[332c10d] | 1 | .. fitting_sq.rst |
---|
| 2 | |
---|
| 3 | .. Much of the following text was scraped from product.py |
---|
| 4 | |
---|
| 5 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
---|
| 6 | |
---|
| 7 | .. _Product Models: |
---|
| 8 | |
---|
| 9 | Fitting Models with Structure Factors |
---|
| 10 | ------------------------------------- |
---|
| 11 | |
---|
| 12 | .. note:: |
---|
| 13 | |
---|
| 14 | This help document is under development |
---|
| 15 | |
---|
| 16 | *Product models*, $P@S$ models for short, multiply the structure factor $S(q)$ by |
---|
| 17 | the form factor $P(q)$, modulated by the *effective radius* of the form factor. |
---|
| 18 | |
---|
| 19 | Many of the parameters in $P@S$ models take on specific meanings so that they |
---|
| 20 | can be handled correctly inside SasView: |
---|
| 21 | |
---|
| 22 | * *scale*: |
---|
| 23 | |
---|
| 24 | The *scale* for $P@S$ models should usually be set to 1.0. |
---|
| 25 | |
---|
| 26 | * *volfraction*: |
---|
| 27 | |
---|
| 28 | For hollow shapes, *volfraction* represents the volume fraction of |
---|
| 29 | material but the $S(q)$ calculation needs the volume fraction *enclosed by* |
---|
| 30 | *the shape.* SasView scales the user-specified volume fraction by the ratio |
---|
| 31 | form:shell computed from the average form volume and average shell volume |
---|
| 32 | returned from the $P(q)$ calculation (the original *volfraction* is divided |
---|
| 33 | by *shell_volume* to compute the number density, and then $P@S$ is scaled |
---|
| 34 | by that to get the absolute scaling on the final $I(q)$). |
---|
| 35 | |
---|
| 36 | * *radius_effective*: |
---|
| 37 | |
---|
| 38 | If part of the $S(q)$ calculation, the value of *radius_effective* may be |
---|
| 39 | polydisperse. If it is calculated by $P(q)$, then it will be the weighted |
---|
| 40 | average of the effective radii computed for the polydisperse shape |
---|
| 41 | parameters. |
---|
| 42 | |
---|
| 43 | * *structure_factor_mode*: |
---|
| 44 | |
---|
| 45 | If the $P@S$ model supports the $\beta(q)$ *correction* [1] then |
---|
| 46 | *structure_factor_mode* will appear in the parameter table after the $S(q)$ |
---|
| 47 | parameters. This mode may be 0 for the local monodisperse approximation: |
---|
| 48 | |
---|
| 49 | $I = (scale / volume)$ x $P$ x $S + background$ |
---|
| 50 | |
---|
| 51 | or 1 for the beta correction: |
---|
| 52 | |
---|
| 53 | $I = (scale$ x $volfraction / volume)$ x $( <FF>$ + $<F>^2 (S-1) ) + background$ |
---|
| 54 | |
---|
| 55 | where $F$ |
---|
| 56 | |
---|
| 57 | More options may appear here in future as more complicated operations are |
---|
| 58 | added. |
---|
| 59 | |
---|
| 60 | References |
---|
| 61 | ^^^^^^^^^^ |
---|
| 62 | |
---|
| 63 | .. [#] Kotlarchyk, M.; Chen, S.-H. *J. Chem. Phys.*, 1983, 79, 2461 |
---|
| 64 | |
---|
| 65 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
---|
| 66 | |
---|
| 67 | *Document History* |
---|
| 68 | |
---|
| 69 | | 2019-03-29 Paul Kienzle & Steve King |
---|