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DE razor geometry. A system for measuring aggressive razors.

Here is an example of why accuracy is only meaningful if it's repeatable, and why the photos are 1000x more important and difficult to do than the measurements. The area that we're measuring is really, really small. This is what the area that I'm working with looks like when I'm working with it in image J. All of the measurements revolve around the edge of the blade, but the edge of the blade is not in the focal plane of the photo, so it kind of vanishes into a haze of pixels. I'm just guessing where it is. The better the focus, the better the measurement.



The problem is depth of focus. The edge of the razor and the edge of the razor blade are not on the same plane. The edge of the razor blade 2.00mm lower than the edge of the razor. The depth of focus of the Pluggable USB 2.0 is only 0.10mm. Put differently, there is a 2,000% disparity between the depth of focus of the camera is capable of and the 2 focal planes of interest (side of the razor, and side of the blade).

The only solution to this problem in 1 picture is to painstaking find the point where these two features are both simultaneously in the best focus together. Basically we're finding the focal point right in the middle, where we are 1.00mm distant from these two features. That's extremely hard to do.

The solution is to take 2 pictures, without moving the camera. The first picture focuses as clearly as possible on the side of the razor blade in the crispest detail possible. The side of the razor will be very blurry in this shot. The second picture is taken without moving the camera, and the focus is adjusted to get the crispest image of the side of the razor where the shave-plane is defined. In this picture, the blade will be a blurry.

The next step is focus stacking. We take both photos, and use software to combine them such that it borrows the best "in-focus" part of both photographs, at every point on both photographs, to create a new photograph where everything is in focus at the same time.

Here is a fantastic 5 minute video that explains it much better. It's actually pretty easy to do.

 
I took these pictures at the same height and focus as the razor pictures to see if they can help with calibration.
View attachment 1279825
Each mark is .01"
View attachment 1279824
I placed a .100" Johansson gage block on the scale to show the effects of moving off center.
View attachment 1279828
On center the edges of the Jo Block are clear and sharp.
View attachment 1279827
The side of the Jo Block can be seen as it is moved to one side as a ghost mirror.
View attachment 1279826
With a true Optical Comparator the sides would not show.


:cornut:
Wow. That ghost mirror effect is mind boggling. I can't wrap my brain around how it happens, but I can see the clear implications for measurement accuracy if whatever you're photographing is not in the center of the picture!

As far as adding to the scale to the photo, I'm not sure how to move a scale from one photo into another. Do you have a way to get a ruler or any other feature with a precisely known size into the photo? Ideally, it needs to be on about the same plane as the side of the razor so that it's more or less in focus in one of the 2 pics. This is what I did in my crappy photos. The larger the object is, the better. If a known feature is 3 pixels tall, and I'm off by 1 pixel, everything I measure is off by 50%. If the object used for scale is 100 pixels, and I'm off by 1 pixel, then everything I measure is off by 1%.

 

Esox

I didnt know
Moderator
The better the focus, the better the measurement.
The higher the cameras resolution, the more pixels per sq.in or sq.mm, the sharper the image.

Understanding Digital Camera Resolution - http://facweb.cs.depaul.edu/sgrais/camera_res.htm

For example, lets say the USB camera used for that picture is 2MP, if you took the same picture with a 10MP camera it would be 5x's as sharp because each pixel would be 5x's smaller. The image would have more data (pixels) in it.
 
New suggestion for the linear regression:
tmp = x*blade exposure + y*free end distance + z*total support surface
result = decimal_scaling(tmp)

where

total support surface [mm^2] = surface of top cap after the blade post(s) + surface of baseplate clamping the blade
The surface can be approximated using a piece of thread, a pencil and a measuring instrument. The thread needs to be below the inserted blade (unless the blade is a winner from the Excalibur experiment) and marked where it loses contact with the blade while in the razor.
x,y,z should sum up to 1.
 
The higher the cameras resolution, the more pixels per sq.in or sq.mm, the sharper the image.

