Underwater wide-angle photography Dome Port virtual imaging distance and close-up focus point correction physics

1. Physical mutation of underwater optics: reduced viewing angle and failure of flat glass

When the camera is put into a waterproof case and dived underwater, the light propagation medium changes drastically:

1. Penalty of Snell's Law of Refraction:

• The refractive index of water $n_{\text{water}} \approx 1.333$, the refractive index of air $n_{\text{empty}} \approx 1.000$;
• If an ordinary flat-bottom glass lens cover (Flat Port) is used: the light is strongly deflected inward when entering the air from water, the equivalent focal length of all lenses is forcibly enlarged by 1.33 times (the angle of view is reduced by 25%), and the ultra-wide-angle lens is instantly reduced to a mediocre mid-focus lens!

2. Optical salvation of the hemispherical optical dome:

• Using concentric hemispherical optical glass/acrylic dome cover;
• When light hits the surface of the dome from all directions, the incident angle is almost strictly perpendicular to the normal of the spherical section ($\theta \approx 0^\circ$), and the light does not undergo refraction, fully retaining the magnificent underwater field of view of the 16mm ultra-wide-angle or even 180-degree fisheye lens.

2. The fatal physical by-product of the dome cover: Virtual Image (Virtual Image)

But the hemispherical dome cover brings about an extreme optical physics phenomenon that goes against common sense:

1. Micro-concave lens divergence effect at water interface:

• The outside is dense high-refractive index water, and the inside is low-refractive index air; the entire dome cover system is equivalent to installing a powerful divergent concave lens in front of the lens!

2. All the real scenery in the distance is compressed into a "miniature arc-shaped virtual image" in front of you:

• Even if turtles and coral reefs are as deep as 10 meters away from the diver;
• After penetrating the dome cover, the optical real image that the camera lens actually sees and can focus on is not 10 meters away, but is physically projected on the arc-shaped "Virtual Image Plane (Virtual Image Plane)" that is only tens of centimeters in front of the dome cover**!

3. Virtual virtual image distance calculation formula:
   $$D_{\text{Virtual Image}} \approx \frac{3 \times R}{2}$$
   (where $R$ is the physical radius of curvature of the dome cover).

• A standard 6-inch (radius $R \approx 7.5\text{cm}$) dome cover: its virtual virtual image is physically located only 15cm to 20cm in front of the lens!

3. Hard threshold for focus correction and lens minimum focusing distance (MOD)

1. Causes of tragedy of virtual focus:

• If the "Minimum Focus Distance" of your ultra-wide-angle lens is 35 cm;
• while the virtual image formed by the 6-inch dome cover is located at 20 cm;
• Even if the lens focusing ring is turned all the way, it will not be able to focus at a distance of 20 cm! The camera's bellows completely failed underwater, and the entire film must have been blurry!

2. Solution A: Switch to a larger diameter dome cover (8" to 9.25"):

• Increase the radius of curvature $R$, push the virtual virtual image distance outward to 30~40 cm, and enter the closest focusing stroke of the lens.

3. Solution B: Install a +2 or +4 high-quality achromatic close-up lens (Diopter):

• Screw a high-quality double-glued +2 close-up lens on the front of the wide-angle lens to forcibly shorten the closest focusing stroke of the lens, allowing it to sharply and accurately focus on the virtual virtual image 15cm in front of you.

4. Shrink the aperture to combat field curvature (f/8 ~ f/11):

• The virtual virtual image is a spherical surface with serious field curvature at the edge of the lens; when shooting underwater wide-angle shots, be sure to shrink the aperture to f/8 or f/11, and use the large depth of field to completely absorb the edge virtual image field deformation to ensure that the details of the four-cornered coral are unstoppable.

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