The Science Of Projection Lenses
A basic understanding of projection optics gives systems integrators a leg up when accurately predicting and troubleshooting the quality of projected images.
Ten years ago, when writing about InfoComm's annual Projection Shootout, I commented that some LCD projectors appeared to have soft images or focus problems. One projector manufacturer's rep responded that “LCD projectors always make sharp images,” implying it wasn't possible to see what I saw. While it may be true that the images formed at the convergence point of the optical prism in an LCD projector indeed are sharp, they can still suffer on the way to the screen if the projection lens isn't up to snuff.
The exchange raised the question of just how much the average AV professional really knows about projection optics, beyond specifying a certain focal length for a specific projection throw and image size. The truth is that projection optics and the quality and type of lens on your projector significantly impact the quality of the projected image.
In the Beginning
People have been projecting images on walls and screenlike surfaces for centuries. References go back to the 5th century in China for pinhole image formation, and the Greeks were aware of the phenomenon by the 4th century.
In a pinhole camera, which you can make out of a cardboard box, a bright object, such as the sun or a building, can be seen as light rays from that object pass through the pinhole and are reflected on the wall of the box. As kids, many of us have used this technique to safely watch a solar eclipse.
By the Middle Ages, the pinhole camera had acquired a new name, the camera obscura, and some models were quite large. Leonardo da Vinci and Johannes Kepler are among the more famous names associated with it (Kepler is credited with naming the camera obscura), and it found a home as a drawing and sketching aid.
Cutaway view of a multielement projection lens, showing the two fixed, aspheric lens elements (in pink) at the fint and rear. Because the lens aperture is fixed, the f-stop number decreases as focal length increases.
But a pinhole camera is not very practical for viewing larger images. Plus, any images it forms are, by necessity, inverted. So it was only a matter of time before some enterprising individuals began experimenting with glass to bend and magnify real-life images.
According to the Magic Lantern Web site (www.magiclantern.org.uk), one early historical reference to a projected image is found in “Liber Instrumentorum,” by Giovanni de Fontana, dating back to 1420. An illustration in this work shows a person projecting a large, right-side-up image of the devil onto the wall from a handheld lantern.
Dutch scientist Christiaan Huygens and Danish mathematician Thomas Rasmussen Walgensten were developing lantern projection systems in the mid-1600s. By the 1700s, so many people were experimenting with these “magic lanterns,” it's difficult to attribute significant developments to any one of them.
In the 1840s, William and Frederick Langenheim of Philadelphia began experimenting with projecting photographic images using a technique to coat glass plates with light-sensitive compounds (halides of silver), first developed by Niepce de Saint-Victor. By contact printing an exposed, negative plate to a second plate, a monochromatic, positive image resulted that could be projected onto light-colored surfaces.
Believe it or not, lantern slide projection continued well into the 20th century, with oil lamps giving way to arc and eventually electric lamps. I once had a lantern slide projector from the 1930s that used 3 ¼-inch by 4 ¼-inch glass plates and a rather unique acorn-shaped lamp, which had been used originally to show advertising in movie theaters.
Top view of the lamp, imagers, integrating prism, and zoom lens assembly inside a Canon REALiS LCOS projector.
Eadweard Muybridge's experiments with sequential images and Thomas Edison's development of motion picture projection brought lens technology more sharply into focus in the late 1800s. Twenty years later, lantern slide projectors and film projectors were both performing yeoman duty in theaters.
As demand for projected images increased, lenses improved in quality. The heavily vignetted, hot-spotted images of early theaters gave way to bright, crisp renderings of black-and-white movies and newsreels. The development of color in the early 1930s (two- and three-strip Technicolor) created additional challenges on lens designers, as did the anamorphic widescreen Cinemascope and Todd-AO formats of the 1950s.
The British Broadcasting Corp. made attempts as far back as the late 1930s to project video images. A Swiss company, Eidophor, developed an electronic video projection system during World War II that used an oil-filled imaging disk and could create very large, monochrome images or color images using a sequential color system. (GE's Talaria projector worked in a similar fashion.)
With the introduction of three-gun cathode-ray tube projectors in the 1970s, lens development took another turn, followed by the first large-panel LCD projectors in the late 1980s and the first portable LCD projectors in the early 1990s. Today, microdisplay projectors are ubiquitous, but that doesn't mean they all have the same quality of optics.
How Lenses Are Made
More than 100 types of raw materials are used to manufacture different types of optical glass. Among them are quartzite, borax, and soda ash. These blended raw materials are placed into a platinum or quartz crucible, and fused at high temperatures in a furnace. The resulting molten glass is poured into a pallet as a liquid, cooled naturally, then crushed into small pieces.
