# Paraxial > Paraxial is the first AI-native optical design platform built from the ground up to replace legacy tools like OpticStudio® (formerly Zemax®) and Code V. It uses differentiable ray tracing and hybrid AI tolerancing to compress optical design workflows by 10–100×, enabling engineers to go from specification to manufacturable design in hours instead of months. ## Site Map - Homepage: https://paraxialoptics.com/ - Research Paper: https://paraxialoptics.com/research - Careers: https://paraxialoptics.com/careers - Full Research Paper (PDF): https://paraxialoptics.com/Hybrid_AI_Optical_Tolerancing_Bhagat_2025.pdf - Waitlist Signup: https://paraxialoptics.com/#waitlist - Contact / LinkedIn: https://www.linkedin.com/in/akilbhagat/ - Email: hello@paraxial.ai --- ## Homepage ### Hero **Headline:** Design World-Class Optical Systems In Days, Not Months **Subheadline:** The first AI-native platform with differentiable ray tracing and hybrid AI tolerancing that compresses optical design workflows by 10–100×. Built from the ground up to replace legacy tools like OpticStudio® and Code V. **Call to Action:** Join the Waitlist — Early access · Development updates · Beta testing opportunities **Trust Signal:** Founded by ex-Zemax® Principal PM · Advised and backed by former Zemax® executive · Seeking pilot partners --- ### The Problem: Legacy Tools Can't Keep Up With Modern Hardware Cycles OpticStudio® and Code V were built in the 1990s. Their physics engines weren't designed to fully leverage modern AI or GPU acceleration, and it shows. **Problem 1 — 4–6 Weeks Just for Setup** Senior optical engineers spend $15K–$25K in labor translating specs into optimizable merit functions before any real design work begins. **Problem 2 — Weeks of Brute-Force Monte Carlo** Tolerance analysis ties up compute clusters for weeks to months, blocking manufacturing sign-off and still missing non-linear sensitivities. **Problem 3 — No Path for Non-Specialists** Mechanical and systems engineers need months of training to contribute meaningfully, creating bottlenecks as teams can't hire enough optical specialists. --- ### How It Works: AI-Native Optical Design Workflow From specification to manufacturable design in hours, not weeks. **Step 1 — AI-Guided Design Exploration** Describe requirements in natural language. AI explores design space, evaluates trade-offs, and delivers an optimized starting point in minutes, not weeks. **Step 2 — Differentiable Ray Tracing** GPU-accelerated gradient-based optimization with automatic differentiation. Global search through design space with real-time feasibility checks. **Step 3 — Hybrid AI Tolerancing** Surrogate-model accelerated yield analysis runs 10–100× faster than Monte Carlo. Captures non-linear manufacturing sensitivities with active learning. **Comparison:** - OpticStudio® / Code V: 4–6 weeks setup, weeks to months for tolerancing - Paraxial: Minutes to hours for setup, hours to days for tolerancing --- ### Applications: Precision Optics Across Industries From AR/VR to autonomous sensing, Paraxial accelerates the most demanding optical design challenges. **AR/VR & Displays** Wide FOV pancake optics, waveguide combiners, and ultra-compact projection systems with sub-5mm eye relief constraints. **LiDAR & Sensing** High-resolution FMCW and ToF systems for autonomous vehicles, robotics, and industrial metrology with sub-millimeter precision. **Quantum & Photonics** Ultra-low loss coupling systems, single-photon collection optics, and free-space quantum communication links. **Biomedical & Imaging** Diffraction-limited microscopy objectives, endoscope relay systems, and high-NA surgical imaging with sub-micron resolution. --- ### Technical Approach: Research-Backed AI-Native Architecture Built from first principles with differentiable physics and active learning, not wrappers around 1990s code. **Automatic Differentiation** GPU-native ray tracing with backpropagation through the entire optical train. Gradients with respect to all surface parameters, coatings, and materials enable global optimization impossible in legacy tools. **Surrogate-Accelerated Tolerancing** Published research methodology combines high-fidelity physics with Gaussian process surrogates and active learning. Captures non-linear manufacturing sensitivities 10–100× faster than brute-force Monte Carlo. **Agentic Integration via MCP (Model Context Protocol)** Model Context Protocol enables Paraxial agents to be called wherever optical calculations are needed. Autonomous agents plug into external APIs, with seamless CAD export eliminating downstream rework. **10–100× Faster Workflows** Compress months of legacy workflows