Prior to the introduction of the CD player, the red He-Ne laser was by far the most common source of inexpensive coherent light on the planet. The following are some typical physical specifications for a variety of red (632.8 nm) He-Ne tubes (all are single transverse mode – TEM00):
Output Tube Voltage Tube Tube Size
Power Operate/Start Current Diam/Length
------------ --------------- ------------ -------------
0.3-0.5 mW 0.8-1.0/6 kV 3.0-4.0 mA 19/135 mm
0.5-1 mW .9-1.0/7 kV 3.2-4.5 mA 25/150 mm
1-2 mW 1.0-1.4/8 kV 4.0-5.0 mA 30/200 mm
2-3 mW 1.1-1.7/8 kV 4.0-6.5 mA 30/260 mm
3-5 mW 1.7-2.4/10 kV 4.5-6.5 mA 37/350 mm
5-10 mW 2.4-3.1/10 kV 6.5-7.0 mA 37/440 mm
10-15 mW 3.0-3.5/10 kV 6.5-7.0 mA 37/460 mm
15-25 mW 3.3-4.0/10 kV 6.5-7.0 mA 37/600 mm
25-35 mW 4.0-5.2/12 kV 7.0-8.0 mA 42/900 mm
- Power Output is the minimum beam power after a specified warm up period over the spec’d life of the tube.
- Tube Operating Voltage is the voltage across the bare tube at the nominal operating current.
- Tube Start Voltage is the minimum voltage across the bare tube required to guarantee starting.
- Tube Size is generally the maximum diameter of the tube envelope and the total length from the outer surfaces of the mirrors.
Tubes like this are generally available in both random and linearly polarized versions which are otherwise similar with respect to the above characteristics (for red tubes at least, more below).
At least one other basic specification may be critical to your application: Which end of the tube the beam exits! There is no real preference from a manufacturing point of view for red He-Ne lasers. (For low gain “other-colour” He-Ne laser tubes, it turns out that anode output results is slightly higher gain and thus slightly higher output for the typical hemispherical cavity because it better utilizes the mode volume.) However, this little detail may matter a great deal if you are attempting to retrofit an existing barcode scanner or other piece of equipment where the tube clips into a holder or where wiring is short, tight, or must be in a fixed location. For example, virtually all cylindrical laser heads require that the beam exits from the cathode-end of the tube. It is possible that you will be able to find two versions of many models of He-Ne tubes if you go directly to the manufacturer and dig deep enough. However, this sort of information may not be stated where you are buying surplus or from a private individual, so you may need to ask.
The examples above (as well as all of the other specifications in this and the following sections) are catalog ratings, NOT what might appear on the CDRH safety sticker (which is typically much higher). See the section: About Laser Power Ratings for info on listed, measured, and CDRH power ratings.
Note how some of the power levels vary widely with respect to tube dimensions, voltage, and current. Generally, higher power implies a longer tube, higher operating/start voltages, and higher operating current – but there are some exceptions. In addition, you will find that physically similar tubes may actually have quite varied power output. This is particularly evident in the manufacturers’ listings. (See the chapter: A HREF=”laserhcl.htm#hcltoc”>Commercial Unstabilized HeNe Lasers.)
These specifications are generally for minimum power over the guaranteed life of the tube. New tubes and individual sample tubes after thousands of hours may be much higher – 1.5X is common and a “hot” sample may hit 2X or more. My guess is that for tubes with identical specifications in terms of physical size, voltage, and current, the differences in power output are due to sample-to-sample variations. Thus, like computer chips, they are selected after manufacture based on actual performance and the higher power tubes are priced accordingly! This isn’t surprising when considering the low efficiency at which these operate – extremely slight variations in mirror reflectivity and trace contaminants in the gas fill can have a dramatic impact on power output.
I have a batch of apparently identical 2 mW Aerotech tubes that vary in power output by a factor of over 1.5 to 1 (2.6 to 1.7 mW printed by hand on the tubes indicating measured power levels at the time of manufacture).
And, power output also changes with use (and mostly in the days of soft-sealed tubes, just with age sitting on the shelf):
(From: Steve Roberts.)
“I have a neat curve from an old Aerotech catalogue of He-Ne laser power versus life. The tubes are overfilled at first, so power is low. They then peak at a power much higher than rated power, followed by a long period of constant power, and then they SLOWLY die. It’s not uncommon for a new He-Ne tube to be in excess of 15% greater than rated power.”
