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Manual

  • Provisional Manual
    • Installation And Prerequisites
      • Basic installation paths
      • Running the layout editor
      • Manual source
    • Core Model: Surfaces And Systems
      • Surface attributes
      • System methods and state
      • Glass catalogs
    • Classes and Attributes
      • Table 1 — surf class attributes
      • Table 2 — system class implementations and attributes
    • Working with the KrakenOS Library
      • 3.1 Ray generation
      • 3.2 Extraction of ray information
      • 3.3 Generation of the optical system graph
        • Raykeeper introspection
    • Parax Tool
    • PupilCalc Tool
      • Pupil parameters
      • Automatic ray generation
      • 5.1 Atmospheric refraction in PupilCalc
    • Pupil Patterns (Source Model: Pupil / field)
      • 2D Pattern Versus 3D Scene Launch
      • Meridional fan
      • Cross fan
      • Fan X
      • Fan Y
      • Hexapolar
      • Square
      • Random disk
      • Chief ray
      • R-theta
      • Summary
    • Analysis Tools (Layout Editor Toolbar)
      • Symbol conventions
      • Shared setup for the code examples
      • Using analyses as optimization targets
        • Why each analysis matters and when to target it
        • Conflicting objectives — what you give up
        • Worked case studies: from a poor start to best
      • Geometric image quality
        • Spot — Spot Diagram
        • RMS — RMS Spot Radius
        • PSF — Point Spread Function
        • MTF — Modulation Transfer Function
      • Pupil and wavefront
        • Pupil — Pupil Diagnostic
        • Seidel — Seidel Aberrations
        • WFront — Wavefront Analysis
        • Zernike — Zernike Polynomial Fit
      • Field-dependent metrics
        • FC/Dist — Field Curvature / Distortion
        • Illum — Relative Illumination
        • LatClr — Lateral Color
        • Pol — Polarization
        • Atmos — Atmospheric Dispersion
      • Map analyses on the detector / pupil
        • PSFMap — Point Spread Function Map
        • FldMap — Field Map
        • IllMap — Illumination Map
        • WfeMap — Wavefront Error Map
        • DetMap — Detector Power Map
        • CohDet — Coherent Detector Field Sum
        • BField — Branch Field
        • Diffr — Diffraction Detector
      • Comparative analyses
        • Interf — Interferogram
        • TolCmp — Tolerance Compare
      • Cross-reference table
    • Captured USAF-1951 MTF
      • Method
      • Python API
      • Command line
      • Measurement limits
    • Editable Table Workflow
      • Loading versus inserting
      • Insertion point
      • Surface and element clipboard
      • Surface right-click menu
      • Compact prescription columns
      • Optimization cell marker
      • Tolerance Monte Carlo report
      • Prisms and cube beam splitters
      • Tilt and decenter tolerance overlays
      • Validation
    • Non-Sequential-First Design Goals
      • Goal 1: non-sequential tracing is the native model
      • Goal 2: 3D tracing is authoritative; 2D is only a slice
      • Goal 3: object and illumination source are separate scene entities
      • Goal 4: every surface interaction obeys physics law
      • Implementation checklist
    • Tracing And Ray Data
      • Scene-first UI model
      • 2D slices, 3D scenes, and CAD envelopes
      • Sequential tracing special case
      • Non-sequential tracing
      • Scene source records
      • Launch sampling metadata
      • Scene target records
      • Possible next scene workflows
      • Optical STL prism check
      • Face-role metadata check
      • Face-anchor snap-to-ray check
      • Face-fit placement check
      • Path-frame face-fit check
      • Virtual internal plane check
      • Optical-solid hit-sequence check
      • Raykeeper data
      • Inspect Ray / Surface Physics
      • Multicore and batch tracing
    • Zemax Rayfile Sources
      • Import workflow
      • Ray sampling
      • Example saved layout source record
      • Validation
      • Current limitations
      • Beam-splitter imaging example
    • Pupil, Paraxial, And Analysis Tools
      • Paraxial tool
      • PupilCalc
      • Atmospheric refraction
      • Wavefront and aberration tools
        • Zemax Wavefront Map comparison
      • Image-quality maps
