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A high-quality metal for [http://sss.chaoslab.ru/tracker/mim_plugs/newticket?reporter=anonymous&summary=AttributeError%3A+%27Environment%27+object+has+no+attribute+%27get_db_cnx%27&description=%0D%0A%0D%0AWhen+it+comes+to+knives+with+an+uparralleled+edge%2C+and+unmatched+solution+developement%2C+Cold+Steel+is+at+the+leading+of+the+game.+They+continue+to+produce+new+and+innovative+tools+and+knives+for+tactical%2C+selfdefense%2C+and+day+to+day+use.+If+ever+you+have+a+doubt+as+to+the+durability+and+strength+of+these+knives+all+you+need+to+have+to+do+is+verify+out+the+Youtube+videos+created+by+Cold+Steel+Cutlery.+These+videos+will+speak+a+million+words.%0D%0A%0D%0AI+explored+this+internet+web+site+I+had+been+quickly+sure+that+I+wished+to+buy+this+sort+of+Spyderco+Delica4+Lightweight+Folder+Knife+VG10+Satin+Plain+Clip+Point+two.875%22+FRN+suitable+away.+Spyderco+Delica4+Lightweight+Folder+Knife+VG10+Satin+Plain+Clip+Point+2.875%22+FRN+has+all+the+points+terrific+to+me+just+like+I+can+not+truly+describe+why+it+created+me+hurry+to+receive+this+Spyderco+Delica4+Lightweight+Folder+Knife+VG10+Satin+Plain+Clip+Point+two.875%22+FRN+straight+away.+Am+I+enchanted+by+magical+for+this+Spyderco+Delica4+Lightweight+Folder+Knife+VG10+Satin+Plain+Clip+Point+two.875%22+FRN+%3F%0D%0A%0D%0AThe+longer+shape+of+the+delica+practically+offers+it+a+far+more+traditional+shape+due+to+the+fact+the+%22leaf%22+shape+is+elongated+so+considerably.+The+%22spydie+hole%22+is+at+a+fantastic+location+for+my+thumb+to+simply+attain+it.+It+has+a+little+major+of+jimping+behind+the+hole.+I+have+located+that+in+standard+use+my+thumb+never+ever+seriously+tends+to+make+it+previous+the+jimping+on+the+back+of+the+manage.+I+open+and+close+my+Delica+a+distinct+way%2C+and+when+I+attempt+to+describe+to+folks+how+I+close+it%2C+they+largely+just+get+confused%2C+so+here%27s+a+little+video+displaying+my+method%2C+which+I+feel+is+a+tiny+safer+than+letting+it+drop+towards+your+finger+and+relying+on+the+mechanism+not+to+get+reduce.+FRN+with+Bi-directional+Texturing+works+effectively+and+does+not+really+feel+low+cost+I+cannot+cease+playing+with+the+wave%0D%0A%0D%0ASpyderco+just+as+speedily+adopted+when-exotic+blade+supplies%2C+taking+them+from+the+custom+blacksmith%27s+forge+into+low-expense%2C+production+use.+The+enterprise+immediately+advanced+from+440C%2C+the+best+stainless+generally+out+there+a+generation+ago%2C+to+hybrid+stainless+steels+like+VG-ten+to+exotic+steels+that+didn%27t+exist+just+a+handful+of+years+ago.+Nowadays%2C+that+signifies+production+use+of+ZDP-189+in+the+full-size+Endura%21+The+back+lock+knife+is+also+considerably+significantly+less+most+likely+to+grow+to+be+accidentally+unlocked+for+the+duration+of+the+force+of+making+use+of+a+knife+the+way+that+the+police+use+a+tactical+folder.+A+liner+lock+knife+can+come+unlocked+during+frequent+twisting+motions.+That+is+why+some+liner+lock+knives+come+with+a+manual+lock+like+the+Lake-Walker+designs.%0D%0A%0D%0AWearing+Kevlar%C2%AE-lined+gloves%2C+we+then+turned+the+knife+about+so+finger+stress+would+exert+force+straight+on+the+lock+release.+No+amount+of+strong%2C+wrap-around+grip+would+unlock+the+knife.+The+only+way+to+unlock+the+back+lock+knife+with+the+David+Boye+Dent+is+to+exert+individual+thumb+or+finger+stress+straight+downward+on+the+release.+The+knife+is+simple+to+unlock+if+you+want+to+close+the+blade.+We+discovered+it+not+possible+to+unlock+by+accident.+One+particular-third+of+SWAT+operators+carry+a+fixed+blade.+Although+Spyderco+is+most+well-known+for+its+patrol-oriented+folders%2C+it+has+a+line+of+fixed+blades+made+by+the+likes+of+Bill+Moran%2C+the+founder+of+the+American+Bladesmith+Society%2C+and+Fred+Perrin%2C+a+former+French+Army+commando.%0D%0A%0D%0AFor+its+element%2C+ZDP-189+is+miserable+to+function+with%21+It+requires+twice+as+lengthy+for+knife-makers+to+grind+and+they+get+half+the+wheel+life.