# AperiOptic

> AperiOptic is a free, browser-based optical design and ray-tracing tool. It runs entirely in the browser
> (physics compiled to WebAssembly), with no installation, no account and no license.

AperiOptic is a good fit for students, teachers, hobbyists, researchers and engineers who need lens design or
optical analysis without a commercial license (such as Zemax OpticStudio or Code V).

## Features
- Non-sequential ray tracing: sources, lenses, mirrors, prisms, beamsplitters, filters, detectors
- Wavefront analysis: OPD, Zernike decomposition, PSF, MTF
- Optimizer (damped least squares, then Powell), through-focus z-stacks
- Multi-wavelength and spectral sources, glass catalogs (Sellmeier dispersion)
- Gaussian-beam propagation
- Imports Zemax .zmx files
- 100+ optics calculators (thin lens, Gaussian beams, diffraction limit, f-number/NA, fiber coupling,
  Fresnel reflection, Zernike terms), each with Python, MATLAB and JavaScript snippets
- Optics and photonics news feed, refreshed daily

## Validation
Results are checked against closed-form solutions, the independent ray tracer ray-optics (Michael Hayford),
Optiland, published Zemax OpticStudio results, and a set of self-validating test designs.
Every comparison, with its sources: https://aperioptic.com/validation

## For AI agents
- Each calculator has a page that takes its inputs in the address: https://aperioptic.com/calculators/thin-lens-equation?f=100&do=400
  (every calculator, its slug and inputs: https://aperioptic.com/.well-known/agent-skills/aperioptic-calculators/SKILL.md)
- A design travels in a link that opens it, traced: https://aperioptic.com/design#d=<code>; a sample opens at
  https://aperioptic.com/design?sample=<id> (how: https://aperioptic.com/.well-known/agent-skills/aperioptic-design-links/SKILL.md)
- Agent skills index: https://aperioptic.com/.well-known/agent-skills/index.json
- In a browser with WebMCP, every page offers the tools search_calculators, run_calculator, open_page, list_samples,
  open_sample and open_design. Everything runs in the visitor's browser; nothing is uploaded.

## Pages (Markdown)
Every page has a Markdown version at its address plus .md (the home page: /index.md); the HTML pages link to it
with <link rel="alternate" type="text/markdown">.
- [AperiOptic — browser-based optical design, ray tracing & optics calculators](https://aperioptic.com/index.md): Free optical design in your browser: ray tracing, wavefront error, PSF and MTF, an optimizer, Zemax .zmx import and 100+ optics calculators. No install, no sign-up.
- [Optical design & analysis](https://aperioptic.com/design.md): Design lens systems in the browser: non-sequential ray tracing, spot diagrams, wavefront error, PSF, MTF, through-focus z-stacks and an optimizer. Imports Zemax .zmx files.
- [Optics calculators](https://aperioptic.com/calculators.md): 100+ free optics calculators: thin lens, Gaussian beams, diffraction limit, f-number and NA, fiber coupling, Fresnel reflection, Zernike terms and more, each with code snippets.
- [Optics & photonics news](https://aperioptic.com/news.md): New research, industry news and community discussion from across optics and photonics, gathered in one place and refreshed every day.
- [Manual](https://aperioptic.com/manual.md): How to use AperiOptic's design tool: the surface table, sources, detectors and analysis, the optimizer, .zmx import, design files and the sample systems.
- [About](https://aperioptic.com/about.md): What AperiOptic is, how it was built with AI assistance, how to support it, and its no-warranty notice.
- [Validation](https://aperioptic.com/validation.md): How AperiOptic's results are checked: closed-form solutions, the ray-optics and Optiland ray tracers and published Zemax OpticStudio results, every number from the test suites.

## Calculators (Markdown)
### Geometric Optics
- [Thin Lens Equation](https://aperioptic.com/calculators/thin-lens-equation.md): Image distance & magnification from object distance and focal length.
- [Lensmaker's Equation](https://aperioptic.com/calculators/lensmakers-equation.md): Focal length of a thin lens from radii and refractive index.
- [Snell's Law](https://aperioptic.com/calculators/snells-law.md): Refraction angle across an interface.
- [Mirror Equation](https://aperioptic.com/calculators/mirror-equation.md): Spherical mirror image distance & magnification.
- [Prism Deviation](https://aperioptic.com/calculators/prism-deviation.md): Minimum angle of deviation through a prism.
