Introduction

Imagine walking from the bright midday sun into a dimly lit room and noticing how the red of a painting seems muted, while the blues deepen and take on a richer quality. Or consider how colors on an HDR display suddenly appear “punchier” compared to standard screens, even though the underlying data values remain unchanged. These everyday experiences hint at a fundamental truth: brightness and perceived color are inseparable.

In this post, we’ll journey through the science of vision—from the microscopic workings of rods and cones to advanced color-appearance models like CIECAM02—to uncover why and how changing light levels can alter hue, saturation, and lightness. Along the way, we’ll introduce key physiological mechanisms, derive core mathematical relationships, and examine practical implications for art, design, and display technology.

By the end, you’ll appreciate that color is not a fixed attribute of objects but a dynamic phenomenon shaped by light intensity, adaptation, and context. Let’s brighten our understanding of color!

The Basics: Luminance vs. Brightness vs. Lightness

  • Luminance (physical quantity) is the measurable flux of light per unit area per unit solid angle (cd/m²).
  • Brightness (psychophysical) is our subjective impression of how much light is emanating from or reflected by a surface.
  • Lightness refers to how bright a surface appears relative to a reference white under the same lighting.

Key point: While luminance is objective, brightness and lightness depend on context—surrounding colors, adaptation level, and importantly, overall illuminance (scene brightness).

2. Physiology of Vision: Rods, Cones, and Adaptation

  1. Cone responses

    • Three cone types (L-, M-, S-cones) with spectral sensitivities $S_L(λ)$, $S_M(λ)$, $S_S(λ)$.
    • At high luminance, cones dominate color perception.

  2. Rod intrusion

    • At low luminance, rods contribute to brightness but not hue, causing desaturation and hue shifts (“Purkinje shift”).
    • Purkinje shift: reds appear darker and blues appear lighter under dim light because rod sensitivity peaks around 507 nm.

  3. Adaptation mechanisms

    • Light adaptation (cones adjust gain downward as scene brightens)
    • Dark adaptation (rods and cones increase sensitivity in darkness)

Opponent-Process and Color Appearance

Human vision transforms cone signals into opponent channels:

\[\begin{aligned} R & = L - M,\\ G & = M - S,\\ B & = L + M + S \; (\text{luminance channel}) \end{aligned}\]
  • Hue and chroma depend on the ratio of $R$ and $G$ channels, but the perceived saturation is modulated by the luminance channel $B$.

Mathematical Models of Color Appearance

CIELAB (1976)

A simple non-linear transform from CIEXYZ to perceptual Lightness \(L^*\), chroma \(a^*, b^*\):

\[\begin{aligned} L^* &= 116\,f\bigl(Y/Y_n\bigr) - 16,\\ a^* &= 500\bigl[f(X/X_n) - f(Y/Y_n)\bigr],\\ b^* &= 200\bigl[f(Y/Y_n) - f(Z/Z_n)\bigr], \end{aligned} \quad f(t) = \begin{cases} t^{1/3}, & t > (6/29)^3,\\ \frac{1}{3}(29/6)^2\,t + \tfrac{4}{29}, & \text{otherwise}. \end{cases}\]
  • Limitation: CIELAB’s $L^*$ correlates with lightness but doesn’t fully predict how hue and chroma shift with overall scene brightness.

CIECAM02

A full color appearance model incorporating:

  • Surround conditions (dark, dim, average)
  • Adaptation luminance $L_A$
  • Chromatic induction by surround
  • Output correlates: Lightness $J$, chroma $C$, hue $h$, brightness $Q$, saturation $s$.

Key equations (simplified):

\[\begin{aligned} &D = F\bigl(1 - \tfrac{1}{3.6}\exp\bigl[-(L_A+42)/92\bigr]\bigr),\\ &J = 100\bigl(A/A_w\bigr)^c,\\ &C = t^{0.9}\sqrt{\frac{J}{100}}\bigl(1.64 - 0.29^n\bigr)^{0.73}, \end{aligned}\]

where $A$, $A_w$ are achromatic responses for the test and whitepoint, and parameters $c, n, t$ depend on surround and viewing conditions – see [Fairchild, 2013] for full derivation.

Takeaway: As adaptation luminance $L_A$ rises, the model predicts decreases in both perceived lightness $J$ for a constant patch and shifts in chroma $C$.

The Helmholtz–Kohlrausch Effect

Even at constant chromaticity, apparent saturation rises with increasing luminance.

