{"id":35871,"date":"2014-11-24T16:11:26","date_gmt":"2014-11-24T16:11:26","guid":{"rendered":"http:\/\/www.labri.fr\/perso\/barla\/blog\/?p=35871"},"modified":"2014-11-24T16:13:27","modified_gmt":"2014-11-24T16:13:27","slug":"clouds-in-a-glass-of-beer","status":"publish","type":"post","link":"https:\/\/www.labri.fr\/perso\/barla\/blog\/?p=35871","title":{"rendered":"Clouds in a Glass of Beer"},"content":{"rendered":"<p id=\"top\" \/>by Craig Bohren<\/p>\n<p>&nbsp;<\/p>\n<h3><b>The green flash<\/b><\/h3>\n<p>In the water the incident wave may be considered to have been extinguished because of interference with all the waves scattered by the molecules and replaced by another wave with a different direction of propagation. Scattering in this special direction is said to be coherent. The word &#8220;cohere&#8221; means to stick together, especially entities that are similar, and this is just what all the waves scattered by the individual water molecules do: in the direction of refraction the crests and troughs of all the waves scattered by the molecules very nearly coincide. As a consequence, total scattering in this special direction is quite strong. p.102<\/p>\n<p>A beam of light in the purest of substances is incoherently scattered, although weakly, in lateral directions. Water is such a substance, and when milk is added to it the amount of incoherent scattering is greatly increased. p.102 <i>Thus reflection and refraction at an interface are the commonest of coherent scatterings.<\/i><\/p>\n<p><b>\u00a0<\/b><\/p>\n<h3><b>Multiple scattering at the breakfast table<\/b><\/h3>\n<p>Its margin is well defined as a consequence of single scatterg: a photon must be scattered at least once for us to see the beam (to be precise, we do not see the beam but rather the light removed from it), but its likelihood of being scattered more than once is small. To increase this likelihood add more milk to the water; that is, increase the concentration of scatterers. p.105<\/p>\n<p>But multiple scattering takes as well as gives: the greater the number of scatterers the greater the chance that a photon will be absorbed; multiple scattering not only increases the pathways by which incident photons can reemerge from a medium, it exposes them to a greater hazard of being absorbed. p.107<\/p>\n<p>The single scattering characteristics of particles in milk are really quite irrelevant to the appearance of a glass of milk. What is relevant is that it is optically thick &#8211; a small glass of milk looks no different from a large glass &#8211; and its particles are very weakly absorbing. Although incident photons corresponding to the color red may have to rattle around more in a glass of milk before re-emerging than thse corresponding to blue, almost all of them ultimately re-emerge having escaped absorption. p.108<\/p>\n<p>A group of water molecules when randomly separated scatter incoherently, when these same molecules condense into a droplet (i.e., they all are part of the same entity rather than independent agents) they scatter coherently. And coherent scattering can be much more intense, all else being equal, than incoherent scattering.\u00a0 Just as coherent (in phase) pushing yields a much greater effect than incoherent pushing, so also is coherent scattering vastly more intense even though the scatterers are the same in both instances. p.110 <i>Thus coherence is merely &#8220;in-phase&#8221; scattering?<\/i><\/p>\n<p>For example, sunlight reflected by a film of water is much brighter than that reflected by a cloud, at least a thousand times greater, possibly much more depending on the angle of incidence of the sunlight (to convince yourself of this compare the reflection of the sun on a pond with light from a cloud). But this reflected light is concentrated in a single direction that given by the law of reflection, whereas the cloud scattets light in all directions. p.110 <i>Is it possible to get coherent scattering in all directions ? This should be different from close-range inter-reflections on a micro-surface, since the scale is not the same here&#8230;<\/i><\/p>\n<p>&nbsp;<\/p>\n<h3><b>Multiple scattering at the beach<\/b><\/h3>\n<p>Photons incident on a scatterer are scattered in all directions, but more scatter in some directions than in others. We may therefore talk. about the probability that an incident photon will be scattered in a particular direction. This, in turn, leads to the concept of the average direction in which photons are scattered. This average direction is strongly dependent on, among other things, the size of the scatterer. For example, scatterers much smaller than the wavelength of the light illuminating them scatter nearly the same in all directions. To be more precise, the average scattering angle &#8211; the angle between the incident and scattered photons &#8211; is 90 degrees: as many photons are scattered into a hemisphere of directions about the forward direction as are scattered into a hemisphere about the backward direction (the forward direction is defined by the direction of the incident beam; the backward direction is opposite to this). In contrast, scatterers much larger than the wavelength of the light illuminating them scatter more strongly about the forward direction: the average scattering angle is less than 90 degrees, perhaps 30 degrees or less. p.115\u00a0 <i>These are properties of the phase functionm and the average angle might be the g parameter&#8230;<\/i><\/p>\n<p>The more closely the optical properties of the surrounding fluid match those of the grains the smaller the average scattering angle. To convince yourself that this is plausible consider the extreme case where the surrounding fluid is optically identical with the grains. In this instance the grains are invisible: the incident light is scattered only in the forward direction. Recall how much more difficult it is to find glassware in water than in air. p.117 <i>At a smaller scale, this may be recast in terms of refraction effects which are more pronounced for high index ratios, which broadens scattered cones.