Certainly the most striking effect of a 3D lenticular picture is its ability to display depth. Consequently, the 3D lenticlar artist is under pressure to maximize this effect by displaying scenes with larger depth. Practice has shown that uncontrolled depth increase leads to a failure. This gives rise to the question: is there a limit to the depth which can be displayed in a 3D lenticular picture? The answer to this question is: Yes!
The theoretical limit is illustrated and explained in the scheme below. It shows schematically the lenticular picture and two imaged objects: foreground and background, each displaced from the picture by a distance h.
In order to maximise the viewing effect one would like to increase h as much as possible. However, h is limited by the formula displayed in the scheme. Any attempt to increase h beyond this limit will introduce increasingly disturbing defects in the picture: blurring, discretization, or both.
Lens thickness t and index of refraction n require no further explanation. The concept of the "Number of resolvable images" is not widely known. It refers to the maximal number of images in a lenticular sequence which can be resolved by the system (printer + lens). This number depends on the printer resolution and the optical characteristics of the lenticular lens. It must be measured experimentally.
The parameter q is used by me to control the tradeoff between depth and picture quality. In my experience choosing the value of 2 for q guarantees a clean and sharp picture. With almost all pictures the value of 3 gives rise to visual defects. Therefore, the optimal value for a given picture lies between 2 and 3, depending on its content. If the picture contains high-resolution features in the foreground or the background, the optimal value is closer to 2. Otherwise, one can choose a value closer to 3.
Here are two examples for our pictures performance with q = 2:
Example 1: 40lpi lens with 2mm thickness has approximately 64mm total displayed depth
Example 2: 25lpi lens with 4mm thickness has approximately 215mm total displayed depth