In my last blog posting, I was excited to show results from version 9 of EDAX OIM Analysis™ for refining EBSD orientation measurements. However, two questions have been gnawing at me since that post. (1) How much does the size of the patterns affect the results? and (2) How sensitive is the refinement to noise in the patterns? To explore these two questions, I will use data from the same silicon single crystal I used in my previous post – a 1 x 1 mm scan with a 30 µm step size. The patterns were 480 x 480 pixels and of excellent quality.
I added two levels of Poisson noise to the patterns, as shown in Figure 1, and will term these noise levels 1 and 2 for the subsequent analysis.
Figure 1. Si single crystal patterns processed with adaptive histogram equalization [1]. (a) initial pattern, (b) pattern after a moderate level of added noise, and (c) pattern after a significant level of added noise.
The next step was to bin the patterns, index them using spherical indexing, and then apply orientation refinement as implemented in version 9 of EDAX OIM Matrix™. To perform the experiments, I binned the patterns to 360 × 360, 240 × 240, 160 × 160, 120 × 120, 96 × 96, 80 × 80, 60 × 60, and 48 × 48. After binning, I re-indexed them using spherical indexing and then calculated kernel average misorientations (KAM). I used the average KAM value as a measure of precision and plotted that against the binned pattern size for all three noise levels (0, 1, and 2). Figure 2 shows the results of the experiments.
Figure 2. Plot of average KAM values vs. pattern width for all three noise levels.
I have a couple of observations from these results.
In general, the first level of noise has only a minimal impact on the precision, whereas the higher level of noise has a more significant impact.
For noise levels 0 and 1, the average KAM values remain relatively constant until the pattern size dips below 120 × 120 pixels. Surprisingly, good results can be obtained until the smallest size of 48 × 48 pixels is reached. For noise level 2, the precision drops off significantly at a pattern size of 96 × 96. Those using Velocity cameras have probably noticed that the default pattern size is 120 × 120 pixels. Similar results to those I’ve presented here lead us to choose 120 × 120 pixels as the default. These results confirm the soundness of that choice.
I hope these results can guide the expectations for what orientation refinement can achieve in your samples. We will announce the official release of EDAX OIM Analysis 9 in the next few weeks. We hope you are excited to apply it to your materials. The orientation refinement tools are part of EDAX OIM Matrix, which is an add-on module. While you wait for your copy of version 9, make sure you save the patterns you plan to apply orientation refinement measurements to. No, I’m not getting paid by the hard drive manufacturers 😉.
Figure 3. Screenshot of EDAX APEX showing where the check-box to save patterns is located within the software.
[1] Pizer, S.M., Amburn, E.P., Austin, J.D., Cromartie, R., Geselowitz, A., Greer, T., ter Haar Romeny, B., Zimmerman, J.B. and Zuiderveld, K., 1987. Adaptive histogram equalization and its variations. Computer vision, graphics, and image processing39: 355-368.
Dr. Shangshang Mu, Applications Engineer, Gatan/EDAX
The new APEX™ 3.0 is the ultimate materials characterization software, integrating Energy Dispersive Spectroscopy (EDS), Electron Backscatter Diffraction (EBSD), and Wavelength Dispersive Spectrometry (WDS) to deliver previously unattainable solutions. This optimized configuration offers the uncompromised performance of each technique and allows users to combine them for the ultimate materials insight. All three techniques seamlessly operate within the APEX, blending powerful elemental and crystallographic analysis routines through an intuitive interface to deliver outstanding data collection, faster analysis, and flexible reporting for users of all levels.
What does APEX WDS look like?
WDS functionalities are implemented seamlessly with the EDS graphical user interface. The user can quickly adapt to the new functionalities and employ WDS when and where EDS reaches the limit. With one-click from start to finish, Auto WDS allows fully automated WDS scan list generation, optimum sample height determination, and spectrum collection. It simultaneously collects EDS and WDS spectra and displays them side-by-side or overlaid for easy data visualization and interpretation (Figure 1), with no overlapping or overloading of windows.
Figure 1. Simultaneous EDS-WDS spectrum acquisition user interface.
