Lens hood petal-shaped (Petal) vs cylindrical (Round) physical optics field of view obstruction calculation

1. Geometric optical deduction of sensor frame ratio and petal-shaped hood

1.1 Four-dimensional diagonal trap of rectangular format (3:2)

The full-frame or APS-C sensor we are using has a standard rectangular shape (aspect ratio 3:2):

Horizontal direction (left and right sides): The widest frame (full frame is 36mm) and the largest field of view;
Vertical direction (upper and lower sides): The frame is narrow (full frame is 24mm), the field of view is medium;
Diagonal direction (four corners): The farthest physical distance from the center of the sensor (the diagonal is 43.3mm long). It is also the most dangerous and dangerous spot in the lens imaging circle that is most easily blocked by physical obstruction and creates dead dark corners!

1.2 Optical physical carving of Petal Hood

Wide-angle lenses (such as 16-35mm, 24-70mm) have extremely large field of view (up to 84° to 107°), and the effective light cone in front of the lens is a four-cornered pyramid that spreads sharply outward.
In order to achieve the physical limit balance between "blocking external stray light" and "not blocking the effective light of the picture", engineers used three-dimensional Boolean subtraction to precisely cut the hood:

[Top and bottom (longer petals)] ──> Corresponding to the sensor 24mm, vertically narrow edges, small field of view, the hood can be extended outward longer to block the harsh midday sunlight from above 
[Left and right sides (second longest petals)] ──> Corresponding to the 36mm horizontal width of the sensor, appropriately converged inward 
[Four diagonal cutouts (extremely deep recesses)] ──> Precisely avoid the widest imaging diagonal beams at the four corners of the sensor. Even extending forward by 1 mm will block the light and form vignetting!

The petal-shaped hood is physically the maximum geometric hood that the lens optical system can achieve without mechanical vignetting!

2. Round Hood: the exclusive domain of telephoto lenses

Why are the lens hoods of mid-telephoto lenses such as 70-200mm, 100-400mm or 85mm F1.4 almost always regular and deep cylindrical?

Narrow FOV: The angle of view of a telephoto lens is usually only 34° to 6° or even narrower, and the light cone is almost similar to a parallel cylindrical beam at the front end of the lens;
The four diagonal light rays cannot spread to the periphery at all, so even if the depth of the cylindrical shape is made very deep, it will never touch the imaging field of view at the four corners. The symmetrical deep cylinder can achieve 360° stray light shielding and strong physical impact buffering without blind spots.

3. Three irreplaceable physical functions of the hood

Reduce secondary reflection stray light (Flare & Glare):
The non-imaging stray light falling diagonally on the front lens will undergo multiple violent internal reflections on the surface of the more than ten precision lenses inside the lens, causing the contrast of the photo to collapse, a gray and foggy white light to appear, and a hexagonal colored flare to appear. The hood blocks these non-axial stray lights at the source;
Physical Shield:
In outdoor rain, snow or sea breeze and dusty weather, the deep hood can block more than 80% of the oncoming drizzle and splashing waves, eliminating the trouble of frequently wiping the lens;
"Crumple Zone" at critical moments:
When the camera and lens accidentally fall forward from a tripod or table, the high-toughness engineering plastic lens hood will be the first to hit the ground, absorbing almost all the impact kinetic energy through its own fragmentation and deformation, saving the expensive front lens and focus motor.

4. Pitfall avoidance and practical common sense

[!CAUTION]

"False black corners" caused by improper installation of the hood:
The petal-shaped hood is fixed with a bayonet mount. If you don't hear a crisp "click" locking sound when rotating and installing, causing the large petals to rotate to a diagonal position, two extremely ugly black arcs will instantly appear on the edge of the viewfinder! When installing, be sure to make sure that the alignment mark (small dot) in the center of the petal is strictly vertically aligned with the center mark line on the top of the lens barrel.

Ultra wide angle lens superimposed with thick frame filter vignetting:
When using a 16mm ultra-wide-angle lens, if a thick-framed UV filter is screwed on the front of the lens, then a thick-framed adjustable ND filter is screwed on, and finally the lens hood is attached - the superposition of the three thicknesses will cause the physical base of the lens hood to move forward by more than 5mm, instantly breaking through the light cone envelope and creating serious mechanical dead angles around the screen! Be sure to use an ultra-thin (Slim) filter frame for wide-angle lenses.