into days with AI-native architecture. Based on published research methodology and early pilot validation. --- ### Quantifiable ROI for Design Teams Real cost savings validated by senior optical engineers across the industry. **$15K–$25K — Labor Cost per Setup** Eliminated by AI co-pilot that generates merit functions and starting layouts in minutes instead of 4–6 weeks. **10–100× — Tolerancing Speedup** Hybrid AI tolerancing cuts yield analysis from weeks/months to hours/days while capturing manufacturing realities Monte Carlo misses. **Weeks Saved — CAD Handoff** Direct mechanical integration eliminates downstream rework between optical models and production CAD assemblies. **Customer Quote:** "Nominal design plus tolerancing together, that's worth much more than Zemax® or Code V. The value is much higher. What popped in my head was $100K–$200K because that's the amount we could save over a few designs." — Expert Optical Engineer, Major Optics Company --- ### Waitlist **Heading:** Join the Future of Optical Design Be among the first to experience AI-native optical design. Early access includes pilot partnerships and direct input on platform development. - Free to join - Early access - Unsubscribe anytime Waitlist signup: https://paraxialoptics.com/#waitlist --- ### Footer © 2026 Paraxial Corporation. All rights reserved. Disclaimer: Zemax® and OpticStudio® are registered trademarks of Ansys, Inc. Paraxial is not affiliated with, endorsed by, or sponsored by Ansys. --- ## Research Page **URL:** https://paraxialoptics.com/research ### Paper Header **Title:** Hybrid AI for Robust Optical Tolerancing: Bridging Machine Learning and Traditional Workflows **Author:** Akil Bhagat **Affiliation:** The Institute of Optics, University of Rochester **Published:** February 14, 2025 **Download:** https://paraxialoptics.com/Hybrid_AI_Optical_Tolerancing_Bhagat_2025.pdf **Suggested Citation:** Bhagat, A. (2025). "Hybrid AI for Robust Optical Tolerancing: Bridging Machine Learning and Traditional Workflows." The Institute of Optics, University of Rochester. February 2025. --- ### TL;DR — Key Takeaways - **10–100×** — Faster than traditional Monte Carlo tolerancing while maintaining accuracy - **Hybrid** — AI surrogates + traditional methods for best of both worlds - **Non-linear** — Captures manufacturing sensitivities missed by linear methods --- ### Abstract Achieving high performance in real-world optical systems hinges on robust tolerancing methods that account for manufacturing imperfections. Traditional techniques like sensitivity analysis, Root-Sum-Square (RSS) budgets, and Monte Carlo (MC) simulation, while essential, can become computationally intractable for complex systems or fail to capture strong non-linear tolerance interactions. This paper explores the integration of Artificial Intelligence (AI) to enhance optical tolerancing workflows. We delve into the mathematical underpinnings of both classical and AI-driven approaches, proposing a novel hybrid methodology that leverages the strengths of each. By combining AI-based surrogate models, such as neural networks and Gaussian processes, with established tolerancing practices, we demonstrate how to achieve significant computational speedups, improved interpretability, and robust statistical yield estimates. This hybrid framework not only quantifies uncertainty and accelerates performance prediction but also guides optical engineers towards more manufacturable and cost-effective designs, effectively bridging the gap between traditional rigor and the efficiency of modern AI techniques. --- ### Key Findings **1. Traditional Methods Face Critical Limitations** Sensitivity Analysis (SA) provides only first-order linear approximations and misses non-linear tolerance interactions. Root Sum Square (RSS) assumes statistical independence and can be overly conservative. Monte Carlo (MC) is accurate but computationally prohibitive for complex systems, requiring weeks to months of compute time. **2. AI Surrogates Provide Massive Speedup** Neural networks and Gaussian processes learn complex tolerance-to-performance mappings from limited training data (hundreds of simulations). Once trained, surrogates enable millions of yield predictions in seconds — achieving 10–100× speedup over traditional Monte Carlo while capturing non-linear sensitivities. **3. Hybrid Workflow Combines Best of Both** The proposed workflow starts with sensitivity analysis for initial budgeting, uses focused Monte Carlo for training data generation, trains AI surrogates for rapid yield assessment, and employs active learning to iteratively refine model accuracy in critical regions. This