At first glance this equation might look a little intimidating.  However, upon further review, we will see that is can be a very useful and friendly equation, given we understand the factors it utilizes.  As we review these factors, we will do so in an order which will provide the best result.  First, let us look at Image Area.  We have learned previously that we must determine the screen size based on the 4 and 6 rule.  Therefore, if we have a room where the MDV (most distant viewer) will be 24' away from the screen, then we would use a screen that is 48" in height for reading applications or 72" in height for applications where inspecting the screen is necessary.  In this case, we are using the inspection rule and based on the fact that our source material has an aspect ratio of 4:3, our optimum screen size would then be 72" by 96".  When we multiply these two numbers together and divide by 144, (inches in one square foot) we learn that our chosen screen size is equivalent to 48 ft².  This will be the number we insert into the equation for the Image Area.

Next, let us look at the Screen Gain portion of the equation.  While this is one of the factors that can be manipulated in order to change the outcome of the equation, it is one of those items where it is best to determine this based on factors such as viewing angle and ambient lighting.  For our example, let us say that we have chosen to use a screen of 1.5 gain based on the fact that our audience is seated within a cone that is equal to 70º from the center of where the screen will be placed and the fact that we are utilizing a ceiling mounted projector.  Therefore, we will plug in 1.5 as the Screen Gain factor. 

Now we look at the ρ portion of the equation.  This is a constant that is based upon whether we are utilizing either front or rear projection.  The constants here are 1.0 if front projection and 0.2 if rear projection.  In this example, we are using a front projection screen.  Therefore, we will plug 1.0 in for the ρ portion of the equation. 

Lastly, let us look at the L_amb portion of the equation.  This is representative of the ambient light that is incident to the screen’s surface, measured in foot-candles.  Utilizing a basic light metering device for existing rooms or giving careful consideration and planning in rooms that are not yet completed can achieve this number.  In an existing application, all that is needed is to point the light meter from the wall where the screen will be placed out towards the audience seating area.  For rooms yet to be built, it becomes a bit more involved.  Here we need to consider what type of lighting is being utilized and determine based on the output of the light source and the direction at which it is aimed, how much will be incident to the screen’s surface.  For example, if we follow the IESNA (Illuminating Engineering Society of North America) Lighting Handbook rules for designing a properly lighted conference / meeting room, we learn that there should be 30 foot candles falling on horizontal surfaces and 5 foot candles falling on vertical surfaces.  Given our screen should be parallel with the vertical surface, we can assume 5 foot candles.  So for the purposes of our equation we will use 5 as our L_amb portion of the equation. 

So, we almost have a completed equation, right?  Technically, yes we do. The only remaining factor is the Minimum Light Output (Lumens).  While all of the other factors in the equation can and do affect the others, this is one of the areas that can be adjusted to meet our minimum requirements for the 10:1 contrast ratio.  After all, the Minimum Light Output (Lumens) is what we are trying to determine based on the other factors.  In other words, we are attempting to determine how much output we need from the projector in order to achieve our desired 10:1 contrast ratio for the projected image. 

We can now complete the equation and see the results.

Minimum Light Output (Lumens) = (9x48x1.0x5) ÷ (1.5-0.2)

Minimum Light Output (Lumens) = (2160) ÷ (1.3)

Minimum Light Output = 1662 Lumens

For purposes of comparison, let us see what happens if we change the screen gain portion of the equation.  Instead of using a 1.5 gain screen, our application requires a screen with a wider viewing angle and the 1.0 gain screen fits that requirement.  In this case, the equation looks like the following:

Even though it has been mentioned a number of times before, you can see based on these numbers that the ambient light in the room has a very significant impact on the amount of light output that is necessary from a projector in order to achieve our 10:1 contrast ratio.  In this example, by reducing the ambient light in half, we are able to use a projector that is also nearly half as bright to achieve the same results.

To take our contrast ratio one step further, we can also review the following formula from the same Volume V of Angles of View.