<\/i><\/p>\n<p>Although embedding a single grain in different transparent fluids does not appreciably change the amount of incident light it scatters and absorbs, it may appreciably change the distribution of the scattered light. A consequence of this change is that the brightness of many grains may be gready diminished merely by wetting them with different liquids. p.117<\/p>\n<p>So it is no wonder that foam is highly reflecting: it is made up of scatterers that are very weakly absorbing. Beer is yellow because it preferentially absorbs visible light of shorter wavelengths. But there is not enough preferential absorption &#8211; indeed, there is very little absorption at all &#8211; of the light incident on the foam, so it is white. p.119<\/p>\n<p>&nbsp;<\/p>\n<h3><b>On a clear day, you can&#8217;t see forever<\/b><\/h3>\n<p>Yet it is not physical distance that determines visibility but rather optical distance. The scattering mean free path is defined as the average distance a photon travels in the medium before it is scattered. The optical thickness of a path connecting any two points in the medium is the distance between them measured in units of mean free paths. Optical thicknesses are dimensionless (i.e., they are measured not in yards or meters or furlongs, but rather are ratios) and may depend on wavelength because the probability of scattering depends on wavelength. A given optical thickness can be obtained with weak scatterers distributed over a long distance (the atmosphere) or strong scatterers distributed oer a short distance (aquarium). Physically, the distances are quite different; optically, they are the same. p.122<\/p>\n<p>&nbsp;<\/p>\n<h3><b>Physics on a manure heap: more about black clouds<\/b><\/h3>\n<p>In the forward direccion, therefore, the intensity of the light scattered by two dipoles is four times that scattered by one; that scattered by four dipoles is 16 times that scattered by one, and so on. In the backward direction, however, scattering does not increase nearly so rapidly with an increase in the number of dipoles because in this direction the dipoles do not necessarily scatter exactly in phase. p.140<\/p>\n<p>Any particle becomes an array of dipoles when illuminated by an electromagnetic wave. The molecules making up the particle are uncharged: the amounts of positive and negative charge are equal. When isolated, the center of the positive charge in a molecule may coincide with that of negative charge. In an electric field, however, these two charge centers are displaced slightly because they are forced in opposite direcions by the field; a dipole is therefore created or induced by the field. If this field is oscillatory, the dipole oscillates and consequently radiates. Thus to deternine how a particle scatters light we could, in principle at least, merely add up the waves scattered by all of its constituent molecules (i.e., dipoles) taking account of their phase differences. p.141<\/p>\n<p>The arguments I made for a few dipoles can be extended to a huge array of them, which is just what any illuminated particle is. Thus the larger the particle (i.e., the more molecules it contains), the more it scatters in the forward direction relative to the backward direction. p.142 <i>Thus the particular shape of a PHASE function is due to the phase alignment of its constituent dipoles, with more dipoles meaning more forward scattering?<\/i><\/p>\n<p>If a particle is much smaller than the wavelength of the light illuminating it, the distance between each pair of its constituent molecules must be similarly small. Two dipoles separated by distances that are small compared with the wavelength scatter in phase in all directions. Thus we expect very small particles to scatter more or less the same in all directions, and this is indeed what is observed. p. 142 <i>Thus the distance between dipoles very much matters for the directionality of a phase function.<\/i><\/p>\n<p>&nbsp;<\/p>\n<h3><b>Polarization of skylight<\/b><\/h3>\n<p>An unpolarized beam is a mixture of two independent, linearly polarized beams of the same intensity, horizontally and vertically polarized, say. Except in the forward and backward directions, these two beams are scattered differently by a small sphere. This difference is greatest at a scattering angle of 90 degrees, where the intensity of the scattered light vanishes for the horizontally polarized beam. At this angle, therefore, the scattered light is completely vertically polarized. At other scattering angles there is some mixture of horizontally and vertically polarized light, although the horizontal component is less intense. Hence the polarization is less than complete: the scattered light is partially polarized perpendicular to the scattering plane. p.147<\/p>\n<p>Clear air contains many small scatterers, the air molecules themselves. As a consequence, skylight is partially polarized because unpolarized sunlight acquires a degree of polarization upon scattering by air molecules. This can be observed by scanning the sky through a polarizing filter while rotating it. The degree of polarization will be greatest at 90 degrees to the sun, although it will never be 100 percent. p.148<\/p>\n<p>The difference between the polarizing properties of small and large scatterers can be put