). Lens entities are distinct from surface and edge entities in ASAP and, at the same time, they share some of their properties. Lens entities were first introduced for the sake of the classically trained optical lens designer, and their implementation carries similarities with conventional sequential ray-tracing codes. Like surface entities, lens entities can be described by a mathematically continuous function and are fast to ray trace. However, unlike surface entities, lens entities can also translate into IGES surface entities. That is why they are limited to conicoid surfaces, which can also be described by a sequence of connected points in space or a parameterized rational Bézier for ease of meshing and CAD export. In short, lens entities cannot be used to describe optical curved surfaces that contain asphericity. In that respect, they are less versatile than surfaces described with the OPTICAL command. In terms of storage, lens entities behave like surface and edge entities. In fact, all entities share a single array for internal storage and have equivalent storage locations. However, they do not necessarily take up the same amount of space. Entities take up only the memory needed to store the data of the entity at that location. This is an important consideration, since the complexity of lens entities may vary from a single element to a complete imaging lens that contains several elements. Other examples of lens entities include triplets, prisms, mirrors and even telescope systems. This means that one ASAP object made with a lens entity may include several optical elements made of different materials.
NOTE General use of the word lens does not imply a single element. Similar to a camera lens that may include several optical components, a lens entity may also contain several elements. In ASAP, lens entities are described as a set of optical elements that can be represented by planes and conicoids. Closely related to classical optical design codes, lens entities are made up of a series of refractive or reflective surfaces (not the ASAP reserved term), bounded by circular apertures and separated by arbitrary media.
ASAP Technical Guide 7 LENS ENTITIES IN ASAP
While it is not difficult to enter a lens by hand using the basic SEQUENCE command, several predefined lens types are supplied: SEQUENCE WEDGE MIRROR AFOCAL SINGLET IDEAL DOUBLET REPEAT MANGIN COMPOSITE RIGHT TELESCOPE PENTA DOME PERFECT
As for surface and edge entities, lens entities can be subjected to linear transformations that can be applied to the object or to the entity. The reference point of lens entities corresponds to the vertex of the first conicoid. It has the following properties: • lenses are defined relative to this point, • lenses are located in space using this point, and • simple translations/shifts of the lenses are performed on the reference point. In addition to linear transformations, two ASAP modifiers—EXPLODE and IMAGE—are closely related to lens entities. The properties of these modifiers are discussed later in this technical guide. A particularity of lens entities is their more sequential nature. This statement alludes to the fact that rays coming from a different object can intersect only the first or last conicoid of a lens entity. Rays (coming from different objects) do not see the sides or the middle elements of an object created with a lens entity. Once rays hit the first or last conicoid of a lens, they propagate in a sequential order dictated by the lens definition. Rays cannot omit any element within a lens. Rays propagate sequentially through the lens until they stop in some way or exit from the other end. The usefulness of lens entities in ASAP resides in their ability to ray trace fast and to be translated into IGES format. Some commands like AFOCAL and TELESCOPE are highly powerful and allow users to create a fairly well designed system with little input. The IDEAL command helps to verify first-order properties of a system, and the IMAGE command is most useful to find object/image conjugates and pupil relays. There are however, some limitations. Curved surface
8 ASAP Technical Guide Explicit Lens Types The SEQUENCE sequence of conicoids: the describe to input explicit require that commands with starts section This Unless otherwise stated, . LENS TYPEDESCRIPTION one—the basic the most with ASAPlenstypesstarting guide introduces This technical highly desirable feature. is a of thecode nature thenon-sequential forwhich applications, instraylight becomes a concern order asphericcoefficients. Moreover, the asphericities cannot beimplemented and flat to optimize a simple lens design. lens a simple optimize to • The long form specifies the global coordinates and the normal vector of the of vector normal the and coordinates global specifies the form long The • form. short orlong the more predefinedutility(like • The short The form uses a morecompact • Finally,follows. we clos conicoid of a conicoid of Distances between conicoids areusedto element media, thickness and spacing. lens modifiers.Theinputparametersin vertex of each conicoid. share asimilar vertex normalvector. TELESCOPE SEQUENCE SEQUENCE SEQUENCE command creates a sequence of coni command. A discussion of the of A discussion command. command. It progresses towa progresses It command. SEQUENCE e with an exampleusing all coordinates areglobal. all coordinates must be entered in the long format. long the in entered be must DOUBLET , MIRROR clude surface curvatureandconicconstant,clude ) to end the description of lens types with of with lens types ) endthedescription to notation and assumes andassumes notation relate eachconicoid.However, the first “sequential” nature of these entities ofentities nature these “sequential” aspheric planes ar aspheric , and LENS ENTITIESIN ASAP LENS EXPLODE ABERRATIONS COMPOSITE rds commands that provide provide that commands rds coids. It canbeusedinits SPTcnclGie9 TechnicalASAP Guide Lens TypeDescription and that allconicoids e limited to fourth- to e limited IMAGE and and REPEAT MINIMIZE modifiers modifiers
. . . . . LENS ENTITIES IN ASAP Lens Type Description
“Example script LENS_SEQUENCE_LONG.INR (top) and plot (bottom)” and “Example script LENS_SEQUENCE_SHORT01.INR (top) and plot (bottom)” on page 11 show examples of the long and short form of the SEQUENCE command.
