## Abstract

A relatively small gray sample looks lighter (darker) when it is placed on darker (lighter) background. This phenomenon is an example of the well-known contrast effect. The purpose of this paper is to make a quantitative determination of the effect, and to derive a formula for it.

For any given gray sample and gray surround on the left side, the observer was instructed to choose, for the different gray surround on the right, a different gray sample appearing as light as that on the left. It was found that sample lightness changes rapidly with reflectance when sample reflectance is close to that of the background. This effect was named the “crispening effect.”

Several models (von Kries coefficient law, Hurvich–Jameson induction) were tried, but none of them reproduced the experimentally discovered crispening effect. A fairly successful empirical formula was developed by adding a term for the crispening effect to the formula for the induction theory.

© 1966 Optical Society of America

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### Equations (17)

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(1)
$${L}_{1}=f({Y}_{1}-C{Y}_{b1})$$
(2)
$${L}_{2}=f({Y}_{2}-C{Y}_{b2}),$$
(3)
$${Y}_{1}-C{Y}_{b1}={Y}_{2}-C{Y}_{b2},$$
(4)
$${Y}_{2}={Y}_{1}+C({Y}_{b2}-{Y}_{b1}).$$
(5)
$${L}_{1}=f[{Y}_{1}/(n{Y}_{b1}+{Y}_{b2})],$$
(6)
$${L}_{2}=f[{Y}_{2}/(n{Y}_{b2}+{Y}_{b1})],$$
(7)
$${Y}_{2}={Y}_{1}(n{Y}_{b2}+{Y}_{b1})/(n{Y}_{b1}+{Y}_{b2}).$$
(8)
$${L}_{1}={V}_{1}-C{V}_{b1}$$
(9)
$${L}_{2}={V}_{2}-C{V}_{b2},$$
(10)
$${V}_{2}={V}_{1}+C({V}_{b2}-{V}_{b1}).$$
(11)
$$L=V-C{V}_{b}+f(V,{V}_{b},{\overline{V}}_{b}).$$
(12)
$$f(V,{V}_{b},{\overline{V}}_{b})={C}_{2}{\overline{V}}_{b}[(V-{V}_{b})/{C}_{3}]{e}^{-\mid V-{V}_{b}\mid /{C}_{3}},$$
(13)
$${L}_{1}={V}_{1}-{C}_{1}{V}_{b1}+{C}_{2}{\overline{V}}_{b}[({V}_{1}-{V}_{b1})/{C}_{3}]{e}^{-\mid {V}_{1}-{V}_{b1}\mid /{C}_{3}}$$
(14)
$${L}_{2}={V}_{2}-{C}_{1}{V}_{b2}+{C}_{2}{\overline{V}}_{b}[({V}_{2}-{V}_{b2})/{C}_{3}]{e}^{-\mid {V}_{2}-{V}_{b2}\mid /{C}_{3}};$$
(15)
$$\begin{array}{l}{L}_{i}={V}_{i}-0.35\hspace{0.17em}{V}_{bi}+0.5\hspace{0.17em}{\overline{V}}_{b}[(Vi-{V}_{b}i)/1.5]{e}^{-\mid Vi-Vbi\mid /1.5}\\ i=1,2\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}{\overline{V}}_{b}=({V}_{b1}+{V}_{b2})/2.\end{array}$$
(16)
$${L}_{i}={V}_{i}-0.30{V}_{bi}+0.4{\overline{V}}_{b}[(Vi-Vbi)/1.4]{e}^{-\mid Vi-Vbi\mid /1.4}.$$
(17)
$${L}_{i}={V}_{i}-0.20\hspace{0.17em}{V}_{bi}+0.15[(Vi-Vbi)/0.8]{e}^{-\mid Vi-Vbi\mid /0.8}.$$