to good use in photography, particularly of clouds. Cloud droplets are much larger than the wavelengths of visible light; and they are not all the same size, especially in cumulus clouds. As a consequence, they do not highly polarize the light they scatter. p.148<\/p>\n<p>Without airlight a cloud would appear redder the farther away it is, even with the sun directly overhead. A distant cloud is much like the sun on the horizon: the light you receive is light that has not been scattered, hence it is reddened because the shorter wavelength components of white light have been preferendally scattered out of your line of sight. Airlight, however, is light that has been scattered toward your eye, hence it is bluer than transmitted cloudlight. The two combine so that the cloud does not appear as red as it would if there were no airlight. But airlight, unlike cloudlight, is partially polarized so it can be partly eliminated by using a polarizing filter. This will tip the balance somewhat in favor of the redder cloudlight. p.149<\/p>\n<p>To obtain 100 percent polarization all the light you receive must have been scattered through 90 degrees. But when you look at a thick collection of particles it is unavoidable that you receive light scattered through many angles, some less than, some greater than 90 degrees. That is, the light is composed of many beams, each with a different degree of polarization. If two or more partially polarized beams are superposed, the degree of polarization of the resultant cannot be greater than that of the most highly polarized component. Indeed, it is usually less, even zero. p.151<\/p>\n<p>The effect of the ground on the polarization of skylight is similar to that of multiple scattering. Reflecting ground is an indirect source of light. Multiple scattering aside, the light you receive from a given patch of sky is sunlight scattered through a single angle and groundlight scattered through many angles. Thus the degree of polarization can only be less than what it would be in the absence of groundlight. p.151<\/p>\n<p>Cellophane tape, frost, and airplane windows may appear at first glance to have little in common. Although they all are transparent to visible light, the point is their birefringence: the speed with which light propagates through them depends on its polarization state. p.152<\/p>\n<p>Ice is birefringent because of its crystallinity: its molecules are arranged in a regular manner, like seats in an auditorium. Glasses and plastics, like liquids, are amorphous, their molecules do not form an ordered array. As a consequence, they do not naturally exhibit birefringence. But it is possible to induce them to do so. By squeezing, for example. Or stretching, as was done to the cellophane tape during its manufacture. Birefringence requires the existence of special directions in a material, either natural or induced. Without aid you cannot see these directions, but polarized light can. p.153<\/p>\n<p>&nbsp;<\/p>\n<h3><b>Colors of sea<\/b><\/h3>\n<p>There is a natural tendency to think that if a little bit of scattering makes the sky blue then a lot of scattering will make it even bluer. But this is incorrect: single scattering giveth, multiple scattering taketh away. If our atmosphere were perhaps ten times more massive, the sky would be white everywhere. If, on the other hand, it were a tenth as massive, the sky would be black overhead and bluer toward the horizon. p.163<\/p>\n<p>Note in Figure 20.7 that the front of a wave is tilted toward him. Thus he receives light from higher in the sky, a darker and purer blue but with a greater reduction in brightness upon reflection, than he would if the sea were flat. p.167 <i>These multiple effects correlate to give sea patterns.<\/i><\/p>\n<p>Note also how the brightness of the sea varies with distance from the shore. Near shore, there is a definite pattern of alternating dark and bright narrow bands. Farther from shore, there is a bright broad band, light from clouds reflected by a fairly calm sea. Farther still, the sea abruptly becomes darker where the sea is rougher; in this region the distance and wave slopes are such that you can see only the fronts of waves. p.167 <i>One may describe a sea with a few high-level parameters and provide an SV-BRDF as a result!<\/i><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>by Craig Bohren &nbsp; The green flash In the water the incident wave may be considered to have been extinguished because of interference with all the waves scattered by the molecules and replaced by another wave with a different direction of propagation. Scattering in this special direction is said to be coherent. The word &#8220;cohere&#8221; &#8230; <a title=\"Clouds in a Glass of Beer\" class=\"read-more\" href=\"https:\/\/www.labri.fr\/perso\/barla\/blog\/?p=35871\" aria-label=\"Read more about Clouds in a Glass of Beer\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[621],"tags":[],"class_list":["post-35871","post","type-post","status-publish","format-standard","hentry","category-books"],"_links":{"self":[{"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/posts\/35871","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=35871"}],"version-history":[{"count":3,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/posts\/35871\/revisions"}],"predecessor-version":[{"id":35891,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/posts\/35871\/revisions\/35891"}],"wp:attachment":[{"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=35871"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=35871"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=35871"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}