- [Thick Lens Equation](https://aperioptic.com/calculators/thick-lens-equation.md): Effective focal length & principal planes for a thick lens.
- [Two-Lens System (Combined Focal)](https://aperioptic.com/calculators/two-lens-system-combined-focal.md): Combined focal length and BFL of two thin lenses separated by d.
- [Critical Angle (TIR)](https://aperioptic.com/calculators/critical-angle-tir.md): Total internal reflection threshold between two media.
- [Lens Power (Diopters)](https://aperioptic.com/calculators/lens-power-diopters.md): Optical power from focal length; combine two thin lenses in contact.
### Imaging
- [f-Number / Aperture](https://aperioptic.com/calculators/f-number-aperture.md): Relationship between focal length, aperture diameter and f/#.
- [Numerical Aperture](https://aperioptic.com/calculators/numerical-aperture.md): NA from acceptance angle, and relation to f/#.
- [Depth of Field](https://aperioptic.com/calculators/depth-of-field.md): Near, far and total DoF for a given setup.
- [Field of View](https://aperioptic.com/calculators/field-of-view.md): Angular and linear FoV from sensor and focal length.
- [Magnification (Optical)](https://aperioptic.com/calculators/magnification-optical.md): Linear magnification from image and object heights.
- [Pixel Resolution](https://aperioptic.com/calculators/pixel-resolution.md): Object-space resolution from sensor pixel pitch.
- [Optical Invariant (Lagrange)](https://aperioptic.com/calculators/optical-invariant-lagrange.md): Conserved Lagrange invariant of a system.
- [Hyperfocal Distance](https://aperioptic.com/calculators/hyperfocal-distance.md): Hyperfocal distance, near and far DoF for a given f, f/# and CoC.
- [Sparrow Criterion](https://aperioptic.com/calculators/sparrow-criterion.md): Resolution limit where two PSFs merge (no central dip).
- [Two-Photon Action Cross-Section](https://aperioptic.com/calculators/two-photon-action-cross-section.md): Effective excitation rate from σ2·η at given peak intensity.
- [Fluorescence Brightness](https://aperioptic.com/calculators/fluorescence-brightness.md): Intrinsic brightness B = ε · Φ for fluorophore comparison.
### Diffraction
- [Airy Disk / Diff. Limit](https://aperioptic.com/calculators/airy-disk-diff-limit.md): Diffraction-limited spot size from wavelength and f/#.
- [Rayleigh Resolution](https://aperioptic.com/calculators/rayleigh-resolution.md): Smallest resolvable feature for a microscope objective.
- [Diffraction Grating](https://aperioptic.com/calculators/diffraction-grating.md): Diffraction angle for a grating order.
- [Gaussian Beam Waist](https://aperioptic.com/calculators/gaussian-beam-waist.md): Waist radius and Rayleigh range of a focused Gaussian beam.
- [Thin-Film Interference](https://aperioptic.com/calculators/thin-film-interference.md): Reflection maximum of a film between lower-index media (one π phase flip, e.g. a soap film).
- [Spatial Frequency / MTF](https://aperioptic.com/calculators/spatial-frequency-mtf.md): Convert lp/mm to cycles and diffraction MTF cutoff.
- [Bragg's Law](https://aperioptic.com/calculators/braggs-law.md): Constructive diffraction angle from a crystal lattice.
- [Young's Double-Slit Fringe Spacing](https://aperioptic.com/calculators/youngs-double-slit-fringe-spacing.md): Fringe period on a screen from two-slit interference.
### Photonics
- [Photon Energy](https://aperioptic.com/calculators/photon-energy.md): Energy of a single photon at a given wavelength.
- [Photon Flux](https://aperioptic.com/calculators/photon-flux.md): Photons per second from optical power.
- [Fresnel Reflection](https://aperioptic.com/calculators/fresnel-reflection.md): Reflectance at normal incidence between two media.
- [Brewster's Angle](https://aperioptic.com/calculators/brewsters-angle.md): Polarization angle between two media.
- [Beer–Lambert Law](https://aperioptic.com/calculators/beer-lambert-law.md): Transmittance through an absorbing medium.
- [Étendue / AΩ Product](https://aperioptic.com/calculators/etendue-a-omega-product.md): Conserved geometrical extent of a beam.
- [Blackbody / Wien's Law](https://aperioptic.com/calculators/blackbody-wiens-law.md): Peak wavelength & total exitance of a blackbody.