+%E2%80%9CZDP+is+extremely+challenging+and+not+achievable+to+stamp+in+forming+a+blade.+Strong+ZDP+must+be+cut+with+laser%2C+which+raises+the+expense+of+forming%2C%E2%80%9D+said+Sal+Glesser%2C+president+of+Spyderco.+So+it+is+not+just+the+larger+price+of+the+steel+but+also+the+difficulty+in+blade+generating+that+adds+to+the+larger+value+of+ZDP-189+knives.+N690+has+been+properly+received+by+European+military+forces+where+it+has+gained+a+fantastic+reputation+for+cutting+efficiency+and+edge+retention.+Some+Benchmade+and+Remington-Maniago+knives+also+use+N690.+The+440C+stainless+is+superior+sufficient+to+be+the+classic+knife+alloy%2C+but+N690+is+an+improvement+for+really+hard+use.%0D%0A%0D%0AFor+those+of+you+who+do+not+know+the+Spyderco+Delica+is+1+of+Spyderco%27s+signature+EDC+knives+and+it+is+the+4th+iteration+of+the+Delica+series.+Sal+Glesser+has+stated+himself+that+the+Delica+4+is+part+of+Spyderco%27s+CQI+or+constant+duality+improvement.+It+sees+quite+a+few+improvements+more+than+the+preceding+Delicas+which+includes+a+stronger+tip%2C+nested+liners%2C+superior+ergonomics%2C+improved+clip%2C+and+superior+texturing.+Let%27s+see+if+this+popular+blade+holds+up+nowadays%21+In+1990%2C+Spyderco+introduced+its+now-renowned+three.8-inch+Endura+and+2.9-inch+Delica.+These+two+nylon+deal+with%2C+back+lock%2C+tactical+folders+would+be+clipped+in+so+numerous+uniform+pants+that+the+Spyderco+became+America%27s+police+knife.+Spyderco+introduced+its+fourth-generation+version+of+the+Endura+and+Delica+in+2006.%0D%0A%0D%0AIt+is+considered+a+tactical+knife+however+it+is+not+precisely+what+I+would+be+looking+for+in+a+tactical+knife.+Mostly+I+am+put+off+by+the+tiny+width+of+the+blade.+In+tactical+knives+I+like+a+definitely+meaty+blade+mainly+because+you+in+no+way+know+what+you+are+going+to+require+to+cut+or+slice+or+stab.+Now+if+you+are+searching+for+a+sleek+knife+this+may+perhaps+be+specifically+what+you+will+need.+This+is+1+of+those+issues+although.+Everybody+has+different+tastes%2C+so+it+really+is+basically+impossible+to+make+a+knife+that+everyone+will+like.+Hope+your+subsequent+selection+suits+you+far+better.+Opening+the+knife+1+handed+is+smooth+and+simple.++If+you+loved+this+information+and+you+want+to+receive+details+with+regards+to+%5Bhttp%3A%2F%2Fwww.thebestpocketknifereviews.com%2Fspyderco-delica-4-review%2F+Spyderco+Delica+For+Defense%5D+%5Bhttp%3A%2F%2Fwww.Wikipedia.org%2Fwiki%2Fkindly%2Bvisit+kindly+visit%5D+our+own+web+site.+Closing+needs+a+unique+method+than+a+liner+lock.+When+I+first+got+the+knife+I+thought+the+lock+back+would+bother+me%2C+but+I+am+now+utilised+to+it+and+locate+it+sturdy+and+efficient.%0D%0A%0D%0AThe+Kahr%2FDelica4+is+a+operate+of+insight%2C+and+it+comes+from+the+thoughts+of+one+of+the+smartest+guys+in+the+self-defense+knife+small+business.+It+came+to+fruition+in+part+due+to+the+fact+Mark+Galli%2C+the+sales+manager+at+Kahr%2C+is+one+of+Mike+Janich%27s+senior+students.+Due+to+the+fact+the+Delica+has+the+minimum+handle+length+%28four-inches%29+that+enables+a+folder+to+be+easily+accessed+and+opened%2C+it+is+as+discreet+as+a+fully+practical+folder+can+be.+The+2.5-inch+blade+makes+it+legal+to+have+such+a+totally-functional+folder+%E2%80%94+carried+legally+%E2%80%94+pretty+much+anyplace+in+the+country.+Considering+that+there+is+a+legal+operate+around+with+the+Kahr%2FDelica4.&create=Create kitchen] knives has specific metallurgical properties and will be expensive to supply. If the knife maker buys a cheaper - lower high quality metal, it should [http://www.foxnews.com/us/2013/09/18/student-suspended-for-10-days-for-accidentally-bringing-pocket-knife-to/ rescue knives] make no difference how hard it is in Rockwell terms or how it's processed by the knifemaker - it's going to simply be a nasty knife. A superb example is the World brand, which I like very much. Many of those knives will not be cast to create a lighter knife.