Matlab Model Optics

Optical Design and Simulation Library

Use this skill when the user is working with the Optical Design and Simulation Library to build, import, analyze, tolerate, or optimize optical systems in MATLAB.

This library may also be referred to as:

• Optical Design and Simulation Library
• Optics Support Package
• Optics Add-On
• Optics Library
• Optics Toolbox

Use Optical Design and Simulation Library as the canonical name in responses unless the user explicitly uses a different name.

When to Use

Use this skill when the user asks about:

• Optical Systems
• Ray Tracing
• Geometric Optics based analysis like lens distortion, spot diagrams, chromatic aberration, astigmatism and ray fans
• Paraxial Optics
• Optical Coatings
• Polarization or EM analysis (computing Fresnel Coefficients)
• Glass Materials and Glass Catalogs
• Zemax import
• Optical Tolerancing
• Optical System Design and Optimization
• Dynamic optical systems in Simulink (see references/dynamic-optical-systems-simulink.md)

When NOT to Use

Do not use this skill when:

• The user is working with physical optics or wave optics (diffraction, interference, coherence)
• The user is working with fiber optics or photonics
• The user needs image processing or computer vision (use Image Processing Toolbox instead)
• The task is purely about Simulink modeling without optical system involvement

First Steps

When helping a user who is new to the library, start with discovery:

help optics

To get more details for a specific function:

help lensDistortion
doc lensDistortion

Many optics APIs are class methods. For class methods, use:

help className/functionName
doc className/functionName

Example:

help opticalSystem/add

Use examples in the documentation when the user asks for a larger end-to-end workflow.

Sample ZMX Files

The Optical Design and Simulation Library ships sample Zemax (.zmx) files in the opticsdata folder within the support package install location. To find the path:

spkgRoot = fullfile(matlabshared.supportpkg.getSupportPackageRoot, "toolbox", "images", "supportpackages", "opticsdata");
dir(fullfile(spkgRoot, "*.zmx"))

When a user asks to work with a standard optical system (e.g., "a Cooke triplet", "a doublet", "a telephoto lens") but does not provide their own file:

• List the available .zmx files in the opticsdata folder
• Pick the sample system that best matches the user's request
• Import it using zmximport

This avoids asking the user for a file path when a suitable sample already exists.

Core Concepts

opticalSystem

opticalSystem is the central object representing a physical optical system.

opsys = opticalSystem(Wavelengths=[486.134 587.562 656.281]);

opticalMaterial

opticalMaterial represents a glass or optical material.

mat = opticalMaterial([1.5168 64.17]);
mat = pickGlass("N-BK7");

opticalCoating

opticalCoating represents a thin-film coating applied to surfaces.

oc = opticalCoating(CoatingMaterial=["MgF2" "TiO2"], LayerMaterialIndex=[1 2 1 2], LayerThickness=[1 0.5 1 0.5], PrimaryWavelength=550);
oc = pickCoating("AR_MgF2_VIS");
addCoating(opsys, oc);
addCoating(opsys, oc, CoatingSide="front");

Coordinate Systems

Refer to the MATLAB Documentation page called "Coordinate Systems in Optical Design" to learn about the coordinate system conventions used to construct optical systems.

Field Point Angle Convention

When creating a field point with fieldPoint(Angles=[Hy Hx]):

• Hy — vertical field angle (degrees)
• Hx — horizontal field angle (degrees)

Example — a field point at 10 degrees vertical:

fp = fieldPoint(Angles=[10 0]);

A field point at 10 degrees horizontal:

fp = fieldPoint(Angles=[0 10]);

TiltAngles Convention

TiltAngles=[Rx Ry Rz] specifies rotations in degrees about each axis:

• Rx (first element) — rotation about the X-axis
• Ry (second element) — rotation about the Y-axis
• Rz (third element) — rotation about the Z-axis

Example — a mirror tilted 45 degrees about the X-axis:

addMirror(opsys, TiltAngles=[45 0 0]);

Common Interaction Patterns

Pattern: Build → Visualize → Analyze

Many user requests follow this sequence:

• Build or import an optical system
• Define field points and wavelengths
• Run an analysis function
• Inspect returned values
• Visualize results

%% 1. Build
opsys = opticalSystem(Wavelengths=587.562);
addRefractiveSurface(opsys, Radius=50, Material=pickGlass("N-BK7"), SemiDiameter=10, DistanceToNext=5);
addRefractiveSurface(opsys, Radius=-50, SemiDiameter=10, DistanceToNext=20);
addImagePlane(opsys, SemiDiameter=10);
opsys.FieldPoints = fieldPoint(Angles=[0 0; 10 0]);

%% 2. Visualize
h2 = view2d(opsys);

%% 3. Analyze
tra = rayAberration(opsys);
hra = show(tra);

Pattern: Compute → Show

Many analyses follow a compute first, visualize second pattern.

spotResult = spot(opsys);
spotDiagram(spotResult);

ldResult = lensDistortion(opsys);
show(ldResult);

Use this pattern when the user wants both a numeric result and a plot.

