Abstract

Introduction

Fig. 1. A mock­mirage green flash, photographed at Alpine, CA, at 7:22:32 pm PDT on 19 April, 1998. (See Paper I [3] for an explanation of mock mirages.)

Many physical scientists assume that because green flashes can be photographed, they are purely physical phenomena due only to atmospheric dispersion, and that effects in the visual system play no part in them. For example, O'Connell, in his well­known book [6], ridicules what he calls the ``physiological explanation.'' Taylor and Matthias [7], because they were able to photograph a green display, concluded that ``no physiological causes need be considered.''

However, as Mr. W. F. Floyd commented after the younger Lord Rayleigh's presentation [8] of a laboratory demonstration, ``I am willing to accept a purely physical explanation of the green flash, but I would suggest that the present paper establishes only one possible explanation. That a physiological effect may contribute to the phenomenon, or may even provide the sole explanation of it, has not been disproved, nor can it be disproved by purely physical arguments.'' Nevertheless, of the principal writers on green flashes, only the Meinels [9] have granted adaptation a role in what is seen at sunset.

In fact, there is solid evidence that visual adaptation is important. One could not ask for a more convincing demonstration than C. Vaughan Starr's report [10] that ``a party of four of us, including two doctors, had discussed the possibility of this phenomenon being due to some effect in one's eyes and not to refraction; to try this out two of us watched the sun carefully until it had set, while the other two looked eastwards and on a signal from the sun watchers turned quickly just as the sun was disappearing. The two who had watched continuously saw the green flash, while to those who did not look till the very last moment, the sun went down orange­yellow, and no green was seen.''

Similarly, a few years earlier, Leopold Neumann had reported [11] that ``once in the decisive moment of the observation my attention was diverted, while my companion did not let his eye leave the horizon. Suddenly he cried `Look there!', and it turned out that he still saw the green ray comparatively long, while I could not notice it.'' Neither of these reports is cited by O'Connell, [6] though Corliss [12] cites Starr's report in a list of unexplained anomalies.

Fig. 2. Schröder's Bildreihe 6. Note the progressive change in perceived color from orange to near­white as the Sun sets. [Note: the printed version does not show the cream-colored part of the Sun in the last 3 images at all well.]

Many other reports contain adaptation effects, including the excellent colored­pencil sketches published by Captain Gustav Schröder, [13] which faithfully portray what he saw. In his sixth series of images, he depicts the setting Sun as changing from orange to a pale yellow in a few minutes (see Fig. 2). This rapid color change cannot be due to a diminution of atmospheric reddening, but must have occurred in the observer's visual system as it adapted to the bright Sun. He remarks that the phenomena were observed independently by the ship's doctor. Schröder was an experienced green­flash observer, and his drawings (some of which [14] are the ``beautiful colored plates'' cited by Minnaert [15]) show that he was both careful and skilled in drawing what he saw.

I shall mention several other accounts that clearly display adaptation effects in connection with particular visual phenomena below. It should be clear that well­established reports indicate that visual­system effects are important in green­flash observations at sunset.

Terminology

Astronomers, meteorologists, and physicists have written the bulk of the green­flash literature, with minor contributions from hydrographers, geographers, and many others. This paper is intended to introduce these physical scientists to relevant results from color science, visual physiology, and perception; it involves photometry and colorimetry, together with photographic sensitometry and color rendition. But because these disparate fields use technical terms in contradictory ways, some discussion of terminology is unavoidable.

Brightness

On the other hand, in perception and color science, ``brightness'' is not a physical quantity at all, but a psychological attribute of visual perception; sometimes it is also called ``luminosity.'' [18] Unfortunately, ``luminosity'' is used by astronomers to denote the total power output of a star (e.g., the Sun's luminosity is about 4 x 10²⁶ watts).

Evidently, much confusion is possible here. If everyone were familiar with photometric quantities, the term ``luminance" would suffice. Unfortunately, not everyone understands what luminance is; and the television industry often uses ``luminance'' for an entirely different quantity.

Not long ago, luminance was called ``photometric brightness,'' a name that is now deprecated as obsolete. But, in a section on ``Photometric Brightness and Illuminance'' in their classic text, Jenkins and White [19] wrote: ``To distinguish [photometric brightness] from the visual sensation of brightness, it is usually termed the luminance in the technical literature, but we shall here use the more common name brightness, with the understanding that it is the photometric quantity that is meant.'' This passage is excerpted by the Oxford English Dictionary in its definition of ``luminance.'' I shall follow the example of the OED and Jenkins & White here.

Those who would like to understand photometric and radiometric units and quantities better are encouraged to read not only Jenkins & White [19], but also the excellent summary by J. Meyer­Arendt [20]. Astronomical readers are particularly directed to Crawford's fine synopsis [21] of photometric quantities.

Photographic Colorimetry

One must also distinguish between the colorimetric properties of a stimulus, and the color perceptions it produces in different conditions. The colors perceived by an eye viewing some light while in a neutral state of adaptation, an eye that has become adapted to this light (or to some other), or an eye viewing a color photograph of the light, all differ.

For readers unfamiliar with colorimetric notation, designation of stimuli by chromaticity coordinates or by dominant wavelength is less useful than the use of color names, which can be assigned to a light of any chromaticity by means of the diagram published by Kelly [22]. As Kelly's color names for lights denote the colors seen by a neutrally adapted eye at moderate photometric brightnesses, I shall call these the ``nominal colors'' of the lights.

For example, Dietze [23] has calculated the spectrum of the Sun at the horizon, and found that for a pure Rayleigh atmosphere, the dominant wavelength is 592 nm and the excitation purity 98% (see his Tabelle 5). According to Kelly's figure, the corresponding nominal color is orange; but the Sun is always redder than this at the horizon, because the air is never free of aerosols. For the largest amount of aerosol extinction considered by Dietze, the dominant wavelength is 627 nm, with 99% purity, corresponding to the nominal color red. For more typical conditions, the nominal color is reddish orange.

However, the color seen differs from the nominal color if the light is very bright (as will be discussed below), or if the eye is strongly adapted by previous exposure to colored light. I shall call the color actually seen by the observer a ``perceived color''. Often, the perceived color of the Sun at the horizon is yellow, because of adaptation effects, even though the nominal color is red or reddish orange.