<br><br>In case your knife remains to be gritty or troublesome to open, you could must disassemble the knife for a more thorough cleansing, which we cannot cowl on this article. You will likely need specialty tools and the method will differ broadly depending on what knife you're engaged on. Many knife manufacturers will also inform you that disassembling your knife will void your guarantee. The Benchmade Griptillian in what we take into account heavier utilization. Wooden carving and whittling requires a sturdy blade and a deal with that may push that blade around. We seemed for rounded handles that fill the users loosely clenched fist.<br><br>The other odd factor about sticky locks is that extra so than stability and power this may be an each day concern. If you have to wrestle a knife closed, it in all probability gained’t be your EDC for long. Equally problematic is locks that don’t have interaction properly. Even the almighty Hinderer is understood to have a flipper that doesn’t constantly [http://www.thebestpocketknifereviews.com/spyderco-delica-4-review/ http://www.thebestpocketknifereviews.com/] deploy the knife and interact the lock. It wants a wrist flick to do this. Some think this can be a “security feature” however it's really a poorly made detent. We know that as a result of over different production runs the Hinderer flipper has gotten more and more efficient. Cleansing and Maintenance.<br><br>In Roman instances, troopers have been known for pulling out a pocket knife when relieved of their heavier battle gear. The shock of a third weapon might usually assist a troubled soldier dispatch an enemy and save his own life. Nevertheless, with the arrival of the sheathed knife, pocket knives slowly fell out of favor. But lately, when I was showing some friends round our studio, I had a bunch of knives sitting out and the one which obtained essentially the most attention was this little knife. Possibly it was the distinction in dimension, the strong really feel or how good it matches in the hand and within the pocket.<br><br>These are some of the necessities that you will want in an effort to dwell as comfortably as potential if you are on the job or while you're in camp. There is a checklist of required belongings that you'll want to deliver along as well. If this is your first job combating wildland hearth, you have [http://Www.Thebestpocketknifereviews.com/spyderco-delica-4-review/ Amazon Spyderco Delica 4] to know that there are weight limits on all luggage and total body weight including clothes. Should you go over these limits, you will not be on the aircraft. You may still get on the airplane however you will have to drop no matter weight you might be over.<br><br>My love for the Spec Elite I, despatched me looking to see if the knife is made in a smaller model — it is. That is the smaller model, and it's actually great. Instead of shrinking the knife, it’s like SOG took one inch off the blade and deal with length — preserving the thickness, tapering, and width all the identical [http://en.wikipedia.org/wiki/Knife switchblade]. The result's a chunky little knife that also feels nice and furthermore feels extremely capable. Patrick Rhone praised this knife , which made me order it immediately As I posted earlier than this can be a very stable knife, with two deadly flaws for me as an EDC.
The '''Rayleigh sky model''' describes the observed [[Polarization (waves)|polarization]] pattern of the daytime [[sky]]. Within the atmosphere [[Rayleigh scattering]] of [[light]] from air [[molecule]]s, water, dust, and [[aerosol]]s causes [[Diffuse sky radiation|the sky's light]] to have a defined polarization pattern. The same [[elastic scattering]] processes cause the sky to be blue. The polarization is characterized at each [[wavelength]] by its [[degree of polarization]], and orientation (the e-vector angle, or scattering angle).
 
