Some time ago Wootz posted reference to the study "Experiments on Knife Sharpening" by John Verhoeven. In the appendix 1 there is a sketch of a laser device for edge angle determination. https://www.wickededgeusa.com/wp-content/uploads/2012/10/knifeshexps.pdf)
I was wondering if it will work with the laser line module which I am utilizing for LOC visualization. Using children mechanical construction set I prepared simple optical bench shown below.
(http://img21.rajce.idnes.cz/d2102/11/11771/11771137_37021e568ec44478b9ce7dc74d286378/images/Laser_edge_angle_1_700DPI.jpg?ver=0)
As I expected it works fine for knives with wide bevels which reflect the laser beam well (e.g. the TORMEK/MORA knife shown). The laser line is splitted and reflected on the knife edge. The reflected rays draw two lines on the cross board. From the separation of those lines and the distance of the cross board from the edge the edge angle can be easily calculated.
(http://img21.rajce.idnes.cz/d2102/11/11771/11771137_37021e568ec44478b9ce7dc74d286378/images/Laser_edge_angle_2_700DPI.jpg?ver=0)
Much less satisfying results I have obtained for my quite new Victorinox kitchen knife where the bevel is narrow (less than 1 mm) and does not have mirror quality finish. With some difficulties I was able to determine the angle of the blade tapering. The lines reflected from the tapered sides were heavily blurred. In my thinking the reason may be that Victorinox side grind is not exactly flat but slightly convex. The estimated angle of the approximately "V" grind was circa 3o.
The reflections from the own bevel were very weak, even in a darkened room, and even more indicating an edge angle of 20o instead of 30o.
So those are my provisional results, I still have to work on that.
Jan
May I suggest a circular target area centered at the knife edge. Mark in degrees divided by two - a 45 will deflect the beam 90 deg, etc.
CATRA makes a handheld unit for about $100.
Steve, thank you for your suggestion! :)
This will completely eliminate any calculations by preparation of the semi-circular scale which will directly provide the bevel edge angle in degrees. (By the way the planar scale can also be calibrated in degrees for a fixed distance from the knife edge.)
You are correct, the scale in degrees should be divided by two, because the laser beam is deflected at an angle which is two times greater than the bevel angle.
At this moment I am experimenting and trying to find optimal distances. You can see that the laser module is movable in both directions, longitudinal and transversal while the knife clamp is movable only longitudinally but can be pivoted around vertical axis.
Jan
Jan, where do you get your lasers ?
Kind regards,
Rich
Rich, I use the same 5 mW focusable laser line modules which are offered e.g. by Amazon. I power it from 3V battery without any resistor.
https://www.amazon.com/Focusable-650nm-Module-driver-Plastic/dp/B012V3U3KK/ref=pd_sim_200_2?ie=UTF8&dpID=41mmSR02trL&dpSrc=sims&preST=_AC_UL160_SR160%2C160_&psc=1&refRID=DYR5W9EK8H60TGMZDRQ7https://www.amazon.com/Focusable-650nm-Module-driver-Plastic/dp/B012V3U3KK/ref=pd_sim_200_2?ie=UTF8&dpID=41mmSR02trL&dpSrc=sims&preST=_AC_UL160_SR160%2C160_&psc=1&refRID=DYR5W9EK8H60TGMZDRQ7
Jan
Quote from: stevebot on July 26, 2016, 04:38:59 PM
CATRA makes a handheld unit for about $100.
Yes Steve, you are correct, the CATRA Hobby laser goniometer "HOBBIGONI" costs US$ 136 + shipping + VAT. :)
The Portable Model laser goniometer Mk1 with aluminium body and focussed laser costs US$ 2200 and the Bench Model laser goniometer is even more expensive. ???
I hope my prototype is in the highest category. I'll have to tell my spouse how much money I had saved. ;)
I am wondering if CATRA uses dot laser modules because the image of the beam reflected at the edge has circular symmetry. I use line laser module which delivers line image of a planar bevel. Both approaches have their pros.
Jan
Jan, that's a very nice setup of yours.
I always wanted to do something alike, but never dared, and finally bought CATRA's hobby goniometer.
Yes, CATRA uses dot laser pointer.
And as you noticed with that other knife, not all edges angle can be measured using the laser method. Now and then I get a knife that CATRA goniometer cannot read, this is sort of expected limitation of the method.