Example script LENS_SEQUENCE_LONG.INR (top) and plot (bottom)
10 ASAP Technical Guide MIRROR design law that light travels only from left from only travels light that law design The MIRROR Example scriptLENS_SEQUENCE_SHOR commandis used to create a si to right, the focal length of a concave length of to right,thefocal mple mirror.mple the universal Under T01.INR (top) and plot (bottom) LENS ENTITIESIN ASAP LENS SPTcnclGie11 TechnicalASAP Guide Lens TypeDescription
. . . . . LENS ENTITIES IN ASAP Lens Type Description
mirror is positive, while the focal length of a convex mirror is negative. See “Example script LENS_MIRROR.INR (top) and plot (bottom)” on page 12.
Example script LENS_MIRROR.INR (top) and plot (bottom)
COMPOSITE AND REPEAT (LENS MODIFIER) The COMPOSITE command combines several lens entities into a single lens entity. See “Example script LENS_TRIPLET_COMPOSITE.INR (top) and plot (bottom)” on page 13. IDEAL lens entities are not allowed in a composite set. The REPEAT command repeats previously defined entity data that may subsequently be changed by linear transformations.
12 ASAP Technical Guide Example script LENS_TRIPLET_COMPO SITE.INR (top) and plot (bottom) (top) andplot SITE.INR LENS ENTITIESIN ASAP LENS SPTcnclGie13 ASAP Technical Guide Lens TypeDescription
. . . . . LENS ENTITIES IN ASAP Lens Type Description
DOME The DOME command creates a dome lens as a single refractive element of axial thickness t and media m with front and back radius of curvature r and r', respectively. The side with the shortest radius is a complete hemisphere, while the other is truncated at the same plane. See “Example Script LENS_DOME01.INR” on page 14 and “LENS_DOME01.INR plot” on page 15.
Example Script LENS_DOME01.INR
14 ASAP Technical Guide ESSPRET3IR(o)adpo bto) npg 16. onpage (bottom)” and plot (top) LENSES_PERFECT03.INR of ratio the to equal a magnification with can beusedtoperfectlyreimagea finite-d Two back-to-back Unlike the Unlike the plane at back focal plane),andnospheri (characteristic) functionforperfect imaging vectors aredeterminedfrom the input ra PERFECT length length The PERFECT f , input height height , input IDEAL command is used to create a perfec command isused tocreate lens, there areblurring ray aber PERFECT h , output distance distance , output lenses,with a small coll LENS_DOME01.INR plot y vectors by the solutions to the eikonal theeikonal to bythesolutions y vectors cal aberrationof the principal points. t theirfocal lengths. See“ExampleScript istance objecttoafinite-distance plane, , and output height height , andoutput of an object plane at infinity (image at infinity plane of anobject LENS ENTITIESIN ASAP LENS rations at all other conjugates. conjugates. other all at rations t (but realistic) lens of focal lens t (butrealistic) SPTcnclGie15 ASAP Technical Guide imated space between them, imated space Lens TypeDescription h' . The output ray
. . . . . LENS ENTITIES IN ASAP Lens Type Description
Example Script LENSES_PERFECT03.INR (top) and plot (bottom)
16 ASAP Technical Guide Predefined Lens Types NOTE account for lens aberrations. first-orderproperties of anoptical system,but they not do model idealfor thinlenses. modeling They themost are helpful shows a first-order design example of 7x35 binoculars. designexample afirst-order shows 19 page plot” “LENS_IDEAL04.INR on 18 and onpage LENS_IDEAL04.INR” beunity, should theray matrix of determinant thatisad-bc=1. script “Example bethesame. areassumed to the Therefore, media andoutput The input called (sometimes rays input of raysareextensions output where Non-lens • magnification Afocal system of angular • length focal Perfect lenswith • guide, Thismoreadvanced matrices. of Jones to affused command canalsobe This matrix. bya ABCD ray vector 2x2 theoutput related to arelinearly ray vectors The IDEAL IDEAL here: andareintroduced utility a predefined provide These curvature entities input. previously,As mentioned lens ASAP some TELESCOPE Ideal orparaxial lenses arereal.Mathematical not toolscan transmission matrix): matrix): transmission IDEAL Polarization , SINGLET commandcreatesanidealizedpara . , . Common idealized optical systems include: RIGHT (a,b,c,d) = (1,t,0,1) = (a,b,c,d) , PENTA f: (a,b,c,d)(1,0,-1/f,1) = , WEDGE ect ray polarization via the implementation topic is treated in the ASAP technical ASAPtechnical inthe istreated topic m: (a,b,c,d) = (1/m,0,0,m) entities do not require explicit surface surface explicit require not do entities . , DOUBLET xial opticalelementwhose input LENS ENTITIESIN ASAP LENS SPTcnclGie17 ASAP Technical Guide , Lens TypeDescription MANGIN , AFOCAL , and , and . . . . . LENS ENTITIES IN ASAP Lens Type Description
