Applying Minnaert Min Liu Professor Marc Levoy The Science of Art February 20, 2003

1. Applying MinnaertMin Liu Professor Marc LevoyThe Science of ArtFebruary 20, 2003

2. All photos were taken with an Olympus D-520 Zoom digital camera

3. Leaves “When the leaf is illuminated from the front (relative to the observer), a bluish hue mingles with the green, and when from the back, a yellow hue.”(Minnaert, 356) One can see that the more yellow leaves are illuminated from the back side and the deeper green-colored leaves are directly illuminated. Minnaert comments that leaves take on complex forms of illumination due to variables that include double-sided illumination, leaf surface texture, chlorophyll presence, and infrastructural intensity that reflects light. -This photo was taken on a sunny late morning in late August, 2002.

4. Leaves, continued “… in a leaf, though much less than 1mm thick, all the processes of reflection, absorption, and scattering take place in the same way as in an ocean tens or hundreds of meters deep. Absorption is caused here by the chlorophyll grains; scattering is probably brought about by innumerable grains of all kinds in which the contents of cells are so rich, or perhaps by the unevenness of the leaf’s surface.” (Minnaert, 356) The intricate infrastructure of leaves is illuminated by sunlight. One can see the play of light on the leaves, emphasizing small dark spots on the clover-like petals (right) and the red hues on the leaves in the photo above. Photos taken late morning, Feb 18, 2003.

5. Leaves, continued “From an optical point of view, a leaf is much more complex than a lake or a sea; … [I]t is illuminated not on one, but on two sides; moreover, one side is matt and the other shiny, while the intensity and color of the incident light are usually different at the two sides. The possible combinations of optical phenomena are astronomical!” (Minnaert, 356) This image of a large clove-like plant has a “matt” or fuzzy underside as the sunlight shows. The shiny front side is absorbing light as well, causing certain areas of the leaf to look yellow-green. Light on both sides create complex green hues on this leaf. Photo taken late morning, Feb 18, 2003.

6. Images of the Sun “In the shade of a group of trees the ground is dappled with spots of light, some small, some large, but all regularly elliptical … they are… sunlight that falls through some opening in the foliage: all we see here and there between the leaves is a blinding ray of light.” (Minnaert, 1-3) The “sunspots” are caused by myriad beams of light that together flood through tiny openings in the foliage. The collective light that floods through the openings and land on the ground is conical because the sun is not a point source; light shines through the foliage opening at different angles, thus filling in an ellipse on the ground. The sunspot is an ellipse because the ground cuts the light cone at a non-right angle. The elliptical sunspots are especially apparent during the morning and afternoon, when the sun is not directly overhead. -This photo was taken during the late morning of Feb, 18, 2003.

7. On the other hand, when the sun is overhead, there is a bigger chance that the sunspots on the ground form circles. Similarly, when light shines through foliage openings and hit a wall in the morning, the sunspots formed tend to be more like circles than ellipses. This is due to the angle at which the sun shines through the foliage opening and the upright angle of the wall.

8. Minnaert states that “we see the sun’s disk at an angle of 1/108 radian.” With this formula, we can calculate the height of the tree and the length of the sunspot from the foliage opening:H = (k/b)L = 108k(k/b) where H = height of tree; L = distance of sunspot to foliage opening; k = minor axis of sunspot; b = major axis of sunspot.I measured the elliptical sunspot of an oak tree. k = 5”; b = 20” ; H = 135” or 11’ 3”; L = 540” or 45’. The results turned out to be erroneous. A problem I encountered was that the sun moved rapidly through the foliage openings, hence changing the ellipse. (Notice the changing shape of the ellipse as I measure the major and minor axes. The time interval between these images was about a minute).

9. Shadows “When you look at your shadow on the ground, you will notice that the shadow of your feet is clearly defined, whereas that of your head is not. The shadow of the bottom part of a tree or post is sharp, while that of the higher part becomes increasingly unclear toward the top.” (Minnaert, 4) Although this is a perspective view of the tree trunk shadow, Minneart’s observations still hold. -This photo was taken in the late afternoon of January 2003.

10. Window glass & Plate glass“The reflections from windows indicate whether they are normal window glass or plate glass; if the latter, the images are fairly clear; if the former, they are so irregular that the unevenesses of the glass can be seen clearly” (Minnaert, 22) Window Glass - “warped” reflection A Stanford engineering building Noon, Feb 18, 2003 Plate Glass - a clearer reflection Elliot Program Center Late morning, Feb 18, 2003

11. Closed Coils of Light “Remarkable is the appearance of closed coils of light seen when the water surges gently, the waves have short crests, and the light source is high … When you look at the water at a sufficiently large angle, you will see the light source reflected by two separate spots of light [S1 and S2] on each wavelet, for instance, one at the crest and the other at the trough of the wavelet … the associated reflections [S1 and S2] are always in the same plane of the wavelet … When you look slightly to the left or right you will see the reflections getting closer and closer together until they fuse into one closed coil whereby annulus is formed. After all, the wavelets not only have a given wavelength, but also a certain crest length; when two crests merge, the tangent is horizontal. But before that, a point must have been reached where the slope was still steep enough to reflect the light source to our eyes: at that point S1 and S2 coincide.” Minneart (30-33) The crests of these closed coils of light on the water reflect the concrete rim of the fountain. -Midday, fountain outside Memorial Auditorium Feb. 18, 2003