    • Gaussian Beam Propagation
      • Beam fundamentals
      • Complex beam parameter and ABCD transformation
      • Input conventions
      • Datasheet diameter/divergence flow
      • Report columns
      • Astigmatic and elliptical beams
      • Phase 8 branch-field propagation
      • Phase 8B oblique astigmatic q baseline
      • Cavity eigenmode flow
      • UI workflow
      • Folded laser scanner example
      • Python example
      • Scope and limitations
      • Source-mode field relevance
    • Beam Splitters
      • Terminology
      • Current capability
      • Split modes
      • UI workflow
      • Path workflow tutorial
      • Two-path doublet example
      • Manual path assignment
      • Path Workbench workflow
      • Separate source and object status
        • Right-angle illumination example
      • Michelson detector/interferogram workflow
      • Twyman-Green example
      • Mach-Zehnder example
      • Automatic path graph
      • Saved metadata
      • Python example
      • Internal branch data
      • Path throughput report
      • Path-filtered detector analyses
        • Concrete DetMap examples
        • Path-analysis validation fixture
      • Phase 2 source and path workflow
      • Resizing a cube beam splitter (coupled cross-section)
        • Recovering the 45° coating as a selectable face
      • Future tilted/folded/non-sequential Gaussian optics
    • Diffuse And BRDF Scattering
      • Surface Type
      • Guided Target Sampling
      • Examples
      • pySCATMECH Optional Backend
    • Lens Fabrication Drawings
      • Surface Property Workflow
      • Supported Fields
      • Example In A Layout File
      • Reference Behaviour
    • Display And Viewers
      • 2D display
        • Lens drawing PDF export
      • 3D display
      • CAD/STL optical solids
        • Placement workflow
      • STEP and CAD overlays
    • Handling the 3D Viewer
    • Quick Estimation (object / image / FOV)
      • The design flow
      • Two readings of the same move
      • Right-click actions
      • Graphical FOV solve (double-click a plane)
      • Variable-thickness solve (Best Focus / Best Collimation)
      • Sensor coverage and recommended sensor
      • Forbidden values
      • Validation
    • Responsive STEP Handling Architecture
      • Problem Statement
      • Current Kraken Bottleneck
      • What CadQuery Shows
      • Target Architecture
      • Interaction Rules
      • Expected Improvement
      • Implementation Plan
      • Recommended Immediate Next Step
    • Manual Example Inventory
    • Appendix — Examples
      • 7.1 Example — Ray
      • 7.2 Example — Perfect Lens
      • 7.3 Example — Doublet Lens 3D Color
      • 7.4 Example — Doublet Lens Tilt
      • 7.5 Example — Doublet Lens (Paraxial Calculations)
      • 7.6 Example — Doublet Lens Tilt Nulls
      • 7.7 Example — Doublet Lens NonSec
      • 7.8 Example — Doublet Lens Zernike
      • 7.9 Example — Doublet Lens Tilt NonSec
      • 7.10 Example — Doublet Lens Pupil
      • 7.11 Example — Doublet Lens Commands System
      • 7.12 Example — Doublet Lens Pupil + Seidel
      • 7.13 Example — Doublet Lens Cylinder
      • 7.14 Example — Axicon
      • 7.15 Example — Axicon and Cylinder
      • 7.16 Example — Flat Mirror 45 Deg
      • 7.17 Example — Parabolic Mirror Shift
      • 7.18 Example — Diffraction Grating in Transmission
      • 7.19 Example — Diffraction Grating in Reflection
      • 7.20 Example — Tel 2M Spyder Spot Diagram
      • 7.21 Example — Tel 2M Spyder Spot, M2 Tilt
      • 7.22 Example — Tel 2M Pupila
      • 7.23 Example — Tel 2M Error Map
      • 7.24 Example — Tel 2M Wavefront Fitting
      • 7.25 Example — Tel 2M STL Image Slicer
      • 7.26 Example — Tel 2M Atmospheric-Refraction Corrector
      • 7.27 Example — ExtraShape Micro Lens Array
      • 7.28 Example — ExtraShape Radial Sine
      • 7.29 Example — ExtraShape XY Cosines
      • 7.30 Example — MultiCore
      • 7.31 Example — Solid Objects STL Array
      • 7.32 Example — Source Distribution Function
    • References

Tutorials

  • Tutorials And Case Studies
    • Case Study 1: Turn A Glass Plate Into A 100 mm PCX Lens
      • Goal
      • Build The Starting Plate
      • Make The Front Surface Variable
      • Set The EFFL Target
      • Place The Image Plane Correctly
