. . . . . . . . . . . . . . . . . . . . . . . . . . .€¦ · system with little input. The IDEAL command helps to verify first-order properties of a system, and the IMAGE command

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Technical Guide

LENS ENTITIES

Breaul t Research Organizat ion, Inc.

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This Technical Guide is for use with ASAP®.

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brotg0916_lens (September 8, 2014)

ASAP Technical Guide 3

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Contents

Lens Entities in ASAP 7

Lens Type Description 9Explicit Lens Types 9

SEQUENCE 9MIRROR 11COMPOSITE and REPEAT (lens modifier) 12DOME 14PERFECT 15

Predefined Lens Types 17IDEAL 17SINGLET 19

Bending Factor 21Lens Designer 21

RIGHT, PENTA and WEDGE 22DOUBLET 22MANGIN 24AFOCAL 24TELESCOPE 26

Entity Modifiers 33EXPLODE 33IMAGE 36

Optimization 38ABERRATIONS 39VARIABLES 39MINIMIZE 40

Tolerancing in ASAP 43Tolerancing in the ASAP Builder 43


Tolerancing in ASAP scripts 45Step 1: Creating a tolerance data file 45Step 2: Performing Monte Carlo Analysis 47Special Syntax Rules for Tolerancing in ASAP Scripts 49Brute Force Tolerancing Using $ITER 51

6 ASAP Technical Guide

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .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.


L E N S E N T I T I E S I N A S A P

While it is not difficult to enter a lens by hand using the basic SEQUENCE command, several predefined lens types are supplied:

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

SEQUENCE WEDGE

MIRROR AFOCAL

SINGLET IDEAL

DOUBLET REPEAT

MANGIN COMPOSITE

RIGHT TELESCOPE

PENTA DOME

PERFECT


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. .L E N S E N T I T I E S I N A S A P

Lens Type Description

asphericities cannot be implemented and flat aspheric planes are limited to fourth-order aspheric coefficients. Moreover, the “sequential” nature of these entities becomes a concern in stray light applications, for which the non-sequential nature of the code is a highly desirable feature.

This technical guide introduces ASAP lens types starting with the most basic one—the SEQUENCE command. It progresses towards commands that provide more predefined utility (like DOUBLET) to end the description of lens types with the TELESCOPE command. A discussion of the EXPLODE and IMAGE modifiers follows. Finally, we close with an example using ABERRATIONS and MINIMIZE to optimize a simple lens design.

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Unless otherwise stated, all coordinates are global.

Expl ic i t Lens TypesThis section starts with commands that require explicit input to describe the sequence of conicoids: SEQUENCE, MIRROR, and COMPOSITE and REPEAT lens modifiers. The input parameters include surface curvature and conic constant, element media, thickness and spacing.

S E Q U E N C E

The SEQUENCE command creates a sequence of conicoids. It can be used in its short or long form.

• The long form specifies the global coordinates and the normal vector of the vertex of each conicoid.

• The short form uses a more compact notation and assumes that all conicoids share a similar vertex normal vector.

Distances between conicoids are used to relate each conicoid. However, the first conicoid of a SEQUENCE must be entered in the long format.




“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)


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Example script LENS_SEQUENCE_SHORT01.INR (top) and plot (bottom)

M I R R O R

The MIRROR command is used to create a simple mirror. Under the universal design law that light travels only from left to right, the focal length of a concave




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)

C O M P O S I T E A N D R E P E A T ( L E N S M O D I F I E R )

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.


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Example script LENS_TRIPLET_COMPOSITE.INR (top) and plot (bottom)




D O M E

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


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LENS_DOME01.INR plot

P E R F E C T

The PERFECT command is used to create a perfect (but realistic) lens of focal length f, input height h, output distance t, and output height h'. The output ray vectors are determined from the input ray vectors by the solutions to the eikonal (characteristic) function for perfect imaging of an object plane at infinity (image plane at back focal plane), and no spherical aberration of the principal points.