APEX allows you to set an intermediate position for the EDS detector to ensure optimal count rates for both techniques.
Figure 2. Simultaneous EDS-WDS mapping user interface.
Sets of combined EDS-WDS spectrum, linescan, and mapping data at different stage positions can be done via automated batch collection routines (Figure 2) to streamline SEM experiments. EDS and WDS data collection settings are managed in one user-friendly batch scan list (Figure 3).
Figure 3. Combined EDS-WDS batch list.
The quantitative elemental analysis supports individual technique or combined EDS-WDS standards. You can easily switch between EDS and WDS standards for each element by clicking on the icon in front of the element (Figure 4).
Figure 4. Quantitative results with combined EDS-WDS standards.
With the addition of WDS capabilities, APEX 3.0 now includes EDS, EBSD, and WDS. Each characterization tool can operate independently to utilize EDAX’s technological advancements or integrates data to provide solutions that were once unachievable.
John Haritos, Regional Sales Manager Southwest USA. EDAX
I recently had the opportunity to host a demo for one of my customers at our Draper, Utah office. This was a long-time EDAX and EBSD user, who was interested in seeing our new Velocity CMOS camera, and to try it on some of their samples.
When I started in this industry back in the late 90s, the cameras were running at a “blazing” 20 points per second and we all thought that this was fast. At that time, collection speed wasn’t the primary issue. What EBSD brought to the table was automated orientation analysis of diffraction patterns. Now users could measure orientations and create beautiful orientation maps with the push of a button, which was a lot easier than manually interpreting these patterns.
Fast forward to 2019 and with the CMOS technology being adapted from other industries to EBSD we are now collecting at 4,500 pps. What took hours and even days to collect at 20 pps now takes a matter of minutes or seconds. Below is a Nickel Superalloy sample collected at 4,500 pps on our Velocity™ Super EBSD camera. This scan shows the grain and twinning structure and was collected in just a few minutes.
Figure 1: Nickel Superalloy
Of course, now that we have improved from 20 pps to 4,500 pps, it’s significantly easier to get a lot more data. So the question becomes, how do we analyze all this data? This is where OIM Analysis v8™ comes to the rescue for the analysis and post processing of these large data sets. OIM Analysis v8™ was designed to take advantage of 64 bit computing and multi-threading so the software can handle large datasets. Below is a grain size map and a grain size distribution chart from an Aluminum friction stir weld sample with over 7 Million points collected with the Velocity™ and processed using OIM Analysis v8™. This example is interesting because the grains on the left side of the image are much larger than the grains on the right side. With the fast collection speeds, a small (250nm) step size could still be used over this larger collection area. This allows for accurate characterization of grain size across this weld interface, and the bimodal grain size distribution is clearly resolved. With a slower camera, it may be impractical to analyze this area in a single scan.
Figure 2: Aluminum Friction Stir Weld
In the past, most customers would setup an overnight EBSD run. You could see the thoughts running through their mind: will my sample drift, will my filament pop, what will the data look like when I come back to work in the morning? Inevitably, the sample would drift, or the filament would pop and this would mean the dreaded “ugh” in the morning. With the Velocity™ and the fast collection speeds, you no longer need to worry about this. You can collect maps in a few minutes and avoid this issue in practice. It’s a hard thing to say in a brochure, but its easy to appreciate when seeing it firsthand.
For me, watching my customer see the analysis of many samples in a single day was impressive. These were not particularly easy samples. They were solar cell and battery materials, with a variety of phases and crystal structures. But under similar conditions to their traditional EBSD work, we could collect better quality data much faster. The future is now. Everyone is excited with what the CMOS technology can offer in the way of productivity and throughput for their EBSD work.
After all these years I still get excited about new technologies and their resulting products, especially when I have had the good fortune to play a part in their development. As I look forward to 2019, there are new and exciting products on the horizon from EDAX, where the engineering teams have been hard at work innovating and enhancing capabilities across all product lines. We are on the verge of having one of our most productive years for product introduction with new technologies expanding our portfolio in electron microscopy and micro-XRF applications.