Example script LENS_IDEAL04.INR
18 ASAP Technical Guide other words, the position of the object and image with respect to the lens, the tothe lens, respect with image and of object words, the the other position aberration andcoma.Sincele constant are automatically calculated calculated areautomatically constant Another way is to use the use the is to way Another curvature orradiivia the a aperture enter lensthickness, height, The • SINGLET the • • ofalens: shape describes the factor the lensbending to specify way is One Calculations of eachsurface curvature or b =1 b =0 b =-1 FL SINGLET (focal length specification) specification) option. (focallength implies a convex-plano or a concave-plano lens. or a concave-plano aconvex-plano implies impliesabiconvexor biconcave element, implies a plano-convex or a plano-concave lens, a plano-concave or plano-convex a implies command creates a simple, one-element, singlet lens. Explicitly Explicitly lens. singlet one-element, a simple, creates command CV APLANAT or ns aberrations depend on system conjugates or, conjugates system depend on ns aberrations in LENS_IDEAL04.INR plot RD key words, useASAP keywords, or option. The bending factor and and one conic factor Thebending option. to produce zerothir nd medium. Either directly specify surface radius canbedone two separate ways. b. LENS ENTITIESIN ASAP LENS This bending or shape factor or shape bending This SPTcnclGie19 ASAP Technical Guide d-order spherical spherical d-order Lens TypeDescription to calculate themvia
b . . . . . LENS ENTITIES IN ASAP Lens Type Description
parameter is used to describe the object position. This is done using the so-called conjugate or magnification factor defined as:
(EQ 1) where m corresponds to the lens magnification.
One-to-one imaging b=0 Infinite object distance b=1 Infinite image distance b=-1
As shown in “Example script LENS_SINGLET02.INR (top) and plot (bottom)” this SINGLET command creates a plano-convex lens.
Example script LENS_SINGLET02.INR (top) and plot (bottom)
20 ASAP Technical Guide object,and they are used high in numericalsystems. aperture typeThis lens of differs from aplanaticsinglet lenses.For the latter, one surfaceis aplanatic and the otherconcentric with aberration. remove to spherical constant conic surface one adding and coma, eliminate to factor bending the spherical aberration and coma also means no aberration exists over exists aberration no means also coma and aberration spherical an In lensdesign jargon, LENS DESIGNER The BENDING FACTOR bending factor describes the shape ofa aplanatic lens system lens.defined as: Itis means no third-order spherical aberration spherical third-order no means some finite field. In ASAP, such a singlet is designed by us by designed is singlet a such ASAP, In field. finite some and no third-order coma. The absenceof coma. The third-order no and LENS ENTITIESIN ASAP LENS SPTcnclGie21 ASAP Technical Guide Lens TypeDescription (EQ 5) (EQ 4) (EQ 3) (EQ 2) (EQ the ing ing . . . . . LENS ENTITIES IN ASAP Lens Type Description
RIGHT, PENTA AND WEDGE The RIGHT, PENTA, and WEDGE lens entities are other examples of commands that provide a predefined utility in ASAP. The RIGHT command creates a simple, right-angle prism with three circular surfaces. Similarly, the PENTA command creates a 90-degree deviation penta prism with four circular surfaces. The WEDGE command creates a wedge of glass with two circular surfaces.
DOUBLET The DOUBLET command creates a cemented doublet lens made of a positive and a negative element that are placed in contact. Such lenses are typically designed to minimize axial color. Aberration theory shows that this condition is met when the sum of the element power () divided by the material Abbé number () is zero:
(EQ 6) In other words, if r is the ratio of the focal length of the first element to the second, then for an achromatic doublet, r is also the ratio of the dispersions. It is the command default setting if r is not given. The thickness of the first element is set to 90% of the doublet total thickness. Similarly to the singlet command, the shape of the first and last surfaces are specified through the bending factor b: • b = -1 implies a plano-convex or a plano-concave lens, • b = 0 implies a biconvex or biconcave element, and • b = 1 implies a convex-plano or a concave-plano lens.
