The grids shown are actually no longer used in order to measure the MTF. Modern MTF-Testers like the ImageMaster® use a single illuminated slit on opaque background as the object. From a mathematical point of view a single slit can be regarded as the sum over all spatial frequencies (Fourier synthesis). All frequencies contribute with the same amplitude (=1) to this slit not taking the finite slit width into account for this description. This single slit will be imaged into the image plane of the sample. Due to diffraction and aberrations there will be no perfect slit image in this plane, instead the slit image is broadened. It represents the so called Line Spread Function (LSF). On the basis of Fourier analysis the contribution of each spatial frequency to the LSF can be calculated. Actually the amplitude of each spatial frequency is equal to the contrast at this frequency. The Fourier analysis of the Lines Spread Function corresponds to the MTF of the sample. Taking a single image of the LSF unveils the complete MTF. Alternatively it is also possible to use a cross (i.e. two perpendicular slits) for the target. This enables the ImageMaster® to measure the MTF in two image directions simultaneously provided a CCD camera is used for the image analyzer. And finally a pinhole target can be used as the object, too. The image of a pinhole target is called Point Spread Function. This function contains the complete MTF information in all image directions. The basic terms and mathematical relations used for MTF are described in the ISO 9334 standard.
The modulation transfer function varies not only related to the spatial frequency but also with the position in the field of view. The MTF measurement along the axis of symmetry of the optical system is known as on-axis measurement.
To completely characterize the imaging performance of an optical system, the MTF must be measured at different positions within the field of view. The MTF measurement within the field of view is known as off-axis measurement. In order to achieve an off-axis measurement, the target is moved in the field of view at the desired object position and the image analyzer to the corresponding image position.
The MTF measurement can be accomplished at a single wavelength or in a spectral range covering a finite band of wavelengths. The resulting measurement data are known as monochromatic or polychromatic MTF values, respectively.
Usually the MTF is used in its one-dimensional form, calculated for one azimuthal section through the image plane. The azimuth (section plane) of the object pattern is called sagittal azimuth when the prolongation of the slit or object passes through the reference axis. When the prolongation of the slit pattern is perpendicular to the reference axis, the azimuth is called tangential azimuth.
In this so-called finite-finite imaging condition the illuminated slit or crosshair target is directly moved in the object plane of the sample. In the more common infinite-finite imaging condition, the illuminated slit or crosshair is part of a collimator projecting the target to infinity. The collimator is then oriented at different off axis angles for characterizing the MTF at the corresponding image fields. Figure 4 shows the typical setup for this imaging condition.