When optical designers attempt to compare the performance of optical systems, a commonly used measure is the modulation transfer function (MTF). MTF is used for components as simple as a spherical singlet lens to those as complex as a multi-element telecentric imaging lens assembly. In order to understand the significance of MTF, consider some general principles and practical examples for defining MTF including its components, importance, and characterization.
THE COMPONENTS OF MTF
To properly define the modulation transfer function, it is necessary to first define two terms required to truly characterize image performance: resolution and contrast.
Resolution is an imaging system's ability to distinguish object detail. It is often expressed in terms of line-pairs per millimeter (where a line-pair is a sequence of one black line and one white line). This measure of line-pairs per millimeter (lp/mm) is also known as frequency. The inverse of the frequency yields the spacing in millimeters between two resolved lines. Bar targets with a series of equally spaced, alternating white and black bars (i.e. a 1951 USAF target or a Ronchi ruling) are ideal for testing system performance. For a more detailed explanation of test targets, view Choosing the Correct Test Target. For all imaging optics, when imaging such a pattern, perfect line edges become blurred to a degree (Figure 1). High-resolution images are those which exhibit a large amount of detail as a result of minimal blurring. Conversely, low-resolution images lack fine detail.
Figure 1: Perfect Line Edges Before (Left) and After (Right) Passing through a Low Resolution Imaging Lens [View Larger Image]
A practical way of understanding line-pairs is to think of them as pixels on a camera sensor, where a single line-pair corresponds to two pixels (Figure 2). Two camera sensor pixels are needed for each line-pair of resolution: one pixel is dedicated to the red line and the other to the blank space between pixels. Using the aforementioned metaphor, image resolution of the camera can now be specified as equal to twice its pixel size.
Figure 2: Imaging Scenarios Where (a) the Line-Pair is NOT Resolved and (b) the Line-Pair is Resolved [View Larger Image]
Correspondingly, object resolution is calculated using the camera resolution and the primary magnification (PMAG) of the imaging lens (Equations 1 – 2). It is important to note that these equations assume the imaging lens contributes no resolution loss.