22 ASAP Technical Guide shows anexampleof the command. scriptLENS_DOUBLET.INR “Example values. opposite (bottom)” andplot (top) of of and radius curvature third equal firstand b=0 value the is The default with Example scriptLENS_DOUBLET .INR (top) and plot (bottom).INR (top)andplot LENS ENTITIESIN ASAP LENS SPTcnclGie23 ASAP Technical Guide Lens TypeDescription
. . . . . LENS ENTITIES IN ASAP Lens Type Description
MANGIN The MANGIN command defines a Mangin mirror, which is essentially a lens with a reflective second surface (conicoid); rays are refracted twice at the first conicoid. As for singlets, you can directly specify the conicoid’s curvatures via the CV or / RD key words, or let ASAP calculate them via the FL (focal length specification) and bending factor option.
AFOCAL The AFOCAL command creates a two-element afocal telescope. Both elements may be refractive, reflective, or mixed. Reflective conicoids are created when the keyword REFL or 1 is used as media assignment (m or m’). Some of the rules that describe the design of the afocal telescope include: • All refractive elements contain a planar conicoid that faces the collimated beam, (note that these surfaces do not introduce third-order aberration). • Spherical aberration introduced by the curved conicoid is corrected by the addition of a conic constant that is equal to minus the square of the element index of refraction (where k = -n2). • l, the overall length does not include the thickness of the elements. It is, therefore, the spacing between the elements. • ASAP automatically assigns the thickness of the refractive elements. The PRINT command is useful for verifying the thickness assignment.
24 ASAP Technical Guide of the of the example showsan (bottom)” andplot (top) LENS_AFOCAL.INR script “Example AFOCAL Example scriptLENS_AFOCAL. command. INR (top) and plot (bottom) LENS ENTITIESIN ASAP LENS SPTcnclGie25 ASAP Technical Guide Lens TypeDescription
. . . . . LENS ENTITIES IN ASAP Lens Type Description
TELESCOPE The TELESCOPE command is one of the most powerful ASAP commands. It creates a one- or two-mirror telescope, ranging from a simple parabola to a system that contains two mirrors, a corrector plate, and a field flattener. The reference point of the system is the vertex of the primary mirror and it is oriented and located given the defined global coordinate axis and location. TELESCOPE has two options:
1 The FL/MAG/BWD option requires general input such as the overall telescope focal length, the secondary magnification (MAG) when needed, and the location of the focal point with respect to the primary location (BWD). 2 The FL1/SEP/FL2 option requires more explicit input like the individual focal length of each mirror and their separation. For a one-mirror telescope, simply specify FL1 or FL and omit SEP/FL2 or MAG/BWD. See “Example script LENS_AFOCAL.INR (top) and plot (bottom)” on page 25 for an example of a one-mirror telescope. Note that the mirror conic constant is 1, which corresponds to a parabola. STOP is the keyword that tells ASAP to add a corrector plate in front of the primary mirror. Corrector plates are usually used to minimize spherical aberration. This corrector plate becomes a stop when the subsequent media input is omitted or is AIR. FOV tells ASAP to add a field flattener at the image or focal plane. Such a lens eliminates third-order field curvature without adding third-order spherical, coma or astigmatism. The TELESCOPE command is programmed to design telescopes that are always corrected for third-order spherical aberration. This is done by either adding a conic constant on the primary mirror or by adding a fourth-order asphere on the corrector plate. As many as possible other third-order aberrations are corrected as you add degrees of freedom in the system (like a corrector plate or a second mirror). Third- order aberrations are generally corrected according to the following priority: spherical aberration, coma, astigmatism, and field curvature. Color correction comes for free in a reflective system. The two typical configurations of two-mirror telescopes are Cassegrain and Grégorian. The second mirror of the Cassegrain configuration has a negative power and a positive magnification. The Grégorian configuration has two positive elements. Ray traces of Grégorian telescope show an intermediate focus.
26 ASAP Technical Guide option of the command, both thecommand, of option Magnification of thesecond elemen FL and t is negative.Whenusingthe MAG values arenegative. values LENS ENTITIESIN ASAP LENS SPTcnclGie27 ASAP Technical Guide Lens TypeDescription FL/MAG/BWD
. . . . . LENS ENTITIES IN ASAP Lens Type Description
“Example script LENS_TELESCOPE_PARABOLIC.INR (top) and plot (bottom)” shows common telescope designs, and illustrate some rules or tips of the TELESCOPE command.
