Lenses for High-Resolution Microdisplays
OPCON Associates, Inc., 3997 McMann Road, Cincinnati, OH 45245, USA
Tel. 513/752-0877, Fax 513/752-1325, e-mail: email@example.com
Recent trends towards the wider use of high information content displays have led to the development of high resolution projection devices which image small size LCD / DMDs having a large number of pixels. The use of these microdisplays poses more stringent demands on the correction of aberrations in projection lenses. This paper addresses the image quality requirements for lenses used in front and rear projection configurations. Examples of various projection lenses for different applications are presented.
Keywords projection displays, lenses, zoom lenses, image quality, aberration corrections, aspherical surfaces, plastic elements.
Recent breakthroughs in manufacturing technology have led to a rise in popularity of microdisplays digital imaging devices such as DMDs, reflective LCDs, etc.. Projection displays based on these devices offer advantages of small size and light weight. A whole new class of ultra portable lightweight projectors operating in front-projection mode and based on some sort of microdisplay has appeared on the market. These devices have a large number of pixels to display images having high information content. Since the devices themselves are small, the individual pixels are small, too. Typical pixel sizes range from 17m for DMD display to approximately 8m or even less for some of the reflective LCDs. This means that the projection lenses used in these systems must have a very high level of correction of aberrations.
Understanding Projection Lens Specification
In order to maintain a reasonable cost of the optics and, at the same time, to satisfy the image quality criteria it is critical to correctly specify the optical performance requirements for projection lenses. The following factors must be taken into account:
Radial distortion can be described as variation of magnification of a lens as a function of the field of view. When present in the lens it will result in the familiar pincushion, for positive distortion, or barrel, for negative distortion, shape of a rectilinear grid. A rectangular grid of lines, like the one used in spreadsheet programs, must be imaged with as little distortion as possible. Even small amounts of distortion will be readily apparent in this application. In CRT based projectors the lens distortion can be compensated for fairly simply by modifying the raster shape. However, in digital devices this compensation is difficult, if not impossible, to accomplish. It is, therefore, extremely desirable to have the radial distortion of the lens corrected very well. The projection lens design specification often refers to the maximum radial distortion of less than a fraction of 1%.
Another aberration that may be easily observed is lateral color. Lateral color can be defined as variation of magnification with wavelength of light. When present in the lens in substantial amounts it will manifest itself as color fringing at the border of light and dark areas. Like distortion, lateral color is a function of the field of view of the lens and usually increases towards the edges of the image format. For color fringing not to be visible in the outer portion of the image, the lateral color must be corrected to better than a pixel and preferably better than one half to one third of a pixel.
System requirements often dictate that projection lenses be telecentric on the short conjugate side. This means that lens forms symmetrical around the aperture stop and, therefore, inherently well corrected for distortion and lateral color can not be used. Under these circumstances the use of aspherical surfaces provides an invaluable tool in designing the required projection lenses.
Rear Projection Systems
To achieve a small package size, rear projection systems generally use wide angle lenses. Often these lenses must be telecentric on the short conjugate side and must have a long back focal distance to accommodate beam-splitters between the lens and the digital display device. Due to lack of symmetry around the aperture stop in this type of lenses, the necessary level of correction of distortion and lateral color is more difficult to achieve.
Shown in Figure 1 [1,2,3] is an example of a wide angle projection lens designed for use in a rear projection system capable of displaying 1920 X 1080 pixels. In addition to the schematic of the lens, the following plots indicating the optical performance of the lens when traced from long conjugate to short are also shown:
The field of view of this lens is ±36.6°, corresponding to the throw ratio of 0.71:1 for 16:9 format. The f-number of the lens is f/5, and the lens is telecentric on the short conjugate side. The lens is designed for the microdisplay dimensions of approximately 16mm X 9mm with the individual pixel width of 8.9 microns. The projected image diagonal can be anywhere between 25" and 70". The retrofocus lens used here consists of two groups separated by the aperture stop. The front group on the long conjugate side and consisting of the first three elements has a net negative power and the rear group has a net positive power. The first and the last elements of the lens are plastic and have aspherical surfaces. These aspherical surfaces allow for very good correction of distortion and spherical aberration of the entrance pupil. The appropriate choice of glass materials in both the front and the rear groups allows for lateral color to be corrected to less than 6 microns over most of the field for a spectral range of 460nm to 620nm. The diffraction MTF graphs indicate MTF response of at least 65% at 60cy/mm throughout the field of view of the lens. Use of plastic aspherical elements permits a very high degree of correction of aberrations at a very reasonable cost. This type of lens is suited to mass production.