Pattern: Fresh Copy of Optical System

Explicitly create a fresh copy of the original system if you want to use it as a starting point for multiple different changes. This is particularly useful for tolerancing and sensitivity analysis, where parameters of the original system are mutated repeatedly.

newSys = copy(opsys);

This avoids accumulating perturbations across trials unless accumulation is explicitly intended.

Task: Construct Optical System from Prescription Table

Sequential optical systems are often specified as prescription tables (common in patent documents, textbooks, and optical design references).

Each row represents a surface or optical element, with columns such as:

• Radius of curvature
• Thickness to next surface
• Material (name or [nd, vd])
• Surface type (implicit or explicit, e.g., stop or image plane)

Users may provide this data as a screenshot, an Excel sheet, or a manually entered table.

Example Prescription Table (Explicit Stop Surface)

| Surface | Radius | Thickness | Material | Type |

|--------|--------|----------|----------|------|

| 1 | 50 | 5 | N-BK7 | Refractive |

| 2 | -50 | 5 | Air | Refractive |

| 3 | — | 5 | — | Stop |

| 4 | 40 | 5 | N-BK7 | Refractive |

| 5 | -40 | 20 | Air | Refractive |

| 6 | Inf | 0 | Image | ImagePlane |

Pattern: Table → Optical System

• Create opticalSystem
• Iterate over rows
• For each row:
• Refractive → addRefractiveSurface
• Stop → addDiaphragm
• ImagePlane → addImagePlane
• Use thickness as DistanceToNext for preceding element

Example Code

opsys = opticalSystem(Wavelengths=587.562);

% Surface 1
addRefractiveSurface(opsys, Radius=50, Material=pickGlass("N-BK7"), DistanceToNext=5);
% Surface 2
addRefractiveSurface(opsys, Radius=-50, DistanceToNext=5);
% Stop (explicit element)
addDiaphragm(opsys, DistanceToNext=5);
% Surface 4
addRefractiveSurface(opsys, Radius=40, Material=pickGlass("N-BK7"), DistanceToNext=5);
% Surface 5
addRefractiveSurface(opsys, Radius=-40,DistanceToNext=20);
% Image plane
addImagePlane(opsys);

h2initial = view2d(opsys, Parent=figure);

Update Semi Diameters of Surfaces

The semi-diameters of all the surfaces is set to the default value because the table does not provide this value. Instead, system descriptions usually provide a field of view (FOV).

Pattern: Set Semi-Diameters from Field of View

After building the optical system:

• Use the field of view to define the target field angle
• Identify the aperture constraint from the system description. See help updateSemiDiameters for valid constraint options.
• Call updateSemiDiameters to compute semi-diameters for all surfaces

FOV = 20;   % degrees
targetFieldAngle = FOV / 2;
updateSemiDiameters(opsys, "EntryPupilRadius", 5, TargetFieldAngle=targetFieldAngle);
h2Final = view2d(opsys, Parent=figure);

Task: Create systems using components

Users often build optical systems by combining off-the-shelf components (e.g., vendor-provided designs such as singlets, doublets, or lens groups).

This workflow involves:

• importing existing designs
• modifying system structure
• explicitly managing gaps between components

Pattern: Extend System with Component

• Load the components or systems that will be used to construct the base system
• Remove terminal components if needed (e.g., image plane)
• Explicitly update gaps as removing components does not update the gap
• Create the base system opticalSystem
• Add loaded components one by one to the base system and set the gap between components suitably

Example Code

% Load existing system
opsysCooke = zmximport("CookeTriplet.zmx");
% Step 1: Remove image plane (if present)
remove(opsysCooke);
% Step 2: Removing a component does NOT remove the gap. Zero out the trailing gap
changeGap(opsysCooke, numel(opsysCooke.Components), 0);

% Step 3: Import singlet component
opsysSinglet = zmximport("singlet.zmx");

% Step 4: Create a new optical System with these two
opsys = opticalSystem(Name="Combined System");
add(opsys, opsysCooke);
changeGap(opsys, numel(opsys.Components), 3, GapLocation="after");

% Step 4: Append singlet to system
add(opsys, opsysSinglet);

h2 = view2d(opsys);

Task: Add Mirrors or Folded Geometry

Use addMirror when the user wants to model reflective systems.

