Abstract: Avoiding fatigue, not age, is the key factor reducing the large exit pupil size that amateur astronomers desire for dark-adapted deep-sky observing. Between the ages of 20 and 60, the exit pupil of the eye reduces only 14%. Fatigue induced by repeated exposure to low level light and loud sounds reduces exit pupil size by 40% older age groups and 30% in younger age groups, resulting in both having about 4mm fatigued exit pupils. For telescopic observing at magnifications higher than about 5x per inch of aperture, exit pupil is not a factor because the light pencil coming out of the eyepiece is smaller than even the reduced exit pupil size of the aged observer.
The relaxed human exit pupil size is key to the ability of an amateur astronomer to see faint magnitudes. How does the relaxed size of the exit pupil change with age?
7mm is frequently quoted by amateur astronomers as the exit pupil size of the relaxed, dark-adapted eye-pupil. Clark (1990) cites the 7mm number but doesnot provide a source. Schaefer (1990) at 213 provides an equation for the relationship between age and dark-adapted eye pupil size:
D_eye_pupil = 7mm exp(0.5 * [Age/100]^2 ) Eq. 1.0
citing Kumnick (1954) and Kadlevoca (1958). Apparently, these two studies are the source of the 7mm relaxed, dark-adapted eye-pupil size.
============================= Table No. 1 - Schaefer's eye-pupil to age equation Age and dark adapted eye pupil size (from Eq. 1.0) Age D_eye_pupil_mm 10 7.0 15 6.9 20 6.9 25 6.8 30 6.7 35 6.6 40 6.5 45 6.3 50 6.2 55 6.0 60 5.8 65 5.7 70 5.5 75 5.3 80 5.1 =============================
Schaefer does not provide a confidence interval for his model.
Kadlecova et al (1958) measured 906 diameters of pupils in 453 persons, including men and women from about age 5 to 85, after 15 minutes of dark adaptation. The measurements were taken in a dark room using infra-red light as a source of illumination. They presented their data - the average measurement and one standard deviation, in graphic form. Kadlecova did not report their data in tabular form
Taking off some rough numbers from Kadlecova's Figure 2:
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Table 2 - Kadlecova's eye-pupil statistics
Pupil size mm
Age Average Upper_std_dev Lower_std_dev
8 7.6 8.2 7.0
20 7.2 7.9 6.8
30 7.2 7.8 6.7
40 6.7 7.5 6.0
50 6.2 7 5.5
60 5.8 6.8 4.7
70 5.8 6.2 4.6
80 5.2 6.2 4.0
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Table 2 shows a large variation in "normal" dark adapted eye pupil size and approximately a 1mm diameter reduction in size (14%) between age 20 and age 60.
Kadlecova found no difference in dark adaptation between men and women or due to eye color.
Kumnick (1954) measured the dark-adapted eye pupils of 94 persons, men and women aged 7.5 to 91 years. Kumnick also used infra-red illumination and film to record the eye pupils. She also applied faint illumination to record the response of the pupil to low light levels. Unlike Kadlecova, Kumnick was not directly interested in measuring dark adapation. Kumnick's research goal was to measure an obscure pupillary response. When a person's eye is dark adapted and then "fatigued" with exposure to light, their maximal pupillary size can be restored by suprising or shocking them. The shock causes the pupil to relax. Kumnick accomplished this with a loud 97db sound. Kumnick took 94 persons, allowed their eyes to dark adapt for 10 minutes. Then their dark adapation and pupillary response was "light fatigued" by brief exposures to a 12.2 ft-candle faint light, sixty-times for one second, at four second intervals. In this manner, 6840 pupil size measurements were taken.
Kumnick presented her data - the average pupil size measurement - in graphic form, but she did not report in tabular form. Taking off some rough numbers from Kumick's Figure 4:
============================= Table 3 - Kumnick's eye-pupil statistics Group I II III IV Age 7.5-15.0 18.1-28.2 30.5-52.7 70.4-90.8 Number in group 21 25 24 24 Initial size in light Ave_size_light 4.2 4.2 3.7 3.2 _constricted Initial size after 10 minutes of dark adaptation Ave_size_dark 6.9 6.8 5.9 4.9 After pupil fatigue by repeated exposure to faint light Ave_size_light 4 3.9 3.6 2.9 _constricted_fatigued =============================
Kumnick found no difference in dark adaptation between men and women or due to eye color.
Table 3 shows the importance of avoiding fatigue and repeated exposure to faint light sources to maintain dark adaptation. The fatigued eye in 30-52 year-olds suffered an approximately 40% reduction in exit pupil diameter.
Where telescopic magnification is used and the eye pupil is larger than the exit pencil of light from the objective, age does not appear to be a factor. Stanton (1999) did not find any correlation between age and the ability to accurately estimate the visual magnitude of stars of varying B-V colors. Stanton (1999) at 109, Figure 6 (no pattern in residual error in estimating magnitudes of stars, telescopically, between v7.5 and v15.2, for observers between 20 and 65 for 650 observations) and at 111 ("Several factors do not appear to be particularly correlated to the color coefficient or observation error. . . . Age (Figure 8) does not appear to be a significant factor.")
No journal articles were found concerning whether age has any impact on the ability to see faint stars with the naked eye. For example, a study were a group of persons between ages 10 and 70 were asked to estimate the naked eye limiting magnitude for a star field. No field studies were found measuring the eye pupil of amateur astronomers under varying all-sky brightnesses at typical observing sites.
