Accessibility Notes

Accessibility is part of scientific accuracy. A figure that cannot be understood without sight, color discrimination, motion tolerance, or a particular screen size is not a finished explanatory object. For quantum mechanics, the stakes are higher because figures often carry mathematical structure: axes, phases, boundary conditions, degeneracies, state labels, and limiting cases.

This page defines the accessibility expectations for figures, plots, diagrams, animations, and datasets. It complements Figure Index, Plot Reproduction, and Licensing.

The Three-Layer Rule

Every non-decorative visual should be understandable through three coordinated layers:

Layer	Job	Should include
Alt text	concise substitute for the image	the kind of visual and its main informational content
Caption	scientific interpretation	what quantity is shown, conventions, and why it matters
Nearby prose	teaching context	assumptions, derivation links, and limitations

Alt text is not a replacement for the caption. The caption is not a replacement for the page explanation. The three layers should reinforce each other without becoming identical copies.

Alt Text by Asset Type

Asset type	Alt text should answer	Example focus
Concept diagram	What structure or relationship is shown?	two bases connected by a unitary change of basis
Plot	What is on the axes and what trend matters?	probability density peaks broaden over time
Spectrum diagram	What levels or degeneracies are shown?	harmonic oscillator levels are equally spaced
Geometry figure	What coordinates, angles, or orientations are defined?	polar angle measured from the positive z-axis
Table image	Why is this an image instead of a real table?	avoid table images when possible
Animation	What changes with time or parameter value?	packet moves right and spreads
Decorative image	Whether it can be hidden from assistive technology	decorative visuals should be rare in technical pages

Avoid alt text such as “figure,” “diagram,” or “plot of data” without content. Also avoid overloading alt text with a full derivation. Put long explanations in prose or a dedicated description.

Captions for Physics Figures

A good caption states:

• the physical or mathematical quantity being shown;
• the system and assumptions;
• units or dimensionless variables;
• parameter values when they affect interpretation;
• the convention for colors, line styles, or labels;
• the conclusion the reader should draw;
• whether the figure is schematic, analytic, numerical, or historical.

For example, a tunneling plot should say whether the vertical axis is wavefunction amplitude, probability density, current, or transmission probability. These are different physical quantities.

Color and Contrast

Do not use color as the only information channel. Distinguish curves or regions with at least one additional cue:

• line style,
• markers,
• direct labels,
• ordering in a legend,
• texture or hatch pattern,
• explicit text in the caption.

Check that a figure remains meaningful in grayscale. Avoid red–green-only distinctions for pass/fail, positive/negative, left/right, or spin-up/spin-down labels.

Text labels should have enough contrast against the background and should not be embedded as tiny raster text. For source-generated SVGs, prefer real text or clean vector labels when the toolchain supports it.

Mathematical Figures

Mathematical figures need extra care because visual placement often encodes a convention. When a figure defines a convention, the page should also state it in text.

Examples:

• A spherical-coordinate diagram should say which angle is $\theta$ and which is $\phi$.
• A Bloch-sphere diagram should identify the poles, equator, and phase convention used.
• A spectrum diagram should state whether the vertical spacing is quantitative or schematic.
• A radial probability plot should say whether the plotted quantity is $R(r)$, $\lvert R(r)\rvert^2$, or $r^2\lvert R(r)\rvert^2$.
• A Clebsch–Gordan diagram should state the coupling convention and ordering.

If the distinction is important enough to draw, it is important enough to write.

Animations and Motion

Animations should be admitted only when motion teaches something that a static sequence cannot teach as well. They should:

• avoid automatic looping when it distracts from reading;
• provide pause or replay controls when practical;
• have a static fallback or textual summary;
• state the time or parameter being varied;
• avoid rapid flashing or high-frequency motion;
• respect reduced-motion settings when implemented in interactive components.

An animation of a spreading wave packet should say whether the packet is free, which frame is position space, and whether normalization is being preserved.

Long Descriptions

Use a longer textual description when the figure carries multiple relationships that cannot fit in concise alt text. A long description can be:

• a paragraph immediately after the figure;
• a list of the figure’s panels;
• a table of plotted curves and parameters;
• a linked reference entry in the figure index;
• a derivation or formula page linked from the caption.

For multi-panel plots, describe the panel order and the main comparison. For example, say that the left panel shows the potential and stationary states while the right panel shows the corresponding probability densities.

Dataset Accessibility

Datasets and exported tables should be accessible as structured data, not only as plotted images. When a dataset is admitted, record:

• column names,
• units,
• variable definitions,
• parameter values,
• missing-value conventions,
• generation or source method,
• checksum or version,
• license and citation.

If a plot is generated from a dataset, the dataset entry should let a reader recover the plotted quantity without reverse-engineering the figure.

Figure Review Checklist

Before accepting a figure, check:

• Does the image have meaningful alt text?
• Does the caption identify the quantity and convention?
• Is color supplemented by another visual cue?
• Are axes, units, and parameters clear?
• Is the figure source tracked?
• Does nearby prose explain the figure’s role?
• Is any animation controllable or summarized statically?
• Is the license or provenance recorded?
• Does the page still make sense if the image fails to load?

Common Mistakes

• Writing alt text that repeats only the filename.
• Relying on color to distinguish quantum numbers or signs.
• Labeling a curve “probability” when it is a density.
• Showing a schematic spectrum without saying it is not to scale.
• Putting essential explanation only inside the image.
• Making a generated plot reproducible but not understandable.
• Treating accessibility as a final decoration step instead of part of figure design.

Cross-Links

• Figure Index
• Diagram Index
• Animation Index
• Datasets
• Plot Reproduction
• Licensing
• Code Style

References

• W3C Web Accessibility Initiative, Images Tutorial.
• W3C Web Accessibility Initiative, Making Content Usable for People with Cognitive and Learning Disabilities.
• E. Tufte, The Visual Display of Quantitative Information, 2nd ed., Graphics Press, 2001.
• C. Ware, Information Visualization: Perception for Design, 4th ed., Morgan Kaufmann, 2021.

Exercises

1. A figure shows three curves for $n=1$, $n=2$, and $n=3$ using only blue, green, and red lines. What accessibility issue should be fixed?

Solution

Color is the only distinguishing cue. Add direct labels, line styles, markers, or a legend that is meaningful without color. The caption should also identify what the three curves represent.

2. A radial hydrogen plot is captioned “Probability versus radius.” What extra information is needed?

Solution

The caption should state the plotted quantity and measure. It might be $R(r)$, $\lvert R(r)\rvert^2$, or the radial probability density $r^2\lvert R(r)\rvert^2$. These have different meanings and shapes.