View Full Version : angle of coverage = focal lenght?

17-Apr-2004, 05:47
please help me on this: if angle of coverage for 75mm lens and 90mm lens is the same (let's say 105 degrees) does it mean that the lenses are the same or is the 75mm wider? In other words: what is angle of coverage (on this page)? thank you in advance, miha

17-Apr-2004, 06:04
No the angle of coverage is a measure of the image coming out of the back of the lens. Two lenses with the same angle will have different coverage because of the focal length.

2xfocal length x tan (angle/2) = lens coverage

A shorter lens is always wider then a longer one.

N Dhananjay
17-Apr-2004, 09:13
Two terms to keep in mind - angle of view and angle of coverage.

For most lenses (i.e., not telephoto or retrofocus designs), the distance behind the lens' nodel point at which an object at infinity is brought to a focus is referred to as the focal length. The shorter the focal length, the wider the angle of view i.e., the more of a scene you will get on the film.

Angle of coverage is the angle subtended behind the lens. With most smaller formats, a lens only needs to be able to cover the film, so the coverage is hardly ever quoted in the specs. With large formats which utilize camera movements, you need much more coverage. Thus, manufacturers will refer to the angle of coverage.

To summarize, angle of view refers to how much of the scene you can get on film (i.e., how wideangle or narrow angle the view is). Angle of coverage refers to the how much coverage the lens affords.

Hope this helps. Cheers, DJ

John D Gerndt
17-Apr-2004, 10:40

I don't know about you but I am now more confused than before I read this post. Angle of view and angle of coverage can, aparently, be disassociated from each other. In the example you gave of a 75mm and a 90mm with angle of coverage of 105 degrees (assuming the same angle of view) the 75 should take in more of the scene and provide a smaller image circle.


jerry brodkey
17-Apr-2004, 11:21
Think of the cone of light coming from the back of each lens 105 degrees wide. Now focus each lens on infinity. The 90mm lens will be farther away from the film plane, so the cone of light as it intersects the film plane will be larger than the cone coming from the back of the 75mm lens. Its image circle will be larger. There are charts which relate the focal length of the lens to the size of the film and give the angle needed to cover that film. I think Wisner has one on his site.


Michael S. Briggs
17-Apr-2004, 12:03
There are four quantitites being discussed here. The answers above are correct but some don't mention all four quantitites.

Focal length is the distance from the lens (rear nodal point to be precise) to the image when the lens is focused on infinity.

Angle of view is how much of the scence ends up on the film (or other sensor). It depends on the focal length F and the size of the film. (All this assumes that the lens has sufficent coverage to entirely cover the film.) If L is a dimension of the film, e.g., length, width or diagonal, the angle of view theta (with the lens focused on infinity) across that dimension is theta = 2 F atan (L/2). This shows how the angle of view depends on the lens focal length F. The equation is from simple geometry and is independent of the lens design for lenses of normal perspective, i.e., it doesn't apply for fisheyes. The equation is even valid for pinholes.

Angle of coverage is the angle of the cone of quality image projected by the lens. It is a characteristic of the lens design, so typically lenses of different focal lengths but of the same design will have the same angle of coverage phi. As an example, all f4.5 Grandagon-N lenses from 65 mm to 90 mm have a 105 degree angle of coverage.

Diameter of coverage is probably more useful to the photographer because it directly indicates whether the lens will cover a particular film format -- the diameter of coverage needs to be at least as large as the diagonal of the film. This is the diameter of the intersection of the cone of coverage with the film plane. So if two lenses of different focal lengths have the same angle of coverage, the longer focal length one will have a larger diameter of coverage because the apex of the cone is farther from the film. The equation to connect diameter of coverage D with angle of coverage phi is D = 2 F tan (phi / 2). So the equation shows that diameter of coverage is proportional to focal length for lenses of the same angle of coverage. For example, the 90 mm f4.5 Grandagon-N will cover a circle X1.38 larger in diamter than the 65 mm version: the two lenses have the same angle of coverage, and the ratio of their focal lengths is 1.38.

Small and medium format manufacturers typically only give the angle of view for their lenses because they know only one format will be used and that movements will not be used. Manufacturers of large format lenses typically publish both the angle of coverage and the diameter of coverage. Frequently they also have tables showing the shifts possible within the circle of coverage for various formats. For example, Rodenstock's brochure on the Grandagon-N gives the angle of coverage of the 90 mm f4.5 Grandagon-N as 105 degrees and the diameter of the coverage as 236 mm. With the equation above, I calculate 234.6 mm -- the difference is from some rounding error. Rodenstock gives the shifts possible on 4x5 as 48 and 54 mm. The two values are for shift and rise with the film in landscape orientation (or rise and shift for portrait orientation), and are for the lens focused on infinity. These values can be calculated from the image dimensions on 4x5 film (which are a bit smaller than the film size) and the diameter of coverage, or by making a drawing and measuring.

The diameter of coverage increases when the lens is focused on closer objects because the lens is farther from the film, and thus the apex of the cone of coverage is farther from the film. The increase is in proportion to lens-to-film distance divided by focal length.

Michael S. Briggs
17-Apr-2004, 13:49
Correction: the equation for the angle of view is theta = 2 atan ( L / (2F) ).

steve simmons
17-Apr-2004, 14:53
angle of coverage - this is a function of the dewsign of the lens and does not depnd on the format. As a general rule shorter than normal lenses for any given format have a wider angle of coverage because they have a shorter distance to project the image circle back to the film plane. For example a 90mm lens for 4x5 will generally have an angle of coverage exceeding 90 degrees. Newer ones have an angle of coverage of 100 degrees or more. A 210mm for a 4x5 will generally have an angle of coverage of 70-80 degrees because it does not need an angle of coverage of 100 degrees to cover the 4x5 format.

Angle of view is generally measured to opposite corners of the film area. A 210mm lens on a 4x5 camera will have an angle of view of X. On the 5x7 format the angle of view will be greater because the distance between the opposite corners is greater on the 5x7. However, the lens' angle of coverage will remain the same.

steve simmons

Bruce Watson
17-Apr-2004, 16:51
You seem to be confusing "angle of coverage" with "angle of view."

The angle of coverage is a lens design parameter which defines the cone of light that enters the lens. The angle of view is what the film sees. It can be calculated as:

view_angle = 2*arctan((format_dimension/2)/focal_length)

or the focal length required is:

focal_length = format_dimension/(2 * tan(view_angle/2))

Thus, your 90mm lens has an angle of view of 70 degrees. That is, the 5" dimension of the film can see an angle of 70 degrees looking out a 90mm lens.

The 75mm lens is a little wider at about an 80 degree angle of view.