Understanding Digital Camera Resolution - http://facweb.cs.depaul.edu/sgrais/camera_res.htm

For example, lets say the USB camera used for that picture is 2MP, if you took the same picture with a 10MP camera it would be 5x's as sharp because each pixel would be 5x's smaller. The image would have more data (pixels) in it.
So if a measurement with precision of a tenth of a millimeter is required, in order to avoid workarounds, more than 1000x magnification would be required? Which in turn would mean at least 5MP, whereas most consumer-grade USB microscopes offer 1920x1080p which is approx. 2MP.
 
I really want to find an affordable solution for this, but so far the two possibilities are as follows:
-Consumer digital camera and macro lens attachment, at least $300 excluding some sort of support
-Better USB microscope, has built in support arm
OpticsPlanet has a Celestron "Pro" with 5MP sensor for $130, but I think that is still above budget

Optics and photography are in my wheelhouse, but as mentioned, not using $12000 worth of equipment is difficult. You can rent all the equipment once you have your method down and have a go at multiple razors at once. That would be $300-$500.:wacko:
 
The higher the cameras resolution, the more pixels per sq.in or sq.mm, the sharper the image.

Understanding Digital Camera Resolution - http://facweb.cs.depaul.edu/sgrais/camera_res.htm

For example, lets say the USB camera used for that picture is 2MP, if you took the same picture with a 10MP camera it would be 5x's as sharp because each pixel would be 5x's smaller. The image would have more data (pixels) in it.
A 10mp camera with good macro capabilities would be awesome. The one's that I've seen have been way out my price range though. A $50 budget doesn't go very far.

Speaking of megapixels. I took a look at a pixel calculator, and it looks like the photos are just under 1 megapixel by the time I get them into ImageJ. When I open the picture is says 1280x720 on the header. I googled "pixel calculator" and it said that was 921.6 kilopixels. Since the USB microscope only supports JPEG compression, I'm sure some resolution is lost by the time it gets to Rosseforp's laptop. Could 50% of the pixels really be lost from the time the camera takes the picture and the time its downloadable from the forum?

Where are all the pixels going?
 
A 10mp camera with good macro capabilities would be awesome. The one's that I've seen have been way out my price range though. A $50 budget doesn't go very far.

Speaking of megapixels. I took a look at a pixel calculator, and it looks like the photos are just under 1 megapixel by the time I get them into ImageJ. When I open the picture is says 1280x720 on the header. I googled "pixel calculator" and it said that was 921.6 kilopixels. Since the USB microscope only supports JPEG compression, I'm sure some resolution is lost by the time it gets to Rosseforp's laptop. Could 50% of the pixels really be lost from the time the camera takes the picture and the time its downloadable from the forum?

Where are all the pixels going?
@Esox will probably give you a detailed answer, but it's worse. They are actually removed to compress the image and recreated based on adjacent pixels when it is opened!
 
I guess I can't edit my post. The Celestron has a pixel size of 1.75 micrometre which .0175mm by 2592 pixels wide gives 4.536mm. I only mention this to illustrate that even a $130 microscope isn't going to get you to .01 accuracy. If you zoomed out, theoretically you could get each pixel to represent .01 or less. But then the image might not be close enough and you would zoom back in digitally anyway. I measured about 6mm wide edge of my razor that would need to be in the photo therefore you could get each pixel to represent .013mm.
 
I really want to find an affordable solution for this, but so far the two possibilities are as follows:
Why makes you think that the $50 Plugable 2.0 won't work? We're only using 1 of it's 2 megapixels at the moment! Others are saying that it's outputting photos at 1600x1200 to their computer, but we're working with 1280x720 pixels at the moment. I think that's a settings issue.

Here is a link to tech support that explains why the device defaults to 1280x720 pixels unless change the settings using their software.