12. Irregularities on a Water Surface “[On a water surface,] tiny mounds of water show up light or dark depending on the direction in which you are looking … [for example,] inside each eddy [in a river] the tension is a little less and its surface is slightly hollowed out to a depth of a few mm. In the vicinity of the boundary between light and dark reflections, you can see clearly even the tiniest eddies. This is an application of natural ‘schlieren’.” (Minnaert, 21-22) Schlieren are “regions of varying refraction in a transparent medium.”* Schlieren in these images are the eddies found between the elliptical water crests. They almost seem like compressed lines of the sun’s reflection, the blue of the tile bottom, and the sky. *http://www.m-w.com/ Irregular water surface from the fountain outside Memorial Auditorium Noon 2/18/2003

13. Refraction by an Undulating Water Surface “When a water surface is not perfectly smooth, this is revealed by a change in direction of broken rays of light and an uneven brightness at the bottom.” Minnaert (46-47) The broken rays and uneven brightness are caused by “rays of light [that] spread at the center and then close up concentrically” on the bottom of the pool. (Minnaert, 47) In this image of the fountain in front of Memorial Auditorium, the tiles at the bottom are lit unevenly due to the light rays that spread out concentrically. The light on the crest of the water above the tiles combined with the refracted rays at the fountain bottom are causing a symphony of reflecting and refracting rays.

14. Differences between an object and its reflection “The closer the objects are to us, the lower their images with respect to that of the background” “Although the reflection is identical to the object, it looks different in perspective because the two are shifted with respect to each other. We see the landscape as if we were looking at it from a point beneath the water’s surface where the image of our eye is. The difference becomes smaller the closer we bring our eyes to the water and the farther away the objects are.” Minnaert (11-13) Although it is difficult to distinguish in this image, the palm tree and the conical tree on the hill appear to be the same height. In the water’s reflection, however, one can see (up close to the image) that the conical tree is lower in the water. This means that the conical tree is closer to us than the palm tree, even though they appear to be of the same height when viewed directly. This optical effect occurs because a reflected image does not represent the true image. Photo taken Feb 18, 2003; Lake Lagunita in the late morning.

15. Reflections in Puddles “The reflection of trees and shrubs in small ponds and puddles at the roadside sometimes have a more pronounced clairty, sharpness, and warmth of color than the objects themselves … The cause of these differences is more psychological than physical … The reduced brightness of the mirror image is in itself beneficial for looking at the sky and clouds, which otherwise are somewhat too bright for our eyes. Furthermore, the reflection is polarized, so that it may attenuate the luster of certain objects and saturate colors.” Minnaert (13) In this image, the puddle is in the shadow of a tree, thus significantly reducing the brightness of the sky. The sky in the puddle has a blue hue opposed to the white sky on that particular day. -Trail alongside Lake Lagunita; late morning. Feb 18, 2003

16. Freak Reflections Freak reflections are caused by windows. “The spots of light caused by standard window glass are irregular, whereas those caused by plate glass are far more uniform.” Minnaert (15) The uniformity and clarity of this reflection shows that the reflecting window was made of plate glass. -The wall of a stairway in Adams dorm. Late afternoon, Feb 18, 2003

17. The Rainbow in Artificial Clouds “The way in which a rainbow arises in a mass of drops of water is immediately visible to us when we see the sun shining on the fine spray floating above fountains and waterfalls … Always look for rainbows in a direction 42 degrees away from the anti-solar point, and preferably against a dark background.” Minnaert (191-192) -Rainbow formed by waterfall spray; Vernal Falls, Yosemite. August, 2002.

18. Parhelic Circle “After the small ring, the mock suns or sun dogs are the most frequently encountered halo phenomenon. These mock suns are two concentrations of light on the small halo at the same altitude as the sun … The intensity of these mock suns is usually very great; they are distinctly red on the inside, then yellow, before changing into a bluish white.” Minnaert (214) Minnaert cites Greenler in explaining parhelic circles; he states that “parhelia are formed when the air contains enough crystals floating horizontally like leaves. Through such prisms, the rays of light no longer travel along the path of minimum deviation, because they do not lie in a plane perpendicular to the axis.” Q: From Greenler, it seems that parhelic circles occur on cold days with floating crystals. This photo, however, was taken on a sunny warm August day in Southern California. Is this really an image of a parhelic circle? Parhelic circle seen with a cloud; mountains above Hetch Hetchy Dam; August 2002

19. Clouds “Those not accustomed to studying the heavens will be surprised to learn that clouds can often show the most glorious and the purest colors, such as green, purple-red, blue …They are distributed irregularly over the clouds in the form of colored edges, spots, and bands; some observers maintain that they have a ‘metallic’ luster; what do that mean? Our feelings at the sight of such lovely clouds are of intense delight, which is difficult to describe, but which is certainly caused, to no small extent, by the purity of the colors, their delicate intermingling, and their radiant light. It is difficult to take your eyes off their exquisite sight.” Minnaert (250)

