Yeah was going to comment on the colour, then the lambda/x thing. Lambda /20 means the surface as a whole doesn't deviate from being flat by that much, they generally give a scratch/dig or similar rating along with that for local deviation/ roughness. A lot of flatness testing in general metrology is done using sodium's yellow lines btw, optics suppliers favour 633
can you please elaborate on how "RMS roughness (Sq)" is obtained? Is it the same thing as RMS of points on a single sweep line, just accounting all the height measurements in the measured area? And the peak numbers at say 2:45 are 30nm above the average and 9nm below the average?
Haha, the same here. The funny thing is, I don't mind at all. That stuff is really cool! I also had a phase where I got ads for 5 Axis simultaneous CNC machining centers, Oscilloscopes, function generators, ... And Amazon is asking me if I want a business account. No, this is for my hobby, lol. Would be nice if I didn't have to pay taxes. xD
Reminds me on having once been told by someone from ASML that the mirrors they use for their latest Extreme Ultraviolet Light Lithography machines are made at a precision (roughness
Fun fact, It is even more extreme than that! I did an internship there. They polish the mirrors to a nanometer-level scale, that would be the same as flattening Germany to a millimeter ;).
In the case of mica, it has what is known as a “cleavage plane”, where the attraction between molecules is strong in a certain direction, but weak in other directions. Muscovite and biotite, both types of mica, exhibit perfect cleavage along a single plane. Halite, which is the crystal formation of NaCl, has three cleavage planes in a cube shape. This is cubic cleavage. Calcite is a mineral often mistaken for quartz, based on appearance alone. The major differences are that quartz is more than twice as hard, quartz doesn’t react to hydrochloric acid while calcite reacts vigorously, the crystal habit is different, and quartz doesn’t cleave, it fractures in what is known as a conchoidal fracture. Quartz has no cleavage planes. Calcite exhibits rhombic cleavage along three planes, all at about 75°. Anyway, I was interested to see mica in the video, as I have been taking geology courses in university.
@@jameswkirk and @Ross Harrison: I was a CE with IBM UK in the 1970s and 80s spanning the era of large multi platter "removable disk packs" to large multi platter fixed disks. I often gave presentations with diagrams showing the flying height of the heads compared with a particle of smoke or a fingerprint. IIRC, the heads had a radius of ~200' (~60m) to enable them to fly like an aeroplane wing. With my limited understanding of aerodynamics I believe that the surfaces of both the disk and the head would need some regular variation to provide optimal lift; much as an aeroplane, especially a glider (sailplane) flying close to the ground obtains an advantage compared to flight at altitude. I doubt that even modern HDDs with 5 nM flying height can compete with 'the smoothest surface' but they probably have strict limits on the variation of the maximum and minimum deviation from the mean.
I worked in the semiconductor industry for 12 years. We could regularly achieve thin films (e.g. Titanium Nitride or Silicon Nitride) on silicon wafers with less than 0.1 nm roughness and flatness.
Just to have a reference, 0.1nm is smaller than the diameter of a hydrogen atom. A single molecule layer of Si3N4 will be much thicker than 0.1nm but the smoothness will be dependent on the underlying layer geometry and topography
The silicon he showed is bad. Silicon out of the box should be up about an angstrom roughness over a few micron scan. Measuring roughness with an AFM is limited by the tip. Older tips will blunt and give a lower roughness
@@BreakingTaps Actually, it might have been better if you aligned these 6 pieces not by the lowest point but by the average point. This way you wouldn't have these plateaus.
those high points on the slide are most likely caused by roll "pic out" when the glass is floated, the roll's that lift it out of the tin bath are touching glass that is 1200ish F. The glass is still slightly tacky, and the roll's can stick and cause these little tiny pulls on the glass as it conveys down the line.
We used to use Mica for LEED or ' Low Energy Electron Diffraction ' because of its atomically flat surface it was used as test samples to put the instrument through its paces, I cant get enough of this stuff !....cheers.
My mother worked for Rec Silicon back in the 80's. she was a machinist and also a lab engineer. sometimes when a wafer would be out of spec, she would make insanely thin throwing stars or snow flakes from them to give to us as little presents. We would also get huge globs of silicon that looked like 5" slugs that melted. Some had some pretty interesting shapes to them, top hat, sausage, spaghetti etc. don't know what happened to them but she told me on several occasions that the materials were worth about 150k a pound before they were messed up.
I work in a fab where wafers are very prominent. Some moron stacked a bunch of wafers on top of each other. Let me tell you getting those apart took some work.. even trying to slide them apart was difficult. Felt like magnets. Cool to learn more detail about them.
I wonder if soaking the stack of wafers in helium or hydrogen gas at a reasonably high temperature would have been a way to separate them especially if you stack them on their side so they didn't have any gravitational force pushing them back together. Basically the gas would intercalate between the sheets and maybe allow them to gradually move apart, especially if they were under tension of some sort
@@michalchik Inside a vacuum,, our machines actually use helium on the bottom side of the wafer to try and push it up when it's stuck. The surface it sits on is so fine that it too feels like a magnet. The surface also gets turned up to 60C to help relieve the stuck-ness. If we attempt to push it up pass a certain flow of helium (5-15 sccm) we risk blowing the wafer to pieces when it releases.
1st time on your channel. I enjoyed it immensely! I knew mica was molecularly cleavable but did not know it was molecularly flat! Here's one for you to check, Scalpels, there are specialized scalpels that use obsidian for the cutting edge because it can ubtain and hold a sharpness down to that molecular edge! I'd be curious to know the actual thickness and what, if any variation on the exact edge is?! (EDIT - My apologies, *OBTAIN not
I grind lenses and mirrors as a hobby, and flat (and smooth, as well) is more difficult to achieve than a figure of revolution. We settle for "quarter wave" but aim for the limits of our [optical] measuring capabilities. For smoothness and final figuring we use a lap of pitch, and cerium oxide or rouge to polish. Great fun for an introvert. PS: I've been buying stuff from Edmund for half a century.
I got to visit a factory in which a lot of Edmund products were manufactured. Gratings, Ronchi Rulings, reticules, first-surface mirrors, all that sort of thing. It was in a formerly industrial area of Philadelphia, and was owned and operated by a somewhat eccentric (but brilliant) man who once worked on the team that developed the guidance system for the Sidewinder missile, back in the 1950s. He told me a fascinating story about how they got that missile to home in on an infrared source in flight, using all analog electronics, no microprocessors, no stepper motors. Truly impressive level of ingenuity.
