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Oct 19

Space-time tradeoffs of lenses and optics via higher category theory

Optics and lenses are abstract categorical gadgets that model systems with bidirectional data flow. In this paper we observe that the denotational definition of optics - identifying two optics as equivalent by observing their behaviour from the outside - is not suitable for operational, software oriented approaches where optics are not merely observed, but built with their internal setups in mind. We identify operational differences between denotationally isomorphic categories of cartesian optics and lenses: their different composition rule and corresponding space-time tradeoffs, positioning them at two opposite ends of a spectrum. With these motivations we lift the existing categorical constructions and their relationships to the 2-categorical level, showing that the relevant operational concerns become visible. We define the 2-category 2-Optic(C) whose 2-cells explicitly track optics' internal configuration. We show that the 1-category Optic(C) arises by locally quotienting out the connected components of this 2-category. We show that the embedding of lenses into cartesian optics gets weakened from a functor to an oplax functor whose oplaxator now detects the different composition rule. We determine the difficulties in showing this functor forms a part of an adjunction in any of the standard 2-categories. We establish a conjecture that the well-known isomorphism between cartesian lenses and optics arises out of the lax 2-adjunction between their double-categorical counterparts. In addition to presenting new research, this paper is also meant to be an accessible introduction to the topic.

  • 1 authors
·
Sep 19, 2022

Guidance Disentanglement Network for Optics-Guided Thermal UAV Image Super-Resolution

Optics-guided Thermal UAV image Super-Resolution (OTUAV-SR) has attracted significant research interest due to its potential applications in security inspection, agricultural measurement, and object detection. Existing methods often employ single guidance model to generate the guidance features from optical images to assist thermal UAV images super-resolution. However, single guidance models make it difficult to generate effective guidance features under favorable and adverse conditions in UAV scenarios, thus limiting the performance of OTUAV-SR. To address this issue, we propose a novel Guidance Disentanglement network (GDNet), which disentangles the optical image representation according to typical UAV scenario attributes to form guidance features under both favorable and adverse conditions, for robust OTUAV-SR. Moreover, we design an attribute-aware fusion module to combine all attribute-based optical guidance features, which could form a more discriminative representation and fit the attribute-agnostic guidance process. To facilitate OTUAV-SR research in complex UAV scenarios, we introduce VGTSR2.0, a large-scale benchmark dataset containing 3,500 aligned optical-thermal image pairs captured under diverse conditions and scenes. Extensive experiments on VGTSR2.0 demonstrate that GDNet significantly improves OTUAV-SR performance over state-of-the-art methods, especially in the challenging low-light and foggy environments commonly encountered in UAV scenarios. The dataset and code will be publicly available at https://github.com/Jocelyney/GDNet.

  • 6 authors
·
Oct 26, 2024

Wave optics lensing of gravitational waves: theory and phenomenology of triple systems in the LISA band

We study lensing of gravitational waves by a black hole in the deep wave optics regime, i.e. when the wavelength is much larger than the black hole Schwarzschild radius. We apply it to triple systems, with a binary of stellar mass objects in the inspiraling phase orbiting around a central massive black hole. We describe the full polarisation structure of the wave and derive predictions for the polarisation modes of the scattered wave measured by the observer. We show that lensing in the wave optics regime is not helicity preserving, as opposed to lensing in the geometric optics regime. The amplitude of the total wave is modulated due to interference between the directly transmitted and lensed components. The relative amplitude of the modulation is fixed by the lensing geometry and can reach unity in the most favourable settings. This indicates that wave optics lensing is potentially detectable by LISA for sufficiently high SNR systems. Our findings show that in the wave optics regime it is necessary to go beyond the usual lensing description where the amplification factor is assumed to be the same for both helicity modes. While motivated by GW190521 and the AGN formation scenario, our results apply more broadly to stellar-mass binaries orbiting a third body described as a Schwarzschild black hole, with a period comparable to the GW observation time.

  • 4 authors
·
Apr 10, 2024

GOBench: Benchmarking Geometric Optics Generation and Understanding of MLLMs

The rapid evolution of Multi-modality Large Language Models (MLLMs) is driving significant advancements in visual understanding and generation. Nevertheless, a comprehensive assessment of their capabilities, concerning the fine-grained physical principles especially in geometric optics, remains underexplored. To address this gap, we introduce GOBench, the first benchmark to systematically evaluate MLLMs' ability across two tasks: 1) Generating Optically Authentic Imagery and 2) Understanding Underlying Optical Phenomena. We curates high-quality prompts of geometric optical scenarios and use MLLMs to construct GOBench-Gen-1k dataset.We then organize subjective experiments to assess the generated imagery based on Optical Authenticity, Aesthetic Quality, and Instruction Fidelity, revealing MLLMs' generation flaws that violate optical principles. For the understanding task, we apply crafted evaluation instructions to test optical understanding ability of eleven prominent MLLMs. The experimental results demonstrate that current models face significant challenges in both optical generation and understanding. The top-performing generative model, GPT-4o-Image, cannot perfectly complete all generation tasks, and the best-performing MLLM model, Gemini-2.5Pro, attains a mere 37.35\% accuracy in optical understanding. Database and codes are publicly available at https://github.com/aiben-ch/GOBench.

  • 9 authors
·
Jun 1, 2025

MODEST: Multi-Optics Depth-of-Field Stereo Dataset

Training and evaluation of state-of-the-art computer vision algorithms for reliable shallow depth of field (DoF) rendering and defocus deblurring remain constrained by a persistent lack of large-scale, full-frame, high fidelity, real-image datasets. Optical effects of shallow DoF and defocus blur depend intimately on camera optical configuration set with focal length and aperture; requiring rigorous evaluation of the models when these parameters systematically change. Further, modern applications such as AR, VR, smartphones, industrial robots, etc. deploy stereo or multi-camera systems. We present MODEST - the first ultra-high-resolution(5472x3648px, 20MP), multi-optics depth of field stereo DSLR dataset that methodically varies focal length and aperture for a series of complex, real-world scenes, capturing the optical realism and complexity of professional camera systems. With 20,000 images across 50 distinct optical configurations, focal length in 28-70mm, aperture in f/22-f/2.8 for multiple stereo viewpoints for 10 scenes; this ultra-high-resolution, full-range optics coverage enables controlled analysis of geometric and optical effects for shallow DoF rendering and defocus deblurring. Each scene is curated to have challenging visual elements: reflective surfaces, transparent glass walls, fine-grained details, point lights, and multi-scale depth illusions. In addition, we provide intrinsics and extrinsics calibration images to support ever-evolving calibration methods. We evaluate several SOTA DoF and defocus deblurring methods and demonstrate failure cases and limitations. Our comprehensive tuning analysis demonstrates how MODEST evaluates sensitivity of the SOTA DoF models for the actual focal configuration of input images. This work attempts to bridge the realism gap between synthetic, low-resolution training data and inference generalization on high-resolution real-camera optics.

  • 3 authors
·
Aug 4