If you wish, I could upload scan of the CATRA manual if their description might help you in any way...
BTW your description of Victorinox blurred reflections is how CATRA describes convex reflections in their manual.
Wootz, thanks for your kind response, appreciated! :)
My setup was inspired by John Verhoeven sketch and only than Steve pointed me to Catra products. I will appreciate if you could upload the Catra manual. I would love to learn how they describe reflections from hollow grind bevels which are our daily bread. ;)
Yesterday night I was experimenting with my bench goniometer and can confirm that in full darkness I was able to measure weak reflections from very narrow secondary bevels also. :)
The Catra dot lasers may be better for curved edges while my line laser shape is good for straight edges. I am using 5 mW laser modules while Catra uses 1 or 2 mW modules. For very weak reflections it is good to have reserve in laser beam intensity. To properly adjust and focus the line laser is more difficult.
Jan
Sent you the link to the uploaded manual via PM, Jan.
Wootz, thanks so much for the manual upload. :)
It is very important for me to know that Catra interprets the screen images of the hollow ground bevels in the same way as I did independently in my thoughts. It was a great pleasure for me to read the relevant section. ;)
Jan
Ok, ya'll gotta stop talking like I'm smart or something. What is a "goniometer" ?
Kind regards,
Rich
Rich, goniometer is an (optical) instrument that measures angles. Originally used in surveying. The correct term for my device is "laser reflecting goniometer". :)
Catra uses the term "laser goniometer" as synonym for "laser knife edge protractor".
Jan
Quote from: Jan on July 26, 2016, 04:24:04 PM
Much less satisfying results I have obtained for my quite new Victorinox kitchen knife where the bevel is narrow (less than 1 mm) and does not have mirror quality finish.
Jan, have you tried polishing the edge with the SJ grindstone?
The reason I ask is that when I use my SG grindstone prepared in the fine state, followed by polishing with Tormek compound on the leather honing wheel, what I see with my dissecting microscope are smooth, mirror surfaces separated by scratches. I conclude tentatively that the 1000 grit grindstone and the leather wheel are too far apart in grit. Something in between is needed to get all the scratches out. Either that, or apply something like the SJ grindstone.
Of course, none of this affects the performance of the knives and tools that I use, so it's just an intellectual curiosity for me.
Herman, I did not polish the Victorinox knife until now, because it is still with the factory grind, untouched by Tormek wheels and my primary interest now is to measure the edge angle of the cutting edge.
I have tuned my laser goniometer setup and now I am able to measure the angles of my Victorinox knife in low ambient light also. Sorry for lower photo quality, they were not enough photons available. ;)
(http://img21.rajce.idnes.cz/d2102/11/11771/11771137_37021e568ec44478b9ce7dc74d286378/images/VICTORINOX_2_700DPI.jpg?ver=0)
Image interpretation:
A and A' are reflections from the cutting edge
C and C' are bands of reflections from the sides of the blade. The sides are probably convex and such a grind is called cannel or rolled. The width of the band tells about the curvature of the grind.
X centralised blade position.
Based on my measurements the edge angle of the cutting edge is circa 20 degrees which is not in compliance with the generally declared 30 degrees. :-\
Jan
Herman
Valve grinding compound applied to a leather honing wheel might be the answer. I have found that it is noticeably faster cutting than the Tormek honing compound. It does not leave as smooth a polish. I use it with a separate leather honing wheel. The honing wheels are easily interchanged in only a few seconds. With two Tormeks, adding the fourth step would add almost no time.
Ken
Quote from: Jan on July 29, 2016, 09:14:46 PM
Herman, did not polish the Victorinox knife until now, because it is still with the factory grind, untouched by Tormek wheels and my primary interest now is to measure the edge angle of the cutting edge.
According to "Cook's Country", the television show that recommended the knife to me, the bevel angle is 15°. That is the angle I grind mine at, and I've come to find that show to be a valid source of information.
If the bevel comes polished to a mirror finish from the factory, that might be the only way you could use your device to measure the bevel angle.
Herman, Ken, I agree with all what you say about polishing and honing. :)
Before I started to measure my Victorinox knife I experimented with utility blades because they are flat and have pronounced primary and secondary bevels. Since their surfaces were not of mirror quality I honed them on the leather honing wheel using the standard Tormek honing compound.