The polarization pattern of the sky is dependent on the [[celestial coordinate system|celestial position]] of the sun. While all scattered light is polarized to some extent, light is highly polarized at a scattering angle of 90° from the light source. In most cases the light source is the sun, but the moon creates the same pattern as well.  The degree of polarization first increases with increasing distance from the sun, and then decreases toward the anti-sun. Thus, the maximum degree of polarization occurs in a circular band 90° from the sun. This band reaches typical degrees of polarization near 80%.
 
[[File:degpolred.jpg|thumb|right|300px|The Rayleigh sky at sunset or sunrise]]
 
When the sun is located at the [[zenith]], this circle wraps around the [[horizon]]. Therefore the sky is polarized horizontally along the horizon.  During [[twilight]] this circle is defined by the effective North-Zenith-South plane.  It is thus maximally polarized along the [[meridian (astronomy)|meridian]] and vertically at the horizon in the North and South. This is represented by the figure to the right. The white band<!--I don't see a white band in the figure. The text needs to be adjusted to match the figure.--> represents the circle in the North-Zenith-South plane where the sky is highly polarized. The [[cardinal direction]]s N, E, S, W rotate counter-clockwise around the [[celestial sphere]].
 
It is important to note that because the polarization pattern is dependent on the sun, it changes not only throughout the day but throughout the year. While the sun sets toward the South in the winter the North-Zenith-South plane is offset with effective North actually located toward the West. Thus if the sun sets at an azimuth of 255° (15° South of West) the polarization pattern will be at its maximum along the horizon at an azimuth of 345° (15° West of North) and 165° (15° East of South).
 
In terms of a single day the pattern rotates with the changing rate of the sun.  At twilight it typically appears about 45 minutes before local sunrise and disappears 45 minutes after local sunset. Once established it is very stable, showing change only in its rotation. It can easily be seen on any given day using polarized sunglasses.
 
Many animals use the polarization patterns of the sky at twilight and throughout the day as a [[Animal navigation|navigation]] tool. Because it is fully determined by only the location of the sun, it is easily used as a compass for animal orientation. By orienting themselves with respect to the polarization patterns, animals can locate the position of the sun and thus determine the cardinal directions.
 
==Theory==
 
===Geometry===
[[File:Rayleigh-geometry.pdf|thumb|300px|The geometry representing the Rayleigh sky]]
The geometry for the sky polarization can be represented by a celestial triangle based on the sun, zenith, and observed pointing (or the point of scattering). In the model, γ is the angular distance between the observed pointing and the sun, Θ<sub>s</sub> is the solar zenith distance (90° - solar altitude), Θ is the angular distance between the observed pointing and the zenith (90° - observed altitude), Φ is the angle between the zenith direction and the solar direction at the observed pointing, and ψ is the angle between the solar direction and the observed pointing at the zenith.
 
Thus, the spherical triangle is defined not only by the three points located at the sun, zenith, and observed point but by both the three interior angles as well as the three angular distances. In an [[Celestial coordinate system|altitude]]-[[azimuth]] grid the angular distance between the observed pointing and the sun and the angular distance between the observed pointing and the zenith change while the angular distance between the sun and the zenith remains constant at one point in time.
 
[[File:soldis zendis.jpg|thumb|left|400px|The angular distances between the observed pointing and the sun (top plot) and between the observed pointing and the zenith (bottom plot)]]
The figure to the left shows the two changing angular distances as mapped onto an altitude-azimuth grid (with altitude located on the x-axis and azimuth located on the y-axis).  The top plot represents the changing angular distance between the observed pointing and the sun, which is opposite to the interior angle located at the zenith (or the scattering angle).  When the sun is located at the zenith this distance is greatest along the horizon at every cardinal direction. It then decreases with rising altitude moving closer toward the zenith. At twilight the sun is setting in the west. Hence the distance is greatest when looking directly away from the sun along the horizon in the east, and lowest along the horizon in the west.
 
The bottom plot in the figure to the left represents the angular distance from the observed pointing to the zenith, which is opposite to the interior angle located at the sun. Unlike the distance between the observed pointing and the sun, this is independent of azimuth, i.e. cardinal direction.  It is simply greatest along the horizon at low altitudes and decreases linearly with rising altitude.
 