Finally, there is the color seen on looking at a color photograph of a light, which I shall call its ``photographic color''. A correctly exposed photograph could record something like the nominal color of the light, if color films had response functions that were linear combinations [24] of the color­matching functions of the eye. However, for technical reasons, color films cannot have this property; consequently, there are lights that appear identical (metameric) to the eye but of different colors on photographs, and lights that are photographic metamers with very different nominal or perceived colors.

Furthermore, each type of color film produces a different mapping of source spectra into photographic colors. For example, the daylight film Kodachrome 25 invariably shows the photographic color of the Sun at the horizon to be orange or red, in agreement with its nominal color; but the tungsten film Ektachrome 64T (EPY) usually shows a yellow­orange photographic color at the horizon, and yellow (if the air is very clear) just a few minutes of arc above it. The accompanying green­flash pictures were taken on EPY film, which explains the yellow colors that appear on them. This film produces photographic colors that are between the nominal and perceived colors of sunsets.

The discrepancy between nominal and photographic colors is particularly large for monochromatic or nearly monochromatic lights; color films are notoriously bad at reproducing the spectrum. Unfortunately, as Dietze [23] has shown, green flashes have very high excitation purities, and therefore lie in parts of the chromaticity diagram that are poorly rendered by color photography. In particular, the spectral transition from green through yellow and orange to red is much more abrupt on color film than in nominal or perceived color.

Photographic Photometry

Because color films are manufactured and processed within narrow tolerances, they are useful for photometric measurements. Furthermore, the high contrast of reversal color films makes pictures taken with exposures differing by half a stop readily distinguishable by even an untrained eye; experienced workers can reliably detect differences of a quarter and in some cases as little as an eighth of a stop. Anyone who has spent several hundred hours trying to extract photometric information from photographs is aware of how sensitive the trained eye is to small differences.

The errors of such photographic photometry, even the crude sort made by visual inspection, are smaller than the brightness variations within a single image of the setting Sun, and very much smaller than brightness variations from one sunset to another, owing to the large variations in transparency of the air. Thus, one has only to look at a properly exposed sunset photograph and know its exposure to do useful sunset photometry: every well­documented and correctly exposed color photograph provides photometric measurements. I shall use this fact below.

Furthermore, comparison of the photographic colors of green flashes with the perceived colors seen in the camera viewfinder provides information on the state of adaptation of the photographer's eye; this is the subject of the next section.

Evidence from Photography

O'Connell quotes extensively from his correspondence with Eastman Kodak, the theme of which is that overexposure could make something green appear yellow instead. This is true, but it misses the point. Green flashes are usually underexposed rather than overexposed; those that are recorded on color film are generally much fainter than the rest of the Sun (see Figs. 1 and 3).

Fig. 3. Two stages of a green­flash sunset photographed at Torrey Pines, CA on 9 Sept., 1996. These versions have been digitally enhanced to emphasize the green features, which are easily visible on the original slides but are too dark to reproduce in normal prints. Upper image: 7:00:54 p.m., PDT; lower image: 7:02:57 p.m., taken with four times longer exposure. The same enhancement was applied to both images. Note the rapid increase of atmospheric extinction and reddening toward the horizon. The small detached area at the top of the lower image corresponds to the deep notch in the lowest part of the upper image. It appeared entirely green to the eye, as seen in the camera viewfinder, though only a trace of green shows at its extreme ends on the photographs. The green outline on the first (upper) image resembles that shown in part d of Schröder's sunset (Fig. 2).

I have had some correspondence with Kodak scientists myself, and they have kindly provided wedge spectrograms of reversal color films. At low light levels, three discrete bands appear in the photograph of a spectrum: red, green, and what is usually called ``blue'' but is really a blue­violet color. These bands of uniform color, which correspond to the three layers in color films, are separated by dark gaps. With increasing exposure, the red and green regions broaden and overlap to produce yellow; but the yellow region encroaches on the red as much as on the green with overexposure. If the red Sun is not yellowed by overexposure, the much dimmer green flash certainly will not be.

Thus, the yellow flashes on color photographs seem to be genuine and not artifacts, which leaves the eye rather than the film as the source of the discrepancy in hue. In discussing this situation with the much more experienced green­flash photographer Pekka Parviainen, I mentioned my suspicion that what I saw through the viewfinder was modified by visual adaptation. He confirmed my impression, pointing out that the other eye (which is usually kept closed) often cannot see the green flashes.

This response encouraged me to investigate further, and after paying more attention to the differences in colors seen by an eye that has stared at the Sun and one that has not, I found that the adaptation can easily be produced artificially by staring directly into an astronomer's red observing flashlight for a minute or two. When the red filament image no longer appears red, but a less­saturated orange, the eye sees low­pressure sodium street lights as yellowish green rather than yellowish orange.

Visual Adaptation

Already by 1887, von Kries [25] remarked that ``as has been known for a long time, yellow light appears greenish to the red­fatigued eye.'' In 1890, Hess [26] found that light of wavelength 575 nm appears ``yellowish green'' after adaptation to deep red light. At the turn of the century, Burch published two papers [27], [28] in which he examined very carefully the changes in hue produced by adaptation to various parts of the spectrum. In 1905, von Kries explicitly stated that after red­fatigue, he saw light of the D lines' wavelength (589 nm) as a green­yellow hue matching 556 nm seen in a retinal area that was not fatigued [29].

In the 1950s, Brindley repeated and refined Burch's earlier work, and found that after adaptation to bright lights of 658 nm wavelength, ``lights of wave­lengths from 540 to 620 [nm] were indistinguishable from each other … all appearing of an unsaturated blue­green.'' [30] Brindley called this condition ``artificial protanopia.'' This observation is directly applicable to observations of green flashes at sunset.

The early experimenters did not measure the absolute photometric brightnesses of the adapting lights. This omission was rectified by Cornsweet et al. [31] and by Rushton [32] in their studies of bleaching and adaptation to very bright lights.

Rushton found that the long­wavelength photopigment is half bleached at retinal illuminance levels of 4.89 log trolands (i.e., at 7.7 x 10⁴ td) in a 10 second exposure, or at 3.8 log td (6300 td) in the steady state. He also found that the time constant for recovery of the red­sensitive cones is about two minutes. As we shall see below, these numbers agree well with certain reports of sunset phenomena.

