Transfer Functions Influence Lens Choices

The MTF for a lens tells you how it affects contrast and resolution.

Samuel Sadoulet, Edmund Scientific, Barrington, NJ -- Test & Measurement World, 8/1/2000

You can quantify the performance of an imaging system based on its ability to provide images of a certain quality. What qualifies as "acceptable" image quality varies from application to application, and it depends on the amount of information needed about an object in the image. Adequate image quality in one application may be insufficient in another. The key components of image quality are resolution, contrast, distortion, and perspective errors.¹ I will describe a measurement that combines resolution and contrast in one standard specification.

Resolution is a measure of an imaging system’s ability to reproduce object detail. A low-resolution image contains blurry scenes in which objects lack detail. A high-resolution image provides crisp edges and includes much detail.

Contrast also factors into image quality because it expresses how well an image differentiates between an object’s shades of gray. An image with low contrast will appear "washed out" because it lacks vivid blacks and whites.

Resolution and contrast are closely related. To understand this, think of imaging a target with alternating equal-width black-and-white lines (Fig. 1a). This target represents 100% contrast. No lens—not even a perfect one—at any resolution can fully transfer this contrast information to the image because of the inherent diffraction limit dictated by physics.

Now imagine that the width of the line pairs on the target decreases (that is, the frequency increases). As the frequency increases, the lens is less and less able to transfer the contrast, so the resulting image has less and less contrast (Fig. 1b). (A line pair is one black and one white line of equal width. The "frequency" of these line pairs is often defined as the number of line pairs per millimeter, or lp/mm.)

MTF Incorporates Resolution and Contrast
When you must characterize the resolution and the contrast provided by a lens, you can refer to modulation transfer function (MTF) supplied by the manufacturer for a specific lens. You do not have to measure the MTF for a lens. The MTF describes the ability to transfer contrast at a particular resolution (frequency) from an object to an image. In other words, the MTF indicates how much of the object’s original contrast gets lost as the frequency in the object being imaged increases. In this way, the MTF combines resolution and contrast in a single specification.

Manufacturers measure the relationship between contrast and resolution and then plot the results as shown in Figure 2 for two lenses. The points on the lines provide the MTF values. Specifically, the graphs plot the percentage of transferred contrast vs. the frequency (lp/mm) of the lines. As mentioned above, the contrast in the image decreases with increased frequency. The MTF illustrated in Figure 2 was measured both on axis (at the center of the image) and for the full field (toward the corner edges of the field, or off axis). These measurements tell you how well the lens can resolve features throughout a field of view. Also, notice that the plot includes both horizontal and vertical performance. The difference between these two measurements indicates the amount of astigmatism present in the image.

To understand the importance of the MTF specification, consider a conventional technique used to predict a system’s performance. For a typical machine-vision system, a designer might estimate the system’s performance using the "weakest link" rule of thumb. The rule holds that the system’s resolution depends mainly on the component with the lowest resolution. This approach proves useful for quick estimates, but systems tend to have lower resolution than predicted by this rule of thumb, because all of the optical and electronic system components reduce resolution to some extent. And the quick estimate includes no consideration of contrast, which is also critical to image quality.

To accurately predict the image quality of the optical system, you must combine the effects of each component to determine how the overall system will affect resolution and contrast. Within a system, every component—the lens, the camera, the cables, the capture board, and so on—has an MTF. The system MTF is the product of all of the component MTF curves.

To accurately determine whether a particular lens provides sufficient image quality, you must multiply its MTF function by the MTF function for each component in the system. You can observe how MTF affects system performance by comparing the resulting MTF for two different lenses used with the same camera. The examples in Figure 2 compare a 25-mm fixed focal-length lens with a 25-mm double-Gauss lens, each mounted on a Sony XC-75 CCD monochrome camera. (This example simplifies the "system" to cover just the camera and the lenses to illustrate how lens MTFs can affect performance.) By analyzing the lens-camera MTF curves for each combination, you can determine which combination will yield sufficient performance for a specific machine-vision application. For this application, assume that you require a minimum contrast of 35% for an image resolution of 30 lp/mm. The double-Gauss lens is the better choice.

Watch Lens MTF Specs
Lens manufacturers often can provide theoretical or nominal MTF graphs for lenses. Although this information can be helpful for planning purposes, it doesn’t indicate the actual performance of a manufactured lens. Manufacturing always introduces some imperfections that degrade the performance of a lens. Accurate MTFs can be obtained either from software (as long as it takes the manufacturing tolerances into consideration) or by measuring the actual MTF of the lens after manufacturing.² Not all lens manufacturers can provide accurate MTF measurements, however. Be sure to ask for measured MTF data when you’re evaluating lenses for machine-vision systems. T&MW

FOOTNOTES

1. "Image Quality," Section 2 Application Notes, Electronic Imaging Resource Guide 1999. Edmund Scientific, Barrington, NJ.

2. The Web site for the Research Libraries Group (Mt. View, CA) provides more information about how to measure MTF: www.rlg.org/preserv/diginews/diginews21.html.  

Samuel Sadoulet is an applications development engineer at the Edmund Industrial Optics design center in Tucson, AZ. He received his B.S. in physics from the University of Rochester.