@Rosseforp, are you taking the pictures from the Plugable app itself? It sounds like you need to install their software to use full camera resolution, and it will only give you full resolution if you do three things:

1. Download and Install the Plugable Microscope software linked in the video below
2. Manually change the device to Microscope as shown in the screenshot and video
3. Manually change the resolution to 1600x1200 as shown in the screenshot and video

Here is a 2 minute video on how to do it. It's a 2 second fix if that's all it is.


 
So if a measurement with precision of a tenth of a millimeter is required, in order to avoid workarounds, more than 1000x magnification would be required? Which in turn would mean at least 5MP, whereas most consumer-grade USB microscopes offer 1920x1080p which is approx. 2MP.
We haven't even come close to getting 100% of the performance that the USB 2.0 Pluggable is capable of. Here is a picture of the bevel of a Wizamet blade when it was brand new vs 8 shaves. This pic was taken with a $20 USB microscope. Lots of guys on the forum are using them for inspecting straight razor edges off the hone.



Mike linked the post earlier in this thread:

 
Why makes you think that the $50 Plugable 2.0 won't work? We're only using 1 of it's 2 megapixels at the moment! Others are saying that it's outputting photos at 1600x1200 to their computer, but we're working with 1280x720 pixels at the moment. I think that's a settings issue.
Whoopsy doodle! I am off by a digit. 2.2 micrometre is .0022 mm. Each .01 of accuracy that you are aiming for gives you 4.5 pixels at 1:1. You are correct that you can do this with a cheap USB microscope. The higher resolution versions have little advantage at a 6mm object width. Other than the quality of the optics maybe.
 
Good catch @APBinNCA :punk:

I was eyeballing the edge of the blade trying to get the best picture of the blade edge, and the razor wasn't completely straight. These pics were taken with the razor properly straightened. :hand: Just like you pointed out.

And to satisfy @Dovo1695, with greater magnification. The difference in heights of the side of the razor and the end of the blade makes it impossible to get both in focus at the same time, so I adjusted the focus in between.
I know @Dovo1695 wants to try focus stacking, but this highlights why I recommended backlighting. If you focus on the blade, you can get the most important details for measuring. By backlighting you can define the profile of the razor(like the comparator). Also by putting the razor in shadow, you eliminate glare and resulting artifacts. A tip that I saw while reading reviews of USB microscopes is to place the item on something that can be pulled(x, y) to adjust, set your focus then pull to center. It seems like simply having something to hold the handle up(fixed Z) so the razor is parallel and placing both on a translucent sheet would be sufficient. I am in the process of testing some things, but the biggest obstacle really is the low cost. As much as I like the images, I am pretty confident it is the least affective method for low budget. The leading contender right now is $60 calipers and the cut in half blade. You only need to measure the blade exit span and the blade edge span. Then subtract the two and dived by 2. The calipers have a resolution of .001mm.
 
New suggestion for the linear regression:
tmp = x*blade exposure + y*free end distance + z*total support surface
result = decimal_scaling(tmp)

where

total support surface [mm^2] = surface of top cap after the blade post(s) + surface of baseplate clamping the blade
The surface can be approximated using a piece of thread, a pencil and a measuring instrument. The thread needs to be below the inserted blade (unless the blade is a winner from the Excalibur experiment) and marked where it loses contact with the blade while in the razor.
x,y,z should sum up to 1.
I've been playing around with this idea in my head but I don't understand the total support surface calculation. I don't follow what the string is measuring, or how it's being measured. It certainly is intriguing though, and I don't understand a lot of simple concepts that are 100% correct. 😋

Could you take a picture or make a quick sketch of what of what you mean?
 
