FRESNEL Quick Guide |
Even if you are cleaning surfaces of the optics of your installation consisting of many elements, some small size dust particles are left. The element "obscuration" is intended for their modeling as well as to model other absorbing inclusions.
Load the scheme obscur.scm and the beam obscur.pls. Inspecting the beam parameters one can see that the circular beam (wavelength 2000 nm) of the diameter 0.6 cm with very soft boundary (softening 0.06 cm) was chosen. Such a softening was taken deliberately to neglect diffraction on the beam boundaries at used propagation distance.
Step of the calculation grid (distance between sampling points) is
D
x=0.0025 cm. On the way of the beam a
dust particle (absorbing disk) of the diameter 0.004 cm with the center at
x=0,y=0 is placed (see left figure, position A). The target, in other words the
plane where the interference of the plane wave of the main beam with the
spherical wave of diffraction on the dust particle is observed, is at distance 2
cm.
After propagation and magnification set Zoom=4. For
contrasting of the 2D picture change Current Max and Min levels to 1.1 and 0.9
J/cm^{2} respectively. It is possible on the profile to define positions
of the maxima and minima and their values. Left figure below shows what you can
see. Right figure shows the beam intensity profile taken through the center of
the diffraction pattern.
Magnification=2, Zoom=4 | |
After examination change position of the obscuration center
in the scheme to the new one (x=0.00375 cm, y=0.00375 cm; see left figure,
position B). If in position A the obstacle was masking only one sampling point,
now it is masking four of them. Nevertheless, performing the calculations anew,
one can see that the interference pattern is not changed. Obviously, its center
is moved in accordance with the change of the dust particle center position.
The displacement of the dust particle center (along X and Y)
for 1.5Dx
was made deliberately as for twofold (and
more) magnification it is possible to check the intensity for the points
situated at the same distances from the obscuration center and to compare them
with previous case (A). One can see that they are completely identical.
It is recommended now to decrease the obscuration size down
to 0.003 cm and to carry out the calculations for the cases A' and B' (right
figure). Although in position B' the obstacle (obscuration) does not mask any
sampling point the interference pattern is completely analogous to the case A',
certainly, except for the displacement of the center of the interference rings.
Comparing interference patterns for the obscurations of 0.004
cm and 0.003 cm one can discover that the modulation depth is decreased
approximately 1.8 times as the theory predicts.
Conclusions
The obscurations permit to model the absorbing screens with the sizes from several Dx up to small portion of Dx. The obscuration can be located arbitrary with respect to sampling points. Independently of how many sampling points the real obscuration is masking (one, several, or even none) its modeling is precise within the angle ± l/4Dx from the calculation axis.
Calculation time for modeling is much less than the time required for one propagation that permits to model easily tens or even hundreds of the dust particles.