@@peteabc1 i worked in an Optical lab, and sometimes we would need Plano lense. I would grind the lenses on a Coburn lens generator, and grind at the flatest curve possible and reposition the lens four times, and it would be bumpy. We take that lens to a Sphere Pot, and use our 0 diopter lap, and rock it in and out of the center, and after awhile it gets quite flat. We sometimes needed a lens that was just Oh So close to flat, but when using the sagometer, it would read just a hair convex, and when we would epoxy it to a flat dive mask, it wouldn't trap bubbles between the stock mask and the Optical lens, and it would seem totally flat, but not quite. When I would grind carbide in a machine shop, we had a large diameter lapping table that would create the first reference side to grind all other sides for carbide cutting tool inserts. It's almost easier to create a pretty good flat, than to purposely miss the mark and make a minute curve I now work in a Granite shop, and Granite countertop materials are only real close to flat, but appear flat.
Have you tried to microscope slide's other side, too? One side was in direct contact withe tin bath and will have tiny particles of tin bonded to it, the upper side was only in contact with air and should have no contaminants embedded. For windows we actually have to identify the "tin side" as it has slightly different reflective properties.
Wow! I knew mica could be cleaved to restore its optical properties in furnace windows, but I wasn't aware how flat it actually was. Another eye opening episode. Oh, and I chuckled at the shirt.
You’re a really good explainer of technical stuff! That was easy to follow, and packed with information. This was the first video I’ve seen of your craft. It was a great introduction. Thank you.
@@springbloom5940 I don’t think many players really prefer a flat fretboard. I’m just trying to make a joke. I mean classical guitars have flat fretboards.Even super-shredder guitars have like a 20 inch radius. 9.5 inches sounds like a wonderful improvement over 7 1/4 inch Fender original. I’ve never played a guitar with a compound radius…that might be interesting.
@@johnnyxmusic Im missing my index and middle fingers, so a tight radius and narrow neck give me better access up at the nut and more leverage in my grip. Fender started using 9.5" in the 90s I think.
Re: the oxide (glass) layer on silicon wafers: I used to have a job at a wafer company. One step of the cleaning process was a soak in hydrofluoric acid, which would dissolve the oxide layer and expose the bare silicon. You could tell when the process worked because silica is hydrophilic, but silicon is hydrophobic. A pre-HF wafer would be "wetted" when rinsed with water, but afterwards the water would bead up.
Quick question: Does the oxide layer on the wafers prevent the semiconductor contacting the cooler/ heat spreader on top of the chip? I always wondered why conductive materials could just be squeezed onto CPUs without messing with the transistors underneath.
I knew they used hydrofluoric making chips because of a terrifying story I heard from a friend who worked for Microsoft in the 90's, but I always wondered what it was actually used for. Thanks Ian
You have all the pieces to do a project I’ve been thinking about for a while. A few years ago as I was leaving an aerospace job, our mechanical guys were raving about a new surface finishing method coming onto the market. Basically, you’d do a Fourier transform of the surface roughness to extract the spatial ‘frequency’ content. Then you’d put your object into a tub filled with a uniformly sized sand-like media, and vibrate it at those frequencies (I forget how they transformed freqs from distance to time), and you could notch down the specific frequency content of the surface roughness. Apparently it gave much much better polish to complex geometries that are hard to polish otherwise.
@@ramradhakrishnan9382 I don't remember all the technical details. But I don't see how that would dig valleys deeper - it could widen them to be sure, but an impact normal to the bottom of a valley would be just as likely as an impact normal to anywhere else. Phase shouldn't matter too much.
I often work with gage blocks and it fascinates me that it's so rough, you should take a look at a milled metal part it's probably very rough but it can sometimes look very nice
This is insanely impressive! We have outcrops of mica around where I live and as kids we would sit sometimes for hours peeling the layers of this mineral!
Interesting. What about microscope cover slips? I'm not sure how they're manufactured, but to my knowledge, the float technique can't produce glass this thin.
I should have some kicking around, I'll give them a scan when I get a chance. IIRC they looked pretty rough/crude when I last looked at them (visually by eye), perhaps they have to be ground down from a larger piece? My coverslips are _super_ cheap chinese variety though, i might try to grab some proper lab grade ones for a fair comparison.
I think the flattest and smoothest surface you can readily find will be a hard-disk platter. They have a roughness of about 0.1nm (!), according to the first source I found on the internet.
632.8 is red HeNe transition, not green. It is typically used for flatness specs so 1/20 lambda would be 632.8/20 I believe the 589.5924 sodium D lins is used for refractive index measurements. No real reason not to use a green wavelength such as 532 yag SHG, except the HeNe lasers are easier to control single frequency or Zeeman split modes for very long coherence length which is needed for precise interferometric measurements. That's why 632.8 is a standard today.
Really fast scans (128x128) are 10-20 seconds, I use those to roughly find interesting features. Moderately fast scans (256x256) are about 80 seconds and I sometimes use those to sanity check a region, make sure there aren't any super large features that might cause problems, etc etc. Most of the scans I end up showing are done at 512x512 which take 3-4 minutes iirc. Haven't timed it but something in that ballpark
very cool! i was able to guess what the smoothest surface was going to be after i saw that atomic terrace surface in the unoxidized silicon wafer scan in that paper there! so i guessed about 5 seconds in advance, i count that as a win
Sorry 2nd comment but I believe you may find this interesting. Oh something I just remembered that is almost pertinent to this vid....! There was an experement done a couple Swedish Sientists to determine human tactile sensitivity! The volunteers used their dominant finger to determine the smoothness of a surface and the results BLEW my brains out behind me and painted the wall exhaust-hood grey! We're able to detect a roughness of, get this, 13nm tall....actually check out Science Asylum's vid "If Earth was small, could we feel the details" @ 8:35 counter time and the details of how sensitive human touch is! Mind blowing...more sinsitive than the 90s man!
Different piece, I filmed the cleavage bit the day before so I ended up cleaving a fresh piece for the actual scan. If you let the freshly-cleaved surface sit too long, it starts to react with the environment and pick up defects (the crystal has a lot of dangling K+ ions, which start to react with water and CO2 to produce tiny carbonate crystals on the surface over time) But it's pretty representative of what you see. Super flat and free of particulate, although if you're unlucky it is still possible to land on a "step" where the layer breaks and you go up or down to a new sheet. You can see those "steps" on the piece I cleaved as little concentric circles. They are like millimeter sized though so pretty easy to avoid.