approach maintains traditional rigor while gaining AI efficiency. **4. Enables Inverse Tolerancing & Robust Design** Trained surrogates can be integrated into optimization loops to minimize design sensitivity to manufacturing tolerances. This enables robust design optimization that produces inherently more manufacturable systems with potentially reduced production costs. --- ### Methodology: Hybrid AI Tolerancing Workflow **Step 1 — Initial Tolerance Budgeting** Perform sensitivity analysis or RSS budgeting to identify critical tolerance parameters and establish preliminary budgets. This provides initial understanding of which parameters most impact performance. **Step 2 — Training Data Generation** Conduct focused Monte Carlo simulation (hundreds of samples) on critical parameter ranges. This generates a labeled dataset of tolerance combinations and corresponding high-fidelity performance metrics for training. **Step 3 — AI Surrogate Training** Train neural network or Gaussian process surrogate to learn tolerance-to-performance mapping. Apply regularization (L2 decay, dropout, Bayesian methods) to prevent overfitting and ensure generalization across tolerance space. **Step 4 — Large-Scale Yield Assessment** Deploy trained surrogate for surrogate-based Monte Carlo (SMC) with millions of samples. Achieve rapid yield estimation and sensitivity re-evaluation in seconds versus weeks of traditional MC compute time. **Step 5 — Active Learning Refinement** Identify high-uncertainty regions in tolerance space. Perform targeted high-fidelity simulations in these areas and retrain surrogate. This iterative process improves accuracy in critical regions while minimizing computational cost. **Step 6 — Robust Design Optimization (Optional)** Integrate surrogate into optimization loop to perform inverse tolerancing. Optimize nominal design parameters to minimize sensitivity to manufacturing variations, producing inherently more robust and cost-effective designs. --- ### Mathematical Foundation **Neural Network Surrogate Models** Feedforward neural networks approximate the tolerance-to-performance mapping f(x) where x is the tolerance parameter vector. A simple single-hidden-layer architecture: ``` f(x) = W₂ · σ(W₁ · x + b₁) + b₂ ``` Training minimizes mean squared error loss over the dataset, with regularization techniques preventing overfitting in high-dimensional tolerance spaces. **Gaussian Process Surrogates** Gaussian processes provide probabilistic predictions with uncertainty quantification: ``` f(x) ~ GP(m(x), k(x, x')) ``` The predictive variance σ²(x*) quantifies model uncertainty at any point x*, enabling identification of regions requiring additional training data through active learning. **Surrogate-Based Monte Carlo (SMC)** Traditional Monte Carlo requires N expensive optical simulations. Surrogate-based MC (SMC) uses only N_train << N simulations for training, then rapidly evaluates the surrogate on N_MC >> N_train samples for accurate yield estimation at a fraction of the computational cost. --- ### Frequently Asked Questions (Research Page) **What is hybrid AI tolerancing?** Hybrid AI tolerancing combines traditional optical tolerancing methods (sensitivity analysis, RSS, Monte Carlo) with AI-based surrogate models like neural networks and Gaussian processes. This approach achieves 10–100× computational speedup while capturing non-linear manufacturing sensitivities that traditional methods miss. **How much faster is AI tolerancing compared to Monte Carlo analysis?** AI-enhanced tolerancing using surrogate models achieves 10–100× speedup compared to traditional Monte Carlo simulation. Training requires hundreds of simulations, but once trained, the surrogate can perform millions of yield predictions in seconds versus weeks of compute time for equivalent Monte Carlo analysis. **What are the limitations of traditional optical tolerancing methods?** Traditional methods have three key limitations: (1) Sensitivity Analysis (SA) is linear and misses non-linear interactions between tolerances; (2) Root Sum Square (RSS) assumes independence and normal distributions, often being overly conservative; (3) Monte Carlo (MC) is accurate but computationally expensive, taking weeks to months for complex systems with high-dimensional tolerance spaces. **Which AI models work best for optical tolerancing?** Neural networks and Gaussian processes each have advantages. Neural networks excel at capturing complex non-linear relationships in high-dimensional spaces and scale well. Gaussian processes provide built-in uncertainty quantification, making them ideal for active learning strategies. The hybrid workflow can leverage either or both depending on the specific tolerancing requirements. **How does active learning improve surrogate accuracy?