Version 5.0


All bug reports and suggestions are welcome!

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.

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Choose lens material from the list of choices (Al, B, Be, B4C (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/cm3). For diamond use 3.5155 g/cm3.) Note also that the density of PEEK depends on the modification (amorphous 1.26 g/cm3/cristalline 1.32 g/cm3). Usually PEEK is some mixture of amorphous and cristalline phases. By default, the calculator assumes 1.3 g/cm3, corresponding to the PEEK sample used at our institute.

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

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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.)


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 L2 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 2R0 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 2R0. This is the case, if exp(-ap) is not neglegible compared to one (B. Lengeler, et al., J. Synchrotron Rad. 6 (6), 1153-1167 (1999)).

Author: Christian Schroer