20. Scattering of Light by Clouds“It is remarkable how certain kinds of cloud obscure the sharp outline of the sun until only a round mass of light remains that grows fainter toward its periphery.” (Minnaert, 283) “Every cloud has a silver lining” Photo taken at 5PM, Feb. 19, 2003

21. Scattering of Light by Clouds, continued “When the sun is hidden behind loose and heavy clouds, and the air is filled with a fine mist, groups of these sunbeams can often be seen darting from the sun through the openings in the clouds, showing a path of light through the mist, thanks to the scattering by the drops of which it is constituted” (Minnaert, 291) These clouds were captured in the late afternoon of Feb. 19, 2003. The sky was particularly clear that day due to morning rain. The rays of the sun spearing through the openings in the clouds are radiant in this image. This photo was taken from a balcony in Governor’s Corner.

22. Scattering of Light by Clouds, continued Minnaert remarks that the best months to study the colors of twilight are October and November (293). During Autumn 2002, I took photographs of various clouds at sunset. Above: the set sun illuminates an impending storm front. Left: these clouds give the appearance of smoke; the sun is hidden behind these thick clouds; notice the beam of light(!).

23. Scattering of Light by Clouds, continued (Above) “The horizontal stripes (of sky) are red only when the air contains dust or water droplets” (Minnaert, 304) Photos taken at sunset Autumn, 2002

24. Blue Lakes “…the water of blue lakes is almost absolutely pure and that the color is caused by absorption by the water in the orange and red parts of the spectrum. To account for colors green, yellow-green, and yellow-brown, there is constantly increasing proportion of iron-salt and humic acids and also scattering by brown-colored particles in these waters.” Minnaert (345) Second to Lake Tahoe and excluding the Pacific Ocean, Hetch Hetchy Dam is one of the bluest bodies of water I’ve seen. Hetch Hetchy Dam; August 2002. Midday.

25. Grass “The emerald green of grass in a bright light is particularly lovely seen from a shady spot against a dark background. It seems as if each little blade were literally burning within a green inward glow. The incident light pouring on it laterally is scattered by the millions of minute grains, so that each blade casts a stream of light sideways towards your eye.” (Minnaert, 357) This picture was taken in the late morning of February 18, 2003. Even then, the brilliance of the meadow dominated the landscape at Governor’s Corner. Some parts of the meadow were shadowed by massive oak trees, creating contrasting hues of green across the landscape. The meadow, covered with millions of dewdrops, created an ever more ephemeral and heavenly effect.

26. Dispersion of light by a dewy meadow “When you … look over the heavily dewed fields or meadows, … you will notice that they disperse a remarkable amount of light into the distance, toward the sun. The color of the grass there can hardly be seen, it is much whiter near you. It is, of course, the dewdrops that reflect light; in the parts of the field nearest you, only separate dots of light can be seen here and there, but farther away, there seem to be many more bright spots” (Minnaert, 285) “The grayish aspect of bedewed grass is caused by the reflection of the rays of light in all the tiny drops, inside as well as outside; a great many of the rays do not even touch the blade of grass. Large flattened drops have a beautiful silver sheen when seen at fairly large angles, because the rays are then totally reflected at the back surface.” (Minnaert, 56) Up front, the dew is scattered. At a certain distance, however, one can see the white blanket of the dew over the grass. Photo taken at Governor’s Corner, February 18, 2003. Late morning.

27. Vertical Reflection “A chimney or a thin mast is reflected clearly, but the strong lines of roofs have disappeared; only the vertical lines are found back in the reflections. Vertical trunks of trees are clearly recognizable, but those that lean over are much less so, while slanting branches have disappeared completely. The slender neck of a swan is reflected as a clear dab of light, but the body of the bird is lost in the movement of the water … In the case of an upright line, the columns are neatly stacked together and magnify each other; in the case of a horizontal line, they lie side by side and broaden the line to a hazy surface.” Minnaert (24) Minnaert explains that vertical shadows and reflections are more prominent because their reflections overlap each other at greater surface areas. On the contrary, horizontal shapes lose their form because their reflections and shadows do not overlap as greatly, thus causing a hazy image. In this image, the vertical shape of the trees are apparent on the water surface when their horizontal aspects are not. The hills are not emphasized in the reflection either. Photo taken Feb. 18, 2003; Lake Lagunita, late morning.

28. Refraction through uneven panes of glass “The window plate is obviously not a parallel plate, but has thinner and thicker parts that act as irregular lenses, spreading out or collecting rays of light and giving fanciful focal lines. Even small deviations of the rays cause appreciable differences in brightness, so that virtually every window of standard glass exhibits the streaks.” (Minnaert, 48) This window is above the entrance to Memorial Auditorium. Storm clouds and Hoover Tower are reflected from the glass. The glass seems to reflect multiple overlapping images due to the uneven glass surface. Like many Stanford windows, this window has horizontally streaked glass. Photo taken midday, Feb. 19, 2003