One would expect to find a reduction in the ability to see faint stars with the naked eye with age, since a reduction from 6.9mm (15 year olds) to a 6.2mm (50 year olds) in average dark adapted eye pupil size corresponds to about a 20% reduction in the eye's light grasp:
============================= Table 4 derived from Eq. 1.0 and Table No. 1 Age 15 40 50 55 70 80+ Eye_pupil_mm 6.90 6.5 6.2 6.0 5.5 5.0 Area_mm 37.4 33.2 30.2 28.3 23.8 19.6 Area_percent 100% 89% 81% 76% 64% 53% =============================
Schaefer captures this relationship algebrically in his telescopic limiting magnitude model for point-sources with:
F_ep = (D_obj/M*D_eye_pupil)^2 if D_eye_pupil < D_obj/M Eq. 2.0
F_ep = 1.0 if D_eye_pupil > D_obj/M Eq. 2.1
Some of the implications of the above are:
1) There is some good news for "older" observers. Even, in your sixties, 25% of you may have dark adapted eye pupil sizes that equal 25% of twenty-year olds.
2) If you want to observe faint objects at low magnification, hammering your eyes by driving to the observing site after dark might light fatigue your eye pupils by repeated exposure to oncoming headlights. Maybe there is some benefit to driving to the observing site in the twilight, taking a nap, and then observing?
3) Home measuring of the dark adapted exit pupil, done by holding up a triangluar of 3mm-10mm widths in front of the exit pupil in front of mirror probably won't work. If you can see the piece of measuring paper, your exit pupil is probably contracting in the faint light.
4) Kumnick's and Kadlecova's instrument setups suggest a star party activity. Measure pupil sizes with a commonly available "night vision" infra-red scope, interposing a reticule printed on computer transparency plastic, that gives the exit pupil measurement (assuming the infrared illumination source on the scope can be safely looked into at small distances). Mount the scope on a 2x4, using the other end as a chin rest set a standard distance from the night vision scope.
5) For telescopic observing at magnifications higher than about 5x per inch of aperture, exit pupil is not a factor because the light pencil coming out of the eyepiece is smaller than even the reduced exit pupil size of the aged observer:
============================= Table 5 - Knisely's Useful Magnifications Modified to add a 5mm exit pupil for "low-medium power" LOW POWER (3.7 to 9.9x per inch of aperture)(6.9mm to 2.6mm exit pupil) LOW-MEDIUM POWER (5.1 to 9.9x per inch of aperture)(5mm to 2.6mm exit pupil) MEDIUM POWER (10x to 17.9x per inch of aperture)(2.5mm to 1.4mm exit pupil) HIGH POWER (18x to 29.9x per inch of aperture)(1.4mm to 0.8mm exit pupil) VERY HIGH POWER (30x to 41.9x per inch of aperture)(0.8mm to 0.6mm exit pupil) EXTREME POWER (42x to 75x per inch)(0.6mm to 0.3mm exit pupil) EMPTY MAGNIFICATION (100x per inch and above) Modified from D. Knisely, 5/14/2004 sci.astro.amateur Usenet post, Thread "Eyepiece advice, again" =============================
Table 6 ties the above together showing the magnification at or below which various scopes have to be used before the eye pupil would become a constraining factor:
============================= Table 6 Minimum magnification, below which, eye-pupil size becomes a constraint by aperature and relaxed exit pupil size Aperature Inches 1 3 3.5 4 4.75 6 8 10 12 mm 25.4 76.2 88.9 101.6 120.7 152.4 203.2 254.0 304.8 Age D_eye_pupil_mm Magnification applied 10 7.0 4 11 13 15 17 22 29 36 44 15 6.9 4 11 13 15 17 22 29 37 44 20 6.9 4 11 13 15 18 22 30 37 44 25 6.8 4 11 13 15 18 22 30 37 45 30 6.7 4 11 13 15 18 23 30 38 46 35 6.6 4 12 14 15 18 23 31 39 46 40 6.5 4 12 14 16 19 24 31 39 47 45 6.3 4 12 14 16 19 24 32 40 48 50 6.2 4 12 14 16 20 25 33 41 49 55 6.0 4 13 15 17 20 25 34 42 51 60 5.8 4 13 15 17 21 26 35 43 52 65 5.7 4 13 16 18 21 27 36 45 54 70 5.5 5 14 16 19 22 28 37 46 56 75 5.3 5 14 17 19 23 29 38 48 58 80 5.1 5 15 17 20 24 30 40 50 60 =============================
Clark, R.N. Visual Astronomy of the Deep Sky. Cambridge Univ. Press. 1990. http://www.clarkvision.com/visastro/appendix-e.html
Kadlecova, V., Peleska, M. and Vasko, A. 1958. Dependence on Age of the Diameter of the Pupil in the Dark. Nature 182:1520.
Kumnick, L.S. Sept. 1954. Pupillary Psychosensory Restitution and Aging. J. Optical Soci. of America 44(9):735. http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1954JOSA...44..735K
Schaefer, B.E. Feb. 1990. Telescopic Limiting Magnitude. PASP 102:212-229. http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1990PASP..102..212S
Stanton, R.H. 1999. Visual magnitudes and the "average observer": The SS Cygni field experiment. JAAVSO 27:97-112 http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1999JAVSO..27...97S