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How can I calculate for a given lens, where in the periphery a theoretical lens hood would become visible?

This seems dependent on the size of the front element, focal length, and possibly other factors I don't understand.

I build attachments for the front of my lenses to shoot through and selecting the appropriate lens has become challenge because I don't understand this relationship. Thanks!

  • A rule of thumb, or general relationship between the relevant factors would also be helpful. – nate Nov 26 '20 at 1:24
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    There have been a few telephoto lenses in the past supplied with two hoods: a shorter one for use with FF cameras and a longer one for use with APS-C cameras. Since the smaller sensor captures less of the image circle projected by the lens, the angle of view is narrower. – Michael C Nov 26 '20 at 7:28
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Angle of view is determined by (real) focal length and sensor/film size. That's your starting point.

AoV=2*arctan(d/2f)

where:

  • AoV is the Angle of View
  • d is the size of the sensor/film in the direction measured
  • f is focal length (in the same units as d)

For a circular hood you would use the diagonal measure of the sensor/film

For a "petal" hood you would need to calculate based on the width and height as well as the diagonal of the sensor/film.

For many lenses aperture and/or focus distance can also play a part if lenses "breathe" (change focal length) as they are stopped down to different apertures and/or focused to different distances. Sometimes this can be rather significant. The AF-S Nikkor 70-200mm f/2.8G VR II, for example, gives an angle-of-view when zoomed to 200mm and focused at the minimum focus distance that is equivalent to a 140mm lens focused at infinity!

An alternative to calculating fields of view and angles/lengths is to download patterns for different lenses from the following:

For APS-C cameras

For Full Frame cameras

Even if you can't find your exact lens, lenses with similar focal lengths/angles of view and front element diameters should be similar.

  • Great answer. Could you clarify for the following example case (which is the primary source of confusion). The Canon RF 35mm f1.8 and the Canon EF 35mm f1.4 have the same focal length and sensor size which predicts the same AoV. Yet the front element is much larger on the 1.4 and the lenses are different lengths. In practice my "lens hood" is not at all the same size for these lenses. This might be succinctly put as: from where do I project the AoV? (But I am not sure.) – nate Nov 26 '20 at 18:51
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    @nate From whatever point along the optical axis so that the projection of a cone intersects the front of the lens at the diameter of the front element. For example, if the front element is 65mm in diameter, project the cone so that it intersects the rim of the front element where your cone is 65mm in diameter. Or more practically, measure 1/2AoV (because the lens' optical axis bisects the AoV) from the edge of the front element. Don't forget to allow for "breathing" of the AoV is wider at shorter focus distances, even with a prime lens. – Michael C Nov 27 '20 at 2:35
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    For wider angle lenses, such as a 35mm lens on a FF camera, calculate the basic cone using the shortest side of the sensor, then calculate your cutouts using the long side of the sensor for the longest point on the two "short" petals and the diagonal for the four shortest cutouts. In essence you're projecting an upside down pyramid (longer on two sides than on the other two) that has 1/2 the diagonal AoV view as the slope of the corners , 1/2 the long side AoV as the slope on the short side, and 1/2 the short side AoV as the slope on the long side of the pyramid. – Michael C Nov 27 '20 at 2:43
  • Yes, ok! Well described. – nate Nov 27 '20 at 19:19
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Disclaimer: this is not exactly an answer to the question, as it doesn't rely on calculation, but experimentation.

I used a do-it-yourself approach for checking lens hoods (and vignetting, to some extent), back in the analog times.

From cardboard, I cut out a 24*36mm rectangle and glued together a box to hold that cutout at the correct distance from the lens mounting flange.

When looking from the back through the cutout into the lens, no part of the lens hood should be visible. If it's visible, estimate the percentage of area obscured by the hood, with 50% covered resulting in 1.0EV vignetting.

Regarding lens vignetting: when looking along the center line, the shape of the lit-up area always looks circular, and that's the reference. Lenses with a vignetting problem can typically be identified when looking from a corner angle: the shape no longer is circular, but looks like the intersection of two overlapping circles: like an ovoid with two sharp edges.

If you aren't afraid of spending some time with cardboard, glue and sharp knives: build a cardboard box with depth equal to the flange focal distance of your camera system, with a front cut out to match the camera/lens mount, and a back coutout resembling your sensor size.

2020's high-tech-version would be to design and print it in 3D.

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