Camera lens size and field of view
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rocco
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Field-of-view is basic geometry (maybe not that basic). There are three points where it can be specified, and three factors that determine it.
It is usually specified horizontally, meaning the angle from the left side to the right side. But it can also be specified vertically and diagonally. Since most sensors are TV aspect ratio (4:3), the 3-4-5 triangle applies. That is to say the ratio of vertical to horizontal to diagonal is equal to 3 to 4 to 5. A field that is 40 degrees wide will be 30 degrees high and 50 degrees diagonally.
Three things determine the field size:
The focal length of the lens.
The size of the sensor.
The distance to the point of focus.
If the lens is focused at infinity, the distance from the nodal point of the lens to the image plane is equal to the focal length. If you are focused closer, this distance increases, but not by much. The formula is:
1/f = 1/p + 1/q, where:
f is the focal length of the lens,
p is the distance from the nodal point of the lens to the object that you are focused on, (called it object plane) and
q is the distance from the nodal point of the lens to the sensor (called the image plane).
Once you know the distance of the lens to the sensor, the field is determined by a simple right triangle. One leg of the triangle is half the length of the image sensor, (along the axis of interest, usually horizontally). Call it .5*L. The distance to the lens is the other leg, which we defined as q. So the angle of one half the field is the arc-tangent of one half the sensor size divided by lens distance (you can just assume that you are focused near infinity, and use the focal length f for q).
So the angle of the field is:
Angle = 2 * ( arc-tangent( .5*L / q ) )
If you wanted to be anal (like me) you would calculate q from f and p. Make sure you convert everything to millimeters. Most image sensors are either 1/4 inch or 1/3 inch, measured diagonally. You can use the 3:4:5 ratio to convert this to horizontal or vertical if you have a TV-shaped sensor.
Sorry if this is much more than you wanted to know.
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Later: Wayne said it a little more concisely.
It is usually specified horizontally, meaning the angle from the left side to the right side. But it can also be specified vertically and diagonally. Since most sensors are TV aspect ratio (4:3), the 3-4-5 triangle applies. That is to say the ratio of vertical to horizontal to diagonal is equal to 3 to 4 to 5. A field that is 40 degrees wide will be 30 degrees high and 50 degrees diagonally.
Three things determine the field size:
The focal length of the lens.
The size of the sensor.
The distance to the point of focus.
If the lens is focused at infinity, the distance from the nodal point of the lens to the image plane is equal to the focal length. If you are focused closer, this distance increases, but not by much. The formula is:
1/f = 1/p + 1/q, where:
f is the focal length of the lens,
p is the distance from the nodal point of the lens to the object that you are focused on, (called it object plane) and
q is the distance from the nodal point of the lens to the sensor (called the image plane).
Once you know the distance of the lens to the sensor, the field is determined by a simple right triangle. One leg of the triangle is half the length of the image sensor, (along the axis of interest, usually horizontally). Call it .5*L. The distance to the lens is the other leg, which we defined as q. So the angle of one half the field is the arc-tangent of one half the sensor size divided by lens distance (you can just assume that you are focused near infinity, and use the focal length f for q).
So the angle of the field is:
Angle = 2 * ( arc-tangent( .5*L / q ) )
If you wanted to be anal (like me) you would calculate q from f and p. Make sure you convert everything to millimeters. Most image sensors are either 1/4 inch or 1/3 inch, measured diagonally. You can use the 3:4:5 ratio to convert this to horizontal or vertical if you have a TV-shaped sensor.
Sorry if this is much more than you wanted to know.
-----
Later: Wayne said it a little more concisely.
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