To my surprise the laser image after the honing changed in a way I did not expect. The freehand honing process radiused the tip of the cutting edge and smoothed the intersection between the primary and secondary bevels. The originally symmetrical reflection image changed to an asymmetrical one. ;)
This experience prevents me to touch the factory grounded Victorinox knife before I finish my edge angle measurements. My accent is on non-destructive angle estimation.
Experimenting with the homemade laser goniometer is useful but also funny matter. If you have a possibility to build a similar setup at home or in the lab, do not hesitate to do it. Children/grandchildren or students may be involved in this interesting exercise in optical imaging. :D
If there is an interest by other forum members I can prepare some cartoons showing how the laser rays behave when they meet the edge. Let me know.
Jan
Quote from: Herman Trivilino on July 30, 2016, 12:03:06 AM
According to "Cook's Country", the television show that recommended the knife to me, the bevel angle is 15°. That is the angle I grind mine at, and I've come to find that show to be a valid source of information.
I also think the source is reliable. The more I am surprised by the fact that I have estimated the size of the Victorinox knife cutting edge angle's to only circa 20
o (bevel angle 10
o). Even more the knife was moderately used for three months. :-\
Quote from: Herman Trivilino on July 30, 2016, 12:03:06 AM
If the bevel comes polished to a mirror finish from the factory, that might be the only way you could use your device to measure the bevel angle.
My last photo (Reply #13) shows that laser reflections from ground surfaces can be observed also. My explanation is that part of the surface marks produced by the abrasive process have some preference orientation which causes that the laser beam is not scattered randomly. It is clear that the absence of a mirror finish weakens the reflections dramatically. ;)
Jan
Quote from: Ken S on July 29, 2016, 10:59:14 PM
Herman
Valve grinding compound applied to a leather honing wheel might be the answer. I have found that it is noticeably faster cutting than the Tormek honing compound. It does not leave as smooth a polish. I use it with a separate leather honing wheel. The honing wheels are easily interchanged in only a few seconds. With two Tormeks, adding the fourth step would add almost no time.
Ken
Apologies for the semi thread jack....
I don't remember if you posted a comparison of the Tormek compound, the Dursol compound, and the valve grinding compound.
Wondering what you find preference, for what? (example, toothy knives for tomato's, use the valve grinding compound)
Thanks
Excellent question, and worthy of some testing, SADW.
Just off the top of my head, based on limited experience, the Tormek compound does a very good all around job. It leaves a very polished surface. Among the reasons I generally use it is that I have accumulated several tubes of it over the years. :)
Dursol has a stronger ammonia smell. It works as honing compound and seems to work very well as a polisher/cleaner.
Valve grinding compound cuts more aggressively. It works nicely to remove surface oxidation. Like the others, it becomes finer with use. It does not leave as highly polished a surface as the Tormek compound.
I have not tested it for more edge tooth, although that thought has occured to me. I also think it might prove to be a useful extra grit between the SG graded fine and the leather honing wheel with Tormek compound. Switching leather honing wheels is very quick.
I need to do more testing with this; it seems promising to me.
Ken
Quote from: Herman Trivilino on July 30, 2016, 12:03:06 AM
According to "Cook's Country", the television show that recommended the knife to me, the bevel angle is 15°. That is the angle I grind mine at, and I've come to find that show to be a valid source of information.
Herman, I have found Victorinox recommendations for knife blades re-grinding. They recommend an edge angle between 30 and 40 degrees depending on knife usage.
https://assets.victorinox.com/medias/servive-cut-drinding-sharpening-en-nov2012.pdf?context=bWFzdGVyfGN1dHwxNzIyNzd8YXBwbGljYXRpb24vcGRmfGg1MC9oZWUvODc5ODIzOTM1OTAwNi5wZGZ8ZGJmOGVkMGRlODEzMGExYTY3Mjc4Y2U0ZmI3NmIwMzAwZjEwZmM1MzIzOWFmYjhjYzE3NTE0NTU0YTk3ZWRlNw
Jan
Interesting, Jan. Thanks for posting. Note that the Victorinox kitchen knives that I've seen have parallel sides, so there is no concern about edge thickness. In other words, the angle of the blade is 0°.
The knife I have is a large slicing knife, not a boning knife, so the angle of the edge should be 30°. This is consistent with the Cook's Country claim that the bevel angle is 15°.