        • Workflow A: solve image distance after EFFL
        • Workflow B: optimize EFFL and focus together
      • What The User Should See
      • Common Mistakes
    • Case Study 2: Focus A Finite Machine-Vision Lens
      • Goal
      • Load The Finite Lens
      • Make A Bad First Analysis
      • Choose The Right Variable
      • Run The Focus Solve
        • Workflow A: best-focus solve
        • Workflow B: general optimizer
      • Verify The Improvement
      • Check The Wide Field
      • What This Proves
      • Common Mistakes
    • Case Study 3: PYRITE 85 mm Machine-Vision Surrogate
      • What The Surrogate Is
      • Vendor STEP Overlay
      • Default UI Settings
      • How The Blackbox Is Built
      • Rendered Layout
      • Known Limits
      • Validation
    • Case Study 4: AZURE ELS-85 mm Machine-Vision Surrogate
      • What The Surrogate Is
      • Vendor STEP Overlay
      • Default UI Settings
      • How The Blackbox Is Built
      • Rendered Layout
      • Known Limits
      • Validation
    • Case Study 4b: AZURE ELS-85 mm On A Right-Angle Mirror
      • A Promoted STEP Mirror, Not A Sequential Mirror Row
      • The Conjugate And Prescription
      • What Is In The Layout
      • Rendered Layout
      • Validation
    • Case Study 4: PYRITE 120 mm Machine-Vision Surrogate
      • What The Surrogate Is
      • Vendor STEP Overlay
      • Default UI Settings
      • How The Blackbox Is Built
      • Rendered Layout
      • Known Limits
      • Validation
    • Case Study 5: Gaussian Laser Beam Expander
      • Goal
      • Load The Laser Line
      • Back-Calculated Waist
      • Insert A 3x Keplerian Expander
      • Verify The Expanded Beam
      • Run BField Analysis
      • What This Proves
      • Common Mistakes
    • Case Study 6: Michelson Beam Splitter And Interferogram
      • Goal
      • Load The Michelson Layout
      • Read The Path Labels
      • Use Path View
      • Run Detector Analyses
      • Show The Interferogram
      • Run Branch Field
      • What This Proves
      • Common Mistakes
    • Case Study 7: Mach-Zehnder Two-Output Interferometer
      • Goal
      • Load The Mach-Zehnder Layout
      • Read The Path Labels
      • Use Path View For Each Output
      • Run Detector Analyses
      • Show The Interferogram
      • Run Branch Field
      • Check The Return Output
      • What This Proves
      • Common Mistakes
    • Case Study 8: Source/Object Split Through A Beam Splitter
      • Goal
      • Load The Layout
      • Read The Physical Paths
      • Use Path View
      • Audit Source Illumination
      • Run The Camera Detector Map
      • Run The Python Example
      • What This Proves
      • Common Mistakes
    • Case Study 9: Zemax LED Source To Diffuse Object Imaging
      • Goal
      • Load The Layout
      • Read The Scatter Paths
      • Use Path View
      • Inspect Diffuse / BRDF Settings
      • Audit Source Illumination
      • Run Image-Plane Analyses
      • Run The Python Example
      • What This Proves
      • Common Mistakes
    • Case Study 10: Multi-Source Illumination
      • Goal
      • Load The Layout
      • Read The Layout
      • Inspect Scene Sources
      • Audit Per-Source Throughput
      • Run Detector Analyses
      • Run The Python Example
      • What This Proves
      • Common Mistakes
    • Case Study 11: Tolerance Monte Carlo And Compensators
      • Goal
      • Load The Native-Variable Layout
      • Choose Tolerance Roles
      • Run Monte Carlo
      • Compare The Worst Sample
      • Plot The Worst-Sample Spot Overlay
      • Read The Stack-Up Bars
      • Run Compensator Sweeps
      • Check MTF Impact
      • Run The Python Example
      • What This Proves
      • Common Mistakes
    • Case Study 12: Optical STL Prism And Face Roles
      • Goal
      • Load The Optical STL Prism
      • Read The 2D Trace
      • Assign Optical Faces
      • Inspect Mesh Readiness
      • Verify The Trace Sequence
      • Run The Python Examples And Validators
      • What This Proves
      • Common Mistakes
    • Case Study 13: Cube Beam Splitter CAD And Virtual Plane
      • Goal
      • Load Or Import The Cube Body
      • Observe The Passive CAD Trace
      • Assign External Faces And Build A Virtual Plane
      • Read The Virtual Plane Report