The half­bleaching level has been investigated by others as well. For example, Geisler [33] considered several sets of data that gave values ranging from Rushton's 3.8 log td to 4.3 log td (2 x 10⁴ td). In a later paper [34], Geisler cited a wider range, from 3.3 to 4.6 log td, and adopted 4.3 log td (2 x 10⁴ td) as a typical value. About the same time, Alpern [35] likewise reviewed a large body of data, and adopted 4.43 log td (2.7 x 10⁴ td). However, Walraven [36] argues that such values are based on adaptation to white or yellow lights that bleach both red­ and green­sensitive cones, so that a light that bleached just one class of cone would need to be only half as bright: ``one may expect that in the case of a deep red light, the half­bleaching constant for the L cones will indeed be close to 4 log td.'' It seems reasonable to adopt this value for our purposes, as the light of the setting Sun is quite red.

At somewhat higher light levels, Cornsweet found a competition between bleaching of the red­sensitive and green­sensitive cones, which causes very bright red lights (above 10⁵ td) to appear green after a few seconds. Marks and Bornstein [37] observed this effect even at retinal illuminances of 3 x 10⁴ td. This phenomenon also seems to appear in some sunset observations.

Cornsweet's mechanism is clearly reviewed by him in a 1962 paper [38], and both Rushton's and Cornsweet's mechanisms were reviewed by Walraven [36], who interprets these phenomena in terms of both retinal bleaching and adaptation in later stages of visual processing.

Application of Visual Adaptation to Sunsets

The varying concentration of aerosols in the lower atmosphere markedly affects the surface brightness of the setting Sun. Some days, it is painfully bright, even at the horizon; on others, the Sun fades into the haze before reaching the horizon. I have photographs of the setting Sun in which the upper limb is seriously overexposed, while the lower limb is barely recorded. Clearly the photometric brightness of the setting Sun varies by orders of magnitude from sunset to sunset, and often by more than an order of magnitude across the Sun itself. Even in the clearest conditions, the upper limb of the Sun at the horizon is more than twice as bright as the lower, because of the difference in extinction at the two altitudes. And even above the atmosphere, limb darkening makes the edge of the disk only 4/5 as bright as the center, apart from further variations due to faculae and sunspots.

Obviously, it is meaningless to speak of the photometric brightness of the setting Sun. However, it is possible to suggest a range of values that occur on days when the air is clear enough to permit observations of green flashes, and to select some typical values for comparison with the laboratory investigations cited above. I shall deliberately err on the fainter side, as brighter values will surely exceed the threshold for significant retinal bleaching.

Given the large real variations in brightness, we need only work to what astronomers call ``astrophysical'' accuracy here: the nearest order of magnitude will suffice. Sky­brightness values have recently been collected in a useful table by Crawford [21] that extends from the surface of the Sun to the darkest night sky ever observed. Outside the atmosphere, the Sun's surface brightness is about 1.6 x 10⁹ cd m^-2; the daytime sky is about 3000 cd m^-2; and the zenith at sunset, about 100 in the same units.

The sky around the setting Sun is certainly brighter than the zenith at sunset, because of forward scattering by aerosols in the solar aureole. A rough estimate might be 1000 cd m^-2. The Sun itself must normally be one or two orders of magnitude brighter than this, as the sky is not usually visible in sunset photographs if the Sun is correctly exposed (see Figs. 1 and 3). Only the haziest sunsets allow the sky to be photographed at all if an appreciable part of the Sun is still visible. Even green flashes, which are appreciably dimmer than the rest of the Sun, usually appear in well­exposed color photographs against a nearly black sky. So a rough estimate of the brightness of the setting Sun is 10⁴ to 10⁵ cd m^-2.

A more accurate estimate can be obtained by comparing normal daytime photographic exposures with exposures required to obtain well­exposed images of the setting Sun on the same film. For example, a normal daytime exposure for Kodachrome 25 film would be 1/125 second at f/8. A typical exposure for the setting Sun for this film under clear conditions is 1/1000 second at f/16, or five stops less. The daytime sky, which is well exposed in the normal daytime exposure, has a photometric brightness of about 3000 cd m^-2. Therefore, the setting Sun is roughly 32 times brighter than this, or about 10⁵ cd m^-2.

Another way to estimate this brightness is to adopt an effective extinction coefficient for vertical transmission, multiply by the airmass at the horizon (nearly 40), and apply this estimated slant­path transmission to the known photometric brightness of the Sun above the atmosphere. Such a calculation is uncertain, because the extinction changes very rapidly with wavelength. However, the extinction is nearly constant between 500 and 600 nm, where the Chappuis bands of ozone (which peak near 600 nm) nearly compensate the decrease in Rayleigh scattering with increasing wavelength. Near sea level, the extinction in this region typically varies from 0.15 stellar magnitudes per airmass (in very clear conditions) to 0.25 mag/airmass in average conditions. [Stellar magnitudes are a logarithmic scale; 5 mag correspond to an intensity ratio of 100.] Adopting a horizontal airmass of 40 (in round numbers), we have from 6 to 10 magnitudes of extinction in the yellow part of the spectrum, corresponding to transmissions from 4 x 10^-3 to 10^-4. These values yield solar brightnesses at the horizon from 6 x 10⁶ to 1.6 x 10⁵ cd m^-2.

All three methods are consistent with approximately 10⁵ cd m^-2 at the horizon, which will be adopted as a nominal value in the following discussion. The reader should realize that actual variations far exceed the range of values discussed above, and that solar brightnesses change by about a factor of two per minute in the last minutes before sunset, so that typical values might be an order of magnitude larger three or four minutes before sunset, when an observer anticipating a green flash will already be casting glances at the Sun.

Retinal illuminances are expressed in trolands, computed by multiplying the photometric brightness of the source in cd m^-2 by the area of the eye pupil in square millimeters. At high light levels, the eye pupil is typically 2.5 to 3 mm in diameter; let us adopt a nominal area of 5 sq. mm. Then the light level at the retina is 5 x 10⁵ td for our nominal horizontal solar brightness of 10⁵ cd m^-2.

This value is 50 times the level of 10⁴ td at which half of the red photopigment is bleached; according to Rushton's work [32], half the pigment should bleach in one or two seconds. This is also well above the level where Cornsweet's phenomenon appears. Thus, it seems inescapable that these bleaching effects, as well as other visual­adaptation phenomena, must occur when the human eye watches a sunset in a clear sky, and must be important in modifying the visual appearance of colors in the setting Sun.

