For systems where sharpening can be controlled, the recommended primary MTF calculation is the slanted-edge, which is calculated from the Fourier transform of the impulse response (i.e., response to a narrow line), which is the derivative ( d/dx or d/dy) of the edge response. This is supplied by large light and dark areas in slanted edges and by features in most patterns used by Imatest, but is not present in lines and grids. To correctly normalize MTF at low spatial frequencies, a test chart must have some low-frequency energy. \(\displaystyle C(f)=\frac\) Note : this normalizes MTF to 100% at low spatial frequencies. The equation for MTF is derived from the sine pattern contrast C(f) at spatial frequency f, where The MTF of a complete imaging system is the product of the MTF of its individual components. Note that b oth frequency and MTF are displayed on logarithmic scales with exponential notation amplitude (middle plot) is displayed on a linear scale. In Figure 6, the MTF is 50% at 61 lp/mm (line pairs per millimeter) and 10% at 183 lp/mm. By definition, the low frequency MTF limit is always 1 (100%).
Amplitude (middle plot) -The middle plot displays the luminance (“modulation” V in the MTF Equation section) of the bar pattern with lens blur (see red curve in Figure 6).
Note that lens blur causes contrast to drop at high spatial frequencies. Bar pattern, Sine pattern (upper plot) -The upper plot illustrates (1) the original sine patterns, (2) the sine pattern with lens blur, (3) the original bar pattern, and (4) the bar pattern with lens blur.Sine and bar patterns, amplitude plot, and Contrast (MTF) plotįigure 6 consists of upper, middle, and lower plots and are described as follows: These components can be thought of as low-pass filters that pass low frequencies and attenuate high frequencies.įigure 6. The response of photographic components (film, lenses, scanners, etc.) tends to “roll off” at high spatial frequencies. High spatial frequencies (on the right) correspond to fine image detail. In other words, system SFR is equivalent to the product of the MTF of each component in the imaging system. SFR is more commonly associated with complete system response, where MTF is commonly associated with the individual effects of a particular component. Note : Imatest uses SFR and MTF interchangeably. In Figure 6, MTF is illustrated with sine and bar patterns, an amplitude plot, and a contrast plot-each of which has spatial frequencies that increase continuously from left to right. The relative contrast at a given spatial frequency (output contrast/input contrast) is called Modulation Transfer Function ( MTF ), which is similar to the Spatial Frequency Response (SFR), and is a key to measuring sharpness. High frequencies correspond to fine detail in the spatial and frequency domains