      • Use The Primitive For Splitter Physics Today
      • Check Mesh Readiness
      • Run The Validators
      • What This Proves
      • Common Mistakes
    • Case Study 14: Vendor Prism CAD Import And Face Placement
      • Goal
      • Bundled Vendor Files
      • Load The Vendor CAD Prism
      • Set Source Divergence
      • Inspect The Converted Mesh
      • Assign Optical Face Roles
      • Understand Side Labels, Axis Fits, And Optical Functions
        • Examples From penta.py
      • Orient From The Input Face
      • Off-Center Entrance Points
      • Read The Fitted Layout
      • Chain Another Prism After A Folded Path
      • Roll Reference Faces
      • Single-Face Fold Mirrors
      • Run The Validators
      • What This Proves
      • Common Mistakes
    • Case Study 15: Multi-Element Lens PDF Drawing Export
      • Goal
      • Input The Surface Table
      • Input Drawing Properties
      • Export The PDF
      • Run The Validator
      • What This Proves
      • Important Limitation
    • Case Study 16: 3D Hardware Alignment Workflows
      • Goal
      • Open The 3D Inspector
      • Use The CAD/STL Placement Handler
      • Read Active-Mode Badges
      • Rotate Imported STEP Hardware
      • Carry Imported STEP Freely
      • Pick Source Targets From 3D
      • What This Proves
      • Common Mistakes
    • Case Study 17: Cooke Triplet Optimization From A Bad Start
      • Goal
      • Load The Poor Triplet
      • Make The Bad Analysis
      • Understand The Variables
      • Apply The Optimized Prescription
      • Verify The Improvement
      • What This Proves
      • Common Mistakes
    • Case Study 18: One Lens, Many Analyses
      • Goal
      • Load The Analysis Layout
      • Spot: Check Geometric Focus
      • PSF: Convert Samples Into Image Intensity
      • MTF: Read Contrast Versus Spatial Frequency
      • Wavefront: Inspect Pupil Phase
      • Zernike: Decompose The Wavefront
      • What This Proves
    • Case Study 19: Galvo F-Theta Laser Scanner
      • Goal
      • Load The Preset
      • Read The Rows
      • Use The Galvo Scan Overlay
      • Check The Scan Plane
      • Validate The F-Theta Lens Alone
      • Why This Is Non-Sequential-First
      • Common Checks
      • What This Proves
    • Optiland-Inspired Case Study Port Backlog
      • Purpose
      • Already Covered In Current KrakenOS UI Docs
      • High-Value Ports
      • Deferred Or Research-Oriented Ports
      • Recommended Next Port

Knowledge Base

  • Knowledge Base
    • Rules of Thumb — Optics, Imaging, Laser
      • How to use this page
      • Section 1 — Geometric / paraxial optics
        • 1.1 Thin-lens imaging equation
        • 1.2 f-number, aperture cone and diffraction limit
        • 1.3 Working f-number for finite conjugates
        • 1.4 Two thin lenses in series
        • 1.5 Macro 2f rule (1:1 imaging)
        • 1.6 Snell’s law and total internal reflection
      • Section 2 — Imaging system rules
        • 2.1 Angle of view and sensor format
        • 2.2 Depth of field
        • 2.3 Hyperfocal distance
        • 2.4 Diffraction & resolution
        • 2.5 Pixel sampling and the Nyquist limit
      • Section 3 — Lasers and Gaussian beams
        • 3.1 Waist, Rayleigh range, divergence
        • 3.2 Focused spot of a Gaussian beam
        • 3.3 Two-mirror cavity stability
        • 3.4 Power density and damage
        • 3.5 Coherence and bandwidth
      • Section 4 — Cross-cutting design heuristics
      • Section 5 — Where to go next
    • Finding the Cardinal Points and Pupils by Ray Tracing
      • Drawing conventions
      • 1. The six cardinal points
      • 2. Locating \(F'\) and \(P'\)
      • 3. Locating \(F\) and \(P\)
      • 4. Nodal points \(N, N'\)
      • 5. Aperture stop, EP and XP
      • 6. Chief and marginal rays — the operational definition
      • 7. Putting it all together
    • Pupil Sampling — A Lecture on Where the Rays Go
      • 1. What makes a sampler “good”?
      • 2. The equal-area mapping
      • 3. Section fans — when one dimension is enough
      • 4. Hexapolar — equal-area rings
      • 5. Square grid — when the detector decides
      • 6. Random disk — the Monte-Carlo baseline
      • 7. The Vogel / golden-angle spiral
        • Definition
        • Why the golden angle?