And the answer to your burning question is: No, you cannot get a 3 mW tube to output 30 mW – even instantaneously – by driving it 10 times as hard!
I have measured the operating voltage and determined the optimum current (by maximizing beam intensity) for the following specific samples – all red (632.8 nm) tubes from various manufacturers. (The starting voltages were estimated.):
Output Tube Voltage Tube Supply Voltage Tube Size
Power Operate/Start Current (75K ballast) Diam/Length
---------- --------------- ------------ ---------------- -------------
.8 mW .9/5 kV 3.2 mA 1.1 kV 19/135 mm
1.0 mW 1.1/7 kV 3.5 mA 1.4 kV 25/150 mm
1.0 mW 1.1/7 kV 3.2 mA 1.4 kV 25/240 mm
2.0 mW 1.2/8 kV 4.0 mA 1.5 kV 30/185 mm
3.0 mW 1.6/8 kV 4.5 mA 1.9 kV 30/235 mm
5.0 mW 1.7/10 kV 6.0 mA 2.2 kV 37/350 mm
12.0 mW 2.5/10 kV 6.0 mA 2.9 kV 37/475 mm
Melles Griot, Uniphase, Siemens, PMS, Aerotech, and other HeNe tubes all show similar values.
The wide variation in physical dimensions also means that when looking at descriptions of He-Ne lasers from surplus outfits or the like, the dimensions can only be used to determine an upper (and possibly lower) bound for the possible output power but not to determine the exact output power (even assuming the tube is in like-new condition). Advertisements often include the rating on the CDRH safety sticker (or say ‘max’ in fine print). This is an upper bound for the laser class (e.g., Class IIIa), not what the particular laser produces or is even capable of producing. It may be much lower. For example, that Class IIIa laser showing 5 mW on the sticker, may actually only be good for 1 mW under any conditions! The power output of a He-Ne laser tube is essentially constant and cannot be changed significantly by using a different power supply or by any other means. See the section: Buyer Beware for Laser Purchases.
Also see the section: Locating Laser Specifications.
In addition to power output, power requirements, and physical dimensions, key performance specifications for He-Ne lasers also include:
- Beam Diameter at the laser’s output aperture and beam profile (Gaussian TEM00 for most small He-Ne laser tubes).
- Beam Divergence (probably far field ignoring beam waist). Note that this may not always be the same as the expected value from the diffraction limit based on beam/bore diameter as it also depends on the combination of the HR and OC mirror (inside) curvature and the shape of the exterior surface of the OC.
- Mode Spacing (frequency) between the multiple longitudinal modes that are active simultaneously in all but single mode frequency stabilized lasers.
With manufacturers like Aerotech, Melles Griot, and Siemens, a certain amount of information can be determined from the model number. For example, here is how to decipher most of those from Melles Griot (e.g., 05-LHP-121-278):
- All Melles Griot He-Ne laser tubes and power supplies start with 05. Matched systems may start with 25 (e.g., laser head and lab-style power supply).
- The first letter will be an L for all He-Ne laser tubes and heads except for perpendicular window terminated tubes (in which case it will be W – this is inconsistent with the rest of their numbering but who am I to complain!), and some of their self contained lasers where it will be S.
- The second letter will be one of: H = red (632.8 nm), G = green (543.5 nm), Y = yellow (594.1 nm), O = orange (611.9 nm), or I = infra-red (1,523 or 3,391 nm). A couple of self contained red lasers use R for red but for most, I guess they got stuck using H (presumably denoting He-Ne) before ‘other colour’ He-Ne lasers were part of their product line. And, their stabilized He-Ne lasers use a T here. Confused yet? 🙂
- The third letter will be one of: R = Randomly polarized, L = linearly polarized, or B = Brewster window at one or both ends.
- The following three digit number determines the physical characteristics of the laser tube to some extent. Unfortunately, there may be no direct mathematical relationship of this number to anything useful. As will be seen below, for some models, it (or some of its digits) sort of correlates with output power or length but for others, they might as well be totally random! However, it does appear as though an identical set of numbers among different colour tubes (see below) will denote similar physical size tubes at least.
