March 2012
Volume 53, Issue 14
ARVO Annual Meeting Abstract  |   March 2012
A Unified Formula For Light-adapted Pupil Size
Author Affiliations & Notes
  • Andrew B. Watson
    NASA Ames Research Center, Moffett Field, California
  • John I. Yellott
    Cognitive Sciences, Univ of California-Irvine, Irvine, California
  • Footnotes
    Commercial Relationships  Andrew B. Watson, None; John I. Yellott, None
  • Footnotes
    Support  NASA Space Human Factors Engineering (WBS 466199)
Investigative Ophthalmology & Visual Science March 2012, Vol.53, 143. doi:
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      Andrew B. Watson, John I. Yellott; A Unified Formula For Light-adapted Pupil Size. Invest. Ophthalmol. Vis. Sci. 2012;53(14):143.

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      © ARVO (1962-2015); The Authors (2016-present)

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The literature contains at least eight different formulae relating pupil diameter to the photopic luminance of an adapting field. There are large unexplained discrepancies among these formulae. Pupil diameter also depends on the area of the adapting field, the age of the observer, and whether one or two eyes are adapted, which may explain some of the differences. We sought to review the existing formulae and to develop a single unified formula incorporating all of these effects.


We converted six formulas to a common set of units to allow comparison (Blackie and Howland, 1999; Crawford, 1936; De Groot and Gebhard, 1952; Holladay, 1926; Moon and Spencer, 1944; Stanley and Davies, 1995). We developed a formula to represent the effect of age, based on the data of Winn et al. (1994), and a formula to represent the effect of monocular adaptation, based on the data of Blanchard (1918) and Reeves (1918). We developed a unified formula, based on Stanley and Davies formula for luminance and field area, but also incorporating the age effect and monocular effect.


The unified formula computes pupil diameter for any combination of photopic luminance, age, field size, and binocular or monocular viewing. It successfully matches the very different formulae of Winn et al. (1994), who used a small field and monocular adaptation, and Moon and Spencer (1944), who used a large field and binocular adaptation. An example of the unified formula, along with the various historical formulae, is shown in the figure. The parameters used were: age = 40 years, field diameter = 20 deg, binocular adaptation.


We have developed a unified formula for pupil diameter as a function of photopic luminance, field size, observer age, and monocular vs binocular adaptation. The unified formula is consistent with most of the classical results. The formula may be useful in estimating pupil diameter when it cannot be easily measured.  

Keywords: pupil • pupillary reflex • visual acuity 

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