Unlike the IDEAL lens, there are blurring ray aberrations at all other conjugates. Two back-to-back PERFECT lenses, with a small collimated space between them, can be used to perfectly reimage a finite-distance object to a finite-distance plane, with a magnification equal to the ratio of their focal lengths. See “Example Script LENSES_PERFECT03.INR (top) and plot (bottom)” on page 16.




Example Script LENSES_PERFECT03.INR (top) and plot (bottom)


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Predef ined Lens TypesAs mentioned previously, some ASAP lens entities do not require explicit surface curvature input. These entities provide a predefined utility and are introduced here: IDEAL, SINGLET, RIGHT, PENTA, WEDGE, DOUBLET, MANGIN, AFOCAL, and TELESCOPE.

I D E A L

The IDEAL command creates an idealized paraxial optical element whose input ray vectors are linearly related to the output ray vector by a 2x2 ABCD matrix. This command can also be used to affect ray polarization via the implementation of Jones matrices. This more advanced topic is treated in the ASAP technical guide, Polarization. Common idealized optical systems include:

• Perfect lens with focal length f: (a,b,c,d) = (1,0,-1/f,1)

• Afocal system of angular magnification m: (a,b,c,d) = (1/m,0,0,m), and

• Non-lens where output rays are extensions of input rays (sometimes called transmission matrix): (a,b,c,d) = (1,t,0,1).

The input and output media are assumed to be the same. Therefore, the determinant of the ray matrix should be unity, that is ad-bc=1. “Example script LENS_IDEAL04.INR” on page 18 and “LENS_IDEAL04.INR plot” on page 19 shows a first-order design example of 7x35 binoculars.

NOTE Ideal or paraxial lenses are not real. Mathematical tools can model ideal thin lenses. They are most helpful for modeling the first-order properties of an optical system, but they do not account for lens aberrations.




Example script LENS_IDEAL04.INR


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LENS_IDEAL04.INR plot

S I N G L E T

The SINGLET command creates a simple, one-element, singlet lens. Explicitly enter lens thickness, aperture height, and medium. Either directly specify surface curvature or radii via the CV or RD key words, or use ASAP to calculate them via the FL (focal length specification) option.

Calculations of each surface curvature or radius can be done two separate ways. One way is to specify the lens bending factor b. This bending or shape factor describes the shape of a lens:

• b = -1 implies a plano-convex or a plano-concave lens,

• b = 0 implies a biconvex or biconcave element,

• b = 1 implies a convex-plano or a concave-plano lens.

Another way is to use the APLANAT option. The bending factor and one conic constant are automatically calculated to produce zero third-order spherical aberration and coma. Since lens aberrations depend on system conjugates or, in other words, the position of the object and image with respect to the lens, the b




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.

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)

One-to-one imaging b=0

Infinite object distance b=1

Infinite image distance b=-1


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B E N D I N G F A C T O R

The bending factor describes the shape of a lens. It is defined as:

(EQ 2)

(EQ 3)

(EQ 4)

(EQ 5)

L E N S D E S I G N E R

In lens design jargon, an aplanatic lens system means no third-order spherical aberration and no third-order coma. The absence of spherical aberration and coma also means no aberration exists over some finite field. In ASAP, such a singlet is designed by using the bending factor to eliminate coma, and adding one surface conic constant to remove spherical aberration.

This type of lens differs from aplanatic singlet lenses. For the latter, one surface is aplanatic and the other concentric with the object, and they are used in high numerical aperture systems.




R I G H T , P E N T A A N D W E D G E

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.

D O U B L E T

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.


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The default value is b = 0 with the first and third radius of curvature of equal and opposite values. “Example script LENS_DOUBLET.INR (top) and plot (bottom)” shows an example of the command.

Example script LENS_DOUBLET.INR (top) and plot (bottom)




M A N G I N

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.

A F O C A L

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.


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“Example script LENS_AFOCAL.INR (top) and plot (bottom)” shows an example of the AFOCAL command.

