Lens hood design calculator

[OlivierAOP]

I thought I'd share some simple formulas to make custom lens hoods. If you have a 3D printer and are familiar with CAD modeling they are relatively easy to make.

To be truly effective in reducing the amount of non-image-forming light from reaching the lens, they need to be tuned to a specific f-no value, and one must locate the entrance pupil of the lens, from which the lens hood length is measured.

In other words, if designed at a given f-no N, the hood obtained using the calculation below will vignette at lower N values and won't be as effective at larger N values. But they would still look cool and protect the lens somewhat.

So, for a given sensor height s, a focal length f, f-no N and hood length L (from the entrance pupil), the hood should have height

H = f/N + L*s/f,

and should have rounded corners with diameter f/N (the entrance pupil size).

This way the hood is just short of vignetting the frame, allows but gradually vignettes a range of light rays outside the FOV, and completely blocks the remainder. This results in minimising the image around the sensor/film, although rear lens or sensor baffles also help in that regard. The length v of the vignetted image next to the sensor edge is

v = f*f/L/N.

So the longer the hood, the more effective it is for a given lens.

For a round hood, s is the diagonal of the sensor. But rectangular hoods are more effective than round hoods.

 

[OlivierAOP]

Sample calculation. 28mm f/2.8 lens with 24x36mm sensor.

For a hood length of 40mm from the pupil, the hood is ~44x61mm with 10mm diameter corners, and restricts the image to a rounded 7mm band around the sensor.

 

[retinax]

There's an Excel sheet named "hoodcalc" floating around the interwebs. It makes do without the entrance pupil, and instead uses the front element, which seems convenient and convincing to me. I haven't taken the time to try and understand the calculations, but could you explain in simple words if the entrance pupil makes a difference? Is it just needed for the more sophisticated calculations regarding straight sides and rounded corners that you do?

 

[OlivierAOP]

Using the entrance pupil is useful if you want to customise the hood to a stopped-down aperture and/or if you want a rectangular hood.

Using the front element size for a round hood is adequate if the lens is used wide open and if the lens does not vignette wide open. This is rarely the case and a hood such designed won't be as effective or may even exacerbate the vignetting.

If I have some time I'll make some diagrams. The derivation is purely geometrical.

 

[jcb4718]

How do you locate the entrance pupil of a lens?

 

[OlivierAOP]

How do you locate the entrance pupil of a lens?

Method 1 (quick and dirty). Stop down the lens and hold it in one hand, looking straight at the pupil. Move your other hand, opened, along the barrel of the lens. Via depth perception you should be able to tell when your hand and the pupil are on the same plane, approximately. Use rule or caliper to estimate distance from the front the lens or other landmark.

Method 2 (better). Put the lens on a table, stopped down. Set 2nd camera on a tripod at the same height of the lens and focus on the aperture. Take a book or whatever and move it along the barrel. When lettering on book is in focus you found the entrance pupil. Use rule or caliper to estimate distance from the front the lens or other landmark.

Method 3 (best). Set lens and 2nd camera as above but with a nodal slide on the tripod. Focus on pupil and make note of slide position. Put a piece of scotch tape with sharpie mark at the front of the lens or a lens cap with contrasting lettering. Move slide back until tape/cap is in focus. The amount the slide moved is the pupil offset from the front landmark.

 

[OlivierAOP]

There's an Excel sheet named "hoodcalc" floating around the interwebs. It makes do without the entrance pupil, and instead uses the front element, which seems convenient and convincing to me. I haven't taken the time to try and understand the calculations, but could you explain in simple words if the entrance pupil makes a difference? Is it just needed for the more sophisticated calculations regarding straight sides and rounded corners that you do?

Here is a little schematic. For most lenses, at large apertures, the front element is within the image-forming FOV light cone. This is the cause of vignetting in the corners on the image (although the rear element can cause it as well). You can observe it in the "cat's eyes" out-of-focus light sources: the entrance pupil is truncated by the front element near the FOV edge.

Using the front element formula to make a hood would follow the dashed lines (hood 1), while a correct light hood would follow the solid lines (hood 2). Hood 1 will accelerate the light fall-off already present, hood 2 is just short of vignetting the frame.

 

[retinax]

Ok that makes sense. Although I believe that "cat's eyes" can also be formed simply because the aperture looks oval from the sides of the field of view, not only when the front element is too small to allow all light in. But I believe you're right that many lenses do have this limitation.