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Visual Thresholds of Steady Point Sources of Light in Fields of Brightness from Dark to Daylight
Abstract
The threshold illumination i at the eye from a steady source of light of 1′ angular diameter in a field of brightness b was measured for b ranging from zero to about 1500 candles per square foot. The data were obtained by five young experienced observers using both eyes unaided and with natural pupil. A bend in the i, b curve at about b = 1000 mµL occurred at the transition from foveal to extra-foveal vision. The relation i= 10-10 (l+b)½, where i is in footcandles and b is in millimicrolamberts, expressed the experimental data within a factor of 3 over the entire range.
... Evaluating Eq. 5 using Planck's equation and the tabulated luminous efficiency functions gives ρ2850 = 1.408. Knoll et al (1946) found thresholds using incandenscent lamps with colour temperature 2360 K (Tousey & Hulburt 1948). If both teams measured a (photopic) luminance at some equal value then the scotopic luminance of Blackwell's light would be greater by a factor ρ2850/ρ2360 = 1.220. ...
... Using Eq. 13 and the previously calculated values of ρT , the corrections for the laboratory temperatures of Blackwell (1946) and Knoll et al (1946) can then be written ...
... The point-source visibility study of Knoll et al (1946) is of special interest because of its role in subsequent astronomical applications. Five young experienced observers used binocular vision to view a projected target of approximate diameter 1 arcmin. ...
The standard visibility model in light pollution studies is the formula of Hecht (1947), as used e.g. by Schaefer (1990). However it is applicable only to point sources and is shown to be of limited accuracy. A new visibility model is presented for uniform achromatic targets of any size against background luminances ranging from zero to full daylight, produced by a systematic procedure applicable to any appropriate data set (e.g Blackwell (1946)), and based on a simple but previously unrecognized empirical relation between contrast threshold and adaptation luminance. The scotopic luminance correction for variable spectral radiance (colour index) is calculated. For point sources the model is more accurate than Hecht's formula and is verified using telescopic data collected at Mount Wilson by Bowen (1947), enabling the sky brightness at that time to be determined. The result is darker than the calculation by Garstang (2004), implying that light pollution grew more rapidly in subsequent decades than has been supposed. The model is applied to the nebular observations of William Herschel, enabling his visual performance to be quantified. Proposals are made regarding sky quality indicators for public use.
... He applied various simplifications to his theory, not all of them acceptable. We rethink Bruin's method by making some corrections: we take into account the variation of the luminance of the Moon with the phase, we use the experimental results of Knoll et al. (1946) on threshold contrast, we apply Riccò's law, and we consider the atmospheric extinction coefficient to be variable. We use the theory to derive the Danjon limit. ...
... we have applied (A.3) and (A.9); then Riccò's law for not resolvable images is Knoll, Tousey, and Hulburt (1946) for a probability of vision of 100%. Table 2 represents coefficient S B according to Blackwell (1946), which corresponds to a probability of vision of 50%. ...
Bruin (1977) devised a procedure to find out the visibility of the first crescent Moon. He applied various simplifications to his theory, not all of them acceptable. We rethink Bruin's method by making some corrections: we take into account the variation of the luminance of the Moon with the phase, we use the experimental results of Knoll et al. (1946) on threshold contrast, we apply Riccò's law, and we consider the atmospheric extinction coefficient to be variable. We use the theory to derive the Danjon limit.
... The threshold illuminance th E is the same for all non-resolvable images regardless of size and only depends on the luminance of the background. Knoll, Tousey, and Hulburt (1946) determined the threshold illumination for circular images of 1 minute of arc of angular diameter on a background with luminance from 0 to 31.83 cd/m 2 and from 318.3 to 14,323.5 cd/m 2 . The experiment was done with five young observers with good vision. ...
... The threshold illuminance does not depend on the size of the image. The data have been taken from table VIII of Blackwell corresponding to an angular size of 0.595 minutes and from the graph of Knoll et al. (1946). We have corrected the Blackwell data by multiplying the threshold contrast by 2 so that it corresponds to a probability of 100%, and we can compare it with the data from Knoll et al. ...
... Naked Eye Limiting Magnitude (NELM) is a formula from Knoll to determine the visibility of comets and astronomical objects (Knoll et al., 1946). The result of NELM and ( ) is then used to determine the Bortle Scale of a potential site. ...
