[Ifeffit] Distortion of transmission spectra due to particle size

[Matt Newville]

Scott,

You said:
> the distortion from nonuniformity is as bad for four strips
> stacked as for the single strip.

As I showed earlier, a four layer sample is more uniform than a one
layer sample, whether the total thickness is preserved or the
thickness per layer is preserved.

> For 1% pinholes:
> # N_layers | % Pinholes | Ave Thickness | Thickness Std Dev |
> #     1    |   1.0      |    0.990      |    0.099          |
> #     5    |   1.0      |    4.950      |    0.225          |
> #    25    |   1.0      |    24.750      |    0.500        |

Yes, the sample with 25 layers has a more uniform thickness.

> As before, the standard deviation increases as square root of N. Using a
> cumulant expansion (admittedly slightly funky for such a broad
> distribution) necessarily yields the same result as the Gaussian
> distribution: the shape of the measured spectrum is independent of the
> number of layers used! And as it turns out, an exact calculation (i.e. not
> using a cumulant expansion) also yields the same result of independence.

OK...  The shape is the same, but the relative widths change.

24.75 +/- 0.50 is a more uniform distribution than 0.99 +/- .099.
Perhaps this is what is confusing you?

> So Lu and Stern got it right. But the idea that we can mitigate pinholes by
> adding more layers is wrong.

Adding more layers does make a sample of more uniform thickness.
Perhaps "mitigate pinholes" means something different to you?

In your original message (in which you set out to "track down" a piece
of "incorrect lore") you said that Lu and Stern assumed that layers
were stacked "so that thick spots are always over thick and thin spots
over thin".  They did not assume that.  Given that initial
misunderstanding, and the fact that you haven't shown any calculations
or simulations, it's a bit hard for me to fathom what you think Lu and
Stern "got right" or wrong.  The main point of their work is that it
is better to use more layers to get to a given thickness.  You seem to
have some objection to this, but I cannot figure out what you're
trying to say.

This is starting to feel like "The Gossage Vardebedian Papers".

--Matt