Weber vs De Vries-Rose luminance regimes, in plain English

Two people take the same at-home contrast test on two different laptops and post two different scores, with the same eyes. Before you blame the eyes, look at the screen. How bright the background is turns out to change what counts as the faintest visible contrast, and it does so in a lawful, well-studied way. Vision scientists have names for the two regimes involved: the De Vries-Rose law and Weber's law. This post is about what those names mean, why the eye switches between them, and why any honest screen-based contrast test has to care about the answer.

The short version: In dim light your eye is limited by the randomness of the light itself, by how many photons happen to arrive, and the faintest contrast you can detect improves in proportion to the square root of the background brightness. That is the De Vries-Rose law. Turn the light up and the eye crosses into the Weber regime, where the faintest detectable contrast stops improving and settles at a roughly constant percentage, the Weber fraction. Because a display's brightness decides which regime you are testing in, the same eye can post different scores on a dim screen and a bright one. That is exactly why calibrating to a known luminance matters.

What "contrast threshold" actually means

Start with two words. Luminance is how much light comes off a surface toward your eye, the physical brightness of a patch of screen or wall, measured in candelas per square metre (often called nits). Contrast is not brightness itself but the difference in brightness between one region and its surroundings, expressed relative to the background. A dark grey letter on a light grey page has low contrast; the same letter in black on white has high contrast, even though the page brightness has not changed.

Your visual system does not have unlimited access to that difference. Below some smallest difference, a feature simply blends into its background and you cannot tell it is there. That smallest still-detectable difference is the contrast threshold: the faintest light-dark variation you can just barely see. Flip it over and you get contrast sensitivity, which is one divided by the threshold. A person who can detect a one percent difference has a threshold of about 0.01 and a sensitivity of about 100. Lower threshold, higher sensitivity, better performance.

The key idea for everything that follows is that this threshold is not a fixed property of your eyes. It moves depending on conditions, and one of the biggest levers is the background luminance. The same pattern, the same eye, tested against a dim background versus a bright one, gives two different thresholds. Two named laws describe how. (Spatial scale matters too, and interacts with all of this; if the term cycles per degree is new, our primer on spatial frequency in plain English is a good companion.)

The De Vries-Rose regime: counting photons in the dark

Light is not a smooth fluid. It arrives in discrete packets, photons, and in dim conditions the eye is catching so few of them that their randomness becomes the dominant fact of the situation. If a patch of retina receives on average one hundred photons in some brief window, the actual count wobbles from moment to moment, and the size of that wobble is about the square root of the average, so roughly ten. That is Poisson statistics: the noise scales as the square root of the signal.

Now think about what detecting contrast requires. To see that one region is brighter than another, the extra photons from the brighter region have to stand out above this random flicker. In the dark, with few photons arriving, the flicker is large relative to the signal, so a feature has to be quite high in contrast before it clears the noise. Add more light and the average count climbs; because the noise grows only as the square root of that count, the signal pulls ahead. The upshot, worked out by Hendrik de Vries in 1943 and put on a rigorous absolute footing by Albert Rose in 1948, is that in this photon-limited regime the threshold contrast falls in proportion to the inverse square root of the background luminance. Quadruple the light and the faintest detectable contrast roughly halves.

Rose framed it by comparing the eye to an ideal detector, one limited only by the unavoidable randomness of the light it collects. Under that limit the product of the scene luminance, the threshold contrast squared, and the object size squared is a constant. Real eyes are not perfectly ideal, but in dim light they track this square-root law closely, which is a striking result: it means near-darkness performance is set less by the biology and more by the physics of how few photons there are to work with. This is the same photon-scarcity story that sits underneath a lot of the dim-room difficulty we cover in low light, low contrast, and poor lighting.

The Weber regime: a fixed percentage in bright light

Keep turning the light up and something changes. Photon noise keeps shrinking relative to the signal, and at some point it stops being the thing that limits you. Other noise sources take over, ones that scale with the signal rather than with its square root, plus the fact that the visual system continuously adapts its own gain to the prevailing light level. When the limit comes from sources that grow in step with the background, improving the light no longer helps: brighter background, proportionally bigger noise, same ratio.

That plateau is Weber's law, an old and general observation in psychophysics: the just-noticeable difference is a roughly constant fraction of the background level. In the contrast world it means the threshold stops falling and levels off at a fixed percentage, the Weber fraction. Under good conditions for contrast that fraction lands in the low single digits, on the order of one to two percent, though the exact value depends on the pattern, its size, and the person. The practical meaning is that once you are bright enough, making the screen brighter still buys you essentially nothing in contrast detection. The eye has switched from caring about absolute photon counts to caring only about relative differences.

It is worth naming why this is such a useful design. A visual system that obeyed Weber's law everywhere would see the world in stable relative terms across an enormous range of lighting, from a dim room to full daylight, which is roughly what ours does across the bright end. The De Vries-Rose regime is what happens when the light gets too scarce for that trick to hold.