- If there are additional numbers, they relate to a special variation on the basic design done for a particular customer. For example, this might be a different curvature on the outer surface of the output mirror to provide a non-standard divergence to eliminate the need for an additional lens in a barcode scanner. Or, an external window for protection from the elements or to deliberately reduce output power. Go figure. 🙂 It may also just denote a specific configuration like -249 (meaning 115 VAC operation, kind of arbitrary, huh?) or -55 (meaning 5.5 mA). In these cases, the user may be able to modify the settings (flip a switch or twiddle a pot) but the warranty may then be void.
The vast majority of Melles Griot lasers you are likely to come across will follow this numbering scheme though there are some exceptions, especially for custom assemblies. (Some surplus places drop the leading ’05-‘ when reselling Melles Griot laser tubes or heads so an 05-LHP-120 would become simply an LHP-120.)
For other manufacturers like Spectra-Physics, the model numbers are totally arbitrary!
Although a red beam is what everyone thinks of when a He-Ne laser is discussed, He-Ne tubes producing green, yellow, and orange beams, as well as several infra-red (IR) wavelengths, are also manufactured. However, they are not found as often on the surplus market because they are not nearly as common as the red variety. In terms of the number of He-Ne lasers manufactured, red is far and away the most popular, with all the others combined accounting for only 1 to 2 percent of the total production. In order of decreasing popularity, it’s probably: red, green, yellow, infra-red (all IR wavelengths), orange. Non-red tubes are also more expensive when new since for a given power level, they must be larger (and thus have higher voltage and current ratings) due to their lower efficiency (the spectral lines being amplified are much weaker than the one at 632.8 nm). Operating current for non-red He-Ne tubes is also more critical than for the common red variety so setting these up with an adjustable power supply or adjusting the ballast resistance for maximum output is recommended.
Maximum available power output is also lower – rarely over 2 mW (and even those tubes are quite large (see the tables below). However, since the eye is more sensitive to the green wavelength (543.5 nm) compared to the red (632.8 nm) by more than a factor of 4, a lower power tube may be more than adequate for many applications. Yellow (594.1 nm) and orange (611.9 nm) He-Ne lasers appear more visible by factors of about 3 and 2 respectively compared to red beams of similar power.
Infrared-emitting He-Ne lasers exist as well. In addition to scientific uses, these were used for testing in the Telecom industry before sufficiently high quality diode lasers became available.Yes, you can have a He-Ne tube and it will light up inside (typical neon glow), but if there is no output beam (at least you cannot see one), you could have been sold an infrared He-Ne tube. However, by far the most likely explanation for no visible output beam is that the mirrors are misaligned or the tube is defective in some other way. Unfortunately, silicon photodiodes or the silicon sensors in CCD or CMOS cameras do not respond to any of the He-Ne IR wavelengths, so the only means of determining if there is an IR beam are to use a GaAs photodiode, IR detector card, or thermal laser power meter. IR He-Ne tubes are unusual enough that it is very unlikely you will ever run into one. However, they may turn up on the surplus market especially if the seller doesn’t test the tubes and thus realize that these behave differently – they are physically similar to red (or other colour) He-Ne tubes except for the reflectivity of the mirrors as a function of wavelength. (There may be some other differences needed to optimize each color like the He:Ne ratio, isotope purity, and gas fill pressure, but the design of the mirrors will be the most significant factor and the one that will be most obvious with a bare eyeball, though the color of the discharge may be more pink for green He-Ne tubes and more orange and brighter for IR He-Ne tubes compared to red ones, more below.) Even if the model number does not identify the tube as green, yellow, orange, red, or infra-red, this difference should be detectable by comparing the appearance of its mirrors (when viewed down the bore of an UNPOWERED tube) with those of a normal (known to be red) He-Ne tube. (Of course, your tube could also fail to lase due to misaligned or damaged mirrors or some other reason.
As noted above, the desired wavelength is selected and the unwanted wavelengths are suppressed mostly by controlling the reflectivity functions of the mirrors. For example, the gains of the green and yellow lines (yellow may be stronger) are both much much lower than red and separated from each other by about 50 nm (543.5 nm versus 594.1 nm). To kill the yellow line in a green laser, the mirrors are designed to reflect green but pass yellow. I have tested the mirrors salvaged from a Melles Griot 05-LGP-170 green He-Ne tube (not mine, from “Dr. Destroyer of Lasers”). The HR (High Reflector) mirror has very nearly 100% reflectivity for green but less than 25% for yellow. The OC (Output Coupler) also has a low enough reflectivity for yellow (about 98%) such that it alone would prevent yellow from lasing. The reflectivities for orange, red, and IR, are even lower so they are also suppressed despite their much higher gain, especially for the normal red (632.8 nm) and even stronger mid-IR (3,391 nm) line.
