South PacificApparent
Study Vol.
20, No. 2,Magnitudeof2000a Visible Star under the Hazard of Light Glare Pollution

7Apparent Magnitude of a Visible Star under the Hazardof Light Glare Pollution
Naoyoshi NAMEDA

Abstract
Kihoku-cho in Kagoshima prefecture is known as one of the best town in our country for detecting andobserving stars.
Kihoku-cho is also selected the place for experimental installation of ideal lighting by the JapaneseEnvironmental Ministry in 1998 fiscal year. For the promotion of the experiment, experts were assembled
in a "committee for the best lighting in Kihoku-cho".

The author was selected as a member of thecommittee and its chairman in November 1998. Usually, light pollution is caused by the upwards straying
artificial light in urban places.

However, in Kihoku-cho town, there is no such artificial lighting. The

most hazardous light for observation of stars is the newly installed lighting apparatus itself, especiallylight beaming in direction of an observer. Hence, a guideline for better lighting without hazard to starobservation was developed theoretically and experimentally, and experimental lighting was installedaccording to the guideline.
Key words ： star watching, light polution, sky glow

Introduction
Guidelines for countermeasures against light pollution were issued by theJapanese Environment Ministry in March 1998.
In reference to the guidelines, special types of illumination whose upwards
straying light is constrained, were recommended.
If lighting is designed strictly according to the guidelines, light pollution isexpected to decrease. The main problem of light pollution in urban areas is thatstars are not observed in the brightened sky. This brighter sky effect is called skyglow. Kihoku-cho in Kagoshima prefecture was selected as one of the best
location for star observation in Japan. In fiscal year 1998, Kihoku-cho was also
selected as the place for the experimenting ideal lighting. For the promotion of
the experiment, experts were assembled in a "committee for ideal lighting in
Kihoku-cho" an electric specialist, a construction specialist, an employee of theKyushu electric power company, an anti-pollution authority of the prefectureand so on. I was also selected as a member of the committee and its chairman inNovember 1998. We had many discussions until October 1999, and carried out
many star observations. Kihoku-cho has very little artificial lighting and no sky
glow of its area and is sheltered by Sakurajima Volcano from the sky glow ofComputer and Systems Engineering Department, Fukuoka Institute of Technology
3-30-1 Wajirohigashi, Higashi-ku, Fukuoka 811-0214, Japan.

South Pacific Study Vol. 20, No. 2, 2000

8Kagoshima City. The most hazardous light for the observation of stars is newly
installed lighting apparatus, especially light emitted in the direction of anobserver, not upwards straying light.
According to the guidelines of the Ministry, the most hazardous light is
supposed to be the upwards straying artificial light. But, in special cases, when alamp is set in a lower position, upward straying light exists and can be directed tothe eye of observer who looks up at the stars, but the straying light in this case isless hazardous. Actually, in Kihoku-cho low light fixtures were installed.
Then, light pollution in Kihoku-cho could not be properly solved by following
the guidelines of the Ministry, and so the author aimed to establish anotherguideline for lighting to ensure better star observation.

The Threshold Magnitude of an Observable Detectable
Star and the Hazard Light Affecting an Observer
The author supposed the degree of hazard is measurable by the threshold
magnitude of star, which is observable, detected under the hazard of artificial
light.

Consequently, the relation between star magnitude and illuminating

factors for an observer must be investigated.
First, N.Pogson defined star magnitude in 1850, and on this basis C.F. Zo¨llnerconstructed a star visual measurement device which was two nickol prisms able
to conduct two light fluxes for two stars (Unzelt, Kodaira K translator, 1968).
Given that its ratio of the two light fluxes is S1/S2, the difference in magnitude(m) of the two stars is follow,
m1-m2=-2.5log(S1/S2) ・ ・ ・ ・ (1)If m2=0, S2 becomes one,
where m1 and m2 are magnitudes of the stars whose light fluxes are S1 and S2
respectively.
Then,
m1=-2.5log(S1）(magnitude) ・ ・ ・ ・ ・ ・ (2)On the other hand, its hazard for observation star corresponds to the disability
glare problem in illuminating engineering.
The luminance difference (delta L, as listed in the handbook of Japanese
Illuminating Engineering Society, 1987) between back ground luminance andobjective luminance is increased by the effect of hazard light as following
formula,Lev=KEv/θ^n ・ ・ ・ ・ ・ ・ ・ ・ ・ (3)Where, Lev is increasing luminance, Ev is the illuminance on an observer's
cornea and θ is the arc angles between the glare source and the observer's
visual direction. k and n are constants.
If the illuminance on the cornea by a star is Es and the illuminance of the glare