Thank you, oh mighty algorithm, for bestowing this wonderfully niche yet fascinating video upon me. I have made the Sign of the Thumb and Rang the Crimson Bell, may the mighty algorithm favor this content and share it with others.
Its because youtube algorythm doesnt recommend his videos very often. I see it first time recommended, and first video watched, and he's up 3 years. So that's the reason.
Great video! But It would be better to trim experimental values only to significant digits: maybe to tens of a nm, i think, as no AFM can give significant data up to 5-6 digits
Any chance you have an old hard disk metal platter and source a newer generation higher density shingle drive platter? It will be an interesting way to see how the storage generations improved overtime and shrunk at a nano scale..
Hmmm... definitely have plenty of old HDDs sitting around. Unsure if I have a newer shingled variety, will see if I do (and/or obtain one). Not sure if anything would show up but I agree it'd be interesting to check!
I really love your work and your videos really communicate the concepts you deal with well. On the other hand I am very curious about how you went from machining videos (breaking taps 😅) to full on physics (breaking minds... 🤯)... I'll be back for the next one... 😌
Thanks! And haha yeah... definitely changed the content a little over time :) So the main reason is that I wanted to run some home experiments and projects a few years ago, but kept wanting/needing custom metal parts. Throw in a bit of This Old Tony binge watching and a cheap milling machine for sale locally, and I got distracted from my original projects and started learning machining instead. Thought it would be fun to document on YT and then one thing led to the next and here I am scanning mica with an AFM :)
@@BreakingTaps I completely understand how a person can get sidetracked working on physics experiments. For me, my greatest manufacturing hurdel is needing custom glass parts (scientific glass blowing) rather than metal parts. I want to replicate the early (middle to late 1800s) vacuum physics experiments that was built using glass. Things like the Sprengel pump and Crookes tube.
I once read a report that said humans can feel surface imperfections that are on the order of nanometers. Can you feel each of those samples and tell any difference between them?
You can maybe _just barely_ feel something on the gage block, particularly if you can catch a nail on one of the scratches. It feels very very smooth though, and it's very subtle so I'm not sure if I'm imagining it or not tbh. The grinding marks are super apparent by eye though, even if you can't feel them very well, they show up under the light. Not sure I can feel anything on the glass samples though. Slightly rougher items around the shop are very noticeable though, particularly when you get to like the 500nm - 1um range. Pretty impressive when you think about it!
Also interesting is if you've a feedback in hand, like an indicator, you can move it by umeters. The brain figures out you can increase precision by pushing from side without knowing anything about cosines.
What you feel is the effect of roughness against your fingerprints. You don't feel the individual bumps per se, but the roughness will affect how much your skin "chatters" as you drag it over the surface with light pressure. In simple terms, you can gauge the friction and feel the difference between roughnesses that differ in nanometers. I remember reading about research into building sensors that work like whiskers, and how the vibration translates into what it's brushing over.
I love high precision work, awesome!!! I’ve never done anything with flatness or smoothness, though I have played with very small increments of time. Some of the things you have to measure in computers and networking only take a fraction of a nanosecond, so you have to think and measure in pico and fempto and yakcto seconds. :) High precision is difficult though fun!
"femto" "yocto" IF you're going for "precision"... (micro-, nano-, pico-, femto-, atto-, zepto-, yocto-, etc.) (And there are still people who believe "zepto" was one of the comedic Marx brothers. ;-D )
great video! aluminium has a better reflectivity than silver in visible light. it is often used for mirrors in high precision instruments because of that. silver is only commonly used in mirrors because of its corrosion resistance.
As long as there are no traces of sulfur in the environment. Otherwise silver does tarnish quite readily. It doesnt develop pits like aluminum oxide does
@@primus711 Silver tarnishes very easily. This creates a lot of resistance. It also doesn't have a high melting temperature, and that could be important if you are passing a lot of current. Meanwhile... I have a bunch of high current relays with silver contacts. 🤷♂️
@@jimurrata6785 I've occasionally come across old silver coated component leads. You need to remove the tarnish layer (either mechanically or chemically) to properly solder it. The RMA fluxes that I usually use for soldering does nothing to cut through the tarnish layer. For relay contacts, hopefully the contacts are designed to provide a small amount of mechanical wipe when closing to break through the tarnish layer to get to the conductive silver.
I suggest the book "The Surface Texture Answer Book" by Malburg and Musolff (2021) for the definitions of roughness, waviness, form, lay, and profile. When you say "RMS", I assume you are referring to Rq or Sq. Great video, again!!
Oh, rad thanks! Will check it out! Definitely not my field of expertise, as evidenced by the sketchy explanation about flatness and roughess (I realized halfway through explaining I wasn't quite sure... you can see the panic haha). But yes you're correct, the RMS numbers I was quoting were "RMS roughness (sq)" values straight from Gwyddion.
I had to pipe gases through stainless steel and was surprised that smoothest interior surface had a matte appearance rather than a mirror. The reason was that the polished mirror surface had sharp crystalline edges when seen under an electron microscope and the etched matte finish had rounded crystalline edges.
I wonder if they were processed with abrasive fluid machining (AKA hydroerosive grinding). A former employer made diesel injectors, and used AFM to radius the orifices and (IIRC) adjust K-factor. Pumping a diamond-powder-bearing fluid around at high pressure... now that's a recipe for a self-destructing machine!
The flattest surfaces cost many, many thousands of dollars, require freaking PhD level techs to set up, calibrate, test, and validate, and the tools they use to do it have Star Trek sounding names. I find it fascinating. I actually stumbled upon the craft when trying to find physical evidence that would show flat earthers how impossible a flat earth would be. Ever since then I’ve wanted an aaaa rated surface plate and all the tools.
Thank you! I find everything in your videos so interesting, but don't have the means to do this kind of thing myself. I find your videos to be very valuable learning resources.
You ought to mention that the mica is only a perfect surface over a certain range. At about 7:46 you see lines where you're jumping from one crystal plane to another. Showing a scan of an area with that change would be really interesting, in order to show just how big the steps are. At any rate, it's easy to find uniform surfaces larger than the FOV of of your microscope, but they are not arbitrarily large.
Something interesting to look at would be a mechanical seal since their flatness is measured in helium light bands, probably not as smooth as some of the other surfaces but they are pretty darn
I am usually hesitant to watch videos with "click-baity" titles (like ______will surprise you!), but I gotta say, that WAS an incredibly flat surface, and I actually WAS surprised by the source! Fair play, sir. Subscribed.
