Projector Brightness and Zoom Lenses
The purpose of this article is to examine the impact of projector brightness, zoom lenses, positioning a projector, and the need for achieving a desired level of brightness and more importantly contrast and grey scale.
We are aware that there is a certain degree of variance in what projector manufacturers' state in their marketing materials and spec sheets as the projector's light output in "ANSI" lumens. Their published specification versus their actual output to a verifiable standard can be a difference in the way (procedure, environment, test patters, etc.) the projector's light output is measured since there are no ANSI "police" and the ANSI "standard" is really no longer in place. In other cases, the discrepancies can be due to manufacturing variances and tolerances. The bottom line is that there can be as much as a 20% discrepancy in what a specification sheet claims and actual performance.
With this in mind, the selection of a specific projector and zoom lens combination becomes even more important because the zoom lens position in relation to where the projector is installed can further reduce light output. The claim of reduction in light output will depend on how the manufacturer measured the light output of the projector with the zoom lens. Was it measured at its brightest/closest setting at full wide angle (most likely) or in the middle range or at the least bright (unlikely) at full telephoto?
In simple terms, when a projector's lens is in full wide angle mode which is the largest image from a given distance, more lumens exit out the lens. In full telephoto mode, less lumen light output is produced. The worst case scenario is a projector that has its light output overstated by 20% and it has a 2:1 lens and is installed at full telephoto in a given application. The implication on true system light output is not to be ignored and this affects both the screen consideration and ultimately the system performance. In the AV industry there is an "old wives tail/general rule "that there is a two to one range of brightness in most zoom lenses. This comes from the "typical" range of zoom lenses out there but this is not a standard by any means. There is in fact a significant shift in brightness that occurs with projectors that are exceptionally flexible in their placement, by virtue of wider range zoom lenses and conversely, less brightness shift or decay on shorter zoom lenses. The general rule is just that, too general.
Many projectors for the home and commercial applications offer 2:1 zoom lenses. That is a placement range from closest to furthest, of 2 to 1. Perhaps, for a 100" diagonal 16:9 screen, that might be from 10.5 feet to 21 feet away. In general terms, if you mount it 10.5 feet from the screen, you will get almost double the lumens as mounting it 21 feet back.
There is no straight and simple universal formula, because different lens designs will have some degree of impact (some more, some less) on the actual amount of change, but, let's say that with a typical 2:1 lens, it will be "close" to a doubling. If, on the other hand, the projector has a far more limited lens, say with a zoom ratio of 1.2:1, then, the change in brightness from one "extreme" to the other, becomes minimal, and not a serious consideration in terms of light decay from one position of the lens to another.
Today, most moderately priced DLP projectors have limited zoom lens ranges (1.1:1 to 1.3:1), so there isn't much to concern ourselves there, but with the 3LCD, and LCoS projectors, where most of them seem to have at least 1.5:1, and many are around 2:1, where you place the projector can matter a lot. The point to consider is that depending upon the actual light output of the projector and the zoom lens in reference to where the projector is place can result in a significant light variation from the optimum suggested in the manufacturer's specifications and the system designers original design concept.
What do lens specifications mean?
Lens specifications tell us two things:
1. The focal length of the lens is usually expressed in millimeters (example: 50‐75mm). The zoom ratio of 75mm to 50mm is about 50%, or 1.5:1. This means the system designer can vary the size of the projected image by 50% without moving the projector closer or further back in the room.
2. The second number or specification of a lens is the aperture or opening of the lens glass surface that actually passes the light. This is usually expressed in f‐stops (example: f2.5‐3.0). F‐stop specifications are guides to relative brightness capability of a given lens or optic when comparing two or more projectors with similar focal length lenses. A projector with a 50‐75mm, f2.5 lens will produce brighter images over the entire zoom range than one with a 50‐75mm, f3.5 lens. Note: Some manufacturers will give an f‐stop specification over the entire focal length of the zoom lens, i.e. 50‐75mm, f2.0 ‐ 2.5. This shows not only the varying f‐stop in a zoom lens but also refers to that fact that there will be light loss as the f‐stop number increases in the zoom range.
Focal Length and f/Stop: the Formula:
The aperture of a lens is simply the opening through which light passes and it is controlled by an adjustable diaphragm or iris. Each setting of the diaphragm is called an f/stop and is always read as a number, not as a fraction or true ratio. It is referred to as the f/stop or the f/stop of the diaphragm opening.
This value is designated by a lowercase f with a slant (/) between the f and the value. For example, f/8 means that the diameter of the opening in the diaphragm is one eighth of the lens focal length, but only "when the lens is focused on infinity." In this example f/8 is the effective aperture. If the lens were focused at other than infinity, f/8 would then be the relative aperture. In the study of the relationship between aperture and image brightness, the term relative aperture is used frequently. The term relative aperture then refers to the ratio between the effective aperture of the lens and its focal length. This relative aperture of the lens is controlled by two factors: (1) the diameter of the beam of light passed by the lens. (2) the focal length of the lens, which governs the size of the area over which the light is spread. The formula to determine the f/stop of a lens is as follows: f=F/D where F is the focal length, D the diameter of the effective aperture and f the f/stop or the relative aperture. To find the f/stop of a lens that has a focal length of 8 inches and the diameter of the effective aperture is 2 inches, use the formula, so: f=8/2=4 Therefore, the lens has a relative aperture of f/4. When the diameter of the opening (aperture) of the lens is made smaller, less light is admitted and the image formed by the beam of light passing through the smaller opening becomes dim. As the size of the opening is reduced, the ratio between the aperture and the focal length increases. So as the f/stop becomes larger, the size of the relative aperture decreases. Since the f/stop is a ratio of focal length to the lens diameter, all lenses with the same f/stops regardless of focal length provide the same amount of light on the focal plane; that is, when all the other factors that affect image brightness remain constant.
Alan C. Brawn
Alan C. Brawn, CTS, ISF, ISF-C, DSCE
2031 Jewell Ridge, Vista CA 92081