Gaussian Peak

Definition

This model describes a Gaussian shaped peak on a flat background

$$ I(q) = (\text{scale}) \exp\left[ -\tfrac12 (q-q_0)^2 / \sigma^2 \right] + \text{background}
$$
with the peak having height of *scale* centered at $q_0$ and having a standard deviation of $\sigma$. The FWHM (full-width half-maximum) is $2.354 \sigma$.

For 2D data, scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as

$$ q = \sqrt{q_x^2 + q_y^2}
$$

References

None.

Authorship and Verification

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