Give a ballpark figure on the cost of the microscope. (the website requires all kinds of data, too much trouble and resulting spam!) I was about equally surprised at the mica and the microscope slide!
Nice comments on flatness and smoothness and yeah atomically flat and optically transparent MICA is the main substrate used in challenging surface forces apparatus (SFA) experiments to study interfacial and surface forces between adsorbed layers of materials on mica. Cheers!!
Originally, Corning's fusion glass process was to make car windshields. However, the float process was invented at the same time and float had adequate flatness but was much cheaper. Corning kept its fusion glass process running making microscope slides. It was useful as microscope slides because it was virtualy perfectly flat as the glass surface was not polished and was never touched by anything but air. The particles on the slide you have are probably chips from the slied cutting process. Of course, eventually LCDs came along that needed fusion glass flatness and that is the primary use of fusion glass today.
I just finished the second Three Body Problem book. The scene where they discover the probe is a perfectly flat surface and what that meant was awesome. Cool to see that even the most flat item you could find is still bumpy by appearance at a micro level is neat.
I love the content, but dang if I don’t wish you’d have the heightmaps of materials in the same scale, such as at 3:46. It should be trivial to use Levels in Photoshop or Gimp or whatever video editing software you use (Premiere, etc.) to remap the color gradient in of the images to match. I.E.: 1. Map each image to grayscale (if you don’t have that already from your scanning software). 2. Pencil & paper algebra where 36.4 nm and 6.2 nm are on the right scale. 3. Linearly (non-gamma) bring down the white point and up the black point of the left image by the right percentages. 4. Draw a scale that goes from 1.0 nm to 52.3 nm and add a linear (non-gamma) grayscale gradient. 5. Map all the grayscale stuff back to your color gradient (I forget the Photoshop menu option, but it’s easy to do). _But I’m the kind of person who always has pet peeves over misrepresented data, like graphs that don’t have the bottom at 0 for the purposes of deceptive marketing._ ¯\_(ツ)_/¯
Speaking of flatness and, even worse, "curved smoothness": How does Zeiss make reflective EUV (soft X-ray, really) optics for ASML photolithography machines?
*Addendum*
- Flat != Smooth, _please_ don't fill the comments with hate.
Did you know that "flat" and "smooth" means different things? 😉
@Breaking Taps pin it to the top!
@@maxmustermann5353 Whoops, cheers. Pinned!
Yeah was going to comment on the colour, then the lambda/x thing. Lambda /20 means the surface as a whole doesn't deviate from being flat by that much, they generally give a scratch/dig or similar rating along with that for local deviation/ roughness. A lot of flatness testing in general metrology is done using sodium's yellow lines btw, optics suppliers favour 633
can you please elaborate on how "RMS roughness (Sq)" is obtained? Is it the same thing as RMS of points on a single sweep line, just accounting all the height measurements in the measured area?
And the peak numbers at say 2:45 are 30nm above the average and 9nm below the average?
You are the reason I am now being aggressively retargeted by atomic force microscope advertisers on UA-cam.
😂 Sorry! haha :)
Just buy one
Haha, the same here. The funny thing is, I don't mind at all. That stuff is really cool! I also had a phase where I got ads for 5 Axis simultaneous CNC machining centers, Oscilloscopes, function generators, ... And Amazon is asking me if I want a business account. No, this is for my hobby, lol. Would be nice if I didn't have to pay taxes. xD
I don’t need one, but it’s now on my Christmas list 😅
ooof no ad blocker
Reminds me on having once been told by someone from ASML that the mirrors they use for their latest Extreme Ultraviolet Light Lithography machines are made at a precision (roughness
Just like the real Netherlands
Sounds about right for the tallest mountains in the Netherlands.
Sounds like saskachewan. It's so flat you can see the curvature of the earth from a fencepost.
Fun fact, It is even more extreme than that! I did an internship there. They polish the mirrors to a nanometer-level scale, that would be the same as flattening Germany to a millimeter ;).
@@inventor121 LOL!!!
"Do you want to experience true level, Morty??"
yes, yes, i'am
lol
LAMBS TO THE COSMIC SLAUGHTER!!!
@Emory Mason was about to say i was about to say a similar joke b4 i saw this
Yup, found the comment I was looking for.
I expected this joke
"One of the flattest materials, and the source will surprise you"
Probably came from my ex-girlfriend...
You beat me to it dammit
Mica is used in cosmetics so maybe there is some truth in this
mean ;(
The flattest surface is the Earth, of course 😉
I very nearly made a joke about that, but decided not to tempt the fates / internet 😂
@@BreakingTaps I've got you man
Shhhhh.... they'll find us! We might want to barricade up.
In all seriousness, this is not a joking matter. Idiocracy was a prophetic documentary...
@@ChrisHarmon1 the smoothness is in the flat-earthers’ brains, then.
In the case of mica, it has what is known as a “cleavage plane”, where the attraction between molecules is strong in a certain direction, but weak in other directions. Muscovite and biotite, both types of mica, exhibit perfect cleavage along a single plane. Halite, which is the crystal formation of NaCl, has three cleavage planes in a cube shape. This is cubic cleavage. Calcite is a mineral often mistaken for quartz, based on appearance alone. The major differences are that quartz is more than twice as hard, quartz doesn’t react to hydrochloric acid while calcite reacts vigorously, the crystal habit is different, and quartz doesn’t cleave, it fractures in what is known as a conchoidal fracture. Quartz has no cleavage planes. Calcite exhibits rhombic cleavage along three planes, all at about 75°. Anyway, I was interested to see mica in the video, as I have been taking geology courses in university.
Wow. Are you a wizard?
@@davidtatum8682 Probably not. I don't always arrive precisely when I mean to.
@@Ben_Kimber Well, I'm sure that you just need to tweak something somewhere.
@@Ben_Kimber So you can understand markings on a page?
@@Ben_Kimber cubic cleavage sounds like something out of a tomb Raider game...
please do a harddrive platter.
And a hard drive read/write head...
@@paulvolz720 thanks for the link
@@tootalldan5702 I do not see a post from @Paul Volz or a link.
@@jameswkirk and @Ross Harrison: I was a CE with IBM UK in the 1970s and 80s spanning the era of large multi platter "removable disk packs" to large multi platter fixed disks. I often gave presentations with diagrams showing the flying height of the heads compared with a particle of smoke or a fingerprint. IIRC, the heads had a radius of ~200' (~60m) to enable them to fly like an aeroplane wing.