Astrotourism is tourism that uses astronomy as its main attraction. As astrotourism requires astronomy phenomena, it requires a location free from light pollution. As some have posited locations free from light pollution as one of the cultivating elements for maintaining sustainability, Astrotourism can be used to achieve sustainability. Sustainability can be put under the umbrella of Maqasid Syariah and halal tourism. It is thus of utmost importance to demonstrate the unique capabilities of Malaysia as a viable Astrotourism attraction and how it can help achieve the goal of sustainability, both of which are the objectives of this research. Two methods are employed in this study; the first is to identify potential Astrotourism sites using the dark sky database, light pollution mapping and Garstang formulation of light pollution. The second method is comprised of identifying the cultivating elements of sustainability. Through this method, three potential Astrotourism sites could enhance the notion of sustainability, including sustainability from the economic, wellbeing and biodiversity aspects and, more importantly, sustainability towards the holistic practice of Islam. This demonstrates the encompassing benefit of Astrotourism towards sustainability and its development potential in Malaysia.
... Also, many researches of the true and pseudo dawns were achieved. Monitoring the dim light (zodiacal light or pseudo dawn or false dawn) and clear light (true dawn) by the naked eye dependents on the contrast threshold of the human eye during the night sky (Richard and Blackwell (1946), Knoll et al. (1946), Pirenne (1967), Roach and Gordan (1973), NPL (2013) and Crumey (2014)). ...
This research is a new addition to the previous work done in Egypt to determine the exact time of the true dawn due to the urgent need of society for that. Twilight observations were carried out by SQM and the naked eye (N.E.) in the high visibility conditions for the morning twilight sky in the time interval (2018-2019) at Fayum in Egypt (29° 17´ N, 30° 03´ E, 50 m Elev.). The true dawn is found to be appear between Do≈14° to 14.8° according four different criteria applied in this work;(1) the threshold of eye in the magnitude, which is as 0.83 m from the full night (Abdel-Hadi and Hassan (2022) (I and II)), (2) the naked eye observations by the group, (3) the relation: H (Horizontal) =πZ (Zenith), (4) at 0.015 cd/m 2 as minimum energy for the mesopic region of twilight. The observations show that the clouds absorb about 19% of the energy (cd.m-2. degree-1) during the full night(Do=26.5˚-18˚), about 2.5% of the energy (cd.m-2 .degree-1) during the twilight period (Do=18˚-2.5˚) from the rays falling on.
... The first area is when the contrast is very high, the probability of vision is 100%: we always see the object. Table 5.-The logarithm of the threshold illuminance th E to see a circular object of one minute of arc in angular diameter against a background of luminance s B , according to Knoll et al. (1946). The luminance is in cd/m 2 , and the threshold illuminance is in lux. ...
We define the width of the window of visibility of the first lunar crescent as the interval of altitudes of the Moon between which we can see the crescent. We define the duration of the visibility window or time during which we see the crescent; and we also define the altitude of optimal vision of the crescent. We check the parameters on which the visibility window depends. We determine the variation of the visibility window with the phase angle, the atmospheric attenuation constant, the latitude of the observation site, and the declinations of the Sun and the Moon.
... Other researchers (Knoll, Tousey & Hulburt, 1946) devised experiments to find the threshold contrast for 100% probability. Comparison of the results of the various visual sensitivity experiments give similar results, but they are highly dependent on the experimental procedure ...
... Other researchers (Knoll, Tousey & Hulburt, 1946) devised experiments to find the threshold contrast for 100% probability. Comparison of the results of the various visual sensitivity experiments give similar results, but they are highly dependent on the experimental procedure ...
Brief report on how to calculate the first visibility of the Moon crescent. We warn against the misinterpretation of Blackwell's threshold visibility experiment. We state that the width of the first lunar crescent is less than the resolving power of the human eye, so the determining factor for visibility is the illuminance of the Moon and not its brightness.
... Also, many researches about true dawn and pseudo dawn were achieved. Monitoring the dim light (zodiacal light or pseudo dawn) and clear light (true dawn) by the naked eye are dependents on the contrast threshold of the human eye during the night sky Knoll et al., 1946;Pirenne, 1967;Roach and Gordan, 1973). ...