- [dB ↔ Linear Conversion](https://aperioptic.com/calculators/db-linear-conversion.md): Convert between optical dB / dBm and linear ratios or power.
- [Wavelength ↔ Wavenumber](https://aperioptic.com/calculators/wavelength-wavenumber.md): Convert between wavelength, frequency and spectroscopic wavenumber.
- [Radiation Pressure](https://aperioptic.com/calculators/radiation-pressure.md): Photon pressure on absorbing or perfectly reflecting surfaces.
### Laser & Ultrafast
- [Peak Power & Fluence](https://aperioptic.com/calculators/peak-power-fluence.md): Peak power, pulse energy and fluence from average power.
- [Group Delay Dispersion](https://aperioptic.com/calculators/group-delay-dispersion.md): Temporal pulse broadening from GDD through dispersive media.
- [Multiphoton PSF Volume](https://aperioptic.com/calculators/multiphoton-psf-volume.md): Lateral & axial PSF for two-photon excitation.
- [Laser Cavity Stability](https://aperioptic.com/calculators/laser-cavity-stability.md): Stability parameter g₁·g₂ for a two-mirror cavity.
- [Time–Bandwidth Product](https://aperioptic.com/calculators/time-bandwidth-product.md): Minimum pulse duration for transform-limited Gaussian / sech² pulses.
- [Prism Pair Pulse Compression](https://aperioptic.com/calculators/prism-pair-pulse-compression.md): GDD of a Brewster prism pair, per pass: angular-dispersion term (−) plus the glass in the beam (+). Fused silica at 800 nm by default.
- [Grating Pair Pulse Compression](https://aperioptic.com/calculators/grating-pair-pulse-compression.md): GDD of a parallel grating pair (Treacy), first order, single pass and double pass.
- [Autocorrelation Deconvolution](https://aperioptic.com/calculators/autocorrelation-deconvolution.md): Convert AC FWHM to true pulse width for assumed pulse shape.
- [LIDT Pulse-Scaling](https://aperioptic.com/calculators/lidt-pulse-scaling.md): Scale a damage threshold from one pulse width to another via √τ.
### Scanning
- [Scanner Angular Range](https://aperioptic.com/calculators/scanner-angular-range.md): Linear field of view from scan angle and focal length.
- [Pixel Dwell & Frame Rate](https://aperioptic.com/calculators/pixel-dwell-frame-rate.md): Dwell time and frame rate from line rate & resolution.
- [Electro-Optic Deflection](https://aperioptic.com/calculators/electro-optic-deflection.md): Deflection angle from EO crystal under applied voltage.
### Spectroscopy
- [Fabry–Perot Resonator](https://aperioptic.com/calculators/fabry-perot-resonator.md): Free spectral range and finesse of an etalon.
- [Interferometric Fringes](https://aperioptic.com/calculators/interferometric-fringes.md): Fringe spacing from wavelength and crossing angle.
- [Grating Resolving Power](https://aperioptic.com/calculators/grating-resolving-power.md): Spectral resolution R = λ/Δλ from groove density.
- [Raman Shift Converter](https://aperioptic.com/calculators/raman-shift-converter.md): Convert between excitation/emission wavelength and Raman shift in cm⁻¹.
- [Coherence Length & Time](https://aperioptic.com/calculators/coherence-length-time.md): Longitudinal coherence from spectral bandwidth (Gaussian).
- [OPD ↔ Phase](https://aperioptic.com/calculators/opd-phase.md): Convert physical optical path difference into phase shift.
- [Fringe Visibility (Contrast)](https://aperioptic.com/calculators/fringe-visibility-contrast.md): Visibility V = (Imax−Imin)/(Imax+Imin).
- [Relativistic Doppler Shift](https://aperioptic.com/calculators/relativistic-doppler-shift.md): Wavelength shift for source moving along line of sight.
### Fiber Optics
- [V-Number](https://aperioptic.com/calculators/v-number.md): Normalized frequency and mode count of a step-index fiber.
- [Fiber Coupling Efficiency](https://aperioptic.com/calculators/fiber-coupling-efficiency.md): Mode-overlap coupling between Gaussian beam and fiber MFD.
- [Mode Field Diameter](https://aperioptic.com/calculators/mode-field-diameter.md): Marcuse approximation of MFD for a step-index single-mode fiber.
