As explained in the previous section, characterising ‘graininess’ by specifying the actual grain size is neither simply possible nor meaningful. The decisive factor is rather the non-uniform brightness structure of a uniformly illuminated surface that results from it. Kodak has proposed the following measuring method: using a microdensitometer with a circular aperture of 48 µm diameter, the optical density of a uniformly illuminated surface of average density D=1 is measured at many different points. The RMS granularity is defined from the scattering width of these measured values obtained in this way, more precisely as the 1,000-fold of the ‘root mean square’ (the mean square deviation from the average value). According to Kodak, this is a good measure of the ‘perceived graininess’ of the film material. (Quote: ‘Recent tests done with large numbers of observers have demonstrated a correlation between relative granularity and relative graininess.’, Kodak Publication E-58).

Background: the range of variation (RMS) of the brightness is determined by the number $N$ of grains in the observation area in a statistical distribution of ‘light-dark objects’ (grains). The number of grains is now equal to the area of the aperture $A$ divided by the area of the individual grain $a$, so one can expect that with an average density of D=1 the RMS behaves as $RMS = 1/\sqrt{\frac{a}{a_k}}=const.\sqrt{a_k}$. The square root of the (mean) area $\sqrt{a_k}$ of the grain is a direct measure of its size, the factor 1000 and the 48 µm are arbitrary constants.

If you do not use a microdensitometer but the digitised microscope image, you can also check this underlying assumption as you can freely select the area (aperture) over which the average is taken. To do this, divide the microscope image into square areas of side length $d$ as shown in Figure 3 and determine the scattering width (RMS) of the mean densities of these squares. From the context mentioned above, it is expected that the product of RMS and $\sqrt{a}$ is constant and that the RMS granularity results directly from this constant (taking into account the 48 μm and the factor 1000).

To avoid the RMS value being distorted by uneven illumination of the image, the difference in the density of neighbouring cells is used instead of the mean density. The RMS value of this difference is $\sqrt{2}$ greater than that of the densities themselves, which can be easily corrected. It must now be taken into account that the above-mentioned relationship between RMS and aperture area only applies if this is sufficiently large in relation to the ‘structure size’ of the grain size $a_k$ . This visible structure size in the image (!) is determined by the grain size and the resolution. If the aperture ‘a’ is reduced further and further, neighbouring cells lie within the same structure and the difference in densities approaches zero. The product of RMS and $\sqrt{a}$ is therefore only constant for $a>>a_k$, in general one expects a relationship according to

$$ RMS * \sqrt{a} = const\frac{\sqrt{a}}{\sqrt{a+a_k}}$$