Applications to Observed Green Flashes

I have mentioned a few examples of green­flash reports in which physiological effects clearly play a part; but the literature contains many more. Some of the more interesting examples follow.

Observers Aware of Adaptive Effects

A very few observers of sunset flashes have realized that both physics and physiology are involved. For example, Pütter [39], while favoring the afterimage theory, granted that ``… certainly particular conditions must be present in the atmosphere for the phenomenon to occur, but that the color depends on physiological conditions.'' Similarly, Worley [40] stated that ``Although the primary cause of the coloured flash may be atmospheric dispersion, simultaneous colour contrast may very considerably modify the subjective colour effect.''

After seeing a few flashes, Commandant Cornu [41] paid special attention to the effects of visual phenomena preceding another flash. ``I determined beforehand that when I looked at the red sky beside the Sun with the naked eye, I saw the Sun red; but when I fixated the Sun, it appeared to me yellow­green at times. In binoculars, the Sun always appeared yellow­orange before finally turning green.'' This seems to be a marginal appearance of the Cornsweet phenomenon.

In a very perceptive paper based on extensive observations of green flashes, Bonacini [42] recognized that red­fatigue would increase the saturation of the perceived green color, ``and so could explain that particular vividness of the green flash that has always amazed all the observers.'' Similarly, Guillaume [43], the Director of the BIPM, after discussing the matter with Henri Chrétien, noted that ``physical fact alone would not explain the remarkable brilliance of the green flash. That depends on a physiological fact: the contrast that it forms with the red color of the sun, which it immediately follows in its action on the eye.''

Adaptive Changes in Solar Color

Somewhat more people have recorded the effects of adaptation without being aware of it. Many reports involve apparent hue shifts from red to yellow in the setting Sun, contrary to the actual effect of increasing atmospheric reddening toward the horizon.

Besides those already mentioned, such as Schröder [13], one can cite Worthington [44], who ``used no dark glass on the telescope,'' and found that ``At first the whole of the visible portion of the disc of the sun turned intense fiery red. Then when a little more than half the disc had disappeared it changed to yellow.'' Similarly, Whitmell [45], using binoculars, first saw the Sun as ``decidedly orange;'' but then ``As it sunk below the horizon, the diminishing segment paled to yellow.''

Other Evidence of Adaptation at Sunset

The effect of image brightness on perceived color was noted by Guglielmo [46], who found that ``If the Sun is still a little above the horizon (more than 5°) and quite bright, and if the image is projected on a screen, the upper limb appears green with a little blue on the outside; if, on the contrary, it is observed directly under the same conditions without reducing the brightness too much, the limb appears blue, and the green is invisible.'' Evidently at the much greater image brightness a few degrees above the horizon, the green­sensitive cones are bleached as well as the red ones. (The airmass at 5° altitude is only about 10, so the extinction there is only a quarter as large as at the horizon; the image is about a hundred times brighter.)

Several observers have seen a sunset flash pass through a white, or nearly white, stage. Since Dietze's detailed calculations [23] of the chromaticity of green flashes indicates that their excitation purity is always very high, on the order of 80 or 90 per cent, perceived colors near white must indicate that the flash passes near the observer's (greatly shifted) adaptation point.

For example, one early observer [47] reported that ``the flash was very distinct, but seemed to my vision to be such a pale green as to be almost white.'' The well­known expert on meteorological optics Felix Exner reported [48] that ``While the Sun's disk showed the customary dark­red color, the last still clearly recognizable part of it appeared almost white, only to vanish with the flashing up of a beautiful emerald­green ray.''

Rahir [49], after noting the ``extremely brilliant luminosity'' of the setting Sun, ``which is very rare,'' observed that when the Sun was reduced to a straight flat band at the horizon, ``this vivid red band instantly took on a quite striking white color, like that of the Sun at noon,'' before assuming ``a magnificent coloration of a beautiful intense green.''

Long­lasting Green Effects

In some of these examples, it is difficult to say how much of the color shift was due to bleaching and how much to ordinary neural adaptation. However, a few cases are unambiguous examples of bleaching. One of the best of these is Franklin's report [50] of having ``twice seen a brilliant green sunset which lasted some minutes.'' On one occasion, ``As the sun began to set … , the large cream building to the east was so brilliantly illuminated with green, that my son whom I called to see it, remarked that he hadn't noticed the workmen were using green paint! (The building was just then being redecorated.) In a few minutes the green faded, and the more usual yellow­red sunset followed.'' This time scale is consistent with that required for the recovery of bleached photopigments; and the appearance of a pale yellow or cream­colored surface as green is quite typical of the red­bleached condition.

Similarly, Chambers [51] reported that ``… though the ball was bright red it was not too bright to allow of direct vision. The ray, which tinged the whole seascape, lasted for about two or three minutes, and was intensely green. I had been looking directly at the sun before it set.'' Again the time scale suggests bleaching was involved.

Another good example seems to be Libert's claim [52] to have seen the Sun green for periods ranging from 107 to 364 seconds on different days. In the latter case, he reported, ``many persons were struck by so prolonged a green coloration.'' These periods of a few minutes are too long to be ordinary green flashes at temperate latitudes, and too short to be either a ``green Sun'' produced by unusual aerosol scattering, or crepuscular rays - both phenomena that are sometimes confused with green flashes. Retinal bleaching seems the only likely explanation.

Perhaps the best example of long­lasting visual effects at sunset is the report by Verschuur [53], who reported that at 6:15 p.m., ``an especially beautiful green ray was observed. When half the solar disk had disappeared behind the horizon, the top part of the still visible Sun was light green, the lowest part harsh green in tint. This harsh green color moved slowly upward, displacing the light green color. When the last harsh green colored little segment had disappeared at the apparent horizon, plume­shaped green rays shot upward. …

``After sunset it came to my attention that all sailors who had come on deck to see the natural phenomenon had such an intensely dark red skin color; arms, face, and hands had a color of dark mahogany. That was also true of myself. On the gilded buttons of my uniform lay a silver lustre, on the white uniform a pink glow. The Moon, which before sunset had been seen very well, was now pale and indistinct. The water was greyish in color, only the bow waves and the wake, which otherwise are white, were now harsh green. The sea phosphoresced light. Looking over the sea, I got the impression that a yellow haze (light topaz color) hung over everything.

