8th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2018)
Evaluation Method to Determine the Focal Spot Size of a CT System with a new
Designed Resolution Test-chart
1University of Padua, Department of Management and Engineering, Stradella San Nicola 3, 36100 Vicenza, Italy
State-of-the-art micro-focus X-ray sources are extensively used in industrial computed tomography systems to achieve
micrometric resolution, which is fundamental when measuring for example micro-components or parts characterized by micro-
features and structures. Resolution limitations are mainly connected to the size of the interaction cross-section between the
electron beam and the target material (i.e. focal spot). Therefore, much effort has been put into research reducing the size of the
focal spot of X-ray sources. However, the accurate measurement of the effective focal spot size is still challenging. Within this
scope, an evaluation method to determine the spot size and shape of the source of a computed tomography system is explained
in detail. The concepts of modulation transfer function in the Fourier regime and the full width at half maximum in the real space
are used for the evaluation. Different voltages and powers are investigated, as the spot size strongly depends on these parameters.
These measurements are compared to computer simulated reference values obtained with a simulated resolution chart.
Keywords: CT metrology, Resolution, Spot size
In the 80’s X-ray computed tomography (CT) has gained high attention in the industrial field for material analysis and non-
destructive testing (NDT). More recently, CT had its breakthrough as tool for coordinate metrology . This progress was
possible also thanks to the development of sufficiently small spot sizes, enabling better resolution and thus the analysis of micro-
components, components with micro-features, or with tighter tolerances. The existing standards for the characterization of the
focal spot size are collected in the series EN 12543  and propose different methods for the evaluation, whereupon the fifth
part of the standard series specifies the determination of micro focus X-ray sources in a range of 5-300 µm.
However, none of these methods is fully comparable to each other and can lead to different results for the same source .
New developments allow spot sizes well below 5 µm but no specific standard for their evaluation has been issued so far.
In 2004, Jobst et. al.  presented a method to estimate the focal spot size by fitting a convolution of the transmission profile
of a line grid with well-known specifications and a virtual spot size against the obtained radiographic transmission.
Unfortunately, this method does not specify at one hand at which point the magnification is high enough to neglect the detectors
point spread function (PSF) (or if it is truly negligible) and at the other hand the contribution of noise is not considered.
Here, the necessary theory is shortly introduced for the evaluation method with the test pattern presented during the poster
session. This method is based on the determination of the Modulation Transfer Function (MTF) in the Fourier space and the
subsequent transformation into values in real space equally to the Full Width at Half Maximum (FHWM). In future, these results
will be compared to knife edge measurements and computer simulations, and a method to quantitatively compare and additionally
convert the results of the different measurements into each other will be derived.
2 Resolution test-chart
The new test pattern has a total size of > 500×500 µm and inhibits features to evaluate spot sizes in the range between 66 µm
down to 200 nm. Thus, the test chart covers a wide range where measurement standards are under development, but has also a
broad overlap with the range already covered by existing standards. In the following, the theoretical background and the
evaluation method of the resolution test pattern is addressed in more detail.
2.1 Theoretical background and evaluation algorithm
The basics of the evaluation algorithm are kept as simple as possible. First, the regions of interest (ROI) are selected from the
full radiograph and stored separately for easier processing. A selected number of pixel lines of the horizontal and vertical
pattern are projected onto a line perpendicular to the pattern direction to get a better statistic, as the contrast between lines and
grooves can be very low.
Afterwards this line projection is split with a gradient based method into line and groove pairs and the maximum intensity of
the grooves and the minimum intensity of the lines is determined. The Michelson Contrast  of each pair is plotted against
the corresponding frequency and scaled to the contrast of the largest line. Additionally, a curve is fitted through the data points
8th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2018)
to obtain the MTF in the Fourier regime. This curve is furthermore transferred into the real space to obtain the shape of the
intensity distribution of the focal spot in one direction. This procedure is repeated for different source parameter settings to get
an idea of the evolution of the spot size while changing the parameter.
The evaluation follows the same principle explained above for the Siemens star pattern, but the maxima and minima cannot
be retrieved easily as the pattern inhibits Intensity variations in radial and angular direction. Thus, the star is split in sections
with a distinct angle and the maxima and minima are determined for the angular range. Thus, the contrast in 360 degrees can
be determined with a fixed sampling rate and thus the MTF as explained previously.
3 Simulation reproducing the obtained attenuation images
In parallel to the above described evaluation procedure, simulations of the whole setup including the measured objects are
conducted. These simulations are necessary to obtain nominal values which can be compared with experimentally measured
results and to be able to compare the obtained values with determined values from other measurements. For the simulation of
the focal spot, initially Gaussian intensity distributions are assumed and the detector PSF from the data sheet is used as a starting
point. Additionally, different noise distributions are applied mimicking the noise that appears in the obtained images. Several
dimensions of the focal spot are simulated to find an optimal match between measured and simulated results in terms of MTF
and FWHM and thus to assess the actual focal spot size. In a next step, the geometry of the X-ray source is also considered as it
can be expected that the circular profile of the electron beam is producing a distorted X-ray beam when hitting the cylindrical
target under an angle.
In a nutshell, this abstract presents a method to evaluate the focal spot size of a micro focus X-ray source and compare them to
nominal values obtained by computer simulations. Up to now, this kind of test-chart is used in general only for visual inspection,
but no quantitative evaluation is conducted. This method allows besides spot size determination by eye also a more quantitative
evaluation and is also not bound to a specific type of system, but can be easily adjusted and applied to any CT system.
This work has received funding from the European Union’s programme PAM2 within Horizon 2020 under grant agreement No
 J. P. Kruth et. al., CIRP Annals, Manufacturing Technology, Vol. 60 (2), 821-842, 2011
 EN 12543 series (1-5):1999, Non-destructive testing. Characteristics of focal spots in industrial X-ray systems for use in
non-destructive testing. European Committee for Standardization.
 A. Jobst et. al., Neue Methode zur Charakterisierung von Brennflecken kleiner als 5 µm, DACH - Jahrestagung
 K. Bavendiek et. al., New Measurement Methods of Focal Spot Size and Shape of X-ray Tubes in Digital Radiological
Applications in Comparison to Current Standards, 18th World Conference on Nondestructive Testing, Conference paper
16-20 April Durban South Africa, 2012
 Smith, Warren J. "Chapter 15.8 The Modulation Transfer Function." In Modern Optical Engineering, 385-90. 4th ed.
New York, NY: McGraw-Hill Education, 2008.