A Matter Of Terminology

It's important to understand the relationship between image brightness and projection distance.
Publish date:

A Matter Of Terminology

It's important to understand the relationship between image brightness and projection distance.

My February 2006 feature article “Choosing The Perfect Projector” resonated with several readers, who wrote in to say that my calculations for image brightness and predictions of image brightness as a function of the distance from projector to screen were flawed.

To set the table, I mentioned that screen brightness, or luminance, is usually measured in foot-Lamberts (ft-L) or candelas per square meter (cd/m2, also known as nits); while projector illuminance is measured in lumens or lux. I went on to state that as the distance between the screen and projector changes, the brightness of the image changes as a square law function of the distance. All well and good.

Now, let's get to the first letter from Alan Sobel: “I'd like to comment on an apparent error about calculating ‘brightness' in your article. You write that the luminous flux on the screen will change as you change the screen-projector distance. This isn't right. The luminous flux is independent of distance, except for atmospheric absorption. Rather, the luminance will change with distance. If you move the test rig by a factor of two, the luminance will change by a factor of four as the illuminated area changes, unless you change the focal length of the projector lens to compensate, and that will change the luminous flux throughput, as you point out on the next page.”

My original statement was “…the inverse square law…states that the increase or decrease in brightness from the projector will be an inverse square function of its distance to the screen.” Alan's point is well taken; a more appropriate wording would have been: “the brightness of the image on the screen (or luminance) will vary as an inverse function of the distance from the projector to the screen.”

Obviously the luminous flux of a projector doesn't change unless you switch lenses, the lamp ages, or you select a low-power or high-power lamp operating mode. The point here is to illustrate the relationship between image brightness and projection distance, assuming a constant lens focal length and aperture setting. Hopefully readers now have a better understanding of that relationship.

Another letter came from Bill Schripsema, who has had stints at GE/Talaria, Barco, and Electrohome. Here's an excerpt: “…If you have a 2,500-lumen projector, it always puts out 2,500 lumens, regardless of the size of the screen...If the only change is the size of the image, lumens are constant. Your measured number varies because the illuminance (or incident) light meter measures foot-candles, not lumens. To convert from foot-candles to lumens, simply multiply the foot-candles you measure by the area of the raster (at the native resolution of the projector) in square feet. Then the number is constant.”

To clarify, the illuminance meter I use (Minolta's CL200) measures lux, which is the metric standard for measuring illuminance from any light source. To convert from lux to lumens, simply multiply the lux readings by the measured image area in square meters, and divide by the screen gain. If I take incident light readings at the screen surface (pointed toward the projector), screen gain doesn't enter into my calculations — only image size does. For example, I take nine illuminance readings across a projected 40-inch by 30-inch white screen with unity gain (1). These readings average 3,500 lux. The projected image measures 0.774 square meters in area. Using the conversion formula — Lumens = Lux (x) Area / Screen Gain — I wind up with a calculation of 2,709 lumens. As you can see, this formula does take into account constant luminous flux from the projector. If I project a larger image, the incident readings will be lower, but the area of the projected image increases. Result? The same lumens calculation as before.

So what's really changing as a function of projection distance is the luminance of the image, or the reflected light. That's because a larger surface area is being illuminated as projection distance increases, and a smaller area as projection distance decreases. The issue here is how manufacturers measure light output from a projector in the first place. If the luminous flux is really 2,500 lumens, then it remains 2,500 lumens all the way out to infinity. The problem is, photons from the projector are diffusing at greater angles as the distance to the screen increases, resulting in dimmer reflected images once it hits the screen.

So while it's true from Schripsema's letter that a 2,500-lumen projector always pumps out 2,500 lumens, regardless of where it's positioned, the brightness readings on the companion screen will change as a function of lens focal length and projection throw distance. And that's what you'll need to take into account when choosing a projector and screen.

A simple factor can be derived by measuring brightness in lux at a given distance, and then determining the actual projection distance you'll need. If you measure 200 lux on a 1,200-square-inch screen at 10 feet, you'll need four times that light reading at a distance of 20 feet to have equivalent incident light readings. Another way to arrive at the desired brightness level is to take screen gain into account and use reflected readings.

Schripsema: “To measure the light reflected off the screen, you need a luminance meter such as the Minolta CS-100. The unit of measurement is foot-lamberts. Given your 1.5 gain screen, your measurement would be 1.5 times the measurement from your incidence meter (assuming you're on axis).”

Correct. In this case, the entire system — projector and screen — is being measured instead of taking illuminance readings at the screen's surface. If you have access to a spot meter, this is easy to do. The screen gain (angles at which light rays are collimated and reflected back at the viewer) should be available from the manufacturer.

Schripsema: “For the example in your article, the numbers look like this (assume that your projector is properly adjusted and is filling the screen, and that your ambient light is zero):

  • 80” screen
  • 256 lux (as measured at the screen)
  • 256 lux = 23.7 foot-candles (metric to English conversion is 10.79 lux = 1 foot-candle)
  • 80” w x 60” h = 33.33 sq ft
  • 23.7 fcl * 33.33 ft2 = 790 lumens from the projector
  • 23.7 fcl * 1.5 screen gain = 35.5 foot-lamberts (That's enough for a PowerPoint presentation or football game in a room with controlled ambient light; too bright for a dark home theater.)”So there's more than one way to arrive at the number you'll need. I find the illuminance meter the simplest way to go, but that's because I've tested hundreds of projectors this way over the years, projecting into black velvet screens and taking nothing but incident light readings. It's simply a matter of what you're comfortable with.One last comment that came from Schripsema was the issue of contrast. Projector contrast specifications are one thing; what you see on the screen is something else. That's because the contrast of reflected images is always affected by ambient light levels. (That's why I measure actual projector contrast by projecting images into velvet stipple screens to minimize light reflection.)As ambient light hits a screen, it degrades contrast. The higher the brightness and contrast numbers in a projector, the higher the ambient light levels you can “get away with.” In general, a minimal contrast level of 10:1 is needed to distinguish text and objects whether viewing printed or projected images. But this can be difficult to achieve if ambient light levels are high. If you take an incident reading of 300 lux from your 2,500 lumens projector, any ambient light striking the screen surface can't exceed 30 lux, or the minimal 10:1 ratio is compressed.While writing this column, I got out the CL200 illuminance meter and took an ambient reading in my controlled-lighting office of 39 lux. The next room over, with full fluorescent lighting, produced a reading in excess of 400 lux! The moral: High contrast in a projector is important. But unless you manage ambient light on and around the screen surface, you won't realize that benefit.Pete Putman is a contributing editor for Pro AV and president of ROAM Consulting, Doylestown, PA. Especially well known for the product testing/development services he provides manufacturers of projectors, monitors, integrated TVs, and display interfaces, he has also authored hundreds of technical articles, reviews, and columns for industry trade and consumer magazines over the last two decades. You can reach him at pete@hdtvexpert.com.