Square hood

[alb59]

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Like many I assume, I like the look of the square hood. It’s found in Leica lenses and other brands. I’m curious, who first created it! Was it Leica? Is there an advantage or disadvantage to a square hood vs round? 
Thank you in advance to your answers and comments.

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A circular lens hood will shade the image circle of the lens. Consider a rectangle that fits inside that circle. That represents the image your sensor receives. A rectangular hood will encroach into the image circle up to the rectangular shape of your image, thus facilitating slightly closer shading for the captured image and thereby improving the image contrast.

[adan]

Square (or more commonly, rectangular) lens shades were developed for and by the motion picture industry - 90 years ago or more.

https://cinemagear.com/details/fox-cine-simplex.html

https://www.antiquephotographica.info/Mitchell Camera Corporation Matte Box No. 982 West Hollywood Web Page 10-3-2019.htm

They also serve as matte-boxes for special effects (e.g. split-screen shots where an actor could also play his own twin brother). Just required adding a cropping mask to the front. Or as filter mounts.

Leica had a few also in the 1930s:

https://wiki.l-camera-forum.com/leica-wiki.en/index.php?title=XIOOM

https://wiki.l-camera-forum.com/leica-wiki.en/index.php?title=SOOMP

Cameras that actually take square pictures (Hasselblad, Rollei, Yashica, etc) do provide truly "square" lens hoods. A Rollei square hood for their 1932 camera:

https://onlinedarkroom.blogspot.com/2016/12/rolleiflex-old-standard-review.html 

The advent of fisheye lenses (~1970), with extremely wide fields of view, brought the creation of the "tulip" lens hood - a square opening (as projected out into 3D space) cut into a circular tube of metal.

https://wiki.l-camera-forum.com/leica-wiki.en/index.php?title=16mm_f/2.8_Fisheye-Elmarit-R

Rectangular hoods - in theory - can crop out excess light right down to the edges of the rectangular picture (film, sensor) area, doing the best possible job of avoiding flare artifacts.

Round hoods, like round lenses, let a lot of useless light into the camera (the full "image circle"). If they don't, they will cause vignetting (dark shadows in the picture corners).

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But round lens hoods have historically been much easier (i.e. cheaper) to manufacture - buy a hollow metal tube right from the metal foundry, cut off the right length needed, machine some threads on the back, screw it on your lens. And, of course, can be build right into a round lens, to telescope

Many companies stayed with round hoods into the AF era (1990s) - or even today. 

(see: Leica's own current 50mm lenses)