@j_bertolotti In my opinion the problem is not in the average itself, but in the assumption we make to belong to a Normal Distribution. It is not always normal to be in Normal as for the N-1 case
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@MCherkashin@JamesDManton Said that, I see on this thread much more authoritative expert in the field than I do. I am sure you can find more precise explanations reading through their articles and book chapters.Happy new year Maxim
@MCherkashin@JamesDManton Yes and not, the light is, indeed, reflected by less uneven surface but it is not really matter of angular distribution. I like to interpret the problem as follows here below, although it might not be super faithful with the exact theory:
@MCherkashin@JamesDManton It follows that the combination of several element mixed up (tends to randomise, if you like better) the pattern on the screen, then the speckle grains are smaller.
@MCherkashin@JamesDManton On the contrary, when the reflected spot is larger, the amount of light reflected is the same (as in the previous) but a lot of portions of light has "experienced" very different roughness. Then, in this case, the reflected field can be decomposed into very numerous elements.
@MCherkashin@JamesDManton The small spot reflects a lot of light that has experienced very similar roughness, then this light can be decomposed into a few elements of an orthonormal basis. Each point on the screen (optical bench surface) is the result from the combination of these independent components.