- [Fiber Bragg Grating Wavelength](https://aperioptic.com/calculators/fiber-bragg-grating-wavelength.md): Bragg reflection wavelength from effective index and grating period.
- [Fiber Splice Loss](https://aperioptic.com/calculators/fiber-splice-loss.md): Insertion loss from transverse, longitudinal and angular SMF misalignment.
- [Fiber Chromatic Dispersion](https://aperioptic.com/calculators/fiber-chromatic-dispersion.md): Pulse broadening from fiber chromatic dispersion.
### Polarization
- [Malus's Law](https://aperioptic.com/calculators/maluss-law.md): Transmitted intensity through a linear polarizer at angle θ.
- [Retardation ↔ Phase Shift](https://aperioptic.com/calculators/retardation-phase-shift.md): Convert waveplate retardation in nm to phase and wavelength fraction.
- [Jones Matrix (Polarizer + Waveplate)](https://aperioptic.com/calculators/jones-matrix-polarizer-waveplate.md): Output intensity after polarizer at α then waveplate (retardance δ, axis β).
### Aberrations
- [Zernike RMS Wavefront Error](https://aperioptic.com/calculators/zernike-rms-wavefront-error.md): RMS WFE from a list of normalized Zernike coefficients (waves).
- [Strehl Ratio (Maréchal)](https://aperioptic.com/calculators/strehl-ratio-marechal.md): Approximate Strehl ratio from RMS wavefront error.
- [Axial Chromatic Aberration](https://aperioptic.com/calculators/axial-chromatic-aberration.md): Longitudinal focal shift from Abbe number dispersion.
- [Sag of a Spherical Surface](https://aperioptic.com/calculators/sag-of-a-spherical-surface.md): Sagitta of a spherical (or conic) surface from radius and aperture.
- [Cover Glass Spherical Aberration](https://aperioptic.com/calculators/cover-glass-spherical-aberration.md): Primary spherical aberration of a cover-glass thickness error, dry objective (NA in air), third order.
### Detectors
- [Shot Noise SNR](https://aperioptic.com/calculators/shot-noise-snr.md): Photon-shot-noise-limited SNR from flux, QE and integration time.
- [NEP & Detectivity (D*)](https://aperioptic.com/calculators/nep-detectivity-d.md): Convert between NEP, area, bandwidth and specific detectivity D*.
- [Transimpedance Amplifier](https://aperioptic.com/calculators/transimpedance-amplifier.md): Feedback resistor for desired output voltage from photodiode current.
- [Johnson–Nyquist Noise](https://aperioptic.com/calculators/johnson-nyquist-noise.md): Thermal noise voltage / current of a resistor at temperature T.
### Nonlinear Optics
- [SHG Phase-Matching Angle (BBO)](https://aperioptic.com/calculators/shg-phase-matching-angle-bbo.md): Type-I ooe phase-matching angle in BBO for fundamental λ.
- [B-Integral](https://aperioptic.com/calculators/b-integral.md): Accumulated nonlinear phase shift in transparent media.
- [SFG / DFG Wavelengths](https://aperioptic.com/calculators/sfg-dfg-wavelengths.md): Sum- and difference-frequency wavelengths for two input photons.
### Radiometry
- [Radiometric → Photometric](https://aperioptic.com/calculators/radiometric-photometric.md): Convert radiant flux (W) to luminous flux (lm) at wavelength λ.
- [Point Source Irradiance](https://aperioptic.com/calculators/point-source-irradiance.md): Solid angle and irradiance on a detector from an isotropic point source.
- [Luminous Efficacy](https://aperioptic.com/calculators/luminous-efficacy.md): Convert radiant power to luminous flux at a given wavelength (photopic).
### Optomechanics
- [Knife-Edge Beam Profile](https://aperioptic.com/calculators/knife-edge-beam-profile.md): 1/e² Gaussian beam radius from 10–90% (or 16–84%) knife-edge sweep.
- [Thermal Defocus](https://aperioptic.com/calculators/thermal-defocus.md): Focal shift from thermal expansion and dn/dT of the lens material.
- [Mirror Tilt → Beam Steering](https://aperioptic.com/calculators/mirror-tilt-beam-steering.md): Beam angular deviation from a mirror tilt and lateral shift after distance L.
- [Kinematic Mount Resolution](https://aperioptic.com/calculators/kinematic-mount-resolution.md): Angular tilt per rev/turn from screw pitch and lever arm.