** Active learning identifies regions in the tolerance space where the surrogate has high prediction uncertainty. Additional high-fidelity simulations are performed strategically in these regions, and the surrogate is retrained with this new data. This iterative refinement concentrates computational resources where they matter most, improving accuracy while minimizing total simulation cost. **Can this methodology be integrated into existing optical design workflows?** Yes, the hybrid approach is designed to augment, not replace, existing workflows. It starts with traditional sensitivity analysis for initial budgeting, uses standard Monte Carlo for training data, then accelerates the yield assessment phase with AI surrogates. The methodology can be implemented as a post-processing step using data from any optical design software (Zemax®, Code V, etc.). **What training data is required for the AI surrogate?** Training typically requires hundreds to low thousands of high-fidelity optical simulations covering the critical tolerance parameter space. The exact number depends on system complexity and dimensionality. Initial sensitivity analysis helps identify which parameters to vary, making training data generation more efficient by focusing on relevant regions of the tolerance space. **How is this research being applied in practice?** This hybrid AI tolerancing methodology forms the foundation of Paraxial's platform. The research has been validated through pilot partnerships with optical design teams working on AR/VR, LiDAR, and high-precision imaging systems. Results show consistent 10–100× speedups in tolerancing workflows while maintaining or improving yield prediction accuracy. --- ### Future Research Directions The field of AI-enhanced optical tolerancing continues to evolve. Key areas for future research include: - Advanced neural architectures specifically designed for optical physics (e.g., physics-informed neural networks) - Multi-fidelity modeling combining fast approximate simulations with selective high-fidelity validation - Transfer learning approaches to apply trained surrogates across similar optical system families - Integration with differentiable ray tracing for end-to-end gradient-based optimization - Uncertainty quantification standards and validation protocols for AI-enhanced tolerancing - Real-time tolerancing for design exploration and interactive merit function optimization --- ## Careers Page **URL:** https://paraxialoptics.com/careers ### Heading **Join Our Team** Help us build the future of optical design. We're looking for exceptional people to join our founding team. ### Open Positions No open positions at this time. Check back soon — we're growing. ### Why Join Paraxial? We're a small, focused team building something that will transform how optical systems are designed. This is your chance to be part of something from the very beginning, with people who care about doing great work together. - **Meaningful, challenging work:** Combine physics simulation, AI/ML, and modern software to solve problems no one else has tackled - **Autonomy and ownership:** Take real responsibility for what you build, with the freedom to make decisions and shape our direction - **A team that respects your time:** We value sustainable pace, clear communication, and getting things done without unnecessary meetings - **Direct customer connection:** Work closely with optical engineers at leading companies who genuinely need what we're building - **Founding team equity:** Join early and share in the upside as we grow --- ## About Paraxial **Founder:** Akil Bhagat (former Zemax® Principal Product Manager) **Advisors/Backers:** Former Zemax® executives **Founded:** 2025 **Status:** Pre-launch, seeking pilot partners and waitlist signups **Contact:** hello@paraxial.ai **LinkedIn:** https://www.linkedin.com/in/akilbhagat/ Paraxial is building a modern optical design platform from first principles. The platform is AI-native — meaning it is not a wrapper around legacy 1990s physics engines, but a ground-up reimplementation using differentiable ray tracing, GPU acceleration, and AI surrogate models. The platform is designed to serve professional optical engineers across precision optics industries, and to lower the barrier for non-specialists (mechanical engineers, systems engineers) to contribute meaningfully to optical design workflows. **Disclaimer:** Zemax® and OpticStudio® are registered trademarks of Ansys, Inc. Paraxial is not affiliated with, endorsed by, or sponsored by Ansys.