However, to manufacture a tube with optimum and stable output power, it isn’t sufficient to just kill lasing for unwanted lines. The resonator must be designed to minimize their contribution to stimulated emission – thus the very low reflectivity of the HR for anything but the desired green wavelength. Otherwise, even though sustained oscillation wouldn’t be possible, unwanted colour photons would still be bouncing back and forth multiple times stealing power from the desired colour. The output would also be erratic as the length of the tube changed during warm up (due to thermal expansion) and this affected the longitudinal mode structure of the competing lines relative to each other. Some larger He-Ne lasers have magnets along the length of the tube to further suppress (mostly) the particularly strong mid-IR line at 3,391 nm. (See the section: Magnets in High Power or Precision HeNe Laser Heads.)
In addition, you can’t just take a tube designed for a red laser, replace the mirrors, and expect to get something that will work well – if at all – for other wavelengths. For one thing, the bore size and mirror curvature for maximum power while maintaining TEM00 operation are affected by wavelength.
Furthermore, for these other colour He-Ne lasers which depend on energy level transitions which have much lower gain than red – especially the yellow and green ones – the gas fill pressure, He:Ne ratio, and isotopic composition and purity of the helium and neon, will be carefully optimized and will be different than for normal red tubes.
Needless to say, the recipes for each type and size laser will be closely guarded trade secrets and only a very few companies have mastered the art of other colour He-Ne lasers, especially for high power (in a relative sort of way) in yellow and green. I am only aware of four companies that currently manufacture their own tubes: Melles Griot, Research Electro-Optics, Uniphase, and LASOS, with the last two having very few models to choose from. Others (like Coherent) simply resell lasers under their own name.
And, the answer to that other burning question should now be obvious: No, you can’t convert an ordinary red internal mirror He-Ne tube to generate some other colour light as it’s (almost) all done with mirrors and they are an integral part of the tube. 🙂 Therefore, your options are severely limited. As in: There are none. (However, going the other way, at least as a fun experiment, may be possible. For a laser with external mirrors, a mirror swap may be possible (though the cavity length may be insufficient to resonate with the reduced gain of other-colour spectral lines once all loses taken into consideration). But realistically, this option doesn’t even exist where the mirrors are sealed into the tube.
There are also a few He-Ne lasers that can output more than one of the possible colors simultaneously (e.g., red+orange, orange+yellow) or selectively by turning knob (which adjusts the angle of a Littrow or other similar dispersion prism) inside the laser cavity using a Brewster window He-Ne tube). But such lasers are not common and are definitely very expensive. So, you won’t likely see one for sale at your local hamfest – if ever! One manufacturer of such lasers is Research Electro-Optics (REO). See the section: Research Electro-Optics’s Tunable HeNe Lasers.
However, occasionally a He-Ne tube turns up that is ‘defective’ due to incorrect mirror reflectivities or excessive gain or magic 🙂 and actually outputs an adjacent colour in addition to what it was designed to produce. I have such a tube that generates about 3 mW of yellow (594.1 nm) and a fraction of a mW of orange (611.9 nm) but isn’t very stable – power fluctuates greatly as it warms up. Another one even produces the other orange line at 611.9 nm, and it’s fairly stable. But, finding magic ‘defective’ tubes such as these by accident is extremely unlikely though I’ve heard of the 640.1 nm (deep red) line showing up on some supposedly good normal red (632.8 nm) He-Ne tubes.
As a side note: It is strange to see the more or less normal red-orange glow in a green He-Ne laser tube but have a green beam emerging. A diffraction grating or prism really shows all the lines that are in the glow discharge. Red through orange, yellow and green, even several blue lines (though they are from the helium and can’t lase under any circumstances)!! The IR lines are present as well – you just cannot see them.