Where the two regimes meet: the transition luminance

So there are two straight-line behaviours, plotted against luminance, and a knee between them. Below the knee, threshold falls as the square root of luminance (De Vries-Rose). Above it, threshold flattens (Weber). The luminance at the knee is the transition luminance, and its location is not a single universal number. It depends on what you are looking at.

The most important dependence is on spatial frequency, how fine the pattern is. Floris van Nes and Maarten Bouman, measuring contrast sensitivity across many light levels in 1967, found that finer patterns stay in the photon-limited regime up to higher luminances, while coarse patterns reach their Weber plateau earlier. Later modelling by Jyrki Rovamo and colleagues in 1994 pinned this down quantitatively: contrast sensitivity grows with the square root of retinal illuminance below a critical level and saturates above it, with the critical level shifting depending on the pattern and the area of retina it stimulates. In rough terms, a coarse pattern might reach its Weber plateau at a modest indoor luminance, while a fine, high-frequency pattern is still improving with added light well past that point.

The takeaway for a tester is not a magic number but a shape. At a given screen brightness, some parts of your contrast curve may already be in the flat Weber regime while other parts, usually the fine-detail high-frequency end, are still down in the sloped De Vries-Rose regime and would improve if the screen were brighter. That is why brightness does not shift a whole score up or down uniformly; it tilts the curve.

Why this matters for testing on a screen at home

Here is where the physics meets the practical problem. A display has a real, physical peak luminance. A phone in a bright room might push four hundred nits; the same phone dimmed for night reading might sit near forty. A laptop on battery-saver mode dims itself without telling you. Auto-brightness quietly changes the setting between one test session and the next. On OLED panels the near-black behaviour is its own puzzle, because how the darkest greys are rendered depends on the panel and its gamma handling, which we get into in the science of why grayscale on monitors can lie.

Every one of those brightness differences moves your eye along the luminance axis we have been describing, and therefore moves your threshold. Test on a dim screen and you may be operating partly in the De Vries-Rose regime, where thresholds are higher, so the very same eye detects less contrast and scores worse. Test on a bright, calibrated screen and you climb toward the Weber plateau, where thresholds are lower and, crucially, stable. Neither result is wrong about the eye. They are measurements of the same eye at two different operating points, and without knowing the luminance you cannot say which is the fair one.

This is the whole argument for calibration. A contrast score is only interpretable, and only comparable across sessions or across people, if the background luminance is fixed to a known value. Set the brightness the same way each time, in a consistently lit room, and the number becomes a measurement of your eyes rather than a measurement of your screen settings. Let brightness float and you are partly testing the hardware.

A note on what this is and is not. A contrast sensitivity test is a screening signal of overall visual function, not a diagnosis of any condition, and it does not replace an eye exam. Calibrating to a known screen luminance is what makes the signal meaningful: it keeps you at a consistent point on the luminance curve so that a change in your score reflects a change in your eyes rather than a change in your display. If your everyday vision has shifted, the right next step is a clinician, not an online tool.

What to do next

The two-regime picture is the reason a good home test asks you to set brightness and room lighting before it asks you to read anything. Once the luminance is fixed, the curve you produce is a fair map of how your eyes trade contrast for light, and it becomes something you can compare against your own past results. If you want to see the idea in action, take a free contrast sensitivity test in a normally-lit room with your screen at a steady brightness, and note the setting so the next session starts from the same place.

References

• De Vries, H. (1943). The quantum character of light and its bearing upon threshold of vision, the differential sensitivity and visual acuity of the eye. Physica, 10(7), 553–564. First framed dark-adapted detection as photon-noise limited, arguing that threshold is set by the statistical fluctuations in the number of light quanta the eye absorbs.
• Rose, A. (1948). The sensitivity performance of the human eye on an absolute scale. Journal of the Optical Society of America, 38(2), 196–208. Derived that for an ideal detector limited only by photon statistics, luminance times threshold contrast squared times object size squared is constant, giving the inverse square-root dependence of threshold on luminance.
• van Nes, F. L., & Bouman, M. A. (1967). Spatial modulation transfer in the human eye. Journal of the Optical Society of America, 57(3), 401–406. Measured contrast sensitivity across spatial frequencies and many light levels, showing sensitivity rises with luminance and then saturates into a Weber plateau, with the transition depending on spatial frequency.
• Rovamo, J., Mustonen, J., & Näsänen, R. (1994). Modelling contrast sensitivity as a function of retinal illuminance and grating area. Vision Research, 34(10), 1301–1314. Built a quantitative model in which contrast sensitivity grows with the square root of retinal illuminance below a critical level (De Vries-Rose) and then saturates to a constant Weber fraction above it.