Those involved in optical design and fabrication understand that lens elements and optical systems are seldom perfect. Despite the presence of the most sophisticated design and manufacturing techniques, lenses can still vary considerably in quality. As the optical industry has grown, and with it the demand for higher quality, higher resolution optical systems, engineers have increasingly turned to the modulation transfer function (MTF) for objective evaluation of optical system performance.
The MTF of an optical system describes how the system's ability to image an object varies depending on the spatial-frequency content of the object. We express it as the ratio of contrast in the image to contrast in the object as a function of spatial frequency. One simple method uses a series of sinusoidal intensity profiles.
Spatial frequency, as measured in the image plane, is expressed in terms of line-pairs per millimeter (lp/mm) or line-pairs per milliradian (lp/mrad). "Cycles" per millimeter, or per milliradian, are alternate units of spatial frequency; therefore, the MTF combines image resolution and contrast into a single specification.
The MTF is a measure of contrast reduction imposed by an imaging system as a function of spatial frequency.
In the simplest form of resolution testing, the U.S. Air Force (USAF) 1951 four-bar target pattern is projected in the object plane and captured as the system output using an imaging device such as a CCD camera or by direct observation. This image is examined by a person, who then makes a subjective determination on the lowest resolvable pattern feature that can be distinguished. Differing USAF four-bar patterns are associated with specific lp/mm values. This approach has limitations, however, as the image resolution is a subjective measurement derived from a person's ability to resolve an image.
The use of the MTF provides an objective measurement of optical systems. Originally, a knife-edge scanner was used to make an intensity profile across a slit target projected from a collimated source. This intensity profile is called the line spread function (LSF). Once the LSF is obtained, a Fourier transform is performed to calculate the modulation versus spatial frequencies of the intensity profile. For visible optics it is possible to use a visible CCD camera, and a pinhole that produces an Airy disk pattern (concentric rings at continuously varying spatial frequencies determined by the aperture size). The CCD array is a 2-D array of detectors of well-known size and pitch. The projected Airy disk image passes through the unit under test and is captured at video rates in both the tangential and sagittal directions by the rows and columns of the CCD array. The array output forms the two LSFs and the MTF calculations are made simultaneously.
These two techniques use well-characterized detectors, relay optics, illumination sources, and precise apertures to produce an objective measurement of image quality that combines resolution and contrast. An MTF test system enables system evaluation in situations similar to those of the actual applications. With the correct configuration, we can replicate or simulate field-angle positions, conjugate ratios, spectral regions, and image plane architecture in the test of an optical system. MTF measurement systems also provide great testing versatility as numerous other measurements can be performed; for instance, an MTF system with appropriate motion-control components can measure such parameters as field curvature, distortion, and blur spot size. MTF testing offers the engineers and test technicians a method for directly measuring image features related to overall system performance, and bridges the gap between lens designers, optical fabricators, and quality-control engineers. oe
Stephen Fantone is president and founder of Optikos Corp., Cambridge, MA.