I'm excited about those close ups! So excited in fact I decided to figure out how to use the ImageJ software, which took me a little while. The software isn't that complicated, but I'm not particularly bright. The reason that I decided to go with ImageJ is that I noticed some oddities in PowerPoint where the angle that a line segment is drawn at influenced the measured length of the segment. It was never designed for measuring small things. Measuring microscopic things is ImageJ's raison d'etre.
Downloaded ImageJ and User Guide, will play with it this weekend! :001_cool:
 
New suggestion for the linear regression:
tmp = x*blade exposure + y*free end distance + z*total support surface
result = decimal_scaling(tmp)

where

total support surface [mm^2] = surface of top cap after the blade post(s) + surface of baseplate clamping the blade
The surface can be approximated using a piece of thread, a pencil and a measuring instrument. The thread needs to be below the inserted blade (unless the blade is a winner from the Excalibur experiment) and marked where it loses contact with the blade while in the razor.
x,y,z should sum up to 1.
I'm not sure if this is what you were getting at, but it gave me an idea. Allow me to introduce a new and totally made up razor parameter: Muzzle Area

Muzzle area is a measurement of support surface area and more importantly, it's a measurement of how easy it is to make a razor bite. Ultimately, the thinner and more steeply curved a guard is, the easier it is going to be to push it into your skin with pressure. Every .01mm you push it into your skin, is an actual increase in effective blade exposure. The ability to push a razor into your skin is what makes it possible for negative exposure razors to shave. Pushing a razor with positive exposure into your skin is what makes it "bite". Hence the name "muzzle". It's admittedly kind of a dumb name, but it's descriptive, and it's an open question whether or not it's an sufficiently worthwhile concept to need a proper name anyhow.

The muzzle area calculation measures the total surface area necessary to double the absolute value of the razor's blade exposure (AV accommodates negative exposure razors). First you measure the blade exposure, then you go back in the opposite direction towards the blade. You draw a muzzle plane, and you measure the area of the metal within it. It takes about 2 minutes. Obviously, this is just a 2 dimensional measurement, but when you multiply times the width of the guard/comb, you have a volume measurement.

Image J makes it pretty easy to take area measurements, even of curved objects. Here is an example of the measurement on the Karve SB-D.



Here is an example of how much this measurement can vary. The muzzle area on a Henson is 100x as big as the one on the example razor above it. I'm guessing it's a hell of a lot harder to make a Henson bite than pretty much any other razor. It's got a heck of a muzzle. 😋

 
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I've been playing around with this idea in my head but I don't understand the total support surface calculation. I don't follow what the string is measuring, or how it's being measured. It certainly is intriguing though, and I don't understand a lot of simple concepts that are 100% correct. 😋

Could you take a picture or make a quick sketch of what of what you mean?
Too early to label my concept "correct", but thanks.
I substituted the string for a sheet of paper, but the principle is the same. I use a sheet of paper between the baseplate (R2 here) and the blade. Then after removing the blade, I use a pencil to draw the surface where the blade has direct contact with the cap and/or the plate, finally measure. My biggest problem is, though, my eyes and my triangle are not precise enough to perform the measurement. In the given example, the baseplate clamping points would be 2 (sides) * 1mm (width) * 4mm (length) + 2 * 2mm * 4mm = 24 mm^2. The reason why I consider this parameter important is that it would enable us to compare OC vs CC without considering the OC teeth (curvature, width, etc.)

20210612_160935.jpg
20210612_161129.jpg
PS. I was several minutes too late it seems. But the clamping surface is different from the muzzle area - would need to think a little on that one.
 
I'm not sure if this is what you were getting at, but it gave me an idea. Allow me to introduce a new and totally made up razor parameter: Muzzle Area

Muzzle area is a measurement of support surface area and more importantly, it's a measurement of how easy it is to make a razor bite. Ultimately, the thinner and more steeply curved a guard is, the easier it is going to be to push it into your skin with pressure. Every .01mm you push it into your skin, is an actual increase in effective blade exposure. The ability to push a razor into your skin is what makes it possible for negative exposure razors to shave. Pushing a razor with positive exposure into your skin is what makes it "bite". Hence the name "muzzle". It's admittedly kind of a dumb name, but it's descriptive, and it's an open question whether or not it's an sufficiently worthwhile concept to need a proper name anyhow.