Our APEX™ software platform will have a new release early this year with substantial feature enhancements for EDS, to be followed by EBSD capabilities later in 2019. APEX™ will also expand its wings to uXRF providing a new GUI and advanced quant functions for bulk and multi-layer analysis.
Our OIM Analysis™ EBSD software will also see a major update with the addition of a new Dictionary Indexing option.
A new addition to our TEM line will be a 160 mm² detector in a 17.5 mm diameter module that provides an exceptional solid angle for the most demanding applications in this field.
Elite T EDS System
Velocity™, EDAX’s low noise CMOS EBSD camera, provides astonishing EBSD performance at greater than 3000 fps with high indexing on a range of materials including deformed samples.
Velocity™ EBSD Camera
Last but not least, being an old x-ray guy, I can’t help being so impressed with the amazing EBSD patterns we are collecting from a ground-breaking direct electron detection (DED) camera with such “Clarity™” and detail, promising a new frontier for EBSD applications!
It will be an exciting year at EDAX and with that, I would like to wish you all a great, prosperous year!
Somewhere around the age of five years old, many of us learn that another way to identify water is by the molecular name, H2O. This usually leads to more questions like: ‘What is H?’, ‘What is O?’, ‘How does that make water?’, ‘Why should I care?’. Over the years, we grow into more advanced chemistry students exploring topics like compound formulas, and we learn that the world we live in is made up of complex associations of combined atoms. A chemical compound is a substance that is composed of two or more chemical elements. The reason that we should care about compounds is that an element such as Oxygen (O) can be very different if it is associated with Hydrogen into H2O to make water, or as SiO2, which is Silicon Dioxide that makes up sand on a beach, or as Fe2O3, which is ferric oxide, loosely known as rust on steel. Therefore, as microanalysts, we should pay close attention to compounds because the elements alone do not always tell us the complete nature of the material we’re analyzing.
Once we grow into an “expert scientist,”* we become deeply entrenched in the details of microanalysis, and we often forget to take a step back to see the big picture. For example, as an EDS analyst, I look at the spectrum below and I think “what a nice sodium peak” or “hmm, am I picking up Al due to scatter at variable pressure?” But unless I’m using it for an introduction to a microscopy and microanalysis student lecture I don’t often simply call it what it is, and that is NaCl, or salt.
Next, we look at the electron image at very low mag and that gives us a better contextual understanding that it is a grain of salt.
When we look back at the spectrum again with a big picture view, we recognize that the main elements present in the spectrum are Na and Cl, and that they make up the compound NaCl, or salt.
In follow up to my recent webinar, I received a lot of questions asking “What are CompoMaps?” and “How can I use CompoMaps?” I was glad to see so much interest in such a valuable routine, and I do hope that users of every level can use this “Compound” view to understand their materials more deeply. To answer the first question, “CompoMaps” is a sophisticated software routine that creates a display of the elemental composition of each pixel. That is, the intensity of the pixel display color is a direct representation of the peak intensity of an element. It is helpful when there is a trace amount of an element, because the routine separates the peak from the background, removing the noise and intensifying the signal. It is perhaps most useful for separating element peaks where there is ambiguity whether there is one element, or another. In the example shown below, I was collecting this data when I happened to get a chance to web connect with an earth sciences professor. After he saw the before and after, he commented that the “after” made much more sense because those two elements would not likely be in combination together in any mineral.
The results here show that Phosphorus in green and Zirconium in purple are definitely located in two different phases.
Before CompoMaps: After CompoMaps: Superimposed into one image: What we didn’t see in the webinar was the Oxygen map, shown here for the first time: The display shows both with (right) and without (left) the Phosphorus and Zirconium superimposed, and this gives us a better understanding about the compound, since Oxygen is present with these elements. After full investigation of all element maps, we find that the two phases are Ca5(PO4)3F, or fluorapatite and ZrSiO4, or Zircon.