Example script LENS_AFOCAL.INR (top) and plot (bottom)




T E L E S C O P E

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.


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Magnification of the second element is negative. When using the FL/MAG/BWD option of the command, both FL and MAG values are negative.




“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)


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NOTE ASAP creates a one mirror telescope with a 40 mm radius of curvature (2xFL). The mirror conic constant is automatically set to -1 for a parabola that corrects spherical aberration.

Example LENS_TELESCOPE_SCHMIDT.INR




LENS_TELESCOPE_SCHMIDT.INR plot


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A detailed prescription of the telescope system can always be obtained using the PRINT command, as shown below.

Output for LENS_TELESCOPE_SCHMIDT.INR with the PRINT command

NOTE ASAP creates a mirror telescope with a 40 mm radius of curvature (2xFL). In this design, the mirror is concentric with the stop (the corrector plate). Such a configuration eliminates third-order coma, astigmatism, and distortion introduced by the mirror. The asphericity of the corrector plate corrects spherical aberration, and the mirror remains spherical with a zero conic constant.




Example LENS_TELESCOPE_CHRETIEN.INR (top) and plot (bottom)


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Output for LENS_TELESCOPE_CHRETIEN.INR with the PRINT command

NOTE ASAP creates a two-mirror telescope with a Cassegrain configuration. The radii of curvature of the primary and secondary mirrors are respectively 400 and 140 mm. The primary mirror obscuration is created automatically. Aberration control is done via the addition of conics on the two mirrors, which eliminates third-order spherical aberration and coma. This results in a Ritchey-Chrétien telescope design that is limited by astigmatism.

Example LENS_TELESCOPE_MAKSUTOV.INR




Example LENS_TELESCOPE_MAKSUTOV.INR plot

Output for LENS_TELESCOPE_MAKSUTOV.INR with the PRINT command


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NOTE In this example, ASAP creates a Maksutov-Cassegrain with two mirrors concentric with the stop. This location of the mirrors eliminates third-order coma, astigmatism, and distortion without the addition of conics on the mirror. However, ASAP always eliminates spherical aberration, which is why the two mirrors have conic constants that correct spherical aberration and coma.

Ent i ty Modi f iersAs mentioned earlier, two ASAP entity modifiers—EXPLODE and IMAGE—are closely related to lens entities. This section includes a brief description of the properties of these modifiers.

E X P L O D E

The EXPLODE command expands lens conicoids into separate SURFACE OBJECTS. By creating objects, it eliminates the need to add an OBJECT command. A common use of this command is to explode a lens sequence to create bounded elements, typically comprised of two surfaces plus a tube. Additional objects—like baffle, mounting, or edge surfaces that connect each coaxial lens surface—are also created when a sign precedes the entity number.

• A minus sign creates direct-sloped cones,

• A plus sign creates right cylinders.

• No sign creates only a series of separate surfaces.

The original lens is not deleted from the entity database and is, therefore, a duplicated entity.

The interfaces of refractive surfaces are automatically set to INTERFACE COATING BARE and SPLIT is automatically raised to level 1. Since the entities are no longer lenses but surfaces, the non-sequential nature of ASAP is re-established. This occurrence is why ray traces show rays that reflect on the surfaces and propagate in the opposite direction. “Example script LENS_EXPLODE_MINUS.INR (top) and plot (bottom)” on page 36 shows the EXPLODE command applied directly to the Cooke triplet, which was shown in “Example script LENS_SEQUENCE_SHORT01.INR (top) and plot (bottom)” on page 11.




Example script LENS_EXPLODE_MINUS.INR (top) and plot (bottom)


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LENS_EXPLODE_PLUS.INR (top) and plot (bottom)




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.

I M A G E

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.


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Example LENS_IMAGE02.INR




LENS_IMAGE02.INR plot

Optimizat ionA 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


. . .



emulated with some additional macro-language programming (for example, $ITER). As a minimum, this specific optimization feature can be used to quickly find (possibly unique) designs that may then be tweaked elsewhere, if necessary.