Example script LENS_TELESCOPE_PARABOLIC.INR (top) and plot (bottom)
28 ASAP Technical Guide NOTE -1 for aparabola that corrects spherical aberration. curvature (2xFL). The mirror conic constant is automatically set to ASAPcreatesonea mirror telescopewithmm radius a40 of Example LENS_TELESCOPE_SCHMIDT.INR LENS ENTITIESIN ASAP LENS SPTcnclGie29 ASAP Technical Guide Lens TypeDescription
. . . . . LENS ENTITIES IN ASAP Lens Type Description
LENS_TELESCOPE_SCHMIDT.INR plot
30 ASAP Technical Guide Output forLENS_TELESCOPE_SCHMIDT.INRwith the NOTE constant. and themirroraberration, remain The asphericity ofcorrector the plate corrects spherical order coma, astigmatism, and distortion introduced by the mirror. stop (the correctorplate).Such aconfiguration eliminates third- curvature (2xFL).this In design, PRINT the using canalwaysbeobtained thetelescope system of prescription A detailed ASAP creates a mirror telesc command, as shown below. asshown command, the mirror is concentric with the with is concentric the mirror s sphericalzeroa with conic ope with a 40 mm radius of PRINT LENS ENTITIESIN ASAP LENS command SPTcnclGie31 ASAP Technical Guide Lens TypeDescription
. . . . . LENS ENTITIES IN ASAP Lens Type Description
Example LENS_TELESCOPE_CHRETIEN.INR (top) and plot (bottom)
32 ASAP Technical Guide NOTE Ritchey-Chrétien telescope design that is limited by astigmatism. by limited is that design telescope Ritchey-Chrétien third-order spherical aberration and coma. Thisresults ina viaaddition theof conics mirrors, ontheeliminates which two obscuration iscreated automatically. Aberration controlis done mirrors are respectively400 and mm. Theprimary 140 mirror configuration.radii The ofcurvature of the primary andsecondary ASAPcreatestwo-mirrora telescope with aCassegrain Output for LENS_TELESCOPE Output for Example LENS_TELESCOPE_MAKSUTOV.INR _CHRETIEN.INR with the LENS ENTITIESIN ASAP LENS SPTcnclGie33 ASAP Technical Guide Lens TypeDescription PRINT command
. . . . . LENS ENTITIES IN ASAP Lens Type Description
Example LENS_TELESCOPE_MAKSUTOV.INR plot
Output for LENS_TELESCOPE_MAKSUTOV.INR with the PRINT command
34 ASAP Technical Guide Entity Modifiers NOTE conic constants thatcorrect spherical aberration andcoma. eliminates spherical aberration, whichwhy the is two mirrors have theaddition of conicsmirror. onthe However, ASAPalways eliminatesthird-order coma, astigmatism,and distortion without st mirrors concentricwiththe two properties of these modifiers. properties ofthese s This entities. lens to related closely ae11. page script LENS_SEQUENCE_SHORT0“Example EXPLODE 36 shows the onpage (bottom)” and plot (top) LENS_EXPLODE_MINUS.INR the opposi in surfaces andpropagate ray is why established. Thisoccurrence are nolonger lenses but surfaces, theno COATING BARE The interfacesofrefractivesurf duplicated th from deleted not is lens original The se sign createsonlya No • A plus sign creates right cylinders. • cones, direct-sloped signcreates minus A • si when a surface—are also created objects—like baffle, mounting, oredge typically bounded elements, command. A common use ofthis command OBJECTS The EXPLODE earlier,As mentioned modifiers— twoASAPentity Inthisexample, ASAPcreates aMaksutov-Cassegrain with EXPLODE
command applied directly to the Cooke triplet, which was in shown which was theCooke triplet, directly to applied command . Bycreatingobjects, it elim entity. command expands lens conicoids into separate and SPLIT ries of separate surfaces. comprised of two surfaces isautomaticallyraised to aces are automatically set to set aces areautomatically gn precedes theentitynumber. te direction.“Examplescript op. Thislocation of the mirrors ection includes includes a brief ofthe ection description inates the need to addan e entitydatabasean surfaces thatconnect n-sequential nature of ASAP is re- ASAP is n-sequential natureof traces show rays that reflect on the that reflecton rays traces show is to explode a lensis toexplode sequencetocreate 1.INR (top) and plot (bottom)” on plot (bottom)” 1.INR (top) and LENS ENTITIESIN ASAP LENS EXPLODE SPTcnclGie35 ASAP Technical Guide plus a tube.Additional plus level 1. Since theentities 1. level Lens TypeDescription d is,therefore,a INTERFACE eachcoaxial lens and SURFACE OBJECT IMAGE
—are
. . . . . LENS ENTITIES IN ASAP Lens Type Description
Example script LENS_EXPLODE_MINUS.INR (top) and plot (bottom)
36 ASAP Technical Guide LENS_EXPLODE_PLUS.INR (t op) and plot (bottom) LENS ENTITIESIN ASAP LENS SPTcnclGie37 ASAP Technical Guide Lens TypeDescription
. . . . . LENS ENTITIES IN ASAP Lens Type Description
The red baffles that connect the elements are now created with right cylinders. NOTE The red cylinders do not mesh when using the PLOT FACETS command, nor do they display in the 3D Viewer with the VIEW command.