Finally, the answer to the question, “How can I use CompoMaps?”, is easy. This is a routine that EDAX has had in all of our software packages from Genesis to TEAM™ (as Net Maps) and now in APEX™. The routine has been optimized for APEX™ with 64-bit architecture and advanced processing capability, along with an easy to use workflow for results in live-time. So, give it a try and see what you can find!
*My personal opinion is that we should never let ourselves call ourselves experts, lest we forget that there is always something new to learn.
Several years ago, I was talking to a customer, who asked whether we could change the color scheme of the EDAX TEAM™ software. He said was that it was hard for him to tell the difference between the spectrum background and the cursor. I replied, “Well, the cursor is a lime green and the background is more like a gray-gre…..Oh, wait, you’re colorblind, aren’t you?” Surely enough he was, and while I can’t “see” his perspective, I can listen to and respect it. Thus, the motivation of this blog is to let our customers know that we in Applications listen to them and take their needs seriously.
In this specific case, I am happy to report that we just recently received feedback on the new EDAX APEX™ software, and one comment was that the user really liked the “contrast” of the red spectrum on the white background – see the image below.
More generally, it is one main goal of the EDAX Applications team to make sure that we capture the “real world” customer feedback and incorporate it as much as possible into future product enhancements, bug fixes and new generations of products. Each of our Worldwide Apps team members can talk to upwards of ten customers a week. These conversations are usually in interactions such as support calls, training sessions and demos. At each opportunity, we hear tremendously valuable real-world customer perspective, and very often we learn what we can’t “see” ourselves. Often, if I’m asked to share my thoughts, my words are just a colorful patchwork of years of customer ideas all melded into a microscopy amalgam.
Customer perspective is so important, in fact, that it is a cornerstone of the EDAX App Lab Mission Statement. A few years ago, I compiled about three pages of descriptions of what people thought of when they thought of Apps, and then condensed them down into the following statement that hangs on our HQ App Lab walls.
The EDAX US App Lab uses technical expertise and creativity plus a strong focus on understanding the needs of our internal and external customers to drive excellence in innovative analytical solutions. The applications group supports company-wide efforts to provide real-life value and benefits to our customers which differentiate our products in materials analysis.
Now to get back to the colors which are available for maps in our software. One of the lesser known functions is the ability to select and edit your color palette:
Using this option, you can choose from a 40-color palette, seen here. Remember to click on the element in the periodic chart first, then select your color.
Since I brought up the topic of colorblindness, I’ll also use a colorblind app that simulates how a Red/Green colorblind person sees the world (or our color palette).
Note the green color of O and P, and see how closely it compares to the yellow color of the lanthanide/actinide series!
Finally, to summarize the Applications message: to our current customers – thank you for sharing your thoughts; to all our applications team colleagues – thank you for gathering so much wide-ranging information and promoting the importance of it internally, and to all our future customers – when you chose EDAX, you’re choosing to join a dynamic microanalysis company, which strives to develop the most meaningful features and functions to meet your microanalysis needs.
Any EDS spectrum will have two distinct components; the characteristic peaks that originate from transitions between the states of the atoms in the sample and the background (Bremsstrahlung) which comes from continuum radiation emitted from electrons being slowed down as they move through the sample. The figure below shows a carbon coated galena sample (PbS) where the background is below the dark blue line while the characteristic peaks are above.
Some people consider the background an artefact and something to be removed from the spectrum (either through electronics filtering or by subtracting it) but in the TEAM™ software we apply a model based on Kramer’s law that looks as follows:where E is the photon energy, N(E) the number of photons, ε(E) the detector efficiency, A(E) the sample self-absorption, E0 the incident beam energy, and a, b, c are fit parameters¹.
This means that the background is tied to the sample composition and detector characteristic and that you can actually use the background shape and fit/misfit as a troubleshooting tool. Often if you have a bad background, it’s because the sample doesn’t meet the model requirements or the data fed to the model is incorrect. The example below shows the galena spectrum where the model has been fed two different tilt conditions and an overshoot of the background can easily be seen with the incorrect 45 degrees tilt. So, if the background is off in the low energy range, it could be an indication that the surface the spectrum came from was tilted, in which case the quant model will lose accuracy (unless it’s fed the correct tilt value).