The muzzle area calculation measures the total surface area necessary to double the absolute value of the razor's blade exposure (AV accommodates negative exposure razors). First you measure the blade exposure, then you go back in the opposite direction towards the blade. You draw a muzzle plane, and you measure the area of the metal within it. It takes about 2 minutes. Obviously, this is just a 2 dimensional measurement, but when you multiply times the width of the guard/comb, you have a volume measurement.

Image J makes it pretty easy to take area measurements, even of curved objects. Here is an example of the measurement on the Karve SB-D.



Here is an example of how much this measurement can vary. The muzzle area on a Henson is 100x as big as the one on the example razor above it. I'm guessing it's a hell of a lot harder to make a Henson bite than pretty much any other razor. It's got a heck of a muzzle. 😋

This is pretty interesting. I am sure that Henson’s designers, although they probably didn’t use the term “muzzle,” thought precisely about this concept when designing their razor, which is intended to make it easy for beginners to shave with a DE without getting injured.
This may also be the reason why at least some seasoned shavers don’t really care for the Henson.
 
Too early to label my concept "correct", but thanks.
I substituted the string for a sheet of paper, but the principle is the same. I use a sheet of paper between the baseplate (R2 here) and the blade. Then after removing the blade, I use a pencil to draw the surface where the blade has direct contact with the cap and/or the plate, finally measure. My biggest problem is, though, my eyes and my triangle are not precise enough to perform the measurement. In the given example, the baseplate clamping points would be 2 (sides) * 1mm (width) * 4mm (length) + 2 * 2mm * 4mm = 24 mm^2. The reason why I consider this parameter important is that it would enable us to compare OC vs CC without considering the OC teeth (curvature, width, etc.)

View attachment 1280661
View attachment 1280662
PS. I was several minutes too late it seems. But the clamping surface is different from the muzzle area - would need to think a little on that one.
I think I get it. It looks like you're measuring the total blade clamping surface area as an indirect measurement of rigidity. Is that correct?

As a side note, I've never noticed it before, but that Rockwell guard has an absolutely massive guard muzzle area. It's nearly as big as the one on the Henson. In order to increase the blade exposure you would have to use a huge amount of pressure. I'm guessing that's a predictable razor that rarely bites.
 
As a side note, I've never noticed it before, but that Rockwell guard has an absolutely massive guard muzzle area. It's nearly as big as the one on the Henson. In order to increase the blade exposure you would have to use a huge amount of pressure. I'm guessing that's a predictable razor that rarely bites.
Now that I think of it, this solves the mystery of plates 1 and 2 on the Rockwell. People have reported for years that they basically don't shave and it's unclear why they exist. I think the reason for this, is that they offer negative exposure (like many razors) however the guard muzzle area is so massive that it's hard to apply enough pressure to bring the blade into contact with the skin (unlike most negative exposure razors)!

The guard muzzle area on the Karve SBD is 0.069mm (there is a decimal error in the diagram). The guard muzzle area on the Rockwell would be 4mm x .1mm = .4mm.

Put differently, it would take 5.79x more pressure on the Rockwell to make it bite than it would on the Karve SB-D. Now let's consider the case of the Karve OC-D which is the open comb version. Let's also make "muzzle area" into "muzzle volume" by multiplying by the width of the guard of 40mm.

Karve OC-D: .069mm^2 * 20.0mm = 1.38mm^3
Rockwell 6C: .4mm^2 * 40.0mm= 16mm^3

It takes 11.6x more force to increase the Rockwell's exposure by 0.10mm, than it does to increase the Karve OC-D's by 0.10mm. That's wild!

*I decided to arbitrarily change the muzzle area calculation to be the surface area of guard/cap 0.10mm towards the blade. This deals more effectively neutral blade exposure and small positive or negative blade exposures.

@Chan Eil Whiskers, this may be of interest to you given your recent discussion of guard span. It's actually related to guard span, or perhaps more accurately it's the other side of the same coin/question "how easy is it for skin to sneak behind the shave plane and into the blade". Start with Post 136 above that describes the parameter "muzzle area".
 
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