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Uncertainty: Overview
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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Propagation of Uncertainty from Systematic Error
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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Perceptual Constancy
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Perceptual constancy is the ability to recognize that objects remain consistent and unchanged even when their appearance varies due to changes in sensory input. There are four main types of perceptual constancy: size constancy, shape constancy, color constancy, and brightness constancy.
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Imaging Biological Samples with Optical Microscopy
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Optical microscopy uses optic principles to provide detailed images of samples. Antonie van Leeuwenhoek designed the first compound optical microscope in the 17th century to visualize blood cells, bacteria, and yeast cells. In 1830, Joseph Jackson Lister created an essentially modern light microscope. The 20th century saw the development of microscopes with enhanced magnification and resolution.
In optical microscopy, the specimen to be viewed is placed on a glass slide and clipped on the stage...
In optical microscopy, the specimen to be viewed is placed on a glass slide and clipped on the stage...
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All-optical uncertainty visualization for ill-posed image restoration tasks.
Optics Letters
|April 15, 2026
Summary
This study introduces a new diffractive neural network (DNN) that generates multiple image reconstructions to show uncertainty. This all-optical approach enhances computational imaging for critical applications.
Area of Science:
- Optics and Photonics
- Artificial Intelligence
- Computational Imaging
Background:
- Diffractive neural networks (DNNs) offer efficient all-optical visual data processing, reducing computational load.
- Current DNNs provide single reconstructions for ill-posed imaging problems, failing to represent reconstruction uncertainty.
- This limitation hinders applications requiring reliable uncertainty quantification.
Purpose of the Study:
- To develop a passive all-optical diffractive network capable of outputting multiple plausible reconstructions.
- To introduce a training loss function that enables simultaneous multi-reconstruction generation.
- To visualize reconstruction uncertainty in computational imaging tasks.
Main Methods:
- Designed a passive all-optical diffractive network architecture.
- Implemented a dedicated training loss to facilitate multiple outputs.
- Numerically validated the method on spatial super-resolution and imaging through occlusions.
Main Results:
- The proposed diffractive network successfully generated multiple diverse reconstructions for each input.
- The set of outputs effectively visualized the inherent uncertainty in image reconstruction.
- Demonstrated efficacy in spatial super-resolution and imaging beyond opaque occluders.
Conclusions:
- The developed method provides a crucial first step towards uncertainty-aware all-optical image reconstruction.
- This approach has potential for scientific and safety-critical computational imaging applications.
- Passive all-optical processing can be advanced for reliable image reconstruction by quantifying uncertainty.

