jcolwell
Offline
• • • • • • •
Upload & Sell: On
|
 p.3 #6 · p.3 #6 · 16-35 f4 vs 17 tse + 24 is usm + 40 stem quality for hiking | |
OntheRez wrote:
Melcat and Jim,
I remember the word trigonometry, ...
Hi Robert,
Geometry rules! Trigonometry and proportional ratios are the norm in photography. I've attached two examples from some of my calculator spreadsheets (which are on my site);
1. a table showing distance from subject for a full-width full-frame image, for different focal lengths.
2. a diagram showing the amount of tilt required to make the plane of focus for a vertical sensor line up with the horizontal plane (i.e. the ground), as a function of height above the ground, with different curves for different focal lengths, based on the Scheimpflug Principle,
Ref. "Harold Merklinger on the Scheimpflug Principle", http://www.trenholm.org/hmmerk/#SR (free document downloads)
Talk about proportional ratios! The "distance table" doesn't even have dimensions (e.g. feet, km, miles), because the relationship between subject width and distance from subject is independent of dimensions (i.e. it's a dimensionless ratio). In this case, the actual numbers are calculated for a subject that fills the 36mm width of a FF DSLR sensor. For example, if you're using a 17mm lens and you want to fill the frame with a subject that's 0.75 feet wide, then you want to place the camera sensor 0.35 feet from the subject. Alternatively, if you want to take a full frame image of a landscape scene that's 10 miles wide, with an 85mm lens, then you place the camera 23.6 miles away from the scene.
The math behind the tilt curves is a little more complicated than the distance-from table, but it's still basic geometry. This graph is called "Mirex T-S Adapter", because the Mirex allows up to 10 degrees of tilt. The Canon TS-E lenses allow up to 8 degrees of tilt. Each of the nine curves in this graph is for a different focal length, with focal length labels shown in the boxes at the right side of the graph. The curves in the graph alternate between thick and thin lines, corresponding to the thick and thin borders on the focal-length label boxes.
So, if I'm using a 150mm lens on my tripod (which puts the camera sensor at about 1.65 m above the ground), then I need about 5.2 degrees of tilt to align the plane of focus with the ground, while the camera is pointed horizontally (say, at the horizon). In this case, the angle between the vertical sensor and the horizontal ground plane is 90 degrees. If I point the camera downwards, then I need less tilt, because the angle between the horizontal ground and now-leaning sensor is less than 90 degrees. That's where the small "correction for body angle" table below the graph comes in. For this example with a 150mm lens on my tripod (1.65 m above the ground), if I tilt the camera body (and untitled lens) down by 30 degrees, then I would use the 0.67 "correction factor', which says I need 5.2 x 0.67 = 3.5 degrees of tilt on the tilt lens.
OTOH, if I'm doing macro photography with a tilt lens, then I'm getting pretty close to the subject, and the height above the horizontal plane (i.e. table top) starts to get pretty small, and so the amount of tilt required increases dramatically.
Anyway, I use the "tilt curves" and "body angle corrections" to roughly determine my initial tilt angle, and then I use the tried-and-true, iterative process of tilt, focus, tilt, focus, tilt... to get to the final solution. I find using an initial tilt angle from these curves speeds things up a bit, but the first combination of tilt angle and focus distance never seems to work out quite right (which is why I use my smart phone as a remote, high mag. screen for this stuff). I generally follow the "tilt near, focus far" school of thought, but some people do it the opposite way. Some people.... 
There are many excellent resources at the Merklinger site for stuff like focusing Large Format cameras (i.e. tilt & shift), focusing in general, and weird bokeh (to name a few).
Cheers,
Jim
 © jcolwell 2016
Distance from subject for full-width FF image (landscape mode)
Tilt angle for horizontal plane of focus (sensor vertical)
|