        • Why optical designers care
      • 8. From disk to hemisphere — Lambertian and lobe scattering
      • 9. KrakenOS code map
      • 10. Choosing in practice
      • Further reading
    • Introduction To Fundamental Lens Design
      • Why “Lens Families” Exist
      • Photographic Lens Families
        • The Double Gauss
        • Tessar
        • Sonnar
        • Cooke Triplet
        • Retrofocus (Inverted Telephoto)
        • Telephoto
        • Petzval
        • Modern Aspheric / Floating-Element Designs
        • Photographic Family Summary
      • Machine Vision Lens Families
        • Fixed-Focal-Length (FFL) Industrial Lenses
        • Retrofocus On Large Sensors
        • Telecentric Lenses
        • Fixed-Magnification Macro / Inspection Lenses
        • Line-Scan Lenses
        • Spectrally Specialized Lenses
        • Machine Vision Family Summary
      • Photography vs. Machine Vision: Side by Side
      • Reading A Prescription In KrakenOS
      • Further Reading
    • Deriving the Axially Symmetric Aberration Polynomial
      • Geometry and convention
      • Why this is the complete starting point
      • First-order terms
      • Third order: the five Seidel terms
      • Fifth order: constructing every allowed angular term
      • The displayed seventh-order term
      • The assembled equations
      • Sanity checks
      • Using the polynomial with KrakenOS
    • Sub-Pixel Hot-Spot Detection in IR Imaging
      • The mixing model
      • A worked numerical example
      • Why visible-light imaging cannot pull this trick
      • The PSF assist
      • What can break the claim
      • Bottom line: detection vs. characterization
    • Machine-Vision Camera and Lens EOL Qualification
      • Camera Replacement Qualification
        • Objectives and release criteria
        • Required equipment and fixtures
        • Camera test summary
        • Detailed experiments and pass/fail rules
        • Camera report checklist
      • Lens Replacement Qualification
        • Objectives and release criteria
        • Required equipment and fixtures
        • Lens test summary
        • Detailed experiments and pass/fail rules
        • Lens report checklist
      • Decision principles
      • Roles and controlled records
      • Define requirements and budgets
      • Baseline, samples, and comparison configurations
        • Baseline selection
        • Minimum comparison matrix
        • Sampling plan
      • Common test setup and conditions
        • Controlled optical bench
        • Default laboratory controls
      • Acceptance model
      • Qualification stages and release gates
      • Special diagnostic: apparent colour aberration after pixel-size change
      • Data package and expected outputs
      • Reference methods
    • Laser Design Engineer Interview Guide
      • What an interviewer is testing
      • Recommended preparation order
        • Role-Specific Interview Playbook
        • DUV Laser Integration and Qualification
        • Laser Theory Essentials
        • Resonators and Gaussian Beams
        • Solid-State Laser Design
        • Diode-Pumped Solid-State Laser Engineering
        • Beam Quality: Specify, Measure, and Interpret
        • Laser-Induced Damage Engineering
        • Hands-On Alignment, Measurement, and Debugging
        • Worked Interview Design Case
        • Interview Questions and Answer Frameworks
        • Source Map and Further Reading
    • STEP Overlay Promotion — Tiers and 2D/3D Parity
      • Why three tiers
        • Tier 1 — STEP overlay
        • Tier 2 — STL optical-solid row
        • Tier 3 — Native analytic rows
        • Saved Tier 2 rows with a source STEP path
      • Flipping a Tier-3 lens: why it’s not a rotation
      • 2D ↔ 3D row-action parity
      • Handle eligibility — the predicate that gates the rotation rings
      • Validation contract
      • Slide along the optical axis
      • Resizing an imported solid (drag a face)
      • Off-beam promoted solids are display-only
      • Diagnosing “my promoted lens does not refract”
      • Known follow-ups
    • Folded Coaxial Illumination — Projection Physics and the MV-150
      • Keep these five quantities separate
      • General rule for an ideal planar fold
        • Derivation by normal and tangential components
      • Case 1 — underfilled square bundle
      • Case 2 — underfilled circular bundle
      • Case 3 — overfilled square bundle
      • Case 4 — overfilled circular bundle
      • External and internal reflection
      • The actual MV-150 beam-splitter geometry
      • Reported physical MV-150 camera result — approximately 35 × 39 mm bright
      • What the latest full KrakenOS recording shows—and does not show
      • The MV-150 source is Lambertian, not collimated
