The MTF or Modulation Transfer Function can be measured in various ways. In the previous MTF-blogs the measurement by means of a Siemens Star testchart was discussed. This method has particular advantages, but also has some limitations, mentioned in earlier blogs. Another evaluation technique to characterize the MTF is based on the so-called slanted-edge method. Explained in words, this method sounds very complicated, but in reality it is really pretty simple.

There are several good references describing the slanted-edge method, e.g. :

- M. Estribeau and P. Magnan., in SPIE Proceedings, Vol. 5251, Sept. 2003,
- T. Dutton et al. in SPIE Proceedings, Vol. 4486, 2002, pp. 219-246,
- P.B. Burns, in Proceedings IS&T, 2000, pp 135-138,
- S.E. Reichenback et al. In Optical Engineering, pp. 170-177, 1991.

This slanted edge method became an ISO standard, namely ISO 12233. This is one of the very few ISO standards for image sensor and/or camera measurements.

The technique of the slanted edge can be described as follows :

- Image a vertically oriented edge (or a horizontal one for the MTF measurement in the other direction) onto the detector. The vertical edge needs to be slightly tilted with respect to the columns of the sensor. The exact tilting is of no importance, it is advisable to have a tilt of minimum 2
^{o}and maximum 10^{o}w.r.t. the column direction. A tilt within these limits gives the best and most reliable results for the MTF characterization. - Each row of the detector gives a different Edge Spread Function (ESF), and the Spatial Frequency Response (SFR) of the slanted edge can be “created” by checking the pixel values in one particular column that is crossing the imaged slanted edge.
- Based on the obtained SFR, the Line Spread Function (LSF) can be calculated, the LSF is simply the first derivative of the SFR.
- Next and final step is calculating the Fourier transform of the LSF. This results in the Modulation Transfer Function, because the MTF is equal to the magnitude of the optical transfer function, being the Fourier transform of the LSF. Plotting the MTF as a function of the spatial frequency can be done after normalizing the MTF to its DC component and normalizing the spatial frequency to the sampling frequency.

(In one of the coming blogs more info will be given on further improvement and/or sophistication of this procedure.)

A very helpful strategy in understanding how this MTF measurement method works and to check the algorithms, is to run a simulation and create an artificial image with a slanted edge that is sampled by an artificial sensor (e.g. with a pixel fillfactor of 100%). Next the theoretical, geometric MTF can be calculated as a sinc-function of the spatial frequency, while the synthetic image can be used as the input image to evaluate the MTF by means of the technique explained above (ESF, SFR, LSF, MTF). Such a simple simulation tool can also be used to check the influence of the various system parameters on the measurement technique. An example of such a simulation is shown in the following figures.

First of all a synthetic image is generated that results in a slanted edged of 4 deg. w.r.t. the column direction. A region-of-interest (ROI) of 200 (H) x 300 (V) pixels is created around the black-white transition of the slanted edge. This synthetic image is shown in Figure 1.

*Figure 1 : ROI containing the slanted edge or black-white transition.*

A particular column is selected (in this example column number 96), and all pixel values in this column are recorded to generate the SFR or Spatial Frequency Response. The result of this operation is shown in Figure 2, with reference to the left vertical axis.

*Figure 2 : Spatial Frequency Response, being the values of the pixels present in column 96 of the image shown in Figure 1, and Line Spread Function, being the first derivative of the SFR.*

Next the LSF or Line Spread Function is generated, simply by numerically calculating the first derivative of the SFR. The LSF is shown in Figure 2 as well, with reference to the right vertical axis.

Once the LSF is known, the magnitude of the FFT of this LSF is calculated. Plotting the FFT magnitude versus spatial frequency results in the MTF of the sensor, as shown in Figure 3. Notice that the MTF is normalized with its value a zero input frequency (= DC), while the spatial frequency is normalized to the spatial sampling frequency of the sensor. In this simulation example, the pixel pitch is equal to 6.5 µm.

*Figure 3 : MTF of the simulated pixel (6.5 µm, 100 % FF), as well as the theoretical, geometric MTF of the same pixel.*

In Figure 3 and next to the outcome of the MTF simulation, also the theoretical geometric MTF of the pixel is shown (6.5 µm, 100 % FF), for comparison reasons. This geometrical MTF is calculated by means of the well-known sinc-function. As can be seen, both curves coincide very nicely, indicating that the slanted edge method and the algorithms used in the calculation seem to do the job that they were developed for !

Before showing real measurements, in the next blog(s) a few additional improvements of the slanted edge method will be highlighted.

Albert, 18-06-2014.