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Φοτογραϕια is all Greek to me

Panoramas
 
I shoot panoramas from a tripod.  If you have a good panorama stitching software package the tripod is not strictly necessary, but the tripod allows you to shoot at slower shutter speeds, allowing smaller aperatures, creating greater depth of field.  The tripod also can be indexed so you can get properly overlapped shots by using index marks on the head.  The head can be indexed both for azimuth and for elevation.
 
Three things have declared themselves to be my enemies when shooting these panoramas: Wind, Sun, and Clouds.
 
Wind makes things move. Features in the overlap area that have moved between shots create problems in choosing control points, not only by moving features that could be used for control points, but also by obscuring good control points from onne shot so that they are not visible in the other.  Using moving points for registering the shots will make for a very bad fit. Choosing points on big solid objects, buildings, tree trunks, rocks, etc. will give best results.  In a similar vein, choosing points in the near foreground is almost as big a problem as the wind due to parallax errors. 
 
The sun is always somewhere in a 360° panorama, meaning you will have to shoot into the sun.  If you can locate your camera in the shadow of a tree or other object, the problem can be ameliorated, but sometimes the best shot means shooting into the sun. And speaking of shadows, don't forget that when the sun is directly behind you, your shadow becomes part of the scene.
 
Clouds are useless for containing control points.  They always move faster than you think.  Clouds obscuring the sun are also a problem in getting the exposures to blend.
 
All three enemies' effects are exacerbated when you shoot multi-tiered pans.  You make a pass at 60° below the horizon, shooting 12 shots then re-index for 30° for the second tier and lots more things can have changed than change between horizontally overlapping shots.
 

The math of panorama shooting
 
This is the techie page so get your triginometry dusted off for a little practical math.

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Angle BOD is called the Field of View or Angle of view.  The angle depends on only two things -- the focal length of the lens (distance OC) and the width of the sensor (2 times distance AC).  Tenth grade (US) geometry says that angle BOD is twice angle COA, and eleventh grade triginometry says that the tangent of angle COA is AC/CO.  So,
       Field of view = 2 * arctan((Sensor Width / 2) / Focal Length).
Notice that unless the sensor is square, the field of view is different in the horizontal and vertical directions.  Example time?
 
I like shooting my panoramas with a 35mm lens on a Nikon DX sensor, Nikon D80 camera.  The sensor for the D80 is 23.6 by 15.8 mm.  So, in landscape orientation the horizontal  FoV is 2*atan(23.6/2/35) or 37.262333 degrees and the vertical FoV is 2*atan(15.8/2/35) or 25.438662 degrees.  Simple, right?  Well it would be if the focal length of a 35mm lens were actually 35 milimeters.  In actual fact 35mm is an approximate value (a fact that I'll discuss when talking about using panorama stitching software.)  For now it is a good enough value to allow you to PLAN a panorama shoot.

 
"PLAN!!?? WE DON'T NEED NO STEEENKIN' PLAN!"  Yeah, that's how I started too, but remember if you shoot too few shots to cover the scene, you've got holes in your final product, and if you shoot too many shots, your software may not be able to cope with the volume of data you're feeding it.

 
"OK, BUT HOW DO I USE THE FOV?"  Think about this, swinging the camera in a full circle covers 360°, right?  Ten horizontal shots would cover 372° plus change. That's a full circle plus a little; but it's only a little little.  Twelve degress divided by the ten shots means you have only 1.2° of overlap per pair of shots.  That's a little thin slice, and may not have enough control points to do a good job of stitching, so how about adding a few extra shots along the way to be sure.  Fifteen shots 24° apart would give you a 13° overlap.  That should be plenty.  I actually only shoot 12 shots 30° apart, since that's easier to index.  (My tripod has a six pointed design on the pivot axles, so I can eyeball my aim points using the points an half way between the points as index marks.)
 
Of course you can do the same calculation in the vertical direction.  Here, covering the whole 180° isn't the issue, but getting enough vertical overlap to register the shots is critical.  Getting started, I had several screwed up shoots where I overestimated (before I figured out how to P*L*A*N the shoot) the vertical overlap and ended up with three tiers of shots that I could not stitch because they did not overlap at all!
 
Let's go through my example of the 35mm lens on a DX sensor again for the vertical.  I like symetry, so I always want one tier at 0° and I want the tiers above and below the horizon to "match up."  The vertical FoV we calculated above was 25°, so if we divide the 180 by 25 and round up...  Wait a minute; if each shot covers 25°, and we separate them by LESS than 25°,  they will overlap, right?  So we can shoot our tiers at 0, +/- 20, +/- 40, +/60, +/-80  or 0, +/-15, +/-30, +/-45, +/-60, +/-75, and maybe a single shot at zenith and nadir (+/-90) to  cover the vertical.
 
Remember though, each tier adds 12 to 15 shots, so you have to decide, "Is that extra tier of featurless sky or photographer's footprints really worth it?"  
 
By the way, on the footprints issue, if you are going to go for a full 360 by 180, always shoot the ground shots first before you track it up with 9 to 11 circles of footprints around the tripod.  Also try to keep your feet out of the shot.  I've got some lovely ground shots of the toes of my mud boots.  In a later post, I'll discuss techniques for keeping your tripod legs out of the shot (as soon as I figure out how to do so.  I still haven't solved that one.)

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