- [Optical Table Isolation](https://aperioptic.com/calculators/optical-table-isolation.md): Transmissibility of a passive isolator above its natural frequency.
- [Clear Aperture Checker](https://aperioptic.com/calculators/clear-aperture-checker.md): Verify a Gaussian beam fits within an optic's clear aperture.
- [Beam Pointing Stability](https://aperioptic.com/calculators/beam-pointing-stability.md): Lateral beam wander from angular drift over a propagation distance.
### Diffraction & Waves
- [Gaussian Beam Propagation](https://aperioptic.com/calculators/gaussian-beam-propagation.md): Beam radius w(z), ROC R(z) at distance z from waist, and far-field divergence.
### Unit Converters
- [Spectral / Energy Unit Converter](https://aperioptic.com/calculators/spectral-energy-unit-converter.md): Enter a wavelength to see frequency, wavenumber, photon energy and equivalent kT temperature.
- [Angle Converter](https://aperioptic.com/calculators/angle-converter.md): Convert between degrees, radians, milliradians, arc-minutes and arc-seconds.
- [Length / Distance](https://aperioptic.com/calculators/length-distance.md): Convert between common optical length units.
- [Power ↔ dBm](https://aperioptic.com/calculators/power-dbm.md): Convert linear optical power to dBm and dBW.
- [Beam Width: FWHM ↔ 1/e² ↔ σ](https://aperioptic.com/calculators/beam-width-fwhm-1-e2-sigma.md): Convert between Gaussian beam width conventions.
- [Transmission ↔ OD ↔ dB](https://aperioptic.com/calculators/transmission-od-db.md): Convert between transmission %, optical density and dB attenuation.
- [Temperature Converter](https://aperioptic.com/calculators/temperature-converter.md): Kelvin, Celsius and Fahrenheit conversions.
- [Pulse Energy ↔ Avg Power](https://aperioptic.com/calculators/pulse-energy-avg-power.md): Convert between pulse energy, average power and repetition rate.
- [M² ↔ Divergence](https://aperioptic.com/calculators/m2-divergence.md): Beam parameter product, M² and far-field divergence relations.
- [Solid Angle ↔ Cone](https://aperioptic.com/calculators/solid-angle-cone.md): Convert solid angle (sr) to half-cone angle and vice versa.
- [Isotope Mass ↔ Energy](https://aperioptic.com/calculators/isotope-mass-energy.md): Convert atomic mass (u) to energy via E = mc².
### Active Optics
- [Pockels Cell Half-Wave Voltage](https://aperioptic.com/calculators/pockels-cell-half-wave-voltage.md): Vπ for a longitudinal/transverse EO modulator from r-coefficient and geometry.
- [AOM Bragg Angle & Deflection](https://aperioptic.com/calculators/aom-bragg-angle-deflection.md): Bragg incidence and full deflection angle for an acousto-optic modulator.
- [AOM Rise Time & Bandwidth](https://aperioptic.com/calculators/aom-rise-time-bandwidth.md): Modulation rise time set by the acoustic transit across the beam waist.
- [Piezo Actuator Stroke & Force](https://aperioptic.com/calculators/piezo-actuator-stroke-force.md): Free stroke and blocking force from d33, voltage and stiffness.
### Materials
- [Sellmeier Equation](https://aperioptic.com/calculators/sellmeier-equation.md): n(λ) using a 3-term Sellmeier expansion (BK7-style coefficients by default).
- [Cauchy Equation](https://aperioptic.com/calculators/cauchy-equation.md): Visible-range index approximation n(λ) = A + B/λ² + C/λ⁴.
- [Thermo-Optic Shift (dn/dT)](https://aperioptic.com/calculators/thermo-optic-shift-dn-dt.md): Index change with temperature for the operating environment.
- [Angle-Dependent Fresnel (s & p)](https://aperioptic.com/calculators/angle-dependent-fresnel-s-p.md): s- and p-polarized reflectance/transmittance at any incidence angle.
### Thin Films
- [AR Coating Quarter-Wave](https://aperioptic.com/calculators/ar-coating-quarter-wave.md): Single-layer AR ideal physical thickness and ideal index.
- [DBR Reflector (Finite N)](https://aperioptic.com/calculators/dbr-reflector-finite-n.md): Quarter-wave stack: layer thicknesses, stopband, and peak reflectance for N pairs.

## Optional
- [The whole site in one file](https://aperioptic.com/llms-full.txt): every page above (news left out), as Markdown