*Version 5.0*

The calculator is based on B. Lengeler, *et al.*, *J. Synchrotron Rad.* **6**
(6), 1153-1167 (1999).
The depth of focus for microbeam applications is described in C. G. Schroer, *et al.*,
in *X-Ray Micro- and Nano-Focusing: Applications and Techniques II*, I. McNulty, ed.,
*Proc. SPIE* **4499** (2001), to be published. The thin lens approximation
is not valid for all imaging geometries, in particular when the lens has a significant
thickness as compared to the focal distance. The current version corrects for thick lens
effects in all parameters that are affected. The calculation of the corrected focal distance
is also given in the SPIE article mentioned above.

Fill in

- the energy of x-rays (500eV - 200,000eV),
- horizontal and vertical source size,
- distance from source,
- intensity just before the lens.
- FWHM of the detector point spread function (det psf)

Choose lens material from the list of choices (Al, B, Be, B_{4}C
(boron carbide), C, Li, LiF, Mg, Ni, Polycarbonate, PEEK, Si). If
you select carbon, make sure the density is correct for the carbon
modification used. (The default is graphite (2.267 g/cm^{3}).
For diamond use 3.5155 g/cm^{3}.) Note also that the density
of PEEK depends on the modification (amorphous 1.26 g/cm^{3}/cristalline
1.32 g/cm^{3}). Usually PEEK is some mixture of amorphous
and cristalline phases. By default, the calculator assumes 1.3
g/cm^{3}, corresponding to the PEEK sample used at our
institute.

If you do not find the lens material in the list of choices, enter

- density (rho) of the material.
- delta/rho, the increment of the refractive index divided by the density rho.
- mu/rho, the absorption coefficient in (cm
^{-1}) divided by the density rho.

Fill in

- the radius of curvature R of the paraboloids,
- the radius of the geometric aperture R
_{0}of the paraboloids. By default, R_{0}is calculated from the thickness W of a single lens, the radius of curvature R, and the distance d between the apices of the paraboloids. To enter a custom value for R_{0}, uncheck the ``lock R_0 to W'' button. - the number N of lenses placed behind each other,
- the distance d between the apices of the paraboloids.
- the roughness of the lens (Note: use the mean square roughness
R
_{a}in direction of the momentum transfer. This is the direction parallel to the optical axes.) - the thickness W of a single lens (1.0mm by default). This parameter
is used to calculate the thickness of the lens and its effect on the
imaging properties. If you want to use the calculator in thin lens
approximation, set this value to 0.0. Note that this requires to uncheck the
``lock R_0 to W'' and to enter a value for R
_{0}.

The calculations are updated everytime you make a change. (As
opposed to earlier versions, it is no longer necessary to hit
*<return>* after each change of parameters.)

Remarks:

- D
_{eff}is the effective aperture limiting the resolution of the image. It is influenced by both diffraction and surface roughness. - The last item in `lens properties' is the lens cross section. Multiplied with the incident intensity it yields the total flux transmitted through the lens, which is shown in the `results for given geometry' panel below the gain.
- In the field `magn.' either the magnification or the demagnification is shown, depending on whether the setup magnifies or demagnifies the object.

You can print the results by choosing `print' from most browsers. This will print what you see on the screen.

I have added an alignment tool that calculates the correction that
has to be applied to L_{2} in order to reach the microbeam focus.
To use it, the microbeam diameter in either horizontal or vertical direction
has to be measured. Enter the measured value in the appropriate text field and
be sure that the button (to the left) of that field is pressed. The two possible
distances from the focus are shown in the two text fields below,
one on either side of the current position. If *NaN* is
displayed as distance from the focus, the measured value is smaller than
what can be obtained with the current parameters. Note that there might be problems
with this scheme when some of the parameters (such as the effective source size) are
not correct.

The MTF panel shows the modulation transfer function of the setup for an
incoherently radiating object. It measures the
contrast of a periodic intensity variation (in % relative to its amplitude)
as a function of its period. On the abscissa, the period of the intensity
variation is shown in micrometers. The vertical red bar shows the lateral resolution
that corresponds to the FWHM criterion described in B. Lengeler, *et al.*,
*J. Synchrotron Rad.* **6** (6), 1153-1167 (1999). A periodic variation with
that period is transferred through the optics with a relative amplitude of about 2.8%.
The calculation of the MTF assumes a large geometric aperture 2R_{0} such that
the transmission function through the lens is Gaussian. This assumption does not hold,
if the lens becomes transparent to a significant degree on the whole geometric
aperture 2R_{0}. This is the case, if exp(-a_{p}) is not neglegible
compared to one (B. Lengeler, *et al.*,
*J. Synchrotron Rad.* **6** (6), 1153-1167 (1999)).

*Author: Christian
Schroer*