Naked eye observations of the morning twilight phenomenon, beginning, end of a pseudo dawn and the true dawn are recorded. These results are an average of 38 observations carried out at Wadi Al Natron (30° 30' N, 30° 09' E) with a desert background during the years 2014-2015. These observations enabled us to get an average depression of the sun below the horizon of about 19.74o (begin of zodiacal light), 15.41° (end of zodiacal light) and the beginning of twilight (true dawn) is 14.57° (The highest value of confidence, mean+ 1SD) which lies in a range between (12.48o ≤ Do ≤ 15.14o). These results show that there is about 5o difference between our obtained value and that currently used in Egypt which is 19.5o. The azimuthally range of observations in the solar vertical direction ranged from 0° to 20°, but this phenomenon was followed from 0° to 10° along the altitudinal range. These results indicate that the currently used angle for calculating morning twilight in Egypt now is the first zodiacal light (pseudo dawn) and not true dawn.
... We can see the difference of pattern of night sky brightness at both location and determine the naked-eye range of visible astronomical bodies. The determination of the visible celestial object by the naked eye is expressed in the log of the night sky brightness magnitude (m) with formula [26] derived from Knoll, where NELM is the naked eye limiting magnitude. NELM = 7.93-5 x log (10 4.316-(m/s) + 1 (4) From this formula we can predict the visible object in the sky theoretical in respect of the distinction of both site profiles. ...
... We can see the difference of pattern of night sky brightness at both location and determine the naked-eye range of visible astronomical bodies. The determination of the visible celestial object by the naked eye is expressed in the log of the night sky brightness magnitude (m) with formula [26] derived from Knoll, where NELM is the naked eye limiting magnitude. NELM = 7.93-5 x log (10 4.316-(m/s) + 1 (4) From this formula we can predict the visible object in the sky theoretical in respect of the distinction of both site profiles. ...
... Typical unaided eyes were a point of research by many investigators, to determine the minimum threshold that dark adapted eyes can characterize, for instance Knoll et al. (1946) and Richard (1946). ...
... Typical unaided eyes were a point of research by many investigators, to determine the minimum threshold that dark adapted eyes can characterize, for instance Knoll et al. (1946) and Richard (1946). ...
... The difference pattern of night sky brightness at both location is then determined and the naked-eye range of visible astronomical bodies. The determination of the visible celestial object by the naked eye is expressed in the log of the night sky brightness magnitude (m) with formula [11] derived from Knoll, where NELM is the naked eye limiting magnitude. NELM = 7.93-5 x log (10 4.316-(m/5) + 1 (1) From this formula we can predict the visible object in the sky theoretically in respect of the distinction of both site profiles. ...
Light pollution is an anthropogenic by-product of modern civilization and heavy economical activity, sourced from artificial light. In addition of its detrimental impact on human, and ecology, light pollution brightens the night sky, limiting the range of visible astronomical bodies detected by naked-eye. Since it is becoming a global concern for astronomers, the level of light pollution needs to be monitored to study its mark on the astronomical data. Using Sky Quality Meter in the period of 5 months, we investigated the links between city population and its vicinity from the city center towards the profile of the night sky and the limiting magnitude of the naked eye. We eliminate the data factored by clouds and moon brightness on account of it has an adverse effect on sky brightness that could disrupt research on light pollution. From the result, we can see population and location distance from the city as major variables of light pollution, as Kuala Lumpur, a city center sky is 5 times brighter than Teluk Kemang, a suburban sky. Some recommendations in reducing the effect of light pollution will be also discussed.
... Typical unaided eyes were a point of research by many investigators, to determine the minimum threshold that dark adapted eyes can characterize, for instance Knoll et al. (1946) and Richard (1946). ...
Twilight observations were carried out by naked eye in the period (2010–2012) for north Sinai (Lat. 31°4′N, Long. 32°52′E) where the background is desert, and for Assiut (Lat. 27°10′N, Long. 31°10′E) in the period (2012–2014) where the background is agricultural land. The purpose of these observations is to calculate the depression of the sun below the horizon at which the normal eye can discriminate the dawn (morning white thread) for two sites. The results indicated that this discrimination takes place at vertical sun depression angles, Do=14.61° and 13.665° at Sinai and Assiut respectively.
... The opacity classes of some clouds were in full agreement with absorption in magnitudes determined by other observers using star count techniques. Typical unaided eyes were a point of research by many investigators, to determine the minimum threshold that dark adapted eyes can characterize, for instance, Knoll et al. (1946), Richard Blackwell (1946), Ashburn (1952) and Tousey and Knoll (1953). Worth to notice that, (Shariff, 2008) had carried out a comparison between the normal human eye and the electronic detectors in relation to morning and evening twilight. ...