      • How to predict dark edges generally
      • KrakenOS descriptor semantics and the legacy MV-150 approximation

Worked Exercise Solutions

  • Worked Exercise Solutions
    • Understanding Lasers
      • Understanding Lasers: Chapter 1 Quiz
        • Source
        • Quick answers
        • 1. Where the word laser came from
        • 2. The incorrect statement about light
        • 3. The most common lasers
        • 4. The emission process used by a laser
        • 5. The active emitter in ruby
        • 6. Why the name diode laser is used
        • 7. Heat from a 1%-efficient laser
        • 8. Heat from a 25%-efficient laser
        • 9. The result of a stable phase relationship
        • 10. Personal laser inventory
        • What this quiz established
      • Understanding Lasers: Chapter 2 Quiz
        • Quick answers
        • Worked reasoning
      • Understanding Lasers: Chapter 3 Quiz
        • Quick answers
        • Worked reasoning
      • Understanding Lasers: Chapter 4 Quiz
        • Quick answers
        • Worked reasoning
      • Understanding Lasers: Chapter 5 Quiz
        • Quick answers
        • Worked reasoning
      • Understanding Lasers: Chapter 6 Quiz
        • Quick answers
        • Worked reasoning
      • Understanding Lasers: Chapter 7 Quiz
        • Quick answers
        • Worked reasoning
      • Understanding Lasers: Chapter 8 Quiz
        • Quick answers
        • Worked reasoning
      • Understanding Lasers: Chapter 9 Quiz
        • Quick answers
        • Worked reasoning
      • Understanding Lasers: Chapter 10 Quiz
        • Quick answers
        • Worked reasoning
      • Understanding Lasers: Chapter 11 Quiz
        • Quick answers
        • Worked reasoning
      • Understanding Lasers: Chapter 12 Quiz
        • Quick answers
        • Worked reasoning
      • Understanding Lasers: Chapter 13 Quiz
        • Quick answers
        • Worked reasoning
      • Understanding Lasers: Chapter 14 Quiz
        • Quick answers
        • Worked reasoning
    • Introduction to Laser Diode-Pumped Solid State Lasers
      • Chapter 3: Pump, Rod, and Resonator Design
        • The energy-to-power conversion
        • Two 40 W end-pump arrays
        • Scheps Section 3.2.2: laser-rod specifications
        • Brewster-angle resonator: does the output power fall?
        • Local references for this design choice
        • Meaning of low threshold and high slope efficiency
        • Scaling rules
    • Photonics Essentials: Worked Problems
      • Photonics Essentials: From Diffusion Current to Equation 3.5
        • Source
        • Question
        • The small-slab picture
        • Step 1: A concentration gradient produces diffusion
        • Step 2: Apply carrier conservation to a thin slab
        • Step 3: Add generation and recombination
        • Step 4: Substitute the diffusion current
        • Why it is second order
        • Unit check
        • Steady-state Equation 3.6
        • Source correction
        • Continue interactively
      • Photonics Essentials: Detector Operating Modes and Camera Pixels
        • Source
        • The two modes in Section 3.3
        • Why photovoltage is nonlinear
        • What mode does a camera pixel use?
        • CMOS and CCD readout
        • Where camera response becomes nonlinear
        • Continue interactively
      • Photonics Essentials: Chapter 3 Interactive Physics Lab
        • Interactive curve explorer
        • Curves and equations
        • Python physics engine
        • Live Jupyter kernel
        • Silicon absorption with and without surface reflection
        • Silicon slab and 1100 nm LED
      • Photonics Essentials: Chapter 2 Problems
        • Source
        • Quick results
        • Worked solutions
      • Photonics Essentials: Chapter 3 Problems
        • Source
        • Quick results
        • Worked solutions
      • Photonics Essentials: Chapter 4 Problems
        • Source
        • Worked solutions
      • Photonics Essentials: Chapter 5 Problems
        • Source
        • Worked solutions
      • Photonics Essentials: Chapter 6 Problems
        • Source
        • Worked solutions
      • Photonics Essentials: Chapter 7 Problems
        • Source
        • Worked solutions
      • Photonics Essentials: Chapter 8 Problems
        • Source
        • Worked solutions
      • Photonics Essentials: Chapter 9 Problems
        • Source
        • Worked solutions
      • Photonics Essentials: Chapter 10 Problems
        • Source
        • Worked solutions
      • Photonics Essentials: Chapter 11 Questions
        • Source
        • Why does laser spectrum depend on current?
        • How does slit width affect mode resolution?
        • How would a calibrated detector array help?
