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# VITESS Module Reflectometer Sample

This module simulates a sample of a reflectometer.

The reflectivity data of a sample are taken from a file that contains the reflectivity R as a function of momentum transfer Q. To be able to get a simulated function R(Q), it is possible to simulate a reference measurement. The reference sample has a reflectivity of 1 for all Q-values.
If offspecular scattering mode is desired, the reflectivity file should contain a look-up table in the form: q_i, q_f,j, R(q_i, q_f,j). Here, q_i is the incoming neutron "scattering" vector: q_i = 2*pi/lambda * sin(theta), where theta is the angle between the sample and the beam axis. q_f,j is an array of possible outgoing scattered vector components : q_f,j = 2*pi/lambda * sin(theta_j), where theta_j=theta is the specular case and theta_j=-theta stands for the direct beam. The reflectivity table thus looks like this:

q_i.................q_f,j.......R(q_i, q_f,j)
0.00255028 -0.0800882 0.001
0.00255028 -0.0797596 0.0005
0.00255028 -0.079431 0.0005
0.00255028 -0.0791025 0.0015
...
0.00255028 0.0876443 0.0005
0.00255028 0.0879728 0.0005
0.00280531 -0.0798336 0.0005
0.00280531 -0.079505 0.0005
0.00280531 -0.0791764 0.0005
0.00280531 -0.0788478 0.0005
0.00280531 -0.0785192 0.001
...
An empty line between two subsequent q_i values is recommended to match the plotting format of gnuplot. An example file with a generic offspecular look-up table is provided in the FILES folder.

The reflectometry sample can now handle incoherent isotropic scattering. It requires information on the scattering path length mu, with P=μ*x being the scattering probability (0.00288 1/cm for D2O), and on some detector parameters. Besides, if the ratio between the area containing the specular signal and the total detector area is known, this is used to scale the incoherent trajectories such that eval_elast can provide the correct backgroun level without additional data treatment inside and outside the specular signal area.

The reflection of neutrons at several angles can be done in one simulation. In this case, a minimal value, a maximal value, and a step size for the reflection angle must be given (see chapter C). If only one angle shall be considered, the step size must be set to zero or minimal and maximal value must be identical.

A. Options

The options are:

1. Sample: | Reflectivity data from the reflectivity file
2. Reference: | Reflectivity R=1 for all angles.

B. Parameter and file descriptions

File | Format | Examples Attached
Parameter File | Includes FILE INPUT PARAMETERS. This file can be read or created/modified by the VITESS shell. Values are read from separate rows i.e. 1 value/row for scalar and 3 values/row for vector type variables. | refl_probe.rpb
Reflectivity File | File that contains the reflectivity of the sample as a function of momentum transfer 1. column: momentum transfer [1/A] 2. column: reflectivity It is only needed for the option 'Sample'. | refl_probe.dat

- MAIN PARAMETERS

Parameter | Physical Symbol, Description | Range, Examples
Axis of rotation | Axis around which the sample is rotated | 'Y' or 'Z'
reflection angle [deg] | q q=0 means: no reflection, sample parallel to incoming beam positive q.value means: reflection towards the positive z- or positive y-direction resp. | -90° .....90° typical. +1°....+4°

- ADVANCED OPTIONS

Parameter | Physical Symbol, Description | Range, Examples
Offspecular scattering | If enabled, the module expects the reflectivity file in a shape shown above | yes or no
Incoherent scattering | If enabled, the module expects additional parameters, see below | yes or no
Incoherent pathlength [1/cm] | μ, needed to calculate the probability of incoherent scattering, calculated as P=μ*x, where x is the pathlength in sample | μ=0.00288 1/cm for D2O
Detector distance [cm] | Detector parameters are needed to scatter trajectories efficiently towards detector surface. The specular signal is expected in the center of the detector. | Typically up to 10 m
Detector width [cm] | Detector parameters are needed to scatter trajectories efficiently towards detector surface. The specular signal is expected in the center of the detector. | Typically up to 1-2 m, assuming flat detector
Detector height [cm] | Detector parameters are needed to scatter trajectories efficiently towards detector surface. The specular signal is expected in the center of the detector. | Typically up to 1-2 m, assuming flat detector
Norm factor | Ratio between the specular area and the total detector area. If given, the background trajectories are scaled and the resulting reflectivity should show the expected background level. | Usually several percent for an area detector, put in 1 otherwise, if unknown.

- FILE INPUT PARAMETERS

Parameter | Physical Symbol, Description | Range, Examples
main position [cm] | x, y, z Generally this position defines the reference point (origin) of the sample in the frame provided by the former module. | x = distance to CE y = z = 0.0
thickness, width, height of CE [cm] | t, w, h Thickness, width and length give the sizes of the (rectangular) sample: for reflection angle 0, the reflecting surface of the sample is in the x-y-plane. The thickness is along the z-axis, width along the y-axis and length along the x-axis. Thickness is used to determine a distance from the surface (by MC choice) where the reflection is supposed to take place. | t = 0.00002 cm w = h = 2.0 cm
frame generation [-] | 'user defined frame' sets the following coordinate system according to the values given below. 'standard frame generation' leaves the coordiate system as it is, i.e. origin at sample centre, x-axis along the incoming beam. |
output angle horizontal, vertical [deg] | F, Q In case of "user defined output frame", a F rotation about the Z axis and then a Qrotation about the (new)Y axis defines a new reference orientation. According to this and the output frame translation vector (see below) the neutrons are written to the output file. If "standard frame generation" is activated, the output frame is not rotated relatively to the original frame. | F = 180°, Q= - 2q
output frame [cm] | x, y, z The position of the output frame origin (O) in the original frame. (x, y, z) represents the translation vector applied to shift the origin of the original (input) frame (O) to the new (output) position. Default setting is: (x, y, z) = (x, y, z) i.e. main position of the sample. |

C. Data Evaluation

If several reflection angles are considered simultaneously, one incoming neutron can cause up to
Nmax = (qmax - qmin) / Dq + 1
outgoing neutrons. (This number is reached, if the sample is hit by the neutron at all angles.)

So the overall neutron flux at the detector is no longer comparable to the flux before the sample. Thus it is senseful to evaluate the data (using the module EVAL_ELAST) to separate the neutrons reflected at the different angles.
An evaluation in scattering angle is possible, if the angle difference Dq is larger than the fluctuation in the orientation of the incoming neutrons. For an evaluation in the momentum transfer Q, the variation in Q of the incoming neutrons (caused by fluctuation in orientation and wavelength) must be smaller than the difference in Q caused by the angle difference Dq.

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Last modified: Tue Jun 13 16:05:32 MET DST 2013