With my limited understanding of aerodynamics I believe that the surfaces of both the disk and the head would need some regular variation to provide optimal lift; much as an aeroplane, especially a glider (sailplane) flying close to the ground obtains an advantage compared to flight at altitude. I doubt that even modern HDDs with 5 nM flying height can compete with 'the smoothest surface' but they probably have strict limits on the variation of the maximum and minimum deviation from the mean.
Oh yeah, good one! 👍👍
I worked in the semiconductor industry for 12 years. We could regularly achieve thin films (e.g. Titanium Nitride or Silicon Nitride) on silicon wafers with less than 0.1 nm roughness and flatness.
Thats... less than 100 picometers- wowzers. I get why quantum entanglement is a concern for those tiny-ass logic gates.
@@dustinyoung3069 your thinking of quantum tunneling
@@owencarter6417 that too
Just to have a reference, 0.1nm is smaller than the diameter of a hydrogen atom. A single molecule layer of Si3N4 will be much thicker than 0.1nm but the smoothness will be dependent on the underlying layer geometry and topography
The silicon he showed is bad. Silicon out of the box should be up about an angstrom roughness over a few micron scan. Measuring roughness with an AFM is limited by the tip. Older tips will blunt and give a lower roughness
The 3d scans you've made are so awesome! Well done.
Thanks! Blender is super rad :)
I think it's a 2D scan. Height is measured and used in the plot.
Definitely nice.
@@BreakingTaps Actually, it might have been better if you aligned these 6 pieces not by the lowest point but by the average point. This way you wouldn't have these plateaus.
@@alexeynezhdanov2362 might that not be due to the speed of the chisel?
say yes please
i am so sure
those high points on the slide are most likely caused by roll "pic out" when the glass is floated, the roll's that lift it out of the tin bath are touching glass that is 1200ish F. The glass is still slightly tacky, and the roll's can stick and cause these little tiny pulls on the glass as it conveys down the line.
Nice info, thanks!
We used to use Mica for LEED or ' Low Energy Electron Diffraction ' because of its atomically flat surface it was used as test samples to put the instrument through its paces, I cant get enough of this stuff !....cheers.
I wonder if the Mica surface coating with a plasma spray would be just as flat.
My mother worked for Rec Silicon back in the 80's. she was a machinist and also a lab engineer. sometimes when a wafer would be out of spec, she would make insanely thin throwing stars or snow flakes from them to give to us as little presents. We would also get huge globs of silicon that looked like 5" slugs that melted. Some had some pretty interesting shapes to them, top hat, sausage, spaghetti etc. don't know what happened to them but she told me on several occasions that the materials were worth about 150k a pound before they were messed up.
I work in a fab where wafers are very prominent. Some moron stacked a bunch of wafers on top of each other. Let me tell you getting those apart took some work.. even trying to slide them apart was difficult. Felt like magnets. Cool to learn more detail about them.
I wonder if soaking the stack of wafers in helium or hydrogen gas at a reasonably high temperature would have been a way to separate them especially if you stack them on their side so they didn't have any gravitational force pushing them back together. Basically the gas would intercalate between the sheets and maybe allow them to gradually move apart, especially if they were under tension of some sort
@@michalchik Inside a vacuum,, our machines actually use helium on the bottom side of the wafer to try and push it up when it's stuck.
The surface it sits on is so fine that it too feels like a magnet. The surface also gets turned up to 60C to help relieve the stuck-ness. If we attempt to push it up pass a certain flow of helium (5-15 sccm) we risk blowing the wafer to pieces when it releases.
work at a fab too.... breaking wafers is far more interesting....
@@MoDawdy And that's why we have a chip shortage
So when you work at the fab do high five and say fabulous 🤩
1st time on your channel. I enjoyed it immensely!
I knew mica was molecularly cleavable but did not know it was molecularly flat!
Here's one for you to check,
Scalpels, there are specialized scalpels that use obsidian for the cutting edge because it can ubtain and hold a sharpness down to that molecular edge!
I'd be curious to know the actual thickness and what, if any variation on the exact edge is?!
(EDIT - My apologies, *OBTAIN not
I grind lenses and mirrors as a hobby, and flat (and smooth, as well) is more difficult to achieve than a figure of revolution. We settle for "quarter wave" but aim for the limits of our [optical] measuring capabilities. For smoothness and final figuring we use a lap of pitch, and cerium oxide or rouge to polish. Great fun for an introvert.
PS: I've been buying stuff from Edmund for half a century.
That's something I want to learn. How it's done? With the 3 flats?
I got to visit a factory in which a lot of Edmund products were manufactured. Gratings, Ronchi Rulings, reticules, first-surface mirrors, all that sort of thing. It was in a formerly industrial area of Philadelphia, and was owned and operated by a somewhat eccentric (but brilliant) man who once worked on the team that developed the guidance system for the Sidewinder missile, back in the 1950s. He told me a fascinating story about how they got that missile to home in on an infrared source in flight, using all analog electronics, no microprocessors, no stepper motors. Truly impressive level of ingenuity.
Use a big piece of Mica?
@@Obladgolated Right up my Dad's alley. He probs would have liked to talk to the guy.
@@peteabc1 i worked in an Optical lab, and sometimes we would need Plano lense.
I would grind the lenses on a Coburn lens generator, and grind at the flatest curve possible and reposition the lens four times, and it would be bumpy.
We take that lens to a Sphere Pot, and use our 0 diopter lap, and rock it in and out of the center, and after awhile it gets quite flat.
We sometimes needed a lens that was just Oh So close to flat, but when using the sagometer, it would read just a hair convex, and when we would epoxy it to a flat dive mask, it wouldn't trap bubbles between the stock mask and the Optical lens, and it would seem totally flat, but not quite.
When I would grind carbide in a machine shop, we had a large diameter lapping table that would create the first reference side to grind all other sides for carbide cutting tool inserts.
It's almost easier to create a pretty good flat, than to purposely miss the mark and make a minute curve
I now work in a Granite shop, and Granite countertop materials are only real close to flat, but appear flat.
Mica is crazy!!! Nature blows away the very best man has to offer. It really is an amazing world.
It blows away the best of what most of man could do. Scientists could do better
2:20 Green wavelength of 630-ish nm? No, that's red (from a red HeNe laser). Green is around 500-530 ish
Sweet lord I'm bad at life. Addendum additions already! 😂 Cheers :)
@@BreakingTaps You're still an exquisite explainer of complicated concepts, and if you didn't make the occasional mistake we would get suspicious :P
He's probably color blind lmao
i was going to comment this but you beat me to it lol
Will be 632.8nm.