Yes Herman, it is consistent with the Cook's Country claim that the bevel angle is 15°. :)
I am wondering if it is a general rule for all Victorinox professional and kitchen knives.
I have still not found an explanation for my laser goniometer measurements shown in reply #13 which resulted in an angle of the blade circa 3 degrees and some 19 to 20 degrees for edge angle. The latter seems to me unrealistically small and so I am looking for an alternative explanation of the measured reflection line (e.g. speckle effect). :-\
My Victorinox knife (6.8003.15) is 15 cm (6") long with max. spine thickness 1.5 mm.
Jan
I suggest you use a Tormek and grind an edge angle of 30° (using the Angle Master to measure) on something, say an old knife or even a piece of flat stock, and see what your goniometer reads.
In the image below you can see laser lines reflected on a knife blade ground to an edge angle of 30°. The USB setup was done using the Dutchman/kenjig approach to avoid the effect of the slightly tapered blade.
(http://img21.rajce.idnes.cz/d2102/11/11771/11771137_37021e568ec44478b9ce7dc74d286378/images/Blansko_1_640DPI.jpg?ver=0)
Image interpretation:
A and A' are reflections from the cutting edge. The calculated edge angle is 29.8°.
C and C' reflections from the sides of the blade. The calculated angle of the blade is 3.4°.
X blade projection
This shows that the laser goniometer readings and following angle calculations are OK. :)
Jan
Quote from: Herman Trivilino on August 02, 2016, 10:11:49 PM
Interesting, Jan. Thanks for posting. Note that the Victorinox kitchen knives that I've seen have parallel sides, so there is no concern about edge thickness. In other words, the angle of the blade is 0°.
Herman, my Victorinox knife does not have parallel sides. It is V grind. It is well visible when inserted between the jaws of a slide bar. The angle of the blade is circa 3°.
(http://img21.rajce.idnes.cz/d2102/11/11771/11771137_37021e568ec44478b9ce7dc74d286378/images/VICTORINOX_Blade_angle_640dpi.jpg?ver=0)
Jan
Quote from: Jan on August 04, 2016, 04:18:59 PM
Herman, my Victorinox knife does not have parallel sides.
You're right, I hadn't noticed that before, but so is mine. I have the Victorinox Fibrox Straight Edge Chef's Knife, 8-Inch.
I found this statement on the Victorinox web site:
QuoteHOW DO I RESHARPEN A VICTORINOX KITCHEN KNIFE?
The kind of edge applied to a blade, determines the sharpness and durability of it. When using a sharpening steel, the angle should be between 30-40°.
I've left a message for their support team asking what the edge angle is set to at the factory. Perhaps it's hollow ground.
This topic brings up my problem with using the Anglemaster with knives. With a chisel or plane blade, the flattened back presents a large flat surface for the Anglemaster to easily and dependably register. Knife sharpeners do not have this luxury. Knife bevels are tiny, and the larger part of the knife is rarely parallel.
I have created a work around by substituting a flat target. I made up a flat piece of metal which protrudes 139mm from the universal support in the knife jig. It should be 2.5mm thick to match the ideal jig thickness and have a bevel ground on the underside.
Using a substitute target in this manner greatly increases the efficiency of the Anglemaster with knives. I use it for the occasional knife which will not fit well with the kenjig.
Ken
Victorinox has confirmed that the bevel angle is indeed 15°. Thus the edge angle is 30°.
Quote from: Ken S on August 04, 2016, 07:57:26 PM
This topic brings up my problem with using the Anglemaster with knives. With a chisel or plane blade, the flattened back presents a large flat surface for the Anglemaster to easily and dependably register. Knife sharpeners do not have this luxury. Knife bevels are tiny, and the larger part of the knife is rarely parallel.
Ken
Ken, you are correct! :)
Tiny knife bevel makes the use of the Anglemaster impossible because the length of the bevel is too short for proper angle setter alignment. When the sides of the blade are parallel we can align the angle setter to the knife blade. But when the sides of the blade are not parallel, the blade is V grind, than the angle setter cannot be set to the desired bevel angle. We have to correct the setting with respect to the angle of the blade.
Ignoring the blade V grind results in enlarging the edge angle by the angle of the blade. In the case of the Victorinox knife's the angle of the blade is circa 3° and so ignoring the blade tapering we will ground and edge angle of 33° instead of 30°.
