Entry surface properties

For most applications involving an underwater camera, the lens system is set to be focused at infinity. This allows a focused image to be obtained from an infinite distance, up to a few centimeters of the entry surface (the minimum focused distance decreases with short focal lengths).The above consideration implies that the photosensitive matrix is almost always located at the image focal point.

Underwater cameras often possess an entry surface where the external surface is a plane. This property can be explained by the necessity of obtaining focused images in water as well as in air conditions.

In fact, an image will remain focused independently of the object medium index if and only if its image focal point remains unchanged through index variation. The image focal point is determined by the distance $S F_i$ (where $S$ denotes the exit surface of the last lens of the optical system).

$$SF_i=SH_i + H_iF_i =SH_i + f_i = \frac{-n_2.tc}{k} \frac{(n-n_1)}{n.r_1} + \frac{n_2}{k}$$ (9)

When $r_1$ grows to infinity (which is equivalent to obtaining a plane surface at the air/water interface), the expression becomes independent of $n_1$:

$$k=\frac{(n_2-n)}{r_2}$$

and $S F_i$ can be written:

$$SF_i= \frac{n_2}{k} = \frac{n_2.r_2}{(n_2-n)}$$ (10)

This location of the image focal point related to the out surface (the one nearest to the CCD matrix) is also independent of $n_1$: the image is focused in air as well as in water.