Example: Periscope system with mirrors at 45 degrees

This periscope folds the beam in the Y-Z plane using X-axis rotations:

opsys = opticalSystem();
addMirror(opsys, Radius=0, SemiDiameter=10, TiltAngles=[45 0 0]);
addGap(opsys, 50);
addMirror(opsys, Radius=0, SemiDiameter=10, TiltAngles=[-45 0 0]);
addGap(opsys, 20);
addImagePlane(opsys, SemiDiameter=10);

h = view2d(opsys);
addRays(h);

To fold in the X-Z plane instead, use Y-axis rotations: TiltAngles=[0 45 0].

Task: Use Ray Data

Use this when the analysis user is looking for is not available out of the box and the user has to derive it themselves using the RayData that is available as part of the RayBundle.

Pattern — plot incident angles on a specific surface using pupil coordinates:

% Import a Cooke triplet
opsys = zmximport("CookeTriplet.zmx");

% Trace from 10-degree field point with incident angle data
fp = fieldPoint(Angles=[10 0]);
sg = samplingGrid("Hexapolar", 8);
rb = traceRays(opsys, FieldPoints=fp, Wavelengths=587.562, SamplingGrid=sg, RayProperties="IncidentAngle");
rd = rb(1).RayData;

% OrientedGrid gives normalized pupil XY for each ray
xy = rd.OrientedGrid;
% Incident angles on surface 4
angles = rd.IncidentAngle(:, 4);

% Scatter plot: position from pupil grid, size and color from angle
figure;
scatter(xy(:,1), xy(:,2), abs(angles)*5, angles, 'filled');
colorbar;
xlabel("Pupil X"); ylabel("Pupil Y");
title("Incident Angle on Surface 4 — Field Angle 10°");
axis equal;

Task: Optimize a Design

Use design optimization when the user wants to improve performance starting from an initial optical system. See references/optical-system-design.md for detailed patterns, code templates, and optimizer selection guidance.

General workflow:

• Define an initial optical system
• Pack design variables (radii, thicknesses, materials, gaps) into a numeric vector
• Create a helper function (x2opsys) to convert the vector back to an opticalSystem
• Define a merit function using weighted performance metrics (focal length, spot RMS, track length)
• Run a bounded optimizer (lsqnonlin for multi-objective, fmincon for scalar)
• Reconstruct the optimized system and verify with paraxialInfo, spot, and view2d

Always call updateSemiDiameters inside the parameter-to-system conversion to maintain the aperture constraint after every parameter change.

Task: Optical Coating Design

Use this when the user wants to design, analyze, or optimize thin-film optical coatings (AR coatings, bandpass filters, longpass/shortpass filters, notch filters). See references/optical-coating-design.md for detailed patterns and optimization templates.

General workflow:

• Define coating materials using pickCoatingMaterial
• Specify layer structure via LayerMaterialIndex (alternating high/low index)
• Create the coating with opticalCoating and layer thicknesses
• Query spectral response with fresnelCoefficients
• For optimization: pack thicknesses into a vector, define spectral band goals, run a bounded optimizer

Key functions:

• pickCoatingMaterial("SiO2") — load a coating material
• opticalCoating(...) — create multi-layer coating
• fresnelCoefficients(oc, Wavelengths=..., IncidentAngles=...) — compute transmittance/reflectance
• Access fq.Ta (total transmittance), fq.Ra (total reflectance), or polarization-resolved properties

Task: Optical Coating Tolerancing

Use this when the user wants to evaluate manufacturing sensitivity or yield of a coating design. See references/optical-coating-tolerance.md for detailed patterns and Monte Carlo templates.

General workflow:

• Define the nominal coating design
• Specify manufacturing tolerances (thickness sigma per material, refractive index sigma)
• Choose analysis type:
• Sensitivity: perturb each layer individually, measure impact on performance
• Monte Carlo yield: run N randomized trials with Gaussian perturbations, compute pass rate
• Evaluate each sample against a pass/fail spec using fresnelCoefficients
• Compute yield percentage and visualize tolerance envelope

Key considerations:

• Use parfor for Monte Carlo trials (each trial is independent)
• Model thickness and refractive index variations as independent Gaussian perturbations
• Material-specific sigma values (high-index materials typically have larger variability)
• 400+ trials for reliable yield estimates; 1000+ for final qualification

Additional Notes

• imref2d can be useful when converting physical locations on a 2D plane into pixel locations.
• For dynamic optical systems in Simulink, see references/dynamic-optical-systems-simulink.md

Embedding view3d / view2d in UI Apps

When placing view3d or view2d inside a uifigure layout, use a uigridlayout (not a uipanel) as the parent so the viewer chart fills the available space:

gl = uigridlayout(parentContainer, [1 1], Padding=[0 0 0 0]);
osv3d = view3d(opsys, Parent=gl);

Chart objects auto-stretch to fill grid layout cells but do not auto-resize inside plain uipanel containers.

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