Twilight observations were carried out in the period between 1984 and 1987 in different seasons at different sites of Egypt (Baharia, Matrouh, Kottamia and Aswan) through a cooperation project between Dar El-Iftaa’ and the Egyptian Academy of Scientific Research and Technology. Naked eye observations of the first light of the dawn were done in parallel to the photoelectric measurements of the twilight phenomena. The depression of the sun below the horizon corresponding to the first light was calculated from the time of observations. Our estimates show that the normal eye can just discriminate the dawn (the first white light thread) at a depression of 14.7° with a maximum value of 15.08° and a minimum value of 12.01°. This result agrees with result obtained by our previous photoelectric measurements.
... From the array of the total sky brightness in V band we can obtain a family of other arrays giving the naked-eye star visibility and the telescopic limiting magnitude. The magnitude over the atmosphere of a star at the threshold of visibility of an observer when the brightness of observed background is b obs in nanolambert and the stimulus size, i.e. the seeing disk diameter, is θ in arcmin, has been given by Garstang (2000b) based on measurements of Blackwell (1946) and Knoll, Tousey & Hulburt(1946) and on a threshold criterion of 98 per cent probability of detection: ...
We apply the sky brightness modelling technique introduced and developed by Roy Garstang to high-resolution DMSP-OLS satellite measurements of upward artificial light flux and to GTOPO30 digital elevation data in order to predict the brightness distribution of the night sky at a given site in the primary astronomical photometric bands for a range of atmospheric aerosol contents. This method, based on global data and accounting for elevation, Earth curvature and mountain screening, allows the evaluation of sky glow conditions over the entire sky for any site in the World, to evaluate its evolution, to disentangle the contribution of individual sources in the surrounding territory, and to identify main contributing sources. Sky brightness, naked eye stellar visibility and telescope limiting magnitude are produced as 3-dimensional arrays whose axes are the position on the sky and the atmospheric clarity. We compared our results to available measurements. Comment: 14 pages, 12 figures, accepted for publication in MNRAS, 17 june 2004
Schaefer (1991) determined the Danjon limit or minimum angle between the Sun and the Moon from which the Moon can be seen shortly after the conjunction. Schaefer's method uses Hapke's (1984) lunar photometric theory and considers a fixed value for the threshold illuminance. We show Schaefer's method and its shortcomings, and we expose a modified theory, where the threshold illuminance to see the lunar crescent depends on several factors, mainly atmospheric absorption. We consider that vision is a probabilistic phenomenon; that is, when we use the experimental data of Blackwell (1946), we cannot be sure whether or not the Moon will be seen. Finally, we conclude that «perhaps» Hapke's theory overestimates the shielding of the sun's rays by the irregularities of the lunar surface at large phase angles.
When considering the threshold values for any visual function, one must take into account that the visual system acts logarithmical and not linear. That means that for the same increase in experience, the ratio between the stimuli, and not the difference between the stimuli, is constant. This constant is often called the Weber fraction. The first aspect of visual performance to consider is that of the primary visual functions.
For suitable illumination and observation conditions, sparkles may be observed in metallic coatings. The visibility of these sparkles depends critically on their intensity, and on the paint medium surrounding the metallic flakes. Based on previous perception studies from other disciplines, we derive equations for the threshold for sparkles to be visible. The resulting equations show how the visibility of sparkles varies with the luminosity and distance of the light source, the diameter of the metallic flakes, and the reflection properties of the paint medium. The predictions are confirmed by common observations on metallic sparkle. For example, under appropriate conditions even metallic flakes as small as 1 μm diameter may be visible as sparkle, whereas under intense spot light the finer grades of metallic coatings do not show sparkle. We show that in direct sunlight, dark coarse metallic coatings show sparkles that are brighter than the brightest stars and planets in the night sky. Finally, we give equations to predict the number of visually distinguishable flake intensities, depending on local conditions. These equations are confirmed by previous results. Several practical examples for applying the equations derived in this article are provided.
From known values of twilight sky brightness, atmospheric transmission, and eye sensitivity, the visibility of planets and stars of magnitudes -2.5 to +4.5 is calculated for the twilight period. The results of the calculations are given in charts which can be applied to various altitudes of the observer and various conditions of observation. The twilight belt is about 1100 sea miles in width, from the sunset or sunrise meridian to full night. The charts show that under good conditions in the first 200 miles of the belt the brighter planets and Sirius become visible, in the next 200 miles first magnitude stars appear, and beyond 500 miles practically all navigational stars can be seen.