These glass fragments are heated again and melted at 1,300°C, mixed and churned, clarified, and then homogenized (free of air bubbles) in a continuous fusing machine. The liquid glass then is shaped into long sheets, which gradually cool to room temperature as they travel through a continuous, slow-cooling furnace. The highly controlled fusing and cooling processes are the most important for quality optical glass.
The next step is inspection. From each block of cooled glass, a test piece is cut, and both surfaces are polished. The test piece is illuminated to check for defects. If it passes, the raw lens moves to the pressing and forming processes. A variety of grinding machines and presses are used, depending on the type and shape of lens to be made.
The necessary volume of glass is calculated precisely, based on lens shape, diameter, and specific gravity. After cutting with a diamond cutter, it is adjusted in units of 1/10 of a gram. Large-aperture lenses are cut by hand, while smaller pieces are handled in automated machines.
For greater precision, lenses undergo additional grinding processes. The glass is heated further, then formed into shape by pressure. Once again, large aperture lenses are pressed by hand, while automated pressing machines handle small lenses. At this point, each piece of glass now looks more like a lens, not just a cut disk of glass.
Each rough lens exhibits high internal thermal stress after cutting and pressing. To remove it, the pressed glass is annealed by first heating it to 500°C in an electric furnace, and then letting it cool gradually. Each lens must now be polished to remove pressmarks from each one's surface.
Using a curve generator, which is a high-speed grinder equipped with an artificial diamond cutter, the surface of each pressed lens is ground until it becomes curved to specified levels of roughness and dimensions. Next, the lens surface is ground with high precision, using an artificial diamond pellet platter. Precision on the order of 1/1000 of a millimeter is required during fine grinding.
Each lens is then polished with an abrasive, sheet-lined platter until the surface roughness reaches a specific level. At the same time, the surface curvature is adjusted precisely to a submicron tolerance. Both front and rear surfaces are polished to transparency, and the surface of the lens becomes more and more transparent during this step.
The precision of the lens surface now is inspected using laser beams. Each lens passes or fails, and those that pass are cleaned in an ultrasonic washer before alignment. During this step, the lens periphery is milled to a specified dimension with symmetrical spacing in the lens' optical axis by using a diamond grindstone.
To prevent unwanted reflection and to protect the glass surface, each lens is coated with a special thin film. After another ultrasonic wash, the lenses are placed into a vacuum evaporator to remove all remaining impurities. At this point, the individual elements are ready to be assembled into a finished lens. Each lens is held into place with tight tolerances, using mounting rings and adhesives. Depending on the number of elements, the lens may be assembled in more than one location before final inspection.
There are two numeric specifications of concern when discussing lenses. The first is focal length, defined as the distance from the surface of the image-forming media (such as a 35mm slide or LCD panel) to the focal point of the lens. Focal length is expressed either in inches or millimeters.
Prime lenses are those with a fixed, single focal length, such as 100 millimeters or 4 inches. Zoom lenses will have multiple focal lengths, such as 100mm to 150mm, or 4 inches to 6 inches. Zoom lenses are, by far and away, the most common type of projection lens, but there are times when a fixed focal-length lens is better suited for a job.
Smaller images are projected over longer distances with lenses of longer focal lengths, while larger images are created with shorter focal lengths. For example, a 2-inch (50mm) lens will project a 1-inch diagonal image from a microdisplay imager about 12 feet wide when positioned 18 feet from a screen. At the same throw distance, a 6-inch lens will project that image 4 feet wide, while a 9-inch lens will result in a 2-foot-wide picture.
The second numeric specification for projection lenses is its aperture, or the glass surface area through which light rays travel on their way to the screen. Lens apertures commonly are expressed in units called f-stops. A low f-stop number represents a large aperture and brighter images, while a higher f-stop number represents a smaller aperture and dimmer images.
The lens aperture conversely affects image sharpness. A small area in front of and behind the focal point of the image also will appear to be sharp. This area is called the lens' depth of field, or depth of focus. As the aperture decreases in size (f-stop number increases), depth of focus increases.
Projection Lens Apertures
Depth of focus is not nearly as much of an issue with projection as it is with photography, which is why most projection lenses have low f-numbers (wide apertures). Brightness is key with projection. However, given that the sharpest setting for a lens usually is two or three f-stops down from fully open, focus uniformity also is important.
Increased depth of focus is necessary when projecting onto uneven surfaces, such as a curved wall or screen. There will be some sacrifice of image brightness, but focus will remain constant across the horizontal and vertical dimensions.