This optimization technique uses the ABERRATIONS, VARIABLES, and MINIMIZE commands.

A B E R R A T I O N S

The ABERRATIONS command displays the image aberrations of all the current lenses or conicoids. Since the analysis is valid only for centered lens systems, the conicoids must have a common axis. If not, the lens is temporarily “unfolded” to make it so.

The first-order operating data must be supplied with the additional entries, which are the data for the marginal axial ray from the center of the object through the edge of the limiting aperture stop, and the chief ray from the edge of the object to the center of this stop.

Surface-by-surface tables and plots can be produced for the paraxial marginal and chief ray traces, the Seidel primary and secondary aberrations, the real marginal and chief ray traces, and the glass and conicoid data.

The final 1st-order (primary color), 3rd-order, 5th-order, and selected 7th/9th-order aberration coefficients (in waves) are listed for actual stop plane coordinates relative to the ideal paraxial focus. These coefficients are computed using both analytical formulas and real-ray data matching.

The ABERRATIONS command can be followed by the VARIABLES and MINIMIZE commands, which are discussed next.

V A R I A B L E S

The VARIABLES command declares which lens construction parameters will be varied during optimization. The basic parameters are the thicknesses, curvatures, and conic constants on any set of conicoids listed after each variable.

Bending is a composite variable that changes the curvature of the given conicoid(s) while keeping constant the difference in curvatures between it and the next conicoid in the lens. This approximately fixes the power and focal length of the two adjacent conicoids, while allowing their aberration contributions to vary. It works with both glass elements and air spaces.




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.

M I N I M I Z E

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.


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Script OPTIMIZATION.INR

The plots resulting from the above script are shown below.




Plots from OPTIMIZATION.INR


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Tolerancing in ASAP

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The idea of tolerancing in ASAP is to see how much a specification can depart from the ideal without jeopardizing the overall design performance. This feature involves perturbing a specification, and looking at the effect on a figure of merit. The perturbation is repeated a sufficient number of times in a random manner, simulating the randomness associated with controlling the specification during a manufacturing process. The results can be displayed graphically, showing the fraction of acceptable results for the figure of merit from the series of random perturbations. Note that tolerancing is not the same as sensitivity analysis.

Tolerancing in the ASAP Bui lderFor each object (or group of objects) that is entered in the Builder, a dialog box for entering tolerance values is available by right-clicking a Builder cell in any column with a numeric field and selecting Tolerance Range from the list. The Tolerancing dialog displays the current tolerance values for the existing parameter.

Next, select the type of perturbation distribution to be used, Gaussian or uniform, and the range of the perturbation. If a figure of merit (FOM) is needed, you must define it in the Builder. Use the $GRAB macro to bring the FOM into the analysis. Otherwise, some other output can be viewed for each run of a perturbed variable.

Click the Builder’s Perturb button to add the FOM to the Perturb Options list, if an FOM is used. The tolerancing analysis is started by selecting OK in the Perturb

Options window. This setup procedure is shown in “Builder window showing Perturb Options and Tolerancing dialog boxes” on page 46.


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 in ASAP

The results of a tolerancing example, using an FOM, are presented below as a graph of the sequence of outputs.

Output viewed in the ASAP Chart Viewer

Tolerancing in ASAP scr iptsAs in the ASAP Builder, tolerancing in the ASAP Editor is a two-step process: First, you create a tolerance data file, and then perform the Monte Carlo analysis. These steps are outlined below.

S T E P 1 : C R E A T I N G A T O L E R A N C E D A T A F I L E

1 Open a new *.inx file. ASAP opens a new Editor window. If you open an existing

*.inr file, you must save the file as an *.inx file type to preserve the tolerance

data.

2 Enter ASAP commands in the Editor window. Before starting the Monte Carlo

analysis, define the Figure(s) of Merit (FOM). All FOMs must be placed at the

beginning of the *.inx file using the “!FOM1=” notation.

3 Assign tolerances to the desired parameters by surrounding each parameter

value with angle brackets, <parameter value >.