``Around the West the color of the clouds was varying between chestnut and the light yellow­brown color of old gold, run through with strips of pink and pearl­gray and quite pale between the gaps through which the blue sky was seen. …

``The port (red light) gave its usual color; that on starboard (green light) however radiated a harsher green light. The aft top­light (white light) shone green blue; the color was approximately like that of a spark between two carbon points. Seen from the bridge, the lights on deck looked, as far as color and shape are concerned, like the blowtorch of an autogenous welding apparatus. Looking at the binnacle I noticed that the brass hood and the [compass] rose were tinted green (light emerald green); likewise the chart, which lay on the table in the chartroom. The light from the lamp above the chart had the color of absinthe.

``This peculiar green tint slowly faded away from all lights. At 6:34 all lights were again of the usual color, but much clearer. Also this greater brightness faded away after approximately 15 minutes.''

The changes in appearance of the Moon and lights on the ship show that these were long­lasting changes in the observer's eye, not just peculiarities of the twilight illumination. I can confirm that I have seen several of these color changes myself, upon bleaching my eye with a red flashlight, as well as at sunset.

Distinguishing Bleaching Effects from Real Green Flashes

As real green flashes can last as long as 15 seconds (although this is possible only for certain rare types of flash), it may be useful to explain how one can tell whether a color change seen on the solar disk is due to bleaching (i.e., physiology) or to atmospheric dispersion (physics). I have noticed that retinal bleaching develops in a patchy fashion, so that the change in hue is uneven, and the Sun appears mottled during the transition. As the mottles are fixed on the retina, they move with the fixation point, and are not fixed with respect to the outline of the Sun.

On the other hand, the refraction effects generally proceed continuously, so that a well­defined hue boundary sweeps rapidly over the affected part of the Sun. The moving boundary is usually fairly symmetrical about a vertical axis, and shares the symmetry of the solar image as it evolves. Furthermore, the colors produced in green flashes are generally extremely saturated, as the stimulus is nearly monochromatic; colors due to bleaching alone are not as vivid.

The Discredited Afterimage Theory

No discussion of physiological effects in green­flash observations can avoid the afterimage theory, which first appeared in Jules Verne's novel [54]. The idea that the sunset flash is merely an afterimage of the disappearing red Sun seems plausible to many who have never seen a green flash. Actually, the two phenomena are so completely unlike that the afterimage explanation seems absurd to anyone who has seen both; only persons who have never seen a green flash can make this error. An observer who deliberately observed the solar afterimage found it ``entirely different'' from a green flash [55]; after seeing a few green flashes, R. W. Wood declared [56] the afterimage theory ``sheer nonsense.''

The solar afterimage is so inconspicuous and rarely seen that only a handful of printed accounts of it exist, and most published reports of the afterimage are accidental observations from people who did not understand what they had seen [57], [58], [59], [60], [61], [62]. As the low Sun is usually orange, its negative afterimage is a dark blue, and is often barely visible against the sky.

Furthermore, as the low Sun is too bright to fixate comfortably, special efforts must ordinarily be made [55] to make its afterimage visible at all. The casual observations of afterimages cited above all have in common very hazy air that allowed the observers to look at the Sun without discomfort, as many of them explicitly state; but green flashes are associated with unusually clear, not unusually hazy, conditions. In clear air, one tends to glance directly at the Sun only briefly and to scan the point of fixation randomly around the Sun, so that a large, ill­defined retinal area becomes bleached without producing a sharply defined image of the Sun itself.

Disproving the afterimage fallacy is the main theme of Mulder's book [63], to which the interested reader should turn for details. Most people are disabused of the error on learning that green flashes are observed at sunrise as well as at sunset, but some fanatical believers in afterimages even maintained that they could be produced at sunrise. Despite sound arguments raised against it, the afterimage theory continued to appear in print long after it was refuted by Lucien Rudaux's photography [64], and it continues to crop up occasionally even today, as in the Economist's completely garbled account [65] of my preliminary report [66] on retinal bleaching at sunset.

A particularly unfortunate example of uninformed debate on the afterimage theory was the exchange in the early 1930s between the younger Lord Rayleigh and the equally noted physiologist J. S. Haldane. Neither of these eminent scientists had ever seen a green flash, nor were they aware of the photographic disproof [64] of the afterimage theory a few years earlier in France. Furthermore, Haldane [67], unaware of the strong atmospheric reddening at the horizon, criticized Rayleigh's first paper [68] for showing a blue upper limb rather than a green one in unrealistic experiments made with the Sun well above the horizon; while Rayleigh [8], in turn, admitted his ``misgiving'' about the physiological questions, ``bred partly of lack of familiarity with this field, and partly from dislike of the vagueness inherent in the use of words for describing subjective colour impression.'' Thus, their debate proceeded with serious ignorance on both sides.

While Haldane [67] rashly concluded that ``the cause of the actual sunset or sunrise coloured ray being vividly green, is the simultaneous contrast effect due to the light coming from round the sun being red,'' and that [69] ``there can be no doubt that the greenness depends on `simultaneous' contrast,'' Rayleigh equally wrongly maintained that normal dispersion could account for published green­flash reports - an error not refuted until 1955, by Dietze [23]. Nevertheless, Rayleigh correctly insisted that atmospheric dispersion was the underlying cause of green flashes; and Haldane [69] correctly cautioned that ``not only physicists, but also many physiologists, have a very imperfect conception of the extent to which physiological contrast enters into what we actually see. According to Newton's teaching the sensation of colour produced by light depends simply on the refrangibility (in more modern language, the wavelength) of the light. This is only true under certain physiological conditions. Under other and quite usual conditions it is not true at all, as can easily be shown experimentally.'' So both Rayleigh and Haldane were partly right and partly wrong: both mechanisms are involved, and both are important.

Discussion

Photography shows that there is a real green flash in some sunsets. Green flashes are not afterimages. Nevertheless, as discussed above, physiological effects in the visual system must usually make the preceding yellow stage of a sunset flash appear green to an attentive observer.