IMAGE The IMAGE command is not a LENS modifier. It is either an EDGE or a RAY modifier that images entities or rays through a specific lens entity. This command can also image a global point through a specific lens entity. The resulting imaging transformation is stigmatic (points go into points), but not necessarily collinear (lines go into lines). Therefore, it is only an approximation, since in any real optical system, the image is aberrated (not a perfect point focus). Common usage of the IMAGE command is to find the conjugate of pupils or images into different space of a lens system. This command is most useful for SCATTER TOWARDS edges that represent images of important areas (like a detector in a stray light analysis). Another common usage is to map a GRID of a ray that is located at an internal stop position into the lens object space. The imaged GRID then matches the entrance pupil, and it is possible to create an efficient ray trace using the GRID SOURCE command. “Example LENS_IMAGE02.INR” on page 39 and “LENS_IMAGE02.INR plot” on page 40 show an example of this technique.
38 ASAP Technical Guide Example LENS_IMAGE02.INR LENS ENTITIESIN ASAP LENS SPTcnclGie39 ASAP Technical Guide Lens TypeDescription
. . . . . LENS ENTITIES IN ASAP Lens Type Description
LENS_IMAGE02.INR plot
Optimization A lens can be optimized using a brute-force algorithm that finds either the nearest minimum or (given enough time) the global minimum—without requiring the merit function to be continuous. This technique also allows constraints to be handled in a straightforward and exact manner. All this is made possible by an extremely fast method for determining the RMS spot size at any field location (for example, it does not have to do iterative ray-aiming to hit the internal stop surface of a wide angle lens). On a typical system, over a million merit function evaluations per minute can be achieved, independent of the number of fields. This ASAP feature is not intended to replace a full-blown lens-design program, since it is currently limited to unvignetted, centered, focal systems—the vast majority of manufactured units, and does not have any built-in, multi- configuration, tolerancing capability. This optimization approach does not handle aspheric terms. However, these and other advanced capabilities can be easily
40 ASAP Technical Guide The VARIABLES The ABERRATIONS uses technique the This optimization may th designs that unique) (possibly find $ITER some additionalmacro- emulated with MINIMIZE the twoadjacent conicoids, while allowingth of the power and focal length fixes Thisapproximately inthe lens. next conicoid thediff constant keeping while conicoid(s) variablethat isa Bending composite and conicconstants on any set of varied during optimization. Thebasicpara lenses orconicoids.Since works with both glass elements andairspaces. The and analytical formulas relative to the idealparaxial focus. Th order aberrationcoefficients (inwaves) 3rd-order, color), (primary 1st-order The final 5th-order, 7th/9th- and selected and chiefraytraces,the glass and conicoid data. chief raytraces, theSeidel primaryand s Surface-by-surface tables and ofthis stop. the center edge of the limitingaperture stop, and thech data forthemarginalthefr are ray axial which entries, the additional with must be supplied data operating The first-order so. it make If axis. havea not, must common conicoids MINIMIZE VARIABLES ABERRATIONS ABERRATIONS ). As a minimum, this optimi this specific ). aminimum, As commands. commands, which are discussed next. arediscussed which commands, command declares which lens construction parameters be parameters will lensconstruction which declares command command displays the image ab command can befollowedbythe real-ray datamatching. the analysis is valid only for centeredlenssystems,the only analysisvalid isthe plots canbeproducedfor conicoids listedafter each variable. changesthecurvatureof given ABERRATIONS ese coefficients are language programming (for example, (forexample, programming language om thecenter of theobjectthrough are listedforactualstopplanecoordinates econdary aberrations,therealmarginal en betweaked elsewhere, ifnecessary. meters arethe thicknesses, curvatures, erence incurvatures between it and the the lens is temporarily “unfolded” to “unfolded” thelensistemporarily ief ray from the edge of the object to the object of from theedge ief ray zation featurecanbeusedtoquickly eir aberration LENS ENTITIESIN ASAP LENS SPTcnclGie41 ASAP Technical Guide errations ofall the current , VARIABLES VARIABLES the paraxialmarginal and computed using both both using computed Lens TypeDescription contributions tovary. It , and and
. . . . . LENS ENTITIES IN ASAP Lens Type Description
In global optimization mode, the optimum glass (or combination of glasses) can be found from all the currently defined MEDIA. Since six variables per conicoid and a maximum of 120 conicoids can potentially exist, an optimization can use up to 720 variables. A large number of variables can quickly become impractical, even for a local optimization, because runtimes go approximately as the cube of the number of variables.