Actually, the colour of the discharge may be subtly different for non-red He-Ne tubes due to modified gas fill and pressure. For example, the discharge of green He-Ne tubes may appear more pink compared to red tubes) which are more orange), mostly due to lower fill pressure. The fill mix and pressure on green He-Ne tubes is a tricky compromise among several objectives that conflict to some extent including lifetime, stability (3.39µm competition), and optical noise. This balancing act and the lower fill pressure are why green He-Ne tubes don’t last as long as reds. Have I totally confused you, colour-wise? 🙂
The expected life of ‘other colour’ He-Ne tubes is generally much shorter than for normal red tubes. This is something that isn’t widely advertised for obvious reasons. Whereas red He-Ne tubes are overfilled initially (which reduces power output) and they actually improve with use to some extent as gas pressure goes down, this luxury isn’t available with the low gain wavelengths – especially green – everything needs to be optimal for decent performance.
The discharge in IR He-Ne tubes may be more orange and brighter due to a higher fill pressure. Again, this is due to the need to optimize parameters for the specific wavelength.
Although most He-Ne lasers are the common red (632.8 nm) variety (whose beam actually appears orange-red), you may come across unmarked He-Ne tubes and just have to know what colour output the produce without being near a He-Ne laser power supply.
Since the mirrors used in all He-Ne lasers are dielectric – functioning as a result of interference – they have high reflectivity only around the laser wavelength and actually transmit light quite well as the wavelength moves away from this peak. By transmitted light, the appearance will tend to be a colour which is the complement of the laser’s output – e.g., cyan or blue-green for a red tube, pink or magenta for a green tube, blue or violet for a yellow tube. Of course, except for the IR variety, if the tube is functional, the difference will be immediately visible when it is powered up!
The actual appearance may also depend on the particular manufacturer and model as well as the length/power output of the laser (which affects the required reflectivity of the OC), as well as the revision number of your eyeballs. 🙂 So, there could be considerable variation in actual perceived colour. Except for the blue-green/magenta combination which pretty much guarantees a green output He-Ne tube, more subtle differences in colour may not indicate anything beyond manufacturing tolerances.
The chart above in conjunction with will help to identify your unmarked He-Ne tube. (For accurate rendition of the graphic, your display should be set up for 24 bit colour and your monitor should be adjusted for proper colour balance.)
HeNe Laser High Reflector (HR) Output Coupler (OC)
Color Wavelength Reflection Transmission Reflection Transmission
Red 632.8 nm Gold/Copper Blue Gold/Yellow Blue/Green
Orange 611.9 nm Whitish-Gold Blue Metallic Green Magenta
Yellow 594.1 nm Whitish-Gold Blue Metallic Green Magenta
Green 543.5 nm Metallic Blue Red/Orange Metallic Green Magenta
Broadband (ROY) Whitish-Gold Blue
IR 1,523 nm Light Green Light Magenta Light Green Light Magenta
IR 3,391 nm Gold (Metal) Coated Neutral Clear
The entry labelled ‘Broadband’ relates to the HR mirror in some unusual multiple colour (combinations of red and/or orange and/or yellow) internal mirror tubes as well as those with an internal HR and Brewster window for external OC optics. And, the yellow and orange tubes may actually use broad band HRs. The OCs would then be selected for the desired wavelength(s) and may also have a broad band coating.
For low gain tubes, they play games with the coatings. I guess it isn’t possible to just make a highly selective coating for one wavelength that’s narrow enough to have low reflectivity at the nearby lines so they won’t lase. So, one mirror will be designed to fall off rapidly on one side of the design wavelength, the other mirror on the other side. That’s one reason front and back mirrors on yellow and green tubes in particular have very different appearances.
As noted, depending on laser tube length/output power, manufacturer, and model, the appearance of the mirrors can actually vary quite a bit but this should be a starting point at least. For example, I have a Melles Griot 05-LHR-170 He-Ne laser tube that should be 594.1 nm (yellow) but actually outputs some 604.6 nm (orange) as well. It’s mirror colours for the HR and OC are almost exactly opposite of those I have shown for the yellow and orange tubes! I don’t know whether this was intentional or part of the problem And, while from this limited sample, it looks like the OCs for orange, yellow, and green He-Ne lasers appear similar, I doubt that they really are in the area that counts – reflectivity/transmission at the relevant wavelengths.
Here are some comments on the difficulty of obtaining useful visible output from He-Ne lasers at wavelengths other than our friendly red (632.8 nm):
(From: Steve Roberts.)