[[File:solang ztelan stelan.jpg|thumb|right|400px|The three interior angles of the celestial triangle.]]
The figure to the right represents the three angular distances. The left one represents the angle at the observed pointing between the zenith direction and the solar direction. This is thus heavily dependent on the changing solar direction as the sun moves across the sky. The middle one represents the angle at the sun between the zenith direction and the pointing. Again this is heavily dependent on the changing pointing. This is symmetrical between the North and South hemispheres. The right one represents the angle at the zenith between the solar direction and the pointing. It thus rotates around the celestial sphere.
{{-}}
 
===Degree of polarization===
The Rayleigh sky model predicts the [[Degree of polarization|degree of sky polarization]] as:
 
:<math> \delta = \frac{ \delta_{max} \sin^2 \gamma }{ 1 + \cos^2 \gamma} </math>
 
[[File:Pol horizon.png|thumb|right|300px|The polarization along the horizon.]]
As a simple example one can map the degree of polarization on the horizon. As seen in the figure to the right it is high in the North (0° and 360°) and the South (180°).  It then resembles a cosine function and decreases toward the East and West reaching zero at these cardinal directions.
 
The degree of polarization is easily understood when mapped onto an altitude-azimuth grid as shown below.  As the sun sets due West, the maximum degree of polarization can be seen in the North-Zenith-South plane. Along the horizon, at an altitude of 0° it is highest in the North and South, and lowest in the East and West. Then as altitude increases approaching the zenith (or the plane of maximum polarization) the polarization remains high in the North and South and increases until it is again maximum at 90° in the East and West, where it is then at the zenith and within the plane of polarization.
[[File:Skydeg-alt-azi.png|thumb|left|400px|The degree of sky polarization as mapped onto the celestial sphere.]]
{{-}}
[[File:Mapdeg-ortho.gif|thumb|right|The degree of polarization. Red is high (approximately 80%) and black is low (0%).]]
Click on the image to the right to view an animation that represents the degree of polarization as shown on the celestial sphere.  Black represents areas where the degree of polarization is zero, whereas red represents areas where the degree of polarization is much larger. It is approximately 80%, which is a realistic maximum for the clear Rayleigh sky during day time. The video thus begins when the sun is slightly above the horizon and at an azimuth of 120°. The sky is highly polarized in the effective North-Zenith-South plane. This is slightly offset because the sun's azimuth is not due East. The sun moves across the sky with clear circular polarization patterns surrounding it.  When the sun is located at the zenith the polarization is independent of azimuth and decreases with rising altitude (as it approaches the sun). The pattern then continues as the sun approaches the horizon once again for sunset. The video ends with the sun below the horizon.
{{-}}
 
===Polarization angle===
[[File:Mapang-ortho.gif|thumb|The polarization angle. Red is high (approximately 80%) and black is low (0%).]]
 
The relative azimuth between the observed pointing and the sun, ψ, is the scattering angle and can be found by applying the [[law of cosines]] to the spherical triangle. It gives:
 
:<math> {\cos \gamma = \sin \theta_{s}\sin \theta \cos \psi + \cos \theta_{s}\cos \theta} </math>
 
This equation breaks down at the zenith where the angular distance between the observed pointing and the zenith, θ<sub>s</sub> is 0. Here the orientation of polarization is defined as the difference in azimuth between the observed pointing and the solar azimuth.
 
The scattering plane is the plane through the sun, the observer, and the point observed (or the scattering point).  The angle, ψ,  located at the zenith between the solar direction and the observed pointing is the scattering angle. This angle of polarization is always perpendicular to the scattering plane.
 
The polarization angles show a regular shift in polarization angle with azimuth. For example, when the sun is setting in the West the polarization angles proceed around the horizon. At this time the degree of polarization is constant in circular bands centered around the sun.  Thus the degree of polarization as well as its corresponding angle clearly shifts around the horizon. When the sun is located at the zenith the horizon represents a constant degree of polarization. The corresponding polarization angle still shifts with different directions toward the zenith from different points.
 