Apparent Magnitude of a Visible Star under the Hazard of Light Glare Pollution

9source is Ev, the observable degree of a star is defined as follows
Observation detected degree of a star=log(Es)- αlog(Ev) ・ ・ ・ (4)In formula (4), Es and Ev expressed by logarithmic function are postulated aslight sensitive value corresponding to biological measures. Then, the Fechner
effect may be considered (Tanaka, 1977).
α is a constant comparing star and glare source smaller than "1".
In formula (2), S1: light flux entering the measurement device, and Es:
illuminance on the observer's cornea, are expected to have a proportional
relation, as follows:
S1＝CEs ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (5)Where C is constant.
Combining formula (5) and formula (2),log(Es)=-m1/2.5+logC ・ ・ ・ ・ ・ (6)Combing (6) and (4), and letting the threshold observably detective degree of astar be zero, then,observable detective degree of a star=0= -m1/2.5+logC - αlog(Ev) ・ ・ (7)m1 is obtained as follows, thenm1＝2.5logC-2.5αlog(Ev) ・ ・ ・ (8)Therefore, the threshold logarithmic magnitude of star is inversely proportional
to the hazardous light logarithmic illuminance on an observer's cornea.

Experimental Results and Discussion
Observation of stars was carried out twice in Kihoku-cho, once in December
1998 and again in August 1999. The experiment in December, was done in thegarden of town office. The observers were six Kihoku-cho officials- three aged
30 years old, and three aged 50 years old. Their visual acuity was more than 1
value by the Randolt ring test chart after accommodation adjustment. They weretasked to approach towards a glare source and declare the limit criteria, which aparticular star was. At this position, illuminant values were measured on thesurface of observers eye by an IM-3 illuminance meter made by Topcon Co., Ltd.
in Japan. The experimental scheme is shown in Fig. 1. The magnitude of the staris confirmed by a star constellation chart which depicts the 4th magnitude of astar (Specially issue Newton, 1995).
Fig. 2 shows the relation between the illuminance and the magnitude ofparticular stars. Their axes are plotted as logarithmic measures. The former
experimental results are indicated as solid circles. Latter experiment wasimplemented in August 1999. Usually the atmosphere contains moisture insummer in Japan, but the sky at Uwaba-park located on a hill in Kihoku-cho, wasSouth Pacific Study Vol. 20, No. 2, 2000

10magnitude of starFig.1 Experimental scheme

IlluminanceFig. 2 Illuminance on the cornea and magnitude of star
Solid circles are 6 SB of 30-50 age of years and open circles are 5 SB of20 age of years.

Apparent Magnitude of a Visible Star under the Hazard of Light Glare Pollution

11clear. The experimental observers were five students in Kagoshima University.
They are all 21 years old and their visual acuity was also over 1 value afteraccommodation. The obtained data are plotted in the open circle in Fig. 2. The
data of the two groups is put in a straight line which shows the relation predictedby formula (7). In Fig. 2, C andα of formula (8) are calculated as 6.3, and 0.4,respectively.
The author proposes this formula is as valid for estimating of the light hazardsof artificial lamps before new lighting installation.

References
Invitation to a star twinkling sky 1995. Specially issue Newton, kyouiku-sha, 7277pp. in JapaneseJapanese illumination engineering society ed 1978. Lighting Handbook, Ohmsha, 349pp. in Japanese
TANAKA Y. 1977. Psychological Measurement Method, Tokyo Daigaku shuppankai, 143pp. in Japanese
UNZELT A.: Kodaira K translator 1968. Modern Astronomy, Iwanami-shoten,
113pp. in Japanese(Accepted 4 January, 2000)