    • Fundamentals of Photonics
      • Mathematical Formula Reference
        • Algebra and dimensional checks
        • Product, quotient, and chain rules
        • Stationary-value condition
        • Optical path and Fermat’s principle
        • Trigonometry and small-angle formulas
        • Solid angle and circular cones
        • Exponentials, logarithms, and complex phasors
        • Integration identities
        • Fourier transform, convolution, and correlation
        • Matrices, determinants, and eigenvalues
        • Vector-calculus identities
        • Common differential equations
        • Probability, expectation, and variance
        • Power, intensity, and decibels
        • Verification methods
      • KrakenOS Formula and Code Map
        • How to read the map
        • Coverage by chapter
        • Chapter 1: ray optics
        • Chapters 2 and 3: waves, gratings, and Gaussian beams
        • Chapter 4: Fourier optics and image quality
        • Chapters 5 and 6: materials and polarization
        • Chapters 10 and 18: cavity and detector helpers
        • Reverse audit: KrakenOS code outside this textbook
        • A short code-to-book workflow
        • Limits of this cross-reference
      • Part I — Fundamentals
        • Chapter 1: Ray Optics
        • Chapter 2: Wave Optics
        • Chapter 3: Beam Optics
        • Chapter 4: Fourier Optics
        • Chapter 5: Electromagnetic Optics
        • Chapter 6: Polarization Optics
      • Part II — Wave Propagation
        • Chapter 7: Photonic-Crystal Optics
        • Chapter 8: Guided-Wave Optics
        • Chapter 9: Fiber Optics
        • Chapter 10: Resonator Optics
        • Chapter 11: Statistical Optics
        • Chapter 12: Photon Optics
      • Part III — Laser Optics
        • Chapter 13: Photons and Atoms
        • Chapter 14: Laser Amplifiers
        • Chapter 15: Lasers
      • Part IV — Optoelectronics
        • Chapter 16: Semiconductor Optics
        • Chapter 17: Semiconductor Photon Sources
        • Chapter 18: Semiconductor Photon Detectors
      • Part V — Lightwave Devices
        • Chapter 19: Acousto-Optics
        • Chapter 20: Electro-Optics
        • Chapter 21: Nonlinear Optics
        • Chapter 22: Ultrafast Optics
      • Part VI — Lightwave Systems
        • Chapter 23: Optical Interconnects and Switches
        • Chapter 24: Optical Fiber Communications
    • Optics, Fifth Edition — Worked Exercise Solutions
      • Foundations
        • Chapter 1: Prolegomenon
        • Chapter 2: Wave Motion
        • Chapter 3: Electromagnetic Theory, Photons, and Light
        • Chapter 4: The Propagation of Light
      • Geometrical and wave optics
        • Chapter 5: Geometrical Optics
        • Chapter 6: More on Geometrical Optics
        • Chapter 7: The Superposition of Waves
        • Chapter 8: Polarization
      • Interference, imaging, and modern optics
        • Chapter 9: Interference
        • Chapter 10: Diffraction
        • Chapter 11: Fourier Optics
        • Chapter 12: Basics of Coherence Theory
        • Chapter 13: Modern Optics: Lasers and Other Topics
    • Siegman’s Lasers — Worked Exercise Solutions
      • Basic laser physics
        • Chapter 1: An Introduction to Lasers
        • Chapter 2: Stimulated Transitions: The Classical Oscillator Model
        • Chapter 3: Electric Dipole Transitions in Real Atoms
        • Chapter 4: Atomic Rate Equations
        • Chapter 5: The Rabi Frequency
        • Chapter 6: Laser Pumping and Population Inversion
        • Chapter 7: Laser Amplification
        • Chapter 8: More on Laser Amplification
        • Chapter 9: Linear Pulse Propagation
        • Chapter 10: Nonlinear Optical Pulse Propagation
        • Chapter 11: Laser Mirrors and Regenerative Feedback
        • Chapter 12: Fundamentals of Laser Oscillation
        • Chapter 13: Oscillation Dynamics and Oscillation Threshold
      • Optical beams and resonators
        • Chapter 14: Optical Beams and Resonators: An Introduction
        • Chapter 15: Ray Optics and Ray Matrices
        • Chapter 16: Wave Optics and Gaussian Beams
        • Chapter 17: Physical Properties of Gaussian Beams
        • Chapter 18: Beam Perturbation and Diffraction
        • Chapter 19: Stable Two-Mirror Resonators
        • Chapter 20: Complex Paraxial Wave Optics
        • Chapter 21: Generalized Paraxial Resonator Theory
        • Chapter 22: Unstable Optical Resonators
        • Chapter 23: More on Unstable Resonators
      • Laser dynamics and advanced topics
        • Chapter 24: Laser Dynamics: The Laser Cavity Equations
        • Chapter 25: Laser Spiking and Mode Competition
        • Chapter 26: Laser Q-Switching
        • Chapter 27: Active Laser Mode Coupling
        • Chapter 28: Passive Mode Locking
        • Chapter 29: Laser Injection Locking
        • Chapter 30: Hole Burning and Saturation Spectroscopy
        • Chapter 31: Magnetic-Dipole Transitions
