When it comes to x-ray resolution, there are no clear answers.

How is the term “resolution” defined, as applied to microfocus x-ray systems?

Simple but important question, needing standardization, right? Otherwise how is one to comparison shop in the market for x-ray equipment? All we need is one simple definition.

Sure.

That’s what I thought too, prior to getting this plethora of answers:
Resolution in terms of electron density is a measure of the resolvability in the electron density map of a molecule. In x-ray crystallography, resolution is the highest resolvable peak in the diffraction pattern, while resolution in cryo-electron microscopy is a frequency space comparison of two halves of the data, which strives to correlate with the x-ray definition. Units of measurement typically in Angstroms.”¹

What?

Resolution is often confused with spot size, or feature recognition. Spot size is the point where electrons hit a target in an x-ray tube after they have been focused. Size is measured by the diameter of the spot, in microns. Measurements are obtained by passing a strong x-ray absorbing material over the focal spot and observing the variations in intensity of the signal at the detector. Measurements also vary with distance, separating absorber and detector. To make matters worse, there is no standard for this measurement. Spot sizes will vary with the user’s definition of absorption limits.

Terrific.

Resolution is a measure of the quality of the data that has been collected on the crystal containing the protein or nucleic acid. If all of the proteins in the crystal are aligned in an identical way, forming a very perfect crystal, then all of the proteins will scatter x-rays the same way, and the diffraction pattern will show the fine details of crystal. On the other hand, if the proteins in the crystal are all slightly different, due to local flexibility or motion, the diffraction pattern will not contain as much fine information. So resolution is a measure of the level of detail present in the diffraction pattern and the level of detail that will be seen when the electron density map is calculated. High-resolution structures, with resolution values of 1Å or so, are highly ordered, and it is easy to see every atom in the electron density map. Lower resolution structures, with resolutions of 3Å or higher, show only the basic contours of the protein chain, and the atomic structure must be inferred. Most crystallographic-defined structures of proteins fall in between these two extremes. As a general rule of thumb, we have more confidence in the location of atoms in structures with resolution values that are small, called “high-resolution structures.”²

Uh oh.

Resolution may be further complicated by the manner in which electrons may be focused to the target. For example, open tube x-ray systems may limit the amount of electrons emanating from the source to only a narrow angle near the input of the tube. This has the effect of reducing the spot size, but it also has the knockoff effect of reducing x-ray flux because fewer x-rays come from the target, since fewer electrons are hitting it in the first place. The practical consequence of this is that it takes far longer in this process to obtain a useful image at the detector. When you are under pressure and in a hurry to determine why your board doesn’t work, short of destructive testing, this extra time matters.

Splendid.

The spatial resolution of x-ray microanalysis in thin foils is defined in terms of the incident electron beam diameter and the average beam broadening. The beam diameter is defined as the full width tenth maximum of a Gaussian intensity distribution. The spatial resolution is calculated by a convolution of the beam diameter and the average beam broadening. This definition of the spatial resolution can be related simply to experimental measurements of composition profiles across interphase interfaces. Monte Carlo calculations using a high-speed parallel supercomputer show good agreement with this definition of the spatial resolution and calculations based on this definition. The agreement is good over a range of specimen thicknesses and atomic number, but is poor when excessive beam tailing distorts the assumed Gaussian electron intensity distributions. Beam tailing occurs in low-Z materials because of fast secondary electrons and in high-Z materials because of plural scattering.³

Yikes.

Spatial resolution of x-ray microanalysis in the (S)TEM is limited by the initial electron probe size and by subsequent beam broadening in the foil. A finite probe size will thus inevitably deteriorate spatial resolution when compared to the resolution figure of a hypothetical point source. It can, however, be argued that this induced alteration is acceptable if the relative deterioration in resolution is either small or in accordance with the system resolution, which is determined by the microscope and energy-dispersive system settings (magnification, number of pixels). When acquiring an x-ray map or a line scan, the probe FWHM or spot size and the sampling interval on the specimen or unmagnified pixel size should be tuned to each other in order to optimize the acquisition with respect to time. This tuning criterion is translated into a set of coupled equations for the spot size and pixel size as function of a measure (to be defined) for the alteration of resolution due to the use of a finite source. These simple analytic equations, which obviously depend on parameters such as accelerating voltage, specimen thickness, density, atomic weight and number, can easily be implemented in the software of any x-ray microanalysis system.”⁴

Clear as mud. Is that writing style taught, or is it the product of natural ability?

“Spatial resolution” is defined as the ability to discern how small of a feature you can detect or see. In order to find this out you need to put a duplex wire gauge at a specific magnification and then calculate the spatial resolution. Resolution is also defined by the amount of magnification one is using in their technique. In order for this to be calculated, you need to take into consideration the amount of geometric magnification you have, along with the size of your DDA and the detector pixel pitch of the DDA that you’re using. Our proprietary formula enables the user to see what magnification they’re at as well as calculate the resolution.⁵

Glad we have that resolved.

In plain English, to measure resolution, you need a known sample, with parallel features of the same width or diameter. For example, two parallel traces of 1µm width, separated by 1µm. If your system can see these traces as separate and distinct images, then your system is said to have a resolution of 1µm. Of course, results may vary depending on the type of detector used, as well as the kV settings used to perform the measurements. Higher kV settings (80-150kV) may generate secondary electrons that have the potential to increase the focal spot, thus invalidating prior measurements.

How reassuring.

What is a prospective user of microfocus x-ray systems to do? How do you compare apples to apples? How can one reasonably determine whether a $100,000 x-ray system (or less) is sufficiently resolute (to coin a phrase) vs. a $300,000 (or greater) x-ray system? How much of a role does ego and one-upmanship (“My x-ray system can beat up your x-ray system”) play in the role of system selection? Are we effectively shooting the proverbial gnat with a howitzer? Nobody’s talking.
A big problem is much x-ray technology currently used in the electronics industry for inspection and failure analysis is derivative from medical applications. Hence much of the explanatory gobbledygook above. Medical folks seem to thrive on language like that. Here on Earth, our industry needs clarity. It ain’t happening.
Another problem is that murkiness fits the interests of many system manufacturers. Better to bury users in reams of data and bewildering specmanship – vigorously implying System A can best System B – without really addressing whether both systems are adequate to the task of cost-effectively inspecting BGA balls, hunting for microcracks, head-in-pillow defects, or whatever else is required.

Maybe this definition will suffice: “Resolution is the measure of the smallest feature that an x-ray system can identify. Often given in micrometers or line pairs per millimeter, it is a measure of image quality.”⁶ Maybe this definition is even better: “Forget the statistics; give me a clear image of what I expect to see. I’ll know it when I see it, and I’ll be able to take proper corrective action from it.”

That works.

References
1. Wikipedia.
2. RCSB Protein Data Bank, “Looking at Structures: Resolution,” rcsb.org, retrieved Dec. 7, 2015.
3. D.B. Williams et al, “The Spatial Resolution of X-Ray Microanalysis in Thin Foils,” Proceedings of the 49th Annual Meeting of the Electron Microscopy Society of America, 1991.
4. Ibid.
5. X-ray equipment supplier’s response to the question, “How does your company define resolution?”
6. Quote from x-ray manufacturer’s website.

Special thanks to Dr. David Bernard of Nordson Dage for technical assistance.

ROBERT BOGUSKI is president of Datest Corp., (datest.com); rboguski@datest.com. His column runs bimonthly.