Using the geometrical Dutchman's approach which is incorporated into the Kenjig concept we can easily avoid all Anlgemaster problems with knives. :)
Jan
Jan, I totally agree. (big surprise :) )
I think Dutchman's geometrical approach has definitely simplified knife set up. Actually, the principles can be applied to other sharpening. They really shine with knives.
I find the Anglemaster an essential tool, however, I find it clumsy with knives. I prefer to reserve it for uses where it is effective. Having to factor in three degree deviations because a blade is not parallel seems a poor use for a good tool.
Ken
Quote from: Ken S on August 04, 2016, 07:57:26 PM
This topic brings up my problem with using the Anglemaster with knives. With a chisel or plane blade, the flattened back presents a large flat surface for the Anglemaster to easily and dependably register. Knife sharpeners do not have this luxury. Knife bevels are tiny, and the larger part of the knife is rarely parallel.
This is an issue I recognized when I bought my Tormek in 2002. Since then I have tried to buy only knives that have parallel sides. For kitchen knives, this easy, but not so for pocket knives.
Quote from: Jan on August 04, 2016, 10:30:04 PM
Ignoring the blade V grind results in enlarging the edge angle by the angle of the blade. In the case of the Victorinox knife's the angle of the blade is circa 3° and so ignoring the blade tapering we will ground and edge angle of 33° instead of 30°.
I think you're off by a factor of 2 here, Jan. First of all, my measurements indicate that the blade tapers by 2 mm at a place where the blade width is 50 mm. This is 4% or about 2°. But the error in the bevel angle would be only half that, about 1°.
When I compensate for this I place the knife on my platform jig and measure the angle using the Angle Master. I then remove the knife and again using the Angle Master measure the angle of the platform. The difference between the the two measurements is angle of the blade taper. Half of that is the error in the bevel angle measurement, so I simply subtract that amount.
For example, if I set my platform at an angle of 20°, place my pocket knife on top of the platform, and measure an angle of 24°. The difference is the taper angle, 4°. Half of that is the error in the bevel angle, 2°. If I want to grind a bevel angle of 20° I therefore lower the angle by 2° and set the Angle Master to 18°.
Quote from: Herman Trivilino on August 05, 2016, 01:36:30 AM
Quote from: Jan on August 04, 2016, 10:30:04 PM
Ignoring the blade V grind results in enlarging the edge angle by the angle of the blade. In the case of the Victorinox knife's the angle of the blade is circa 3° and so ignoring the blade tapering we will ground and edge angle of 33° instead of 30°.
I think you're off by a factor of 2 here, Jan. First of all, my measurements indicate that the blade tapers by 2 mm at a place where the blade width is 50 mm. This is 4% or about 2°. But the error in the bevel angle would be only half that, about 1°.
I do not think I am off by a factor of 2 here, Herman. I think we are in compliance. :)
First of all, yours and mine Victorinox knife are different. You have Chef's Knife, 8-Inch long while I have Victorinox carving knife, 6-Inch long with max. blade width some 30 mm. The blade angle of your knife is slightly above 2°, the blade angle of my knife is circa 3°.
Ignoring the blade tapper when using the Knife jig and Anglemaster will result in an increase of the desired bevel angle by the half of the angle of the blade. In my case 15°+ 3°/2 = 16.5°. Thus ignoring the blade tapper we would sharpen an edge angle of 16.5° * 2 = 33°.
To obtain the desired edge angle of 30° we have to set the Anglemaster to (30° - 3°) / 2 = 13.5°.
(http://img21.rajce.idnes.cz/d2102/11/11771/11771137_37021e568ec44478b9ce7dc74d286378/images/Anglemaster_640dpi.jpg?ver=0)
Your thoughts concerning your platform are correct and well documented by the pocket knife example. When you would ignore the blade tapering you would get an edge angle of 2 * 20° + 4° = 44°.
Jan
Quote from: Jan on August 05, 2016, 01:28:33 PM
I do not think I am off by a factor of 2 here, Herman. I think we are in compliance. :)
Yes, you're correct, Jan.
QuoteIgnoring the blade tapper when using the Knife jig and Anglemaster will result in an increase of the desired bevel angle by the half of the angle of the blade.
I thought Ken's point in Reply #30 was that the kenjig is immune to this problem!
Yes Herman, the Kenjig is immune to this problem! In the quoted sentence I am mentioning Tormek Knife jig.