MINIMIZE The MINIMIZE command minimizes the RMS spot size or the average of the previously specified fields. If the image quality of a design does not get better during an optimization, it is usually due to conflicting constraint violations, or constraint violations not affected by the specified variables. Normal optimization controls include the maximum number of multiple trial solutions attempted MULT, a random SEED value, and a target RMS spot size value TARG that stops the optimization process when the calculated RMS spot size drops below the target value. Advanced optimization controls include a tolerance describing a fractional change in the merit function at local minima, and a maximum allowable randomization of normalized variables. These advanced controls are automatically determined by the MULT value and the number of variables. In rare circumstances, they may have to be set explicitly. The underlying design engine has a comprehensive “pickup” (a conicoid variable is constrained to follow one at a previous conicoid), and “paraxial solve” (a conicoid variable is determined from paraxial ray-trace requirements) capability. The ASAP script for an optimization of a three-element lens design is shown in “Script OPTIMIZATION.INR” on page 43 and “Plots from OPTIMIZATION.INR” on page 44.
42 ASAP Technical Guide The plots resulting from the above script are shown areshown below. above script from the The plots resulting Script OPTIMIZATION.INR LENS ENTITIESIN ASAP LENS SPTcnclGie43 ASAP Technical Guide Lens TypeDescription
. . . . . LENS ENTITIES IN ASAP Lens Type Description
Plots from OPTIMIZATION.INR
44 ASAP Technical Guide Tolerancing inthe ASAP Builder Click theBuilder’s Otherwise, someotheroutputcan be view FOM is used. The tolerancing analysis is started by selecting byselecting isstarted analysis Thetolerancing used. is FOM column with a numeric field andselecting a column with valuesisavailabl entering tolerance For each object (orgroupofob fraction ofacceptableresults graphically, process.Theresults can bedisplayed manufacturing the showing during a specification the controlling with associated the randomness simulating The perturbation is repeated asufficient andlooki a perturbing specification, involves jeop idealwithout from the isto in ASAP The ideaoftolerancing . TOLERANCING INASAP Options etr pin n oeacn ilgbxs npg 46. and Tolerancing Options Perturb onpage boxes” dialog define it in the Builder.Use the isneeded,you must (FOM) Ifa ofmerit figure and the range of the perturbation. distri ofperturbation selectthe type Next, Tolerancing tole current the displays dialog perturbations. Note that tolerancing is not the same as sensitivity analysis. thesameas is not that sensitivity tolerancing perturbations. Note window. showing window is in “Builder procedure shown Thissetup Perturb button to add the FOM to the Perturb Options list, if an if list, Perturb Options the to FOM the add to button ardizing the overall design for the figure ofmerit fr jects) that is entered inth that is jects) $GRAB e by right-clicking inany a Builder cell e byright-clicking see how mucha specification candepart macro to bring the FOM into the analysis. the analysis. into FOM the bring macro to numberof timesrandom in a manner, bution tobeused,Gaussianor uniform, bution ed foreachrun of a Tolerance Range rance values for theexisting parameter. ng attheeffect ona figure of merit. LENS ENTITIESIN ASAP LENS SPTcnclGie45 ASAP Technical Guide om the series of random performance. Thisfeature e Builder,e a dialogboxfor Tolerancing inASAP from the list. The thelist. from OK perturbed variable. in the inthe Perturb
. . . . . Builder window showing Perturb Options and Tolerancing dialog boxes Based on the information entered in the Builder spreadsheet, an automatic Monte Carlo analysis generates random perturbations (uniform or normal distribution) to an existing geometry. After you define the source, ASAP performs ray traces and analyses in the usual way. A new set of random perturbations is generated, and the ray traces and analyses are repeated. This feature eliminates the need to define variable names for each parameter or place random variables in your geometry. A double-pass system is used to avoid double-counting iterations. You can also perform a merit function (much as you can with the $ITER macro command) from the Perturb Options dialog box. ASAP then repetitively runs the procedure to produce a plot of merit function versus trial number. Tolerancing inASAP scripts An example of a tolerancing (*.inx) file is shown below. shown is file (*.inx) ofatolerancing An example 3 2 1 CREATING ATOLERANCESTEP 1: FILE DATA below.are outlined These steps to you create a First, As intheASAP process: Builder, isa Editor two-step in the ASAP tolerancing graph of ofoutputs. the sequence The results ofa tolerancing example, us value with angle brackets, withangle
. . . . . LENS ENTITIES IN ASAP Tolerancing in ASAP
Example of a tolerancing (*.inx) file
4 Click the Tolerance Editor button. ASAP opens the Tolerance Editor spreadsheet at the bottom of the window. Columns in this spreadsheet are defined in the Tolerancing Spreadsheet in the Editor.
