English: Basic sketch of the view out off an optically dense medium.

Ideal resizing to a multiple of 193 x 151 pixels.

Model of a fisheye projection by Professor Robert W. Wood. Using the refractive index of water, this projection shows how a fish perceives the surroundings outside the water.

Mapping function: ${\displaystyle r=f{\frac {\sin \theta }{\sqrt {1-{\frac {\sin ^{2}\theta }{n^{2}}}}}}}$

${\displaystyle r}$ image position as distance to the center of the image

${\displaystyle f}$(central) focal length, also considers reduction 

${\displaystyle f={\frac {s}{n}}}$

${\displaystyle s}$ image distance between aperture diaphragm (hole) and image plane

${\displaystyle \theta }$ polar angle of the outdoor object to be imaged

${\displaystyle n}$ refractive index of the medium

The three-dimensional environment is projected onto a sphere (red dots). The black circle represents this surrounding sphere with its center as projection point. The blue semicircle is concentric to the black circle and has ${\displaystyle n}$ times his radius. The blue arrows fulfills the law of refraction. The refracted environment lies onto the blue semicircle (yellow dots). From there the projection takes place in radius direction of the arc (green arrows) to the image line. Because the image line lies on the semicircle instead of the circle, the reduction by the refraction is compensated.