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The basic lens fomula is
f = focal length of lens (for example - 50 mm lens)What is a principle point?
d1 = distance from detector plane to the principle point of the lens
d2 = distance from the principle point of the lens to the object
Note: if d2 = infinity then d1 = f. So the principle point is f away from the array when the lens is focussed at infinity.
Note: lenses focus by moving the optics further from the detector (increasing d1. If you know the minimum object distance (d2) for a lens, you can figure out where d1 is when the lens is focussed close. But it usually varies just a few millimeters from the focal length f.
Most lenses act geometrically like a pinhole lens placed at the principle point. we will use this model. If you are designing the next Hubble telescope, go find a good textbook on optics. Otherwise this will get you started just fine. The principle point is usually inside the lens glass, but in a telephoto lens, this point is in front of the lens!
So how do I figure my field of view? Now since this lens acts like a pinhole, the field
of view (FOV) is found by :
A = distance on the detector (array size)The good news is you don't have to find d1 or the principle point. Combining formulas
or
Watch your units! This formula lets you figure out field of view and working distance for a given camera.
Notice that d2 is roughly the "working distance" from the lens to the object. Strictly speaking the working distance is from the front of the lens to the object.
For large working distances :
so the formula reduces to
or
Let's take an example : What is your working distance to get an
10" field of view with a 50mm lens on a linescan camera with array length 0.6"?
This is the approximate working distance.
- Things to watch out for:
- Make sure your lens will image a large enough
area. Small C-Mount lenses for 1/2" CCD are not large enough for a 0.6" array.
Use a 2/3" or 1" format lens.
If d2 is small, then your lens may not focus that close. You may want to figure out d1 and then figure out what extension tubes you will need.
Let's take another example
: Suppose you want to use a 75mm lens
to get 1:1 magnification. What extension tube is needed?
Here the assumption that working distance = d2 may not be close enough.
Since FOV = A, then
So your distance from the array to your object is d1 + d2 = 4f = 300mm
Since d1 needs to be pushed out to
150mm, and your 75mm lens only moves d1 from 75 to 80mm (figure this
out based on working distance range) then you will need extension tubes that
are 70-75 mm long!
You can figure your working distance based on the physical measurements of the
lens. Remember the principle point is usually inside the lens! This is usually
easier to setup and measure, but it can be calculated.
Good Luck!