This of course means that if your background is off, you can easily spend a long time figuring out what went wrong and why, although it often doesn’t matter too much. To get rid of this complexity we have included a different approach in our APEX™ software that is meant for the entry level user. Instead of doing a full model calculation we apply a Statistics-sensitive Non-linear Iterative Peak-clipping (SNIP) routine². This means that you will always get a good background fit though you lose some of the additional information you get from the Bremsstrahlung model. The images below show part of the difference where the full model includes the steps in the background caused by sample self-absorption while the SNIP filter returns a flat background.
So, which one is better? Well, it depends on where the question is coming from. As a scientist, I would always choose a model where the individual components can be addressed individually and if something looks strange, there will be a physical reason for it. But I also understand that a lot of people are not interested in the details and “just want something that works”. Both the Bremsstrahlung model and the SNIP filter will produce good results as shown in the table below that compares the quantification numbers from the galena sample.
While there’s a slight difference between the two models, the variation is well within what is expected based on statistics and especially considering that the sample is a bit oxidized (as can be seen from the oxygen peak in the spectrum). But the complexity of the SNIP background is significantly reduced relative to the full model and there’s no user input, making it the better choice for the novice analyst of infrequent user.
¹ F. Eggert, Microchim Acta 155, 129–136 (2006), DOI 10.1007/s00604-006-0530-0
² C.G. RYAN et al, Nuclear Instruments and Methods in Physics Research 934 (1988) 396-402
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 credit-nasa.gov
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 – nasa.gov
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.
It has been an exciting month here in our Draper Utah lab, as we have received and installed our new FEI Teneo FEG SEM. We are a small lab, focusing on EBSD development and applications, and without a loading dock, so timing is critical when scheduling the delivery. So, 3 months ago, we looked at the calendar to pick a day with sunshine and without snow. Luckily, we picked well.
Figure 1: Our new SEM coming off the truck.
Once we got the new instrument up and running, of course the next step was to start playing with it. This new SEM has a lot more imaging detectors than our older SEM, so I wanted to see what I could see with it. I chose a nickel superalloy turbine blade with a thermal barrier coating, as it had many phases for imaging and microanalysis. The first image I collected was with the Everhart-Thornley Detector (ETD). For each image shown, I relied on the auto contrast and brightness adjustment to optimize the image.
Figure 2: ETD image
With imaging, contrast is information. The contrast in this image shows phase contrast. On the left, gamma/gamma prime contrast is visible in the Nickel superalloy while different distinct regions of the barrier coating are seen towards the right. The next image I collected was with the Area Backscatter Detector (ABS). This is a detector that is positioned under the pole piece for imaging. With this detector, I can use the entire detector, the inner annular portion of the detector, or any of three regions towards the outer perimeter of the detector.
Figure 3: ABS Detector image.
I tried each of the different options, and I selected the inner annular ring portion of the detector. Each option provided similar contrast as seen in Figure 3, but I went with this based on personal preference. The contrast is like the ETD contrast is Figure 2. I also compared with the imaging options using the detector in Concentric Backscatter (CBS) mode, where 4 different concentric annular detectors are available.
Figure 4: T1 Detector (a-b mode).
My next image used the T1 detector, which to my understanding is an in-lens detector. In this mode, I selected the a – b mode, so the final image is obtained by subtracting the image from the b portion of the detector from the a portion of the detector. I selected this image because the resultant contrast is reversed from the first couple of images. Here phases that were bright are now dark, and detail within the phases is suppressed.
Figure 5: T2 Detector.
My final SEM image was collected with the T2 detector, another in-lens detector option. Here we see the same general phase contrast, but the contrast range is more limited and the detail within regions is again suppressed.
I have chosen to show this set of images to illustrate how different detectors, and their positioning, can generate different images from the area, and that the contrast/information obtained with each image can change. Now I have done a cursory interpretation of the image contrast, but a better understanding may come from reading the manual and knowing the effects of the imaging parameters used.
Figure 6: Always Read the Manual!