An example of a tolerancing (*.inx) file is shown below.



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


. . .


Tolerancing in ASAP

6 Enter tolerance data values for the applicable columns. Tolerance default values

are displayed for applicable columns.

7 Select Save on the File menu to save the tolerance data file. The tolerance data,

as well as the ASAP commands in the Editor window, are saved to an XML file

format (INX).

To display the Parameter Name for an ASAP command (or Object Name) that contains optional parameters, specify all parameters. For example, to assign a tolerance to the semi-width field of the OPTICAL command, enter the following script in the Editor:

OPTICAL Z 4 44.5 0 0 0 0 0 0 0 0 0 0 ELLIPSE <10>

S T E P 2 : P E R F O R M I N G M O N T E C A R L O A N A L Y S I S

1 Select the Perturb button on the Editor toolbar. The names displayed in the

Figure(s) of Merit box are the variables you defined at the top of the *.inx file.

Perturb Options dialog showing Figure(s) of Merit

2 ASAP performs an automatic Monte Carlo analysis. The numerical information is

displayed in the Command Output window and the GRAPH command produces

the tolerancing picture.



Tolerancing in ASAP

Command Output window showing numerical information


. . .


Tolerancing in ASAP

Chart produced by GRAPH command

S P E C I A L S Y N T A X R U L E S F O R T O L E R A N C I N G I N A S A P

S C R I P T S

If you are planning to use the ASAP Editor for tolerancing analysis, it is important to know and follow the special syntax rules in order to assure that your script is properly constructed. A discussion of these rules with examples follows.

The following commands can contain tolerancing values:

SINGLET, PLANE, BICONIC, ELLIPSOID, MEDIA, OPTICAL, TORUS, COATINGS/COATING, POINTS, SPHERICAL, PARABOLIC

A line containing one of these commands (SURFACE, LENSES, EDGES, ENT OBJECT and ENT OBJ) must be followed by another line containing a command that is allowable for tolerancing. For example,

SURFACE

PLANE Y <0>

Abbreviating command names or parameters is not supported, except for ENT OBJ and ENT OBJECT. For example, the ELLIPSE command is incorrectly abbreviated in the following syntax:



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 <LOC> 1 !! where LOC is a previously defined variable.

MEDIA; <2*1.4> ‘GLASS’

POINTS Z 0 <1> 1 1

0 2 1

1 3 1

3 3 1

4 2 1

3 1 1

PLANE <Z> 0 1

All commands must include all required and all optional parameters up to the toleranced parameter, so that the correct parameter names can be displayed. For example, to assign a tolerance to the semi-width field of the OPTICAL command, the following command script must be entered:

OPTICAL Z 4 44.5 0 0 0 0 0 0 0 0 0 0 ELLIPSE <10>

Do NOT add any spaces between the command and the semicolon (;).

Only one white space between a command and a toleranced parameter value is supported.

The MEDIA command must have one of the following forms:

MEDIA; <1.613> 'SK4'

MEDIA

<1.00> 'GLASS'

<1.30> 'MGFL2'

MEDIA;


. . .


Tolerancing in ASAP

<1.51> 'GLASS'; <1.38> 'MGFL2'

MEDIA <1.5> ‘GLASS’; <1.38> ‘MGFL2’

The COATING/COATINGS command must have one of the following forms:

COATINGS LAYERS <122.43>; 0 0 MGFL2 23.12 TI02 50.44 MGFL2 <16.33> TI02 'AR'

COATINGS LAYERS <122.43>

0 0 MGFL2 23.12 TI02 50.44 MGFL2 <16.33> TI02 'AR'

B R U T E F O R C E T O L E R A N C I N G U S I N G $ I T E R

We can also simulate the above tolerancing by using the $ITER command. An example of this approach can be found in the Example Scripts on the Quick Start toolbar, under the keyword “Tolerancing”.

Tolerancing using $ITER



Tolerancing in ASAP

Results of running example script for brute force tolerancing


Documents

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