In most cases, the plane of focus for a projected image is very shallow (perhaps less than an inch) so as to be essentially two-dimensional. As a result, projection lenses typically have low f-stop numbers, providing a larger aperture and, consequently, brighter images on the screen.
The ratio of image brightness to lens aperture easily can be determined. All things being equal, a projection lens with an aperture of f-2.0 will produce images twice as bright (1 f-stop) as a lens with an aperture of f-2.8. The catch is that many short and long focal-length lenses are not available in equivalent apertures.
Let's assume you'd like to move a projector further back in a room while maintaining the same image size. You are using a 1.3:1 ratio zoom lens with an f-stop of 2.0. The manufacturer has a 3:1 zoom available that will do the trick, but its aperture is specified as f-3.5. Will the image be as bright?
No. In this case, the image will drop in brightness about 1.5 f-stops. If you have measured 2,000 lumens of image brightness with the 1.3:1 lens, switching to the longer zoom will result in a measurement of about 750 lumens.
You'd have to increase the aperture of the longer lens back to f-2.0 to maintain the image brightness you had before. However, this wider-aperture lens would be much larger and heavier (if you could find such a lens) because of the greatly increased size and diameter of the glass elements.
In effect, the glass elements in the 3:1 zoom would require twice the diameter of the 1.3:1 zoom to achieve the same lens aperture and pass an equivalent amount of light. As focal lengths increase, lens apertures typically decrease since the manufacturer is trying to maintain a constant lens size and shape. Lenses with very short focal lengths (under 1:1) also typically have smaller apertures than medium-focal length lenses.
Geometry and Distortion
The predominant lens design for microdisplay projectors is the flat-field type, where the focal length to all areas of the imaging medium from the rear lens element is constant and in the same plane. This design ensures that when we focus our projector's lens once, the entire image comes into and stays in focus.
Curved-field lens designs are used more commonly on CRT projectors. The surface area of the imaging device (the CRT) film is not uniformly flat, so a flat-field lens couldn't maintain critical focus across all parts of the image plane at the same time.
Zoom lenses vary considerably in quality, with inferior models exhibiting "pincushioning" and uneven focus at the upper and lower limits of their focal lengths. These distortions can adversely affect sharpness across the width of the projected image, making it difficult, if not impossible, to read small text and numbers.
Another form of optical distortion, known as spherical distortion, is caused by the uneven focus of light rays as they pass through the lens. It can manifest across the image or in one area of the image. No amount of focusing will ever bring the entire image into clarity at the same time.
The best way to correct this condition is to use an aspheric lens structure. This type of lens was quite difficult to grind precisely for some time but is now common in higher-end projection and camera lenses. The asphericity ensures that as many rays of light as possible come to the exact same focal plane for uniform sharpness.
Refraction and reflection are other challenges for lens designers. There is no such thing as a perfect lens. All lenses scatter and refract a portion of the light that passes through them. Any light reflected back toward the source out of phase causes cancellation and lowers image contrast. Special coatings on the lens surfaces are applied to minimize refraction and reflection.
Chromatic aberrations are also common in lower-cost lenses. Light waves cover quite a range of frequencies, with blue near 400 nanometers and red closer to 700 nanometers. If these different colors don't come to the exact same focus, a blur or halo may be seen, or a color may appear to be out of convergence.
Multi-element lenses are designed to compensate for the differences in optical wavelengths by bending different color light rays at different points, not all of which do so at the same point as a single lens element. In combination, the different degrees of focus offset converge through the final element so that all colors are precisely registered.
The most common form of image distortion arises not from the lens, but from the projection angle. This geometric distortion, known as keystone distortion, is caused by tilting the projector up, down, or to either side of the projection screen's optical centerline. At this point, the plane of the screen is not parallel to the plane of the projector, and an uneven, trapezoidal image results, rather than a rectangle.
You can correct keystone distortion — or more scientifically put, parallax distortion — two ways. The first is to make sure the projector's lens is parallel to the screen surface in both the horizontal and vertical planes. However, this may obstruct the screen for many viewers, unless the projector is behind the screen.
Another approach is to incorporate some sort of mechanical lens shift into the projector. This control works just like an old-fashioned view camera, raising or lowering the front lens element with respect to the rear. The projected image is then shifted up or down from the optical center of the lens without introducing any geometric picture distortion.
The cheaper, more expedient approach is to resize electronically the imaging pixels, and literally create a counter-keystone image before it is projected. The problem with electronic keystone correction is that it does not solve any depth-of-focus problems caused by angular projection, and it throws away pixel resolution.
Projection lens research and development never stops. It seems the lenses just keep getting better and better. With all of the new widescreen, high-definition projectors coming to market, that's definitely a good thing.
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 firstname.lastname@example.org.