Of course, I’m an EBSD guy, so I also want to compare this to what I can get using our TEAM™ software with Hikari EBSD detectors. One unique feature we have in our software is PRIAS™, which uses the EBSD detector as an imaging system. With the default imaging mode, it subsets the phosphor screen image into 25 different ROI imaging detectors, and generates an image from each when the beam is scanned across the area of interest. Once these images are collected, they can be reviewed, mixed, added, subtracted, and colored to show the contrast of interest, similar to the SEM imaging approach described above.
The 3 most common contrasts we see with PRIAS™ are phase, orientation, and topographic. To capture these, we also have a mode where 3 pre-defined regional detectors are collected during EBSD mapping, and the resulting images available with the EBSD (and simultaneous EDS) data.
Figure 7: PRIAS™ Top Detector Image.
The first ROI is positioned at the top of the phosphor screen, and the resulting phase contrast is very similar to the contrast obtained with the ETD and ABS imaging modes on the SEM.
Figure 8: PRIAS™ Center Detector Image.
The second ROI is positioned at the center of the phosphor screen. This image shows more orientation contrast.
Figure 9: PRIAS™ Bottom Detector Image.
The third ROI is positioned at the bottom of the phosphor screen. This image shows more topographical contrast. All three of these images are complementary, both to each other but also to the different SEM images. They all give part of the total picture of the sample.
Figure 10: Defining Custom ROIs in PRIAS™.
With PRIAS™ it is also possible to define custom ROIs. In Figure 10, 3 different ROIs have been drawn within the phosphor screen area. The 3 corresponding images are then generated, and these can be reviewed, mixed, and then selected. In this case, I selected an ROI that reversed the phase contrast, like the contrast seen with the T1 detector in Figure 4.
Figure 11: PRIAS™ Center Image with EDS Bland Map (Red-Ni, Blue – Al, Green-Zr)
Figure 12: PRIAS™ Center Image with Orientation Map (IPF Map Surface Normal Direction).
Of course, the PRIAS™ information can also be directly correlated with the EDS and EBSD information collected during the mapping. Figure 11 shows an RGB EDS map while Figure 12 shows an IPF orientation map (surface normal direction with the corresponding orientation key) blended with the PRIAS™ center image. Having this available adds more information (via contrast) to the total microstructural characterization package.
I look forward to using our new SEM, to develop new ideas into tools and features for our users. I imagine a few new blogs posts should come from it as well!
Dr. Patrick Camus, Director of Research and Innovation, EDAX
The beginning of the new calendar year is a time to reflect and evaluate important items in your life. At work, it might also be a time to evaluate the age and capabilities of the technical equipment in your lab. If you are a lucky employee, you may work in a newly refurbished lab where most of your equipment is less than 3 years old. If you are such a fortunate worker, the other colleagues in the field will be envious. They usually have equipment that is much more than 5 years old, some of it possibly dating from the last century!
Old Jalopy circa 1970
EDAX windowless Si(Li) detector circa early 70’s
In my case, at home my phone is 3 years old and my 3 vehicles are 18, 16, and 3 years old. We are definitely evaluating the household budget this year to upgrade the oldest automobile. We need to decide what are the highest priority items and which are not so important for our usage. It’s often important to sort through the different features offered and decide what’s most relevant … whether that’s at home or in the lab.
Octane Elite Silicon Drift Detector 2017
Dr. Pat’s Possible New Vehicle 2017
If your lab equipment is older than your vehicles, you need to determine whether the latest generation of equipment will improve either your throughput or the quality of your work. The latest generations of EDAX equipment can enormously speed up throughput and the improve quality of your analysis over that of previous generations – it’s just a matter of convincing your boss that this has value for the company. There is no time like the present for you to gather your arguments into a proposal to get the budget for the new generation of equipment that will benefit both you and the company.
Best of luck in the new year!
![Si single crystal patterns processed with adaptive histogram equalization [1]. (a) initial pattern, (b) pattern after a moderate level of added noise, and (c) pattern after a significant level of added noise.](https://i0.wp.com/edaxblog.com/wp-content/uploads/2023/09/Figure1.jpg?ssl=1)