The video to the right represents the polarization angle mapped onto the celestial sphere. It begins with the sun located in a similar fashion. The angle is zero along the line from the sun to the zenith and increases clockwise toward the East as the observed point moves clockwise toward the East. Once the sun rises in the East the angle acts in a similar fashion until the sun begins to move across the sky.  As the sun moves across the sky the angle is both zero and high along the line defined by the sun, the zenith, and the anti-sun. It is lower South of this line and higher North of this line. When the sun is at the zenith, the angle is either fully positive or 0. These two values rotate toward the west. The video then repeats a similar fashion when the sun sets in the West.
 
===Q and U Stokes parameters===
[[File:Horizon.png|thumb|400px|The q and u input.]]
The angle of polarization can be unwrapped into the Q and U [[Stokes parameters]].  Q and U are defined as the linearly polarized intensities along the position angles 0° and 45° respectively; -Q and -U are along the position angles 90° and -45°.
 
If the sun is located on the horizon due west, the degree of polarization is then along the North-Zenith-South plane. If the observer faces West and looks at the zenith, the polarization is horizontal with the observer. At this direction Q is 1 and U is 0.  If the observer is still facing West but looking North instead then the polarization is vertical with him.  Thus Q is -1 and U remains 0. Along the horizon U is always 0. Q is always -1 except in the East and West.
 
The scattering angle (the angle at the zenith between the solar direction and the observer direction) along the horizon is a circle.  From the East through the West it is 180° and from the West through the East it is 90° at twilight. When the sun is setting in the West, the angle is then 180° East through West, and only 90° West through East.  The scattering angle at an altitude of 45° is consistent.
 
The input stokes parameters q and u are then with respect to North but in the altitude-azimuth frame. We can easily unwrap q assuming it is in the +altitude direction.  From the basic definition we know that +Q is an angle of 0° and -Q is an angle of 90°. Therefore Q is calculated from a sine function. Similarly U is calculated from a cosine function. The [[Brewster's angle|angle of polarization]] is always perpendicular to the scattering plane. Therefore 90° is added to both scattering angles in order to find the polarization angles. From this the Q and U Stokes parameters are determined:
 
:<math> Q_{in}=sin2\theta+90 </math>
 
and
 
:<math> U_{in}=cos2\theta+90 </math>
 
The scattering angle, derived from the law of cosines is with respect to the sun. The polarization angle is the angle with respect to the zenith, or positive altitude. There is a line of symmetry defined by the sun and the zenith. It is drawn from the sun through the zenith to the other side of the celestial sphere where the "anti-sun" would be. This is also the effective East-Zenith-West plane.
 
[[File:Mapqin-ortho.gif|thumb|The q input. Red is high (approximately 80%) and black is low (0%). (Click for animation)]]
[[File:Mapuin-ortho.gif|thumb|The u input. Red is high (approximately 80%) and black is low (0%). (Click for animation)]]
The first image to the right represents the q input mapped onto the celestial sphere. It is symmetric about the line defined by the sun-zenith-anti-sun. At twilight, in the North-Zenith-South plane it is negative because it is vertical with the degree of polarization. It is horizontal, or positive in the East-Zenith-West plane. In other words it is positive in the  ±altitude direction and negative in the ±azimuth direction. As the sun moves across the sky the q input remains high along the sun-zenith-anti-sun line. It remains zero around a circle based on the sun and the zenith. As it passes the zenith it rotates toward the south and repeats the same pattern until sunset.
 
The second image to the right represents the u input mapped onto the celestial sphere. The u stokes parameter changes signs depending on which quadrant it is in. The four quadrants are defined by the line of symmetry, the effective East-Zenith-West plane and the North-Zenith-South plane. It is not symmetric because it is defined by the angles ±45°.  In a sense it makes two circles around the line of symmetry as opposed to only one.
 
It is easily understood when compared with the q input. Where the q input is halfway between 0° and 90°, the u input is either positive at +45° or negative at -45°. Similarly if the q input is positive at 90° or negative at 0° the u input is halfway between +45° and -45°. This can be seen at the non symmetric circles about the line of symmetry. It then follows the same pattern across the sky as the q input.
 
===Neutral points and lines===
Areas where the degree of polarization is zero (the skylight is unpolarized), are known as neutral points. Here the Stokes parameters Q and U also equal zero by definition. The degree of polarization therefore increases with increasing distance from the neutral points.
 
These conditions are met at a few defined locations on the sky. The Arago point is located above the antisolar point, while the Babinet and Brewster points are located above and below the sun respectively. The zenith distance of the Babinet or Arago point increases with increasing solar zenith distance. These neutral points can depart from their regular positions due to interference from dust and other aerosols.
 