Because atmospheric extinction increases rapidly with decreasing wavelength, the yellow stage is in fact much brighter than the green one (see Figs. 3 and 4); in many sunsets, the extinction is so large that the yellow stage is the last one visible, and no light that would ordinarily appear green is transmitted at the horizon. In these sunsets, a human observer may still see an apparently green flash, though only yellow is recorded by color film.

Fig. 4. An inferior­mirage flash photographed near Scripps Pier on March 30, 1998. This was a moderately bright naked­eye flash that had appeared completely green to the eye for over half a second before this picture was taken. The yellow stage of the flash is disappearing, but still photographable, in the middle of the photographic green part. The full width of this flash is about 5 arc minutes; for a comparison with the whole disk of the Sun, see Fig. 5 of Young. [1]

The yellow stage of a sunset flash begins considerably earlier than the photographable green phase. Indeed, many flashes seen as green turn out indistinguishable on color film from adjacent areas of the Sun (see the lower image in Fig.3), which indicates that the eye saw green before the refractive cutoff of long wavelengths had reached a wavelength where the red­sensitive layer of color film has appreciable sensitivity. The long­wavelength tail of the eye's sensitivity has a much smaller slope than that of color films, whose red­sensitive layer usually peaks around 650 nm and drops to a negligible value by 680 nm; so the eye may see green when wavelengths longer than about 670 nm have disappeared, though this would make little change in the color recorded on film. Because green appears to the watchful eye about a second before any green can be photographed, I have learned to wait a second or so after first seeing green before tripping the shutter release, if a green flash is to be recorded on film. Even so, the result often shows yellow as well as, or instead of, green; see Figs. 3 and 4.

Detailed comparison of visual and photographic colors depends on the spectral responses of both the eye and film, as well as the atmospheric transmission at the horizon under different conditions, and is therefore rather complicated; it deserves a separate paper. However, the empirical difference of about a second between the first visual green sensation and the first appearance of a photographable green color indicates that visual effects account for much of the discrepancy between observed and calculated durations of sunset green flashes.

Durations

If the yellow stage is ordinarily perceived as green at sunset, it would alleviate the long­standing discrepancy between calculated and observed durations of green flashes at sunset. The observed durations are typically around two seconds, but the calculated duration is only half of this.

The classical study of observed duration is P. Feenstra Kuiper's thesis [70]. He analyzed over 300 flashes that must be mostly inferior­mirage flashes, and calculated several different mean values, ranging from 1.84 to 2.05 seconds, depending on which data were excluded as atypical. The estimates were made by professional seamen, whose lives and livelihoods depended on being able to count seconds accurately for navigational purposes at sea. Anyone experienced in counting seconds can measure time intervals of a few seconds with an error on the order of ten per cent, plus perhaps an additional personal error of a quarter of a second for short intervals. Feenstra Kuiper's adopted means should be reliable to one or two tenths of a second.

However, there are much larger real variations in flash duration from one sunset to another. The two­second width of the histogram of durations plotted by Feenstra Kuiper [70] is primarily due to real variations from one flash to another, not to measurement error. Already by 1873 Winstanley [71] had estimated that the more than 50 flashes he had seen ranged from half a second to two and a half, with perhaps one and a quarter seconds as the typical duration.

Also, of the several types of flash, the classical textbook model for their duration, which does not consider mirage effects, applies only to some (e.g., the inferior­mirage flash) and not to others, which can last much longer. (Feenstra Kuiper was careful to exclude long­lasting flashes from his discussion.) Although I have seen flashes lasting as long as five seconds, and several reliably measured durations from ten to fifteen seconds exist, these are certainly not the ordinary inferior­mirage flash to which the standard theoretical duration applies; my own observations of over a hundred green flashes of inferior­mirage and mock­mirage flashes indicate that two seconds is indeed a typical duration in clear sunset conditions. I adopt two seconds as a nominal value of observed duration for comparison with the standard model.

The textbook model [72], [23] for flash duration neglects mirage effects, and supposes that an undistorted Sun is occulted by the apparent horizon. The duration then depends on the width of the green rim due to standard refraction, and to the rate of descent of the Sun due to its diurnal motion, which depends primarily on the cosine of the observer's latitude.

The many published calculations of expected duration all assume the refraction at the horizon simply scales with the refractivity of air, which is not correct; but the error is only a few per cent. Prosper Henry [73] calculated the first theoretical duration, ``about a second.'' W. H. Julius [74] estimated the green as half the distance between F and C, making the dispersion 1/200 of the refraction, and giving a green rim 10 arc sec wide that would last 2/3 of a second at low latitudes; he recognized that the observations already available gave durations ``not only much longer … but also quite variable,'' and concluded that ``ordinary refraction does not suffice to account for the facts.'' Rambaut [72] decided the rim was 30 arc seconds wide, which is excessive; he seems never to have observed a green flash himself. The younger Rayleigh [68] used the whole interval from C to F; the same objections apply. Guillaume [43], the Director of the BIPM, used more realistic numbers to estimate a duration between the disappearance of the red and the green of just one second; this assumes the intervening colors are absorbed by the atmosphere, which is obviously not the case, so it really is only an upper limit.

If one chooses from Kelly's spectrum locus [22] the range of nominal colors from bluish green through yellowish green, the corresponding range of wavelengths is 493 to 559 nm, and the fractional change in refractivity of air in this range is about 1/186, corresponding to a green rim of maximum width about 11 seconds of arc, or very nearly what Julius adopted. Even if Kelly's ``blue green'' and ``yellow green'' are included, the maximum nominally ``green'' interval would extend only from 487 to 570 nm, and the fractional refractivity is 1/149, giving less than 14 arc sec of green rim, and a nominally green flash just under 1 second of time at low latitudes, and no more than a second and a half even at the latitude of Paris.

The actual discrepancy is larger than would appear from these numbers, because many flashes are cut off by atmospheric extinction well before they reach the middle of the nominally green region. So the theoretical duration of about a second should be compared to the durations of the longest observed inferior­mirage flashes, which is to say, two and a half or even three seconds.

However, if the evidence from photography discussed at the beginning of this section (namely, that green can be perceived by a bleached retina as soon as wavelengths longer than 670 nm have been cut off) is adopted, then the calculated dispersion from nominal ``bluish green'' to 670 nm is 1/90 of the refraction, and that from ``blue green'' to 670 nm is 1/86. These figures predict perceived green for just over twice the time predicted by Julius, in good agreement with the observations.