    • Yariv and Yeh Photonics — Worked Exercise Solutions
      • Foundations, beams, and resonators
        • Chapter 1: Electromagnetic Fields and Waves
        • Chapter 2: Rays and Optical Beams
        • Chapter 3: Guided Waves in Dielectric Slabs and Fibers
        • Chapter 4: Optical Resonators
      • Lasers, modulation, noise, and detection
        • Chapter 5: Interaction of Radiation and Atomic Systems
        • Chapter 6: Theory of Laser Oscillation and Laser Systems
        • Chapter 7: Chromatic Dispersion and Polarization-Mode Dispersion
        • Chapter 8: Nonlinear Optics
        • Chapter 9: Electro-optic Modulation of Laser Beams
        • Chapter 10: Noise in Optical Detection and Generation
        • Chapter 11: Detection of Optical Radiation
      • Periodic media, waveguides, fibers, and devices
        • Chapter 12: Wave Propagation in Periodic Media
        • Chapter 13: Waveguide Coupling
        • Chapter 14: Nonlinear Optical Effects in Fibers
        • Chapter 15: Semiconductor Lasers: Theory and Applications
        • Chapter 16: Advanced Semiconductor Lasers
        • Chapter 17: Optical Amplifiers
        • Chapter 18: Classical Treatment of Quantum Noise and Squeezed States
    • Introduction to Matrix Methods in Optics — Worked Solutions
      • Foundations and paraxial systems
        • Chapter I: Introduction to Matrix Calculations
        • Chapter II: Matrix Methods in Paraxial Optics
        • Matrix-Optics Reference Tables
      • Resonators, polarization, and crystals
        • Chapter III: Optical Resonators and Laser Beam Propagation
        • Chapter IV: Matrices in Polarization Optics
        • Chapter V: Propagation of Light Through Crystals
      • Appendix exercise
        • Appendix A: Aperture Properties of Centered Systems
    • Schaum’s Outline of Optics — Supplementary Problem Solutions
      • Chapter 1: Wave Motion
        • The wave equation
        • Sinusoidal waves
        • Phase and phase velocity
        • Complex-number representation
        • Three-dimensional waves
      • Chapter 2: Electromagnetic Waves and Photons
        • Maxwell equations and electromagnetic waves
        • Index of refraction
        • Irradiance
        • Photon energy and momentum
        • Electromagnetic-photon spectrum
      • Chapter 3: Reflection and Transmission
        • Laws of reflection and refraction
        • Fermat’s principle
        • Fresnel equations
        • Critical angle and total internal reflection
      • Chapter 4: Geometrical Optics
        • Aspherical refracting surfaces
        • Spherical refracting surfaces
        • Thin-lens equation and imagery
        • Compound thin lenses
        • Thick lenses
        • Lens combinations
        • Planar, aspherical, and spherical mirrors
      • Chapter 5: Polarization
        • Plane polarization
        • Circular polarization
        • Elliptical polarization
        • Natural and partially polarized light
        • Dichroism and Polaroid
        • Polarization by reflection
        • Birefringence
      • Chapter 6: Interference and Coherence
        • Interference of two waves
        • Wavefront-splitting interferometers
        • Amplitude splitting by thin films
        • Amplitude-splitting interferometers
        • Coherence
      • Chapter 7: Diffraction
        • Radiation from a coherent line source
        • Fraunhofer diffraction by one and two narrow slits
        • Multiple narrow slits and diffraction gratings
        • Rectangular and circular apertures: Fraunhofer diffraction
        • Fresnel diffraction: circular systems
        • Fresnel diffraction: straight edges
      • Chapter 8: Introduction to Fourier Optics
        • Periodic waves and Fourier series
        • Fourier transforms
        • Convolution
    • KrakenOS Textbook Cross-References
      • Choose a reference
        • Optical System Design
        • Modern Optical Engineering
        • Introduction to Lens Design
        • Stray Light Analysis and Control
        • Modulation Transfer Function
      • Best route through the five books
      • Source boundary
    • How to Write a Worked Solution
      • 1. Identify the exercise
      • 2. Draw and choose conventions
      • 3. List knowns and unknowns
      • 4. Select the governing equation
      • 5. Rearrange before substituting
      • 6. Substitute values with units
      • 7. State and interpret the answer
      • 8. Check the result
      • Sphinx equation syntax
      • Template for the next exercise
    • Worked Example: Image Distance of a Thin Lens
      • Problem in our own words
      • What is known
      • Step 1: Choose the model
      • Step 2: Rearrange the equation
      • Step 3: Substitute and calculate
      • Step 4: Interpret the result
      • Check 1: Substitute back
      • Check 2: Estimate physically
      • Final answer
      • Try it yourself
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