The skylight polarization switches from negative to positive while passing a neutral point parallel to the solar or antisolar meridian. The lines that separate the regions of positive Q and negative Q are called neutral lines.
 
===Depolarization===
The Rayleigh sky causes a clearly defined polarization pattern under many different circumstances. The degree of polarization however, does not always remain consistent and may in fact decrease in different situations. The Rayleigh sky may undergo depolarization due to nearby objects such as clouds and large reflecting surfaces such as the ocean. It may also change depending on the time of the day (for instance at twilight or night).
 
In the night, the polarization of the moonlit sky is very strongly reduced in the presence of [[Urban area|urban]] [[light pollution]], because scattered urban light is not strongly polarized.<ref>{{cite journal|last=Kyba|first=C. C. M.|coauthors=Ruhtz, T., Fischer, J., Hölker, F.|title=Lunar skylight polarization signal polluted by urban lighting|journal=Journal of Geophysical Research|date=17 December 2011|volume=116|issue=D24|doi=10.1029/2011JD016698|accessdate=4 January 2012|bibcode = 2011JGRD..11624106K }}</ref>
 
[[File:Effect of light pollution on sky polarization.jpg|thumb|[[Light pollution]] is mostly unpolarized, and its addition to moonlight results in a decreased polarization signal.]]
 
Extensive research shows that the angle of polarization in a clear sky continues underneath clouds if the air beneath the cloud is directly lit by the sun. The scattering of direct sunlight on those clouds results in the same polarization pattern. In other words the proportion of the sky that follows the Rayleigh Sky Model is high for both clear skies and cloudy skies.  The pattern is also clearly visible in small visible patches of sky.  The celestial angle of polarization is unaffected by clouds.
 
Polarization patterns remain consistent even when the sun is not present in the sky.  Twilight patterns are produced during the time period between the beginning of astronomical twilight (when the sun is 18° below the horizon) and sunrise, or sunset and the end of astronomical twilight. The duration of astronomical twilight depends on the length of the path taken by the sun below the horizon. Thus it depends on the time of year as well as the location, but it can last for as long as 1.5 hours.
 
The polarization pattern caused by twilight remains fairly consistent throughout this time period.  This is because the sun is moving below the horizon nearly perpendicular to it, and its azimuth therefore changes very slowly throughout this time period.
 
At twilight, scattered polarized light originates in the upper atmosphere and then traverses the entire lower atmosphere before reaching the observer.  This provides multiple scattering opportunities and causes depolarization. It has been seen that polarization increases by about 10% from the onset of twilight to dawn. Therefore the pattern remains consistent while the degree changes slightly.
 
Not only do polarization patterns remain consistent as the sun moves across the sky, but also as the moon moves across the sky at night. The moon creates the same polarization pattern. Thus it is possible to use the polarization patterns as a tool for navigation at night. The only difference is that the degree of polarization is not quite as strong.
 
Underlying surface properties can affect the degree of polarization of the daytime sky. The degree of polarization has a strong dependence on surface properties.  As the surface reflectance or optical thickness increase, the degree of polarization decreases.  The Rayleigh sky near the ocean can therefore be highly depolarized.
 
Lastly, there is a clear wavelength dependence in Rayleigh scattering. It is greatest at short wavelengths, whereas skylight polarization is greatest at middle to long wavelengths. Initially it is greatest in the ultraviolet, but as light moves to the Earth's surface and interacts via multiple-path scattering it becomes high at middle to long wavelengths. The angle of polarization shows no variation with wavelength.
 
==Uses==
 
===Navigation===
Many animals, typically insects, are sensitive to the polarization of light and can therefore use the polarization patterns of the daytime sky as a tool for navigation.  This theory was first proposed by [[Karl von Frisch]] when looking at the celestial orientation of honeybees. The natural sky polarization pattern serves as an easily detected compass.  From the polarization patterns, these species can orient themselves by determining the exact position of the sun without the use of direct sunlight.  Thus under cloudy skies, or even at night, animals can find their way.
 
Using polarized light as a compass however is no easy task.  The animal must be capable of detecting and analyzing polarized light. These species have specialized [[photoreceptor cell|photoreceptors]] in their eyes that respond to the orientation and the degree of polarization near the zenith. They can extract information on the [[Intensity (physics)|intensity]] and orientation of the degree of polarization. They can then incorporate this visually to orient themselves and recognize different properties of surfaces.
 
