Now that we know how to apply the slanted edge method, it is time to play around with it and gather some interesting results.

The camera under test is provided with a special lens that has a variable iris setting with a click system, so that it is becoming easy to define and change the F-number of the lens during the measurements. Using a green LED light source with a wavelength of 525 nm, a set of MTF measurements is made at various settings of the F-number. The result is shown in Figure 1.

*Figure 1 : MTF measurement for green light, as a function of the F-number of the lens.*

While changing the F-number, the exposure time setting of the camera is optimized so that a constant output signal is obtained. For every change of one F-stop, the exposure time is adapted by a factor of 2. As can be seen from Figure 1, starting with a low F-number and moving towards higher values, the MTF increases from F1.4 till F8 and then starts decreasing again till F16. This effect of increase and decrease can be explained by the interaction of three effects :

- Most lens aberrations are becoming worse for lower F-numbers. So changing the lens setting from a low F-number to a larger F-number will decrease the lens aberrations and will increase the sharpness of the image projected on the sensor. Consequently, the MTF will increase,

- Low F-numbers result in larger angles under which the rays are hitting the sensor. If the angle of the incoming rays deviates more from the normal, the chance of generating optical and electrical cross talk is becoming larger. So higher F-numbers result in less cross-talk and better MTF,

- Even with a perfect lens, a point at the object plane will result in a disk at the image plane. This so-called Airy disk has a diameter equal to *2.44xlxF*, in which* l* represents the wavelength of the incoming light. Taking into account a pixel size of 6 um and a wavelength of 0.525 um, the size of the Airy disk is becoming equal to pixel pitch for F4.7, the size of the Airy disk is becoming equal to 2 times the pixel pitch for F=9.4, the size of the Airy disk is becoming equal to 3 times the pixel pitch for F14.1. So if the F-number is becoming larger, the spot size is becoming larger as well and the image at the sensor level is becoming more blurred. This effect is making the MTF lower, which can be observed for a F8 and higher.

The dependency on the F-number is better observable in Figure 2, which illustrates the MTF at 3 different values of the spatial frequency (10 %, 25 % and 40 % of the sampling frequency).

*Figure 2 : MTF as a function of the F-number for 3 different spatial frequencies : 10 %, 25 % and 40 % of the sampling frequency, and Airy disk size as a function of F-number.*

Also the size of the Airy disk as a function of the lens F-number is shown, referring to the right vertical axis. As can be seen, for green light F8 seems to be the optimum setting of the lens as far as MTF of the camera system is concerned. More on this topic next time !

Albert, 28-10-2014.