Have you tried to microscope slide's other side, too? One side was in direct contact withe tin bath and will have tiny particles of tin bonded to it, the upper side was only in contact with air and should have no contaminants embedded. For windows we actually have to identify the "tin side" as it has slightly different reflective properties.
Was looking for this comment!
How do you identify the tin side?
@@terrygoyan second this question
@@terrygoyan By looking at it, and you can tell because of the way it is.
TSMC: Check out this super smooth wafer.
Mica: *laughs in atomic flatness*
Wow! I knew mica could be cleaved to restore its optical properties in furnace windows, but I wasn't aware how flat it actually was. Another eye opening episode. Oh, and I chuckled at the shirt.
You’re a really good explainer of technical stuff! That was easy to follow, and packed with information. This was the first video I’ve seen of your craft. It was a great introduction. Thank you.
That one dislike was a disappointed flat earther
na it was your smooth brain.
@@lordjaashin no u
It was probably someone who is against the unethical Mica mining which is basically 80% Child Slave Labour.
I ground my own 1/16 wave secondary, from a pyrex blank. The technical term for 'flat', is 'infinite radius'.
Some guitar players like it that way.
@@johnnyxmusic
I prefer a 9.5" radius
@@springbloom5940 I don’t think many players really prefer a flat fretboard. I’m just trying to make a joke. I mean classical guitars have flat fretboards.Even super-shredder guitars have like a 20 inch radius. 9.5 inches sounds like a wonderful improvement over 7 1/4 inch Fender original. I’ve never played a guitar with a compound radius…that might be interesting.
@@johnnyxmusic
Im missing my index and middle fingers, so a tight radius and narrow neck give me better access up at the nut and more leverage in my grip. Fender started using 9.5" in the 90s I think.
Re: the oxide (glass) layer on silicon wafers: I used to have a job at a wafer company. One step of the cleaning process was a soak in hydrofluoric acid, which would dissolve the oxide layer and expose the bare silicon. You could tell when the process worked because silica is hydrophilic, but silicon is hydrophobic. A pre-HF wafer would be "wetted" when rinsed with water, but afterwards the water would bead up.
Quick question: Does the oxide layer on the wafers prevent the semiconductor contacting the cooler/ heat spreader on top of the chip? I always wondered why conductive materials could just be squeezed onto CPUs without messing with the transistors underneath.
@@eagames456 finished CPUs and other chips are coated in a protective layer of epoxy. You never actually see the silicon itself in a finished chip.
I knew they used hydrofluoric making chips because of a terrifying story I heard from a friend who worked for Microsoft in the 90's, but I always wondered what it was actually used for. Thanks Ian
Oh damn, bone hurting juice
You have all the pieces to do a project I’ve been thinking about for a while. A few years ago as I was leaving an aerospace job, our mechanical guys were raving about a new surface finishing method coming onto the market. Basically, you’d do a Fourier transform of the surface roughness to extract the spatial ‘frequency’ content. Then you’d put your object into a tub filled with a uniformly sized sand-like media, and vibrate it at those frequencies (I forget how they transformed freqs from distance to time), and you could notch down the specific frequency content of the surface roughness. Apparently it gave much much better polish to complex geometries that are hard to polish otherwise.
Frequency, yes. But how would the phase be controlled - would there not be a kind off bad phase-lock that would dig the valleys deeper?
@@ramradhakrishnan9382 I don't remember all the technical details. But I don't see how that would dig valleys deeper - it could widen them to be sure, but an impact normal to the bottom of a valley would be just as likely as an impact normal to anywhere else. Phase shouldn't matter too much.
Weird to think that a 7nm chip a single transistor would fit on that measured section of silicone. Thanks for the great video!
"Nothing but a flat surface"
Mica-chan: "b-b-baka! Im not flat !!"
Hahahahaha
rushia chan ;)
I often work with gage blocks and it fascinates me that it's so rough, you should take a look at a milled metal part it's probably very rough but it can sometimes look very nice
This is insanely impressive! We have outcrops of mica around where I live and as kids we would sit sometimes for hours peeling the layers of this mineral!
Same
Interesting. What about microscope cover slips? I'm not sure how they're manufactured, but to my knowledge, the float technique can't produce glass this thin.
I should have some kicking around, I'll give them a scan when I get a chance. IIRC they looked pretty rough/crude when I last looked at them (visually by eye), perhaps they have to be ground down from a larger piece? My coverslips are _super_ cheap chinese variety though, i might try to grab some proper lab grade ones for a fair comparison.
@@BreakingTaps Would be super cool! :-)
I think the flattest and smoothest surface you can readily find will be a hard-disk platter. They have a roughness of about 0.1nm (!), according to the first source I found on the internet.
You are such an underrated channel. You explain things so wonderfully, and your passion about the topics are evident. I love it!
I think that he ranks up there with Destin, Kevin, Steve Mould, Tom Scott, Captain Disillusion and Beekman.
632.8 is red HeNe transition, not green. It is typically used for flatness specs so 1/20 lambda would be 632.8/20
I believe the 589.5924 sodium D lins is used for refractive index measurements.
No real reason not to use a green wavelength such as 532 yag SHG, except the HeNe lasers are easier to control single frequency or Zeeman split modes for very long coherence length which is needed for precise interferometric measurements. That's why 632.8 is a standard today.
I was going to comment on this also - glad to see someone else noticed.
How long do these scans take?
Really fast scans (128x128) are 10-20 seconds, I use those to roughly find interesting features. Moderately fast scans (256x256) are about 80 seconds and I sometimes use those to sanity check a region, make sure there aren't any super large features that might cause problems, etc etc. Most of the scans I end up showing are done at 512x512 which take 3-4 minutes iirc. Haven't timed it but something in that ballpark
@@BreakingTaps Thanks; faster than I expected. I did electron microscope install/repair in the '70s and kept my interest in microscopy.
If you ever do another part, could you do a fiber optic cable? We cleave those to get an atomically-flat face as well.
very cool! i was able to guess what the smoothest surface was going to be after i saw that atomic terrace surface in the unoxidized silicon wafer scan in that paper there! so i guessed about 5 seconds in advance, i count that as a win
Not only a win, but possibly an 8 outta 10 on the psychic forecasting scale!
@@WJRHalyn-jw2ho rockhounding as a kid has paid dividends!
Sorry 2nd comment but I believe you may find this interesting.
Oh something I just remembered that is almost pertinent to this vid....!