Front Projection Systems
Projection lenses used for front projection systems usually have longer focal lengths for longer throw distances. However, the field of view is not reduced proportionally to the increase in the focal length because these lenses must often accommodate an offset between the optical axis of the lens and the geometrical center of the display device in order to project the image above the optical axis of the lens without keystone distortion. The amount of offset can often be as high as 100%. Under these circumstances, since the projection lens essentially operates off-axis, the correction of radial distortion and lateral color are even more critical.
As mentioned before, the projection lens may need to be telecentric on the short conjugate side. It is also desirable to have the lens as small as possible, especially when used in portable lightweight projectors.
An example of a lens suitable for front projection application is shown in Figure 2. 
This lens covers the 1024 X 768 pixels XGA format DMD with the individual pixel width of 17 microns. The offset is 100%, corresponding to a half field of view of the lens of approximately 27.5°. The ANSI throw ratio is 1.75:1. The f-number of the lens is f/2.88, and the lens is telecentric on the short conjugate side. The first two meniscus elements as well as the last element are aspherical. The configuration of the lens shown here is practical only because of availability of technology for molding aspherical elements. The use of aspherical surfaces allows for necessary correction of monochromatic aberrations to be achieved within a very small overall size, and with a minimum number of elements. As can be seen from the optical performance graphs in Figure 2, the radial distortion is fully corrected and the lateral color is about 10 microns for a spectral range of 460nm to 620nm, corresponding to just over half of the 17 micron pixel of the DMD. As seen from MTF plots, the field curvature and astigmatism are well corrected, providing for the maximum depth of focus. At the system limiting frequency of 33 cy/mm, MTF is at least 70% to 75% for the most of the field of view. Achieving the same level of image quality without the use of aspherical surfaces would lead to a substantially larger and more expensive lens.
The most desirable lenses for front projection applications are zoom lenses. As with the projection optics described above, they must be well corrected for aberrations, particularly for distortion and lateral color.
An example of a zoom lens designed for use with a 1.8" diagonal LCD having 1280 X 1024 pixels with the individual pixel width of 28.1 microns is shown in Figures 3 and 4 . The focal length range of the lens is 50mm, shown in Figure 3, to 75mm, shown in Figure 4 . The corresponding throw ratios are 1.35 : 1 at the wide angle end and 2 : 1 at the long end of the zoom range. The lens is capable of handling a 100% offset, corresponding to a maximum half field of view of 33° and 24° at the two ends of the zoom range. The f-number of the lens is f/2.81, and the lens is telecentric on the short conjugate side. The optical performance graphs in the corresponding figures indicate that the radial distortion is less than one percent pincushion at the wide angle and is fully corrected at the long end of the zoom range. The lateral color is less than half of the pixel for a spectral range of 465nm to 620nm, and the MTF response at the limiting frequency of 18cy/mm is higher than 80% over most of the field of view throughout the zoom range of the lens. Not having the freedom to use aspherical surfaces to assist in correcting the aberrations would make this lens much more complex.
Radial distortion and lateral color in a projection lens are apparent to an observer. Therefore, it is very important to correct these aberrations in lenses used for high resolution digital projection displays. By understanding the projection system specifications and by focusing on the critical points in designing the lens, the use of aspherical plastic elements in combination with glass optics makes it possible to meet strict image quality requirements with cost effective lenses suitable for mass production.
The author is grateful to B. H. Welham of US Precision Lens, Inc. and Dr. M. H. Kreitzer of OPCON Associates, Inc. for many fruitful discussions.
All the lens examples shown in the paper are provided courtesy of US Precision Lens, Inc. of Cincinnati, OH, USA.