From the theory of the passage of light through a telescope and into the eye, formulas are derived for the improvement in the visual threshold of a point source, as a star, viewed in a field of light, as the sky, in terms of telescope parameters, as magnification, transmission, and entrance and exit pupils. For fields of the brightness of the daylight sky the first parameter is the most important and the others are of less importance. Observations of artificial stars in the laboratory and of real stars in the daylight sky are given, which were in fair accord with the theory.
The daylight visibility of stars has been investigated for an observer altitude of 100 000 ft, using published visual threshold data and calculated sky luminance. Venus, Jupiter, and Sirius, plus Mars at its brighter phases, can be detected with the naked eye if the observer knows where to look for them in the sky. Saturn and Canopus may be seen only under rare circumstances. A random search of the sky will reveal neither planets nor stars except possibly Venus. If a 10-power telescope of large exit pupil is used, there is a possibility of detecting an occasional star by careful search of the sky. The daytime sky will not exhibit nighttime luminance until an altitude of roughly 100 km has been reached, assuming no contribution from airglow.
The VTOL and V/STOL flight regimes are sufficiently different from those of fixed wing aircraft to magnify certain aspects of the collision avoidance problem. For example, high rates of climb and the capability for lateral translation may require increased visibility vertically and laterally. In addition, the contrasts and intensities required for light visibility against high luminance day-lighted surfaces are very different from those required for night flight conditions. These considerations have initiated a review and re- examination of anticollision lighting requirements.
Nuclear detonations in the vicinity of the moon are considered in this report along with scientific information which might be obtained from such explosions. The military aspect is aided by investigation of space environment, detection of nuclear device testing, and capability of weapons in space. A study was conducted of various theories of the moon's structure and origin, and a description of the probable nature of the lunar surface is given. The areas discussed in some detail are optical lunar studies, seismic observations, lunar surface and magnetic fields, plasma and magneti3 field effects, and organic matter on the moon. (Author)
A survey has been made of literature pertinent to the design of hand held binoculars (hereafter simply referred to as binoculars) intended to be used visually. This survey covered over 5,000 open and classified literature items published during the past one hundred and sixteen years, the majority of the more important works of which were completed during the World War II years. The results of the literature survey clearly indicate that the design of binoculars has not been based on visual tasks intended to be performed using such devices. It has largely been governed by preceding designs and the limitations imposed by technological skill in producing instruments at a rate said to be necessary to meet military requirements. This procedure may have resulted in the design of binoculars of higher quality (and hence more costly) than is required for many military purposes. Accordingly it has been concluded that the procedure of designing binoculars should be changed by making allowances for the end use to which such devices are to be put. Such allowances would include the limitations imposed by the characteristics of the target, the properties of medium between the target and the binocular, and the response of the human observer.
This report presents a synopsis of the literature search and testing conducted by ASD from 3 June 1975 to 22 October 1976 in an attempt to determine the specification requirements for strobe anticollision lights. The literature search resulted in a draft military specification for aircraft anticollision strobe lights which was circulated to the using commands and industry for comments 27 February 1976. Since the literature search had not provided quantitative data relative to required intensity, further investigation was deemed necessary. Testing was designed to generate data which could be extrapolated to determine intensity requirements for the specification. Test results indicate that strobe lights of intensities far exceeding those practical for aircraft installation would be required. The total effort resulted in the ASD recommendation that the proposed strobe light specification not be published as the visibility enhancement characteristics of the strobe lights when compared to the midair threat environment, offer very little, if any, added protection against midair collisions. ASD also recommended that the 'Force Wide Retrofit' action item of the General Officer Panel for Safety Matters be deleted. Any future strobe light activity should be based upon potential Life Cycle Cost advantages when they are used as functional replacements for the present rotating beacons. It was also recommended that the Midair Prevention System program, which was an outgrowth of early ASD proposals and provides a systematic approach to the midair collision problem, be continued. (Author)
By use of the values of the sky twilight brightness deduced at sea level at Abu Simbel in 1980 during the high solar activity period, the visibility of stars and planets of magnitudes less than 5.5 during twilight are obtained. The results are given in charts for each one degree of Sun''s depression below the horizon. These charts can be applied for different altitudes above the horizon and different bearing angles from direction of sunset. Tables of corrections for different values of atmospheric attenuation and solar activity are given.
