Depth Range is a subjective judgment method to measure 3D, not a mathematical one.
Lenny Liptons term "Depth Range" which sounds like what Bernard Mendiburu is calling "Depth Budget" is cute but tells us nothing about apparent distance. I wondered why Lipton chose such a subjective way to measure a 3D scene given the fact that he has access to a wide range of math formulas. It's lead to a lot of people throwing away the math all together. I found a comment on his web site asking him to include a calculation for apparent distance and his response was "I have flipped more to the gut feeling and subjective judgement side of the seesaw and while math is useful the fact that digital stereo allows for observtion and interaction trumps the calculator.". Lenny Lipton - July 4, 2010 at 11:40 am - http://lennylipton.wordpress.com/2009/03/16/glossary/
So Lenny Lipton believes that subjective judgment trumps the math. Interesting.
Because I agree with that in some scenarios I am going to go one step further and say that "Subjective judgment trumps math when the viewer is aware of his surroundings (including the screen), and math trumps subjective judgment when the viewer is unaware of his surroundings (including the screen).". I don't know how to write that in detail so let me expand a little bit more. Being aware of the screen would be a TV in your living room with the house lights are on. But lets be honest. A child sitting up close to the screen could be paying no attention to the screen at all simply because they are so infatuated with the content and I think in that case the math takes over again. In a theater for example your peripheral vision could be saturated, the lights are dim and the people in front of you are hopefully not obstructing your view. Perfect example is a real IMAX screen. In this case your judgment is thrown right out the window. Even when watching a 2D movie.
The mathematical equivalent of Depth Range (aka Depth Budget) is "Apparent Distance". So if you want to backup your Depth Budget with math you have to calculate the Apparent Distance in your scene. Lets talk about that in another blog.