Sunrise and sunset

The bleaching of the long­wavelength cones that is primarily responsible for anomalous color perceptions at sunset can be avoided by observing green flashes at sunrise, where the green stage (if it occurs) is not preceded by a view of the bright solar disk. Then sunrise flashes should be shorter than sunset flashes by about a second, which is the time elapsed at sunset between the first visible green and the first photographable green. This expectation is borne out by the experience of Lipp [75], who observed 25 sunrise and 38 sunset flashes from the Zugspitze in the course of a year. He found that the mean duration at sunrise was 0.77 seconds, just about a second shorter than the mean of 1.80 sec for sunset flashes.

Conclusion

The setting Sun is so bright that it usually bleaches a large fraction of the red­sensitive pigment from the retina of an attentive observer. To the bleached eye, light that would normally be perceived as yellow appears green. Thus, most sunset green flashes are actually yellow for about a second before any photographable green appears; typically, this is the first half of the visually green sunset flash. Even when the atmospheric aerosol loading is so great that no green light is transmitted at the horizon, a green flash may still be seen during the brighter yellow stage. The retinal bleaching that causes yellow light to be perceived as green helps explain the difficulty of photographing green flashes at sunset.

One should not forget that green flashes are also seen at sunrise, when the eye has not been previously exposed to bright light, and the retina is in its normal, unbleached state. Sunrise flashes are therefore seen more nearly in their intrinsic colors.

Acknowledgments

References

[1] A. T. Young, ``Green flashes and mirages,'' Optics and Photonics News 10, no. 3, 31-37 (March, 1999).

[2] A. T. Young, ``De groene flits, hemelsverschijnsel tussen wal en schip,'' Zenit 26, 248-254 (1999).

[3] A. T. Young, G. W. Kattawar, and P. Parviainen, ``Sunset Science. I. The Mock Mirage,'' Appl. Opt. 36, 2689-2700 (1997).

[4] A. T. Young and G. W. Kattawar, ``Sunset Science. II. A Useful Diagram,'' Appl. Opt. 37, 3785-3792 (1998).

[5] W. J. Humphreys, Physics of the Air, Third Edition (McGraw­Hill, New York, 1940).

[6] D. J. K. O'Connell, The Green Flash and Other Low Sun Phenomena (North Holland, Amsterdam, 1958).

[7] J. H. Taylor and B. T. Matthias, ``Green flash from high altitude,'' Nature 222, 157 (1969).

[8] Lord Rayleigh, ``Further experiments in illustration of the green flash at sunset,'' Proc. Phys. Soc. 46, 487-498 (1934).

[9] A. Meinel and M. Meinel, Sunsets, Twilights, and Evening Skies (Cambridge University Press, Cambridge, 1983).

[10] C. Vaughan Starr, ``The green flash,'' Met. Mag. 64, 290-291 (1930).

[11] T. Kellen, ``Nochmals der Grüne Strahl,'' Kosmos (Stuttgart) 24, 282-285 (1927).

[12] W. R. Corliss, Rare Halos, Mirages, Anomalous Rainbows and Related Electromagnetic Phenomena (Sourcebook Project, Glen Arm, MD, 1984).

[13] G. Schröder, ``Beobachtungen des `Grünen Strahls','' Ann. d. Hydr. u. Maritim. Met. 63, 336-340 (1935).

[14] G. Schröder, ``Vom `Grünen Strahl'. … II. Der Grüne Strahl an einem 140 Seemeilen entfernten Bergabhang,'' Ann. d. Hydr. u. Maritim. Met. 65, 492-493 (1937).

[15] M. Minnaert, The Nature of Light and Colour in the Open Air (Dover Publications, New York, 1954).

[16] E. S. Steeb and W. E. Forsythe, ``Photometry and Illumination,'' in Handbook of Physics, E. U. Condon and H. Odishaw, eds. (McGraw­Hill, New York, 1958), p. 6-47.

[17] C. W. Allen, Astrophysical Quantities, 3rd edition (Athlone Press, London, 1973), pp. 26, 127, 169, 173.

[18] G. Wyszecki, ``Colorimetry,'' in Handbook of Optics, W. G. Driscoll and W. Vaughan, eds. (McGraw­Hill, New York, 1978), p. 9-2.

[19] F. A. Jenkins and H. E. White, Fundamentals of Optics, Third Edition (McGraw­Hill, New York, 1957), p. 109.

[20] J. R. Meyer­Arendt, ``Radiometry and photometry: units and conversion factors,'' Appl. Opt. 7, 2081-2084 (1968).

[21] D. L. Crawford, ``Photometry: terminology and units in the lighting and astronomical sciences,'' Observatory 117, 14-18 (1997).

[22] K. L. Kelly, ``Color designations for lights,'' J. Opt. Soc. Amer. 33, 627-632 (1943).

[23] G. Dietze, ``Die Sichtbarkeit des `grünen Strahls','' Zeitschr. f. Meteorologie 9, 169-178 (1955).

[24] A. T. Young, ``Improvements to photometry VI. Passbands and transformations,'' Astron. Astrophys. 288, 683-696 (1994).

[25] J. von Kries, ``Entgegnung an Herrn E. Hering,'' Pflügers Arch. Physiol. 41, 389-397 (1887).

[26] C. Hess, ``Ueber die Tonänderungen der Spectralfarben durch Ermüdung der Netzhaut mit homogenem Lichte,'' Albrecht von Graefes Archiv für Ophthalmologie 36, 1-32 (1890).

[27] G. J. Burch, ``On artificial temporary colour­blindness, with an examination of the colour sensations of 109 persons,'' Phil. Trans. Roy. Soc. Lond. 191, 1-34 (1899).

[28] G. J. Burch, ``On the relation of artificial colour­blindness to successive contrast,'' Proc. Roy. Soc. (Lond.) 66, 204-216 (1900).

[29] J. von Kries, ``Die Gesichtsempfindungen,'' in Handbuch der Physiologie des Menschen vol. 3; W. Nagel, ed. (Friedrich Vieweg und Sohn, Braunschweig, 1905), pp. 109-280.

[30] G. S. Brindley, ``The effects on colour vision of adaptation to very bright lights,'' J. Physiol. 122, 332-350 (1953).