Edward O. Hulburt initiated optical research at The Naval Research Laboratory in June 1924, choosing, fields of investigation such as the upper atmosphere of the earth, especially the ionosphere, gas discharges, the optical properties of the atmosphere and of the sea, visibility, ultraviolet and infrared physics, photoelasticity, and similar subjects. Ultraviolet and x-ray experiments from rockets were an outgrowth from continuing interest in the upper atmosphere, ultimately leading to the establishment of the E. O. Hulburt Center for Space Research in February 1963. Several divisions of the NRL conduct optical research in chemical spectroscopy, the properties of solids, and plasma physics, in addition to broad programs in the Optical Physics Division.
The question of lunar occultation visibility of stars is examined from both a theoretical and an observational viewpoint. The background light caused by the lunar surface, the brightness caused by the lunar glare, the brightness of the sky for dark, twilight, and daytime conditions, and the effects of the telescopic optics are taken into consideration. The results are compared to give the limit on stellar visibility at the time of a lunar occultation, and the model results are graphically demonstrated as a function of various input parameters. Comparisons with observations show good agreement, with an uncertainty of about one-third of a magnitude.
An analysis of the Tiffany data resulted in new relationships between the contrast threshold response of the human eye, the foveola region, and foveal-parafoveal vision as a function of background luminance for various stimulus diameters.
A photoelectric analog of the visual system is constructed in conformance with anatomical data. The analog has the form of a color television camera chain feeding electrical signals to a “computer” (the brain). Evaluation of characteristics is limited to elements preceding the computer, and particularly to the “luminance channel” of the color system.
The absolute visual threshold for an area 40° by 100° visual angle at a color temperature of 2050°K was obtained for seven observers. Two conditions were used, (1) turning the light on and (2) turning the light both on and off before a judgment was made. The average threshold for the six observers in the 24–36 year age range was 2.35 log µµL. No difference in threshold was found between the two conditions. High rank order correlations were found between threshold (µµL) and size of the dark adapted pupil and between threshold (trolands) and age.
We extend the method introduced by Cinzano et al. to map the artificial sky brightness in large territories from DMSP satellite
data, in order to map the naked-eye star visibility and telescopic limiting magnitudes. For these purposes we take into account
the altitude of each land area from GTOPO30 world elevation data, the natural sky brightness in the chosen sky direction,
based on Garstang modelling, the eye capability with the naked eye or a telescope, based on the Schaefer and Garstang approach,
and the stellar extinction in the visual photometric band. For near-zenith sky directions we also take into account screening
by terrain elevation. Maps of naked-eye star visibility and telescopic limiting magnitudes are useful for quantifying the
capability of the population to perceive our Universe, evaluating the future evolution, making cross-correlations with statistical
parameters, and recognizing areas where astronomical observations or popularization can still acceptably be made. We present,
as an application, maps of naked-eye star visibility and total sky brightness in the V band in Europe at the zenith with a resolution of approximately 1 km.
It is generally believed that the explosion which gave birth to the Cassiopeia A supernova remmant resulted from core collapse of a hydrogen-deficient star. A progenitor that has lost all its hydrogen envelope and part of its helium envelope would lead to an explosion with the optical properties of a Type Ic supernova. There is evidence, if not general agreement, that Flamsteed observed the Cas A supernova as a sixth magnitude object in August, 1680. If an explosion with a typical SNIc light curve at the position and distance of Cas A attained maximum luminosity during the winter of 1679-1680, it would at that time have been poorly situated for visual observation, as its upper culmination would have taken place during daylight, while in August, between 170-200 days after peak luminosity, it would have been a sixth magnitude star.
Visibility of point sources.—Laboratory experiments have been devised to make measurements of the visibility of light signals under conditions essentially similar to those encountered by the aviator or the navigator. Data have been collected on the direct visibility of flashing point sources of light of different colors, flash lengths and intervals, against different backgrounds; the time it takes to locate a visible beacon was studied as a function of the beacon intensity and frequency of flashing. The threshold candle power C required for visibility of a point source at distance D (cm) against a background of brightness H (candles × cm–2) is given by the empirical equation C/D2 = 3.5 × 10–9H1/2. Colored point sources were not found to be useful except in the case of red lights with background intensities above moonlight. For an airplane approaching a beacon it is advantageous to use frequencies of flashing as high as 12 to 30 per minute, although with exceptionally clear atmosphere, lower frequencies may be better.