Mathematica Solution for Optics

Optimize systems of symbolically defined lenses and mirrors, test optical components with built-in image processing or data analysis functions, and calculate complex ray-tracing models.

The Mathematica optics solution integrates these capabilities with built-in special functions; advanced differential equation solvers; and the most automated and reliable computation, development, and deployment environment available.

Analyzing data from optical testing

Intensity maps using built-in Zernike polynomials, plotted in three dimensions, for three types of aberration varying from a circle: tilt, defocus, and astigmatism

Key Capabilities

Why Choose Mathematica

Ways to Use

Mathematica includes thousands of built-in functions for computation, modeling, visualization, development, and deployment »
Optics specific capabilities:
Both numeric and symbolic computations for accurately calculating reusable models or determining aberrations
Perform optical calculations from point spread functions to full theories of microscopes with calculus and differential equation solving capabilities »
Built-in optical special functions including Fresnel integrals, Zernike polynomials, and Bessel functions »
Advanced statistical and curve fitting functions for analyzing data »
Functions for automatically computing probabilities and expectations of any event, allowing quick calculations for many problems
Perform convolutions and correlations on numerical data to deblur and denoise images »
Automated precision control with specified input or output precision to automatically adjust computations to maintain or achieve precise results
Java and .NET linking to communicate with equipment connected to a serial or USB port, or with equipment that uses GPIB, VISA, IVI, and more
2D and 3D graphing capabilities for standard optical plots, including scatter, density, and contour plots »

Access curated scientific data from Wolfram|Alpha, immediately ready for analysis, interactively or programmatically »
Use image processing and filtering functions to model the effects of diffraction, perform deconvolutions, and more, using built-in functions and your own custom algorithms »
Fully integrated discrete or continuous high-performance wavelet analysis for thresholding and visualizing in any dimension »
Load and access dynamic libraries and use built-in support for GPU computation with CUDA or OpenCL for high-speed, memory-efficient execution
Powerful programming language and built-in parallel computing for developing new analysis algorithms or solving complicated ray-tracing problems
Integration with C/C++, Python, Java, databases, and other applications »
Sequential and nonsequential ray-tracing, symbolic modeling, and optimization of three-dimensional optical systems with Optica
Optica imports CAD models, Zemax files, and Code V files
Optica has a database of optical materials, more than 6800 commercial optical parts, more than a hundred optical components, lenses, mirrors, light sources, and more
Symbolic optical functions, pupil function, point spread function, modulation transfer function, and more built into Optica
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Why Choose Mathematica

Key Capabilities

Why Choose Mathematica

Ways to Use

Compare Mathematica to your current tools. Do they have these advantages?
Create interactive tools for designing optical systems, curve fitting, or data analysis that provide visual feedback to make debugging and testing innovative instrumentation easier »
Competitor note: Code V and Zemax do not offer custom interactive tools
Free-form linguistic input produces immediate results without the need for syntax »
Competitor note: Unique to Mathematica
Get accurate results in optical model calculations with fully automated precision control and arbitrary-precision arithmetic »
Competitor note: Matlab and other systems relying on machine arithmetic can show critical errors due to numerical accuracy failure
Rapidly prototype new algorithms more quickly than in other software by choosing from procedural, functional, and rule-based programming paradigms as desired »
Competitor note: Code V and Zemax use a procedural language

Import or acquire data, analyze it, and deliver results in one document instead of across several applications »
Competitor note: Unique to Mathematica
Highly optimized superfunctions analyze your equations and automatically select the right algorithms to get accurate results quickly—sometimes switching mid-calculation for further optimization »
Competitor note: Non-Mathematica computation systems make you analyze your equations manually to determine which function to apply—e.g., where in Mathematica you use NDSolve, in Matlab you must correctly choose among ode45, ode23, ode113, ode15s, bvp4c, pdepe, and so on, or risk wrong answers
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Ways to Use

Key Capabilities

Why Choose Mathematica

Ways to Use

Quickly simulate behavior of lenses, mirrors, and other optical components »
Design solar concentrators, lasers, camera lenses, and more
Animate graphics to see how results change while adjusting optical components
Create interactive interfaces for designing optical systems or performing analyses
Design, test, and interact with light scattering instruments »
Use high-powered mathematics to optimize designs, reducing research time and expense »
Perform optical modeling for microlithography or optimize microscopy instrumentation

Visualize interferograms to test mirrors and lenses »
Optimize pulse formation and control in new laser designs
Develop new imaging techniques for research in a variety of scientific or medical fields
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Key Capabilities