  • Empirical relation:

    \[R_{\mathrm{HK}} = k \,(L^*)^\alpha\]

    where $R_{\mathrm{HK}}$ is the extra perceived chroma, $k\approx 0.0378$, $\alpha\approx 0.53$ under average surround [Hunt, 1952].

This effect explains why bright, pure colors (e.g., neon signs) appear more vivid than dim ones, even if their chromaticity hasn’t changed.

Putting It All Together: Color Shift with Brightness

  1. Hue shift

    • At low light, rods skew perceived hue toward shorter wavelengths (Purkinje shift).

  2. Chroma shift

    • Helmholtz–Kohlrausch boosts vividness with luminance:

      \[C_{\mathrm{perceived}} = C_{\mathrm{chromaticity}} + R_{\mathrm{HK}}(L^*).\]

  3. Lightness non-linearity

    • CIELAB’s \(L^*\) cube-root compresses low luminance more than high.

Proof sketch:

  • Start with a constant radiant distribution \(X,Y,Z\).
  • Increase all three by factor \(\beta>1\).
  • Compute new \(L^*_{\rm new} = 116(\beta\,Y/Y_n)^{1/3}-16\).
  • The ratio \(\frac{L^*_{\rm new}}{L^*} = \beta^{1/3}\).
  • Meanwhile, the Helmholtz–Kohlrausch term adds \(\Delta C = k\,(L^*_{\rm new})^\alpha - k\,(L^*)^\alpha>0\).
  • Thus both lightness and chroma increase, altering perceived color.

Real-World Examples

Scenario Observation
Street lights (dusk) Whites appear yellowish; blues deeper (Purkinje shift + low cone gain)
HDR display vs. SDR Same RGB values but HDR’s higher luminance → “punchier” colors
Art gallery lighting Dim accent lights can desaturate colors, altering mood dramatically

Practical Implications

  • Photography & Display: Tone-mapping algorithms must correct for Helmholtz–Kohlrausch to avoid “flat” images.
  • Lighting design: Museums use low illuminance to protect art, but this changes color fidelity—trade-off between preservation and appearance.
  • Vision science: Understanding adaptation crucial for color-blind test design and for reliable color matching in industry.

Conclusion

As we’ve explored in this deep dive, perceived color is a dynamic construct—far more than the fixed wavelengths recorded by a light meter. Changes in scene brightness engage a cascade of physiological and psychological processes:

  1. Photoreceptor Adaptation

    • Cones and rods adjust their sensitivity continuously. In bright light, cone gains decrease to prevent overstimulation, while in dim light, rod signals dominate, introducing hue biases (the Purkinje shift).

  2. Opponent Processing and Nonlinear Transformations

    • The brain’s conversion of cone inputs into opponent channels and nonlinear mappings (as in CIELAB’s cube‐root function) ensure that identical spectral stimuli yield different perceptions at different luminances.

  3. Color Appearance Phenomena

    • The Helmholtz–Kohlrausch effect shows that increased luminance alone makes colors appear more saturated, even if their chromaticity coordinates remain unchanged.
    • Modern appearance models like CIECAM02 quantitatively predict how hue, lightness, brightness, and chroma shift with both adaptation level and surround context.

  4. Practical Implications

    • From HDR tone mapping to museum lighting and display calibration, engineers and designers must account for these brightness-dependent shifts to maintain color fidelity—or to exploit them for dramatic effect.

Key takeaway: Color perception is inherently context‐dependent. Brightness does not merely make objects lighter or darker; it subtly and systematically alters hue and saturation. Next time you dim your room lights or toggle your display’s brightness, pause to notice how the very essence of color seems to change—because, in the interplay between photons and photoreceptors, nothing is ever quite constant.

Thank you for reading! If you have questions about the models or want to explore simulations of these effects, leave a comment below.

References

  1. Hunt, R. W. G. (1952). The Helmholtz–Kohlrausch effect. Optica Acta, 49(3), 213–223.
  2. Fairchild, M. D. (2013). Color Appearance Models (3rd ed.). Wiley-IS\&T.
  3. Wyszecki, G., & Stiles, W. S. (2000). Color Science: Concepts and Methods, Quantitative Data and Formulae (2nd ed.). Wiley.
  4. Brainard, D. H., & Stockman, A. (2010). Color vision mechanisms. In O. N. Jameson & T. Gegenfurtner (Eds.), High-Level Vision: Object Recognition and Modern Color Science. MIT Press.

*This deep dive highlights that color is never purely a function of wavelength—it dances with light level, adaptation, and context. Next time you adjust the brightness on your screen, notice how the reds come alive and the blues sink back! *