Jan
There is one area where the kenjig has a possible lack of immunity. By design, the kenjig is very simple. Please note that simplicity does not imply any lack of accuracy.
In the design I posted on the forum, the kenjig was set up with a protrusion distance (jig plus blade) of 139mm. Using this protrusion, the distance between the universal support and the grinding wheel is 80mm (using Dutchman's tables) to produce a fifteen degree bevel angle with a grinding wheel diameter of 250mm.
This works well until the wheel wears to somewhere less than 240mm. At 240mm, the distance groove needs to be made one mm longer to 81mm. This is easily done with a small saw. However, the kenjig will no longer be accurate with a new 250mm diameter wheel.
Rich Colvin suggested a very simple, elegant solution for this problem. Rich's idea is to make a set of kenjigs, with distance grooves calibrated for different wheel diameters. Cutting out kenjig blanks is quick and easy. The kenjig is essentially a rectangle of plywood or cardboard approximately 150mm x 30mm (6" x 1 1/4"). Cutting half a dozen requires almost no more time than making one. Cost is minimal. Make a pencil mark 139mm on one side. Cut a groove the thickness of the universal support (12mm) to the length shown in Dutchman's tables)
In Rich's version, make kenjigs calibrated for each 10mm of diameter wear. Mark the jigs with the diameter. Keep out the size which matches your grinding wheel. Put the rest in a drawer. When your wheel wears by 10mm, switch kenjigs.
For those of you like Wootz (and me) who go back and forth between wheels of different diameters, just keep the wheel and jig together.
Thanks for the good idea, Rich. It is a few minutes and a dollar or two well spent. It eliminates the weak spot in the kenjig.
Ken
Quote from: Jan on August 05, 2016, 07:34:14 PM
Yes Herman, the Kenjig is immune to this problem! In the quoted sentence I am mentioning Tormek Knife jig.
Jan
So you are! Sorry about that.
Herman, you are welcome. :) The Kenjig concept is really immune to the tapering problem provided the blade is properly mounted into the Knife jig. In the past I faced some difficulties with strongly tapered blade of my older Solingen boning knife because the grip of the Knife jig was not sufficient.
Jan
Is the tapering really a problem? I know forged knives are tapered, but aren't most stamped knives tapered as well, in the manufacturing/grinding process?
What does one need to determine the taper? Does it come with a Tormek? (thinking of newbies here)
What about professionals, such as Stevebot? (time to measure if doing a bunch of knives, etc)
SADW, you can measure the angle of the blade by suitable angle protractor tool and correct the angle set by the Anglemaster. This can take some 30 seconds. :)
When you ignore the tapper you will sharpen an edge angle which is by the angle of the blade larger than the desired edge angle. :-\
Jan
I have redesigned the prototype of my laser goniometer. I have used hand adjustable clamp for smooth knife alignment and calibrated the scale in bevel angle degrees. The separation between the thick lines of the scale is 5° and between the thin lines 1° of bevel angle. :)
I have tested Steve suggestion to prepare a semi-circular scale but kept the planar one because its reading is easier and more sensitive. ;)
Jan
For a knife with optical bevel finish the angle measurement is easy and accurate to +/- 0.5°. For the shown Mora Knife - Tormek Edition the bevel angle is circa 11.5° for both sides. For me it is surprisingly sharp outdoor knife. ;)
Jan
My oldest granddaughter, who is 14, was tasked to prepare for a physics lesson a short essay on an arbitrary topic from optics. Because she saw my laser goniometer for measuring bevel angles she asked me to lend it to her.
So I still had to make a sketch of how there the laser beam runs. The sketch shows the situation for a 20 degrees bevel angle alpha.
Sorry for the labels in Czech. :-\
Jan
P.S.: The sketch assumes a flat ground bevel with mirror finish. For hollow grind we get a bunch of reflections where the bevel angle corresponds to the onset i.e. the inner most line of the bunch. For a husky convex grind it is vice versa.
Jan,
Great project to share with your granddaughter. I expect to learn good things about her work as she completes her education. She is off to a good start with a fine tutor.
I had a little training in fiber optics. (I worked on T1 and T3 data circuits.) What amazes me is how we can simultaneously transmit multiple light frequencies on a single path.
Keep up the good tutoring.
Ken
Ken, thank you for your kind words, appreciated. :)
Jan