There was an experement done a couple Swedish Sientists to determine human tactile sensitivity! The volunteers used their dominant finger to determine the smoothness of a surface and the results BLEW my brains out behind me and painted the wall exhaust-hood grey!
We're able to detect a roughness of, get this, 13nm tall....actually check out Science Asylum's vid "If Earth was small, could we feel the details" @ 8:35 counter time and the details of how sensitive human touch is!
Mind blowing...more sinsitive than the 90s man!
So was the mica you scanned the piece that you had just sliced? Or does it look that nice right from the beginning? Really cool video!
Different piece, I filmed the cleavage bit the day before so I ended up cleaving a fresh piece for the actual scan. If you let the freshly-cleaved surface sit too long, it starts to react with the environment and pick up defects (the crystal has a lot of dangling K+ ions, which start to react with water and CO2 to produce tiny carbonate crystals on the surface over time) But it's pretty representative of what you see. Super flat and free of particulate, although if you're unlucky it is still possible to land on a "step" where the layer breaks and you go up or down to a new sheet. You can see those "steps" on the piece I cleaved as little concentric circles. They are like millimeter sized though so pretty easy to avoid.
Thank you, oh mighty algorithm, for bestowing this wonderfully niche yet fascinating video upon me. I have made the Sign of the Thumb and Rang the Crimson Bell, may the mighty algorithm favor this content and share it with others.
How your channel has not blown up completely is beyond me.
Its because youtube algorythm doesnt recommend his videos very often. I see it first time recommended, and first video watched, and he's up 3 years. So that's the reason.
My gf chest is flatter… jk I love her ❤️
the end surfaces of bearing rollers (good quality) are comparable to gauge blocks. The wringing trick works.
Wrong. Just completely wrong.
The world's flatest thing in existence is that emo girl we all know and don't like
Great video!
But It would be better to trim experimental values only to significant digits: maybe to tens of a nm, i think, as no AFM can give significant data up to 5-6 digits
Yep, very fair point! Was just being lazy copy/pasting from Gwyddion 😅
There are two types of comments on this video, 1 being insanely smart people making recommendations, and 2 is "hehehe no booby funny"
Any chance you have an old hard disk metal platter and source a newer generation higher density shingle drive platter? It will be an interesting way to see how the storage generations improved overtime and shrunk at a nano scale..
Hmmm... definitely have plenty of old HDDs sitting around. Unsure if I have a newer shingled variety, will see if I do (and/or obtain one). Not sure if anything would show up but I agree it'd be interesting to check!
@@BreakingTapsThat would be cool! 👍
8:03 smoothness of a Twitter user’s brain
Rushia-chan fans: "Well I know about a surface that is even more fla... AHHH!!!"
=^) I think the answer of why YT put this in our recommendations
@@Protect_all_ljf3forms Can confirm. See you on the other sid-
The flattest thing ever: my ex’s chest
I really love your work and your videos really communicate the concepts you deal with well. On the other hand I am very curious about how you went from machining videos (breaking taps 😅) to full on physics (breaking minds... 🤯)...
I'll be back for the next one... 😌
Thanks! And haha yeah... definitely changed the content a little over time :) So the main reason is that I wanted to run some home experiments and projects a few years ago, but kept wanting/needing custom metal parts. Throw in a bit of This Old Tony binge watching and a cheap milling machine for sale locally, and I got distracted from my original projects and started learning machining instead. Thought it would be fun to document on YT and then one thing led to the next and here I am scanning mica with an AFM :)
@@BreakingTaps
I completely understand how a person can get sidetracked working on physics experiments. For me, my greatest manufacturing hurdel is needing custom glass parts (scientific glass blowing) rather than metal parts. I want to replicate the early (middle to late 1800s) vacuum physics experiments that was built using glass.
Things like the Sprengel pump and Crookes tube.
As a laser guy it is painful to watch this poor silver mirror 😢
I once read a report that said humans can feel surface imperfections that are on the order of nanometers. Can you feel each of those samples and tell any difference between them?
You can maybe _just barely_ feel something on the gage block, particularly if you can catch a nail on one of the scratches. It feels very very smooth though, and it's very subtle so I'm not sure if I'm imagining it or not tbh. The grinding marks are super apparent by eye though, even if you can't feel them very well, they show up under the light. Not sure I can feel anything on the glass samples though. Slightly rougher items around the shop are very noticeable though, particularly when you get to like the 500nm - 1um range. Pretty impressive when you think about it!
Also interesting is if you've a feedback in hand, like an indicator, you can move it by umeters. The brain figures out you can increase precision by pushing from side without knowing anything about cosines.
What you feel is the effect of roughness against your fingerprints. You don't feel the individual bumps per se, but the roughness will affect how much your skin "chatters" as you drag it over the surface with light pressure. In simple terms, you can gauge the friction and feel the difference between roughnesses that differ in nanometers.
I remember reading about research into building sensors that work like whiskers, and how the vibration translates into what it's brushing over.
The tongue is far more sensitive than the fingers. Windows are in fact pretty smooth. Ask me how I know? :D
@@squelchstuff Professional window licker. Wow.
not exactly what i'd expect choosing to watch while eating but yes very interesting...
I love high precision work, awesome!!! I’ve never done anything with flatness or smoothness, though I have played with very small increments of time. Some of the things you have to measure in computers and networking only take a fraction of a nanosecond, so you have to think and measure in pico and fempto and yakcto seconds. :) High precision is difficult though fun!
Gesundheit
"femto"
"yocto"
IF you're going for "precision"...
(micro-, nano-, pico-, femto-, atto-, zepto-, yocto-, etc.)
(And there are still people who believe "zepto" was one of the comedic Marx brothers. ;-D )
Why I'm watching so many videos of this channel.... 😂😂😂
Flatest surfaces include some waifus
Rushia will find you.
10:32 why not try precisely that, put some particles or interesting stuff on mica and scan it :)
hey, some good stuff! was quite surprised to learn about precision ground quartz, about normal glass slide and mica.
I wonder if you could use the thinnest slice of Mica as a membrane surface for a micro-speaker (IEM, headphones). Would it be superior to graphene ?
i think it’s too brittle
great video! aluminium has a better reflectivity than silver in visible light. it is often used for mirrors in high precision instruments because of that. silver is only commonly used in mirrors because of its corrosion resistance.
As long as there are no traces of sulfur in the environment.
Otherwise silver does tarnish quite readily.
It doesnt develop pits like aluminum oxide does
Why silver isnt used for contact pads in electronics even though its the best conductor
@@primus711 Silver tarnishes very easily. This creates a lot of resistance.