[31] T. N. Cornsweet, H. Fowler, R. G. Radebeau, R. E. Whalen, and D. R. Williams, ``Changes in the perceived color of very bright stimuli,'' Science 128, 898-899 (1958).

[32] W. A. H. Rushton, ``Cone pigment kinetics in the deuteranope,'' J. Physiol. 176, 38-45 (1965).

[33] W. S. Geisler, ``The effects of photopigment depletion on brightness and threshold,'' Vision Res. 18, 269-278 (1978).

[34] W. S. Geisler, ``Evidence for the equivalent­background hypothesis in cones,'' Vision Res. 19, 799-805 (1979).

[35] M. Alpern, ``Lack of uniformity in colour matching,'' J. Physiol. 288, 85-105 (1979).

[36] J. Walraven, ``Perceived colour under conditions of chromatic adaptation: evidence for gain control by $\pi$ mechanisms,'' Vision Res. 21, 611-630 (1981).

[37] L. E. Marks and M. H. Bornstein, ``Spectral sensitivity by constant CFF: effect of chromatic adaptation,'' JOSA 63, 220-226 (1973).

[38] T. N. Cornsweet, ``Changes in the appearance of stimuli of very high luminance,'' Psychological Rev. 69, 257-273 (1962).

[39] A. Pütter, ``Zur Kenntnis des grünen Strahls,'' Die Naturwissenschaften 8, 497 (1920).

[40] F. P. Worley, ``The green flash at sunset,'' Nature 135, 760 (1935).

[41] Commandant Cornu, ``Optique atmosphérique,'' Bull. Soc. Astron. Fr. 63, 341-342 (1949).

[42] C. Bonacini, ``Sul fenomeno del `Raggio Verde','' Pubblicazioni dell'Osservatorio Geofisico dell'Università di Modena No. 39, 115-130 (1927).

[43] Ch.­Ed. Guillaume, ``Le rayon vert,'' B. S. A. F. 33, 515-516 (1919).

[44] J. H. Worthington, ``The green flash at sunset,'' Knowledge (new series) 3, 376 (1906).

[45] C. T. Whitmell, ``The green flash [letter 543],'' English Mechanic 79, 556 (1904).

[46] G. Guglielmo, ``Intorno ad alcune particolarità del raggio verde,'' Boll. bimens. Soc. meteor. ital. (Torino) 36, 49-50 (1917).

[47] ``Meteor'', ``The weather in the British Isles in October, 1902 [439.] The `green flash','' English Mechanic 76, 317 (1902).

[48] F. Exner, ``Der Grüne Strahl der untergehenden Sonne,'' Meteorol. Zs. 20, 42 (1903).

[49] E. Rahir, ``Observation sur le rayon vert au coucher du soleil,'' Ciel et Terre 51, 158-160 (1935).

[50] A. L. Franklin, ``Green flash (letter to the editor),'' Weather 12, 265-266 (1957).

[51] R. M. Chambers, ``The Green Ray ,'' Times (Lond.) 10 (2 June, 1933).

[52] L. Libert, ``Déformations solaires et rayon vert,'' La Nature 30:2, 332 (1902).

[53] A. D. Verschuur, ``Groene straal,'' De Zee 48, 446-448 (1926).

[54] J. Verne, Le Rayon­Vert (Hetzel, Paris, 1882).

[55] ``M. D. '', ``The green flash at sunset,'' T. P. 's Weekly 4, 284 (1904).

[56] R. W. Wood, Physical Optics, 3rd Ed (Macmillan, New York, 1934), p. 84.

[57] E. Acharius, ``Beschreibung eines besondern Meteors,'' Gilb. Ann. Phys. 52, 235-239 (1816).

[58] ``M. '', ``Eine Bemerkung über das besondere, von Herrn Acharius beschriebene Meteor, welches vor einigen Jahren in Schweden gesehen worden ist,'' Gilb. Ann. Phys. 52, 342-343 (1816).

[59] G. Giordano, ``Singolari apparenze osservate nel tramonto del sole,'' Rend. Accad. Sci. Fis. Mat. 10, 230-231 (1871).

[60] Kr(itzinger), ``Der grüne Strahl,'' Sirius 47, 209-210 (1914).

[61] G. Grandjean, ``Optique atmosphérique,'' Bull. Soc. Astron. France 41, 105 (1927).

[62] P. J. E. Marshall, ``Abnormal refraction, North Atlantic Ocean,'' Marine Obs. 22, 125 (1952).

[63] M. E. Mulder, The ``Green Ray'' or ``Green Flash'' (Rayon Vert) at Rising and Setting of the Sun (T.Fisher Unwin, Ltd., London, 1922).

[64] L. Rudaux, ``Photographie du rayon vert,'' La Nature 53:2, 303-304 (7 Nov., 1925).

[65] anonymous, ``In a flash,'' Economist 347, 95 (June 20, 1998).

[66] A. T. Young, ``Understanding green flashes,'' Bull. Amer. Astron. Soc. 30, 934-935 (1998).

[67] J. S. Haldane, ``The physiological significance of Weber's law and colour contrast in vision,'' J. Physiol. 79, 121-138 (1933).

[68] Lord Rayleigh, ``Normal atmospheric dispersion as the cause of the `Green Flash' at sunset, with illustrative experiments,'' Proc. Roy. Soc. A 126, 311-318 (1930).

[69] J. S. Haldane, ``The Green Ray,'' Times (Lond.) 13 (10 June, 1933).

[70] P. Feenstra Kuiper, De Groene Straal (C.de Boer Jr., Helder, 1926).

[71] D. Winstanley, ``Atmospheric Refraction and the last rays of the Setting Sun,'' Proc. Manchester Lit. Phil. Soc. 13, 1-4 (1873).

[72] A. A. Rambaut, ``The green flash on the horizon,'' Symons's Met. Mag. 41, 21-23, 41-45 (1906).

[73] P. Henry, ``Sur une méthode de mesure de la dispersion atmosphérique,'' C. R. 112, 377-380 (1891).

[74] W. H. Julius, ``Le rayon vert,'' Arch. Néerlandaises des sciences exactes et naturelles 6, 385-389 (1901).

[75] H. Lipp, ``Beobachtungen des grünen Strahles auf der Zugspitze,'' Met. Z. 47, 113-115 (1930).