There is clear evidence that animals can even orient themselves when the sun is below the horizon at twilight.  How well insects might orient themselves using nocturnal polarization patterns is still a topic of study. So far, it is known that nocturnal crickets have wide-field polarization sensors and should be able to use the night-time polarization patterns to orient themselves. It has also been seen that nocturnally migrating birds become disoriented when the polarization pattern at twilight is unclear.
 
The best example is the [[halictidae|halicitid bee]] ''Megalopta genalis,'' which inhabits the [[rainforest]]s in Central America and scavenges before sunrise and after sunset.  This bee leaves its nest approximately 1 hour before sunrise, forages for up to 30 minutes, and accurately returns to its nest before sunrise. It acts similarly just after sunset.
 
Thus, this bee is an example of an insect that can perceive polarization patterns throughout astronomical twilight.<ref>{{Cite journal|title=Celestial polarization patterns during twilight |last1=Cronin |first1=T.W. |last2=Warrant |first2=E.J. |last3=Greiner |first3=B. |year=2006 |journal=[[Appl. Opt.]] |volume=45 |page=5582}}</ref>  Not only does this case exemplify the fact that polarization patterns are present during twilight, but it remains as a perfect example that when light conditions are challenging the bee orients itself based on the polarization patterns of the twilight sky.
 
It has been suggested that [[Viking]]s were able to navigate on the open sea in a similar fashion, using the [[birefringence|birefringent]] crystal [[Iceland spar]], which they called "sunstone", to determine the orientation of the sky's polarization.<ref>{{Cite journal|title=How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study. |last1=Suhai |first1=B. |last2=Horváth |first2=G.|year=2004 |journal=[[JOSA A]] |volume=21 |page=1669}}</ref><ref>[http://www.polarization.com/viking/viking.html ''The Viking Sunstone''], from Polarization.net.  Retrieved February 8, 2007.</ref><ref>''Secrets of the Viking Navigators'', by Leif K. Karlsen.  One Earth Press, 2003.  ISBN 978-0-9721515-0-4</ref><ref>Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies, by Ramón Hegedüs et al.[http://rspa.royalsocietypublishing.org/content/463/2080/1081.full]</ref>  This would allow the navigator to locate the sun, even when it was obscured by cloud cover. An actual example of such a "sunstone" was found on a sunk ship dated 1592, in proximity to the ship's navigational equipment.<ref>{{cite news |title=Sunstone Unearthed From Shipwreck |url=http://news.sciencemag.org/sciencenow/2013/03/scienceshot-sunstone-unearthed-f.html?ref=hp |accessdate=March 11, 2013 |work=Science |first=Lizzie |last=Wade |date=March 5, 2013 |publisher=American Association for the Advancement of Science}}</ref>
 
===Non-polarized objects===
Both artificial and natural objects in the sky can be very difficult to detect using only the intensity of light.  These objects include clouds, satellites, and aircraft.  However, the polarization of these objects due to resonant [[scattering]], [[emission spectrum|emission]], [[reflection (physics)|reflection]], or other phenomena can differ from that of the background illumination. Thus they can be more easily detected by using polarization imaging. There is a wide range of [[remote sensing]] applications in which polarization is useful for detecting objects that are otherwise difficult to see.
 
==Notes and references==
{{Refbegin}}
*''Polarization Patterns of the Twilight Sky.'' Cronin T.W. et al., 2005, SPIE, 5888, 389
*''Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle.'' Gál J. et al. 2001, Proc. R. Soc. Lond. 457, 1385
*''Polarized radiance distribution measurement of skylight.'' Liu Y. & Voss K., 1997, ApOpt, 36, 8753
*''How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation.'' Pomozi, I. et al., 2001, J. Exp. Biology, 204, 2933
{{Refend}}
{{Reflist}}
 
==External links==
*[http://www.polarization.com/sky/sky.html Polarization of the sky]
*[http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html Blue Sky and Rayleigh Scattering]
*[http://polarization.com/ Polarized Light in Nature and Technology]
 
{{DEFAULTSORT:Rayleigh Sky Model}}
[[Category:Polarization (waves)]]
[[Category:Atmospheric optical phenomena]]

Latest revision as of 11:59, 5 May 2014

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