It also doesn't have a high melting temperature, and that could be important if you are passing a lot of current.
Meanwhile... I have a bunch of high current relays with silver contacts. 🤷♂️
@@jimurrata6785 I've occasionally come across old silver coated component leads. You need to remove the tarnish layer (either mechanically or chemically) to properly solder it. The RMA fluxes that I usually use for soldering does nothing to cut through the tarnish layer. For relay contacts, hopefully the contacts are designed to provide a small amount of mechanical wipe when closing to break through the tarnish layer to get to the conductive silver.
I don't know what is more fascinating: your videos or a wonderful bunch of experts and/or knowledgeable nerds they attract. 👍
I suggest the book "The Surface Texture Answer Book" by Malburg and Musolff (2021) for the definitions of roughness, waviness, form, lay, and profile. When you say "RMS", I assume you are referring to Rq or Sq. Great video, again!!
Oh, rad thanks! Will check it out! Definitely not my field of expertise, as evidenced by the sketchy explanation about flatness and roughess (I realized halfway through explaining I wasn't quite sure... you can see the panic haha). But yes you're correct, the RMS numbers I was quoting were "RMS roughness (sq)" values straight from Gwyddion.
mica very common in rocky areas of midwest, find chunks of muscovite stacks at random. i think was used as window material before glass in the West
I had to pipe gases through stainless steel and was surprised that smoothest interior surface had a matte appearance rather than a mirror. The reason was that the polished mirror surface had sharp crystalline edges when seen under an electron microscope and the etched matte finish had rounded crystalline edges.
I wonder if they were processed with abrasive fluid machining (AKA hydroerosive grinding). A former employer made diesel injectors, and used AFM to radius the orifices and (IIRC) adjust K-factor. Pumping a diamond-powder-bearing fluid around at high pressure... now that's a recipe for a self-destructing machine!
@@markp5726 We were told it was hydrofluoric acid etched.
The flattest surfaces cost many, many thousands of dollars, require freaking PhD level techs to set up, calibrate, test, and validate, and the tools they use to do it have Star Trek sounding names. I find it fascinating. I actually stumbled upon the craft when trying to find physical evidence that would show flat earthers how impossible a flat earth would be. Ever since then I’ve wanted an aaaa rated surface plate and all the tools.
I’ve never learned about mica before this though. Looks like I’m gonna be splitting crystals.
Thank you! I find everything in your videos so interesting, but don't have the means to do this kind of thing myself. I find your videos to be very valuable learning resources.
You ought to mention that the mica is only a perfect surface over a certain range. At about 7:46 you see lines where you're jumping from one crystal plane to another. Showing a scan of an area with that change would be really interesting, in order to show just how big the steps are. At any rate, it's easy to find uniform surfaces larger than the FOV of of your microscope, but they are not arbitrarily large.
Yep that's a good point! And that the surface degrades over time as it's exposed to air.
Something interesting to look at would be a mechanical seal since their flatness is measured in helium light bands, probably not as smooth as some of the other surfaces but they are pretty darn
everybody knows that the flattest surface in the universe is your gf
I understand the science… what I need an explanation of, is that shirt…
I am usually hesitant to watch videos with "click-baity" titles (like ______will surprise you!), but I gotta say, that WAS an incredibly flat surface, and I actually WAS surprised by the source! Fair play, sir. Subscribed.
there is a joke to be made here
They found it when they looked at Gawr Gura's chest
Fun fact: if the earth was the size of a pool ball it would be smoother than the pool ball
i genuinely predicted mica being 1 after reading the title, nice video
Give a ballpark figure on the cost of the microscope. (the website requires all kinds of data, too much trouble and resulting spam!) I was about equally surprised at the mica and the microscope slide!
I bet you read "automatically" the first time.
how do you tag some1 here cause I need to tag my friend
Can’t believe they made a video about your girlfriend
Nice comments on flatness and smoothness and yeah atomically flat and optically transparent MICA is the main substrate used in challenging surface forces apparatus (SFA) experiments to study interfacial and surface forces between adsorbed layers of materials on mica.
Cheers!!
damn i havent found any "anime" references in the comment section
that just really blew my mind. thank you so much for doing this! It really makes me appreciate my glass slides more... amazing.
I like your funny words Magic Man.
I was thinking it was a video about my wife
This reminds me of the one episode of Rick and Morty
Welcome to today's lecture. Title: "Resolution of Reality"
5:44 why is the max peak lower than the median
"this silicon wafer I had around the shop"
Goals
Originally, Corning's fusion glass process was to make car windshields. However, the float process was invented at the same time and float had adequate flatness but was much cheaper. Corning kept its fusion glass process running making microscope slides. It was useful as microscope slides because it was virtualy perfectly flat as the glass surface was not polished and was never touched by anything but air. The particles on the slide you have are probably chips from the slied cutting process.
Of course, eventually LCDs came along that needed fusion glass flatness and that is the primary use of fusion glass today.
Stanley would beg to differ.
I just finished the second Three Body Problem book. The scene where they discover the probe is a perfectly flat surface and what that meant was awesome. Cool to see that even the most flat item you could find is still bumpy by appearance at a micro level is neat.
My chest is the flattest surface on earth
This video missed out on mentioning my ex.
one of the flattest materials is joe mama
My girl be like
It's clearly a flat earthers tears smh.
For float glass, the roughness is probably so low because of surface tension.
I love the content, but dang if I don’t wish you’d have the heightmaps of materials in the same scale, such as at 3:46. It should be trivial to use Levels in Photoshop or Gimp or whatever video editing software you use (Premiere, etc.) to remap the color gradient in of the images to match.
I.E.:
1. Map each image to grayscale (if you don’t have that already from your scanning software).
2. Pencil & paper algebra where 36.4 nm and 6.2 nm are on the right scale.
3. Linearly (non-gamma) bring down the white point and up the black point of the left image by the right percentages.
4. Draw a scale that goes from 1.0 nm to 52.3 nm and add a linear (non-gamma) grayscale gradient.
5. Map all the grayscale stuff back to your color gradient (I forget the Photoshop menu option, but it’s easy to do).
_But I’m the kind of person who always has pet peeves over misrepresented data, like graphs that don’t have the bottom at 0 for the purposes of deceptive marketing._ ¯\_(ツ)_/¯
Speaking of flatness and, even worse, "curved smoothness":
How does Zeiss make reflective EUV (soft X-ray, really) optics for ASML photolithography machines?