You do need a isotope change in the gases for green, and a He:Ne ratio change for the other orange and yellow lines. In addition, the mirrors to go to another line will have a much lower output transmission. The only possible lines you’ll get on a large frame He-Ne laser will be the 611.9 nm orange and 594.1 nm yellow. The green requires external mirror tubes in excess of a meter and a half long and a Littrow prism to overcome the Brewster losses and suppress the IR.
The original work on green was done by Rigden and Wright. The short tubes have lower losses because they have no Brewsters and thus can concentrate on tuning the coatings to 99.9999% reflectivity and maximum IR transmission. There is one tunable low power unit on the market that does 6 lines or so, but only 1 line at a time, and the $6,000 cost is kind of prohibitive for a few milliwatts of red and fractional milliwatt powers on the other lines. But, it will do green and has the coatings on the back side of the prism to kill the losses.
Also look for papers by Erkins and Lee. They are the fellows who did the green and yellow for Melles Griot and they published one with the energy states as part of a poster session at some conference. Melles Griot used to hand it out, that’s how I had a copy, recently thrown away.
Even large He-Ne lasers such as the SP-125 (rated at 50mW of red) will only do about 20mW of yellow, with a 35mW SP-127 you’re probably only looking at 3 to 5mW of yellow. And, for much less then the cost of the custom optics to do a conversion, you can get two or three 4 to 5 mW yellow heads from Melles Griot. I know for a fact that a SP-127 only does about 3mW of 611.9 with a external prism and a remote cavity mirror, when it does 32mW of 632.8nm.
So in the end, unless you have a research use for a special line, it’s cheaper to dig up a head already made for the line you seek, unless you have your own optics coating lab that can fabricate state-of-the-art mirrors.
I have some experience in this, as I spent months looking for a source of the optics below $3,000.
I do have a short (265 mm) one-Brewster He-Ne tube (Melles Griot 05-LGB-580) with its internal HR optimized for green that operates happily with a matching external green HR mirror (resulting in a nice amount of circulating power) but probably not with anything having much lower reflectivity to get a useful output beam. In fact, I could not get reliable operation even with the HR from a dead green He-Ne laser tube as the Brewster window would not remain clean enough for the time required to align the mirror.
I would expect an SP-127 to do more than 3 to 5 mW of yellow, my guess would be 10 to 15 mW with optimized mirrors but no tuning prism. If I can dig up appropriate mirrors, I intend to try modifying an SP-127 to make it tunable and/or do yellow or green. 🙂
(From: Lynn Strickland (firstname.lastname@example.org).)
You can find 640.1 nm in a lot of red He-Ne lasers. I have a paper on it somewhere, and cavity design can influence it to a large extent. If you have a decent quality grating, it’s pretty easy to pick up. 629 nm is the one you don’t see too much.
I’m no physicist, but the lower gain lines can lase simultaneously with the higher gain lines, no problem, as long as there is sufficient gain available in the plasma. It’s really pretty easy to get a He-Ne laser to output on all lines at the same time (if you have the right mirrors). The trick is optimizing the bore-to-mode ratio, gas pressure, and isotope mixture to get good TEM00 power. Usually the all-lines He-Ne lasers are multi (transverse) mode. I don’t know of anyone who makes them commercially though – at least not intentionally.
Generally, when a gas laser is superradiant, there is a limit to its maximum power output (with exceptions for nitrogen and copper vapour laser, although nitrogen’s upper limit is defined by the maximum cavity length into which you can generate a 300ns or less excitation pulse.
The 3.39µm He-Ne laser’s gain is still, like all other He-Ne lines limited by a wall collision to return the excited atoms to the ground state. 3.39 µm He-Ne lasers have larger bores then normal He-Ne lasers, and the bores are acid etched to fog them and create more surface area, but still the most power I’ve ever seen published was 40 mW – nothing to write home about. The massive SP-125, the largest commercial He-Ne laser, could be ordered with a special tube and special optics for 3.39µm, and it still only did about 1/3rd the visible power. Superradiance and ultimate power are not tied together.
The reason 3.39µm got all the writeups it did was that it started on the same upper state as all the other He-Ne lines, was easily noticed when it sapped power from the visible line, and was, at the time, a exotic wavelength for which there were few other sources.