Empty spreadsheet in the Tolerancing Editor
5 Make script changes in the Editor, and update the Tolerance spreadsheet by clicking the Update Tolerance Editor button.
Updated spreadsheet
48 ASAP Technical Guide 2 1 CARLO ANALYSISPERFORMING MONTE STEP 2: OPTICAL Z 444.50 0 ELLIPSE<10> intheEditor: script ofthe field to the semi-width tolerance all specify parameters, optional contains To Name for theParameter an display 7 6 the tolerancing picture. the tolerancing displayed in the Command Output window and the the and window Output Command the in displayed ASAP performs anautomaticM of y Figure(s) Merit boxarethevariables Editortoolbar. onthe button Perturb the Select inthe The names displayed format (INX). as well as theASAP commands in the Edit data, tolerance The data file. tolerance savethe to menu File the on Save Select columns. for applicable are displayed Tolerance columns. applicable for the data values Enter tolerance values default Perturb Optionsdi onte Carloanalysis. The nu alog showingFigure(s)Merit of ASAP command (or Object Name)that OPTICAL parameters. Forexample, to assign a ou defined at *.inxfile. the top of the ou defined or window, aresaved to anXMLfile LENS ENTITIESIN ASAP LENS command, enter the following enterthefollowing command, SPTcnclGie49 ASAP Technical Guide GRAPH Tolerancing inASAP merical information is command command produces
. . . . . LENS ENTITIES IN ASAP Tolerancing in ASAP
Command Output window showing numerical information
50 ASAP Technical Guide abbreviated in the following syntax: inthe following abbreviated OBJ Abbreviating command names or parame or names command Abbreviating PLANE Y <0> SURFACE command thatisallowablefo ENT OBJECT andENTOBJ commands ( these line containing oneof A TORUS, COATINGS/COATING, POINTS, SPHERICAL,PARABOLIC SINGLET, PLANE,BICONIC,ELLIPSOID, MEDIA,OPTICAL, The followingcommands can follows. examples ofthese with A discussion properly constructed. rules to knowandfollowthespecialsyntaxrules usetheASAP fo If youare to Editor planning SCRIPTS SPECIAL SYNTAXTOLERANCING RULESFOR INASAP and ENT OBJECT Chart produced by GRAPH command . Forexample, the r tolerancing. For example, For r tolerancing. contain tolerancing values: values: tolerancing contain ) must be followed be by ) must followed ters is notsupported, except for ELLIPSE SURFACE, LENSES,EDGES, in order to assure that that your script is toassure in order r tolerancing analysis, it is important is it important analysis, r tolerancing LENS ENTITIESIN ASAP LENS SPTcnclGie51 ASAP Technical Guide command isincorrectly another line containinga another Tolerancing inASAP ENT
. . . . . LENS ENTITIES IN ASAP Tolerancing in ASAP
OPTICAL Z 0 1 ELL 1 0 0 A correct command syntax for ELLIPSE when tolerancing is: OPTICAL Z 0 1 ELLIPSE 1 0 0 Tolerancing on variables, expressions, axes or matrix values is not supported. For example, all the following command scripts are invalid: OPTICAL Z
52 ASAP Technical Guide toolbar,“Tolerancing”. keyword the under example of this approachcanbefound the We using by tolerancing above the simulate also can BRUTE FORCETOLERANCING USING $ITER 0 MGFL2 23.12TI0250.44 MGFL2 <16.33>TI02'AR' COATINGS LAYERS<122.43> MGFL2 <16.33> TI02'AR' COATINGS LAYERS<122.43>;0 0MGFL223.12TI02 50.44 The MEDIA <1.5> ‘GLASS’;<1.38> ‘MGFL2’ <1.51> 'GLASS';<1.38>'MGFL2' COATING/COATINGS command must have one of the following forms: have oneof following must the command Tolerancing using $ITER in the ExampleScript in LENS ENTITIESIN ASAP LENS SPTcnclGie53 ASAP Technical Guide $ITER Tolerancing inASAP s on the Quick Starts ontheQuick command.An
. . . . . LENS ENTITIES IN ASAP Tolerancing in ASAP
Results of running example script for brute force tolerancing
54 ASAP Technical Guide