solid angle

What an Eclipse can teach us about our EDS Detectors

Shawn Wallace, Applications Engineer, EDAX

A large portion of the US today saw a real-world teaching moment about something microanalysts think about every day.

Figure 1. Total solar eclipse.                                  Image

With today’s Solar Eclipse, you could see two objects that have the same solid angle in the sky, assuming you are in the path of totality. Which is bigger, the Sun or the Moon? We all know that the Sun is bigger, its radius is nearly 400x that of the moon.

Figure 2. How it works.                                             Image credit –

Luckily for us nerds, it is also 400x further away from the Earth than the moon is. This is what makes the solid angle of both objects the same, so that from the perspective of viewers from the Earth, they take up the same area in the sphere of the sky.

The EDAX team observes the solar eclipse in NJ, without looking at the sun!

Why does all this matter for a microanalyst? We always want to get the most out of our detectors and that means maximizing the solid angle. To maximize it, you really have two parameters to play with: how big the detector is and how close the detector is to the sample. ‘How big is the detector’ is easy to play with. Bigger is better, right? Not always, as the bigger it gets, the more you start running in to challenges with pushing charge around that can lead to issues like incomplete charge collection, ballistic deficits, and other problems that many people never think about.

All these factors tend to lead to lower resolution spectra and worse performance at fast pulse processing times.
What about getting closer? Often, we aim for a take-off angle of 350 and want to ensure that the detector does not protrude below the pole piece to avoid hitting the sample. On different microscopes, this can put severe restrictions on how and where the detector can be mounted and we can end up with the situation where we need to move a large detector further back to make it fit within the constraining parameters. So, getting closer isn’t always an option and sometimes going bigger means moving further back.

Figure 3. Schematic showing different detector sizes with the same solid angle. The detector size can govern the distance from the sample.

In the end, bigger is not always better. When looking at EDS systems, you have to compare the geometry just as much as anything else. The events happening today remind of us that. Sure the Sun is bigger than Moon, but the latter does just as good a job of making a part of the sky dark as the Sun does making it bright.

For more information on optimizing your analysis with EDS and EBSD, see our webinar, ‘Why Microanalysis Performance Matters’.

Solid Angle Tool

Dr. Patrick Camus
Principal Product Developer, EDAX

It recently was brought to my attention that there is a solid angle (SA) calculator on the web. It is provided by Dr. Nestor Zaluzec of Argonne National Lab. It can be found at :

This web site is of interest to me and many of our customers and potential customers because the SA of your EDS detector is a measure of its efficiency in detecting X-rays. A large SA detector will provide a higher detection rate of X-rays than a smaller SA detector.

Historically, the SA of a detector was approximated by the simplistic equation SA = A / d2 where A is the active area of the detector and d is the detector to sample distance. For small detectors at large distances, this approximation is quite good. However, for large area detectors (which are currently quite popular) and for most TEM applications (which use very short values for d), this simple equation is not valid. This web site is very useful because it provides a much more accurate calculation for the solid angle for any detector size and position. In addition, it can accurately predict values when the additional geometric complication of an off-axis detector is required.

I will use this web site to compare a few representative geometries of SA calculations for round EDS detectors. The web site also has the capability of calculating the SA for rectangular and annular detectors, but I will leave those examples for the user.

In the first example, a typical SEM geometry will be examined where 10 mm2 and 30 mm2 detectors are compared. Most designs for these detectors have the same d, for instance 45 mm in this example.

Using these values, simplistic and calculated SA values can be found.

d (mm) A (mm2) Simple SA (msR) Calculated SA (msR)
45 10 5 5
45 30 15 15

In this example, both SA methods provide the same values. There is no primary benefit to using the calculation method.

The next example is for a TEM geometry for 10 mm2 and 30 mm2 detectors are compared. The primary differences to the SEM example are that (1) d=10 which is significantly shorter than for the SEM geometry, and (2) the axis of the detector does not point to the sample. This geometry is very typical for TEM that have a side entry mount location. In addition, this geometry also needs a take-off angle, for which 20 degrees is used.

Using these values, simplistic and calculated SA values can be found.

d (mm) A (mm2) Simple SA (msR) Calculated SA (msR)
10 10 94 88
10 30 282 249

In this example, the simple SA method over estimates the true SA values by 7% and 13% for the 2 detectors. SA values for TEM geometries should not be reported using the simple method but should always use the more accurate calculated method.

A final example shows a practical application of the SA calculations in comparing potential EDS detector geometries. When comparing detectors and considering SA values, the A is not always the primary consideration for the efficiency because the d term can have a significant effect. This usually occurs when the tubing for the detectors is not the same and the d must increase for a fatter mounting tube to avoid hitting any item with in the SEM chamber, usually the pole piece. This example compares a 60 mm2 in a small diameter tube mounted at 40 mm and an 80 mm2 detector in a larger diameter tube that must be mounted at a larger d of 50 mm.

Using these values, simplistic and calculated SA values can be found.

d (mm) A (mm2) Simple SA (msR) Calculated SA (msR)
40 60 36 36
50 80 32 31

Firstly, the values provided by the 2 calculation methods are essentially the same (within round-off errors) for both detectors. Intuition would indicate that the larger 80 mm2 detector should provide the greater SA value. However, the increased d actually reduces its SA value to less than that for the smaller 60 mm2 detector.

Solid angle values for EDS detectors are an indication of the X-ray detection efficiency of the system. A web site is available to calculate the values very accurately once the detector geometry is defined. Comparisons of detector geometry can aid a customer in selecting the best detector for their application.