Cutoff radius in diffraction pattern varies non-linearly with respect to max scattering angle

[Manoj]

Dear all,

I am trying to calculate the maximum allowable spatial frequency for a given maximum scattering angle accepted by an objective aperture. To do this I am using the following equation:

kmax = alpha / lambda. I am showing the calculations in the following image. 

But when I read off the values from QSTEM diffraction pattern I get much higher value compared to the value obtained using the above equation. In the image below, the maximum spatial frequency obtained using the above equation and the value read off from the diffraction pattern are shown for 15 mrad, 11 mrad and 7 mrad objective apertures. Also, the ratio of values obtained from QSTEM with values obtained from the above equation is also not same across the differently sized apertures. 

Is it the case that the ratio (which could be treated as a multiplicative factor) depends on the maximum scattering angle accepted by the objective aperture?

I am not entirely sure why this is happening and the reason for it. Kindly provide any suggestions or reasons for this.

Thank you.

Sincerely,

Manoj Settem 

[Christoph Koch]

Dear Manoj Settem,

 

The objective aperture has two parameters, the first is the radius of the objective aperture, and the second is the range over which this aperture will be faded out to zero, using a cosine function. This ‘edge width’ of the aperture ensures that you do not get any unwanted fringes in the images that may result from a sharp aperture edge. Setting this edge width to zero should give you the radius you desire.

 

Best regards,

Christoph

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