I have recently been having a discussion with a friend as to the merits of using a lens classified as HD.

It has always been my opinion that the quality of the lens optics sent to the camera would be what would determine the image quality recorded, and that it was the camera's electronics/chips that would process the image derived from the lens. Thus, a really good ENG lens would be capable of producing an image of equal/better quality than the standard supplied HD lens that came with my PMW 320.

Following on from this, would it be fair to say that there is no such thing as an HD lens in terms of the image quality aspect, rather than how it has been designed to fit/work with HD cameras?

I would very much welcome the views of those technically knowledgeable members to settle this argument.

Lenses are designed to meet certain criterion. For an SD camera why make a lens that will have a higher resolution and better contrast (MTF) than the camera can reproduce, as this would make the lens more expensive.
So, yes there are SD, HD, 4K, 8K and so on lenses.

In addition there is a very big difference between the way most typical ENG lens focus and the way an EX1/3, PMW-320 or PMW-200 lens focusses. An ENG lens will be a Par Focal lens, a lens that maintains constant focus throughout the zoom range. This is incredibly difficult to design especially with large zoom ranges and is one of the reasons ENG zooms are normally expensive pieces of glass.
The lenses used on the EX1/EX3, PMW-320 are not Par Focal, this makes them much cheaper, the focus shifts and changes as you zoom..... But clever electronics inside the camera and lens compensates for this by adjusting the lenses focus as you zoom so that in practice the lens appears to stay in perfect focus. This is much cheaper than a sophisticated typical ENG type zoom.
Another factor is that as you increase the resolution of a lens, trying to bring everything in to focus on an ever smaller point, you run in to more and more problems with chromatic aberrations. Different wavelengths (and thus colours) of light get bent by different amounts when they pass through a glass lens. As you make the focussed light for one single colour smaller and sharper, the other colours of the spectrum become more dispersed. As a result, generally a softer lens (lower MTF) will exhibit fewer colour aberrations than a sharper lens. To compensate for these aberrations lens manufactures use very exotic types of glass with different refraction indexes to try to cancel out or at least minimise CA (chromatic aberration), but this glass is extremely expensive. The higher the resolution of the lens, the more expensive the glass gets.
With a camera like the EX1/EX3, PMW-320, PMW-200 when you know the exact characteristics of the lens (as they all use essentially the same lens) instead of employing exotic glass, you can program the camera to electronically remove or reduce the appearance of the CA and this happens inside the EX1/EX3, 320 and PMW-200 etc.
Next you must take in to account pixel size. In simple terms to achieve any given resolution the lens has to be able to focus a point of light small enough to hit only one pixel. A typical 2/3" HD camera has much bigger pixels that the pixels on the 1/2" sensor of the PMW-320. As a result a lens that is only just able to achieve HD resolution on a 2/3" camera, will not achieve HD resolution on the PMW-320 with it's smaller pixels. This means that you really need an HD lens designed for the 1/2" sensor size and the corresponding pixel size.
These factors combined mean that the standard kit lens on the EX3, PMW-320 etc appears to perform very well and it takes a much more expensive, designed for 1/2" lens to even match this apparent performance.
Very often it is hard to tell the difference between an SD and HD lens. As well as higher resolution HD lenses tend to have better contrast and this is less easy to visually spot on simple test charts. A better test is for MTF (modulation transfer function) as this measures both resolution and contrast. A higher contrast image will result in a richer and more pleasing picture.

Many thanks Alister for that very detailed explanation.

I am currently using a Canon ENG lens of 2/3rds inch size (mounted via an adaptor) The lens cost as much as the PMW 320 camera did and so should be better quality than the lens supplied with the PMW 320.

Having recorded material using this lens, to the eye, it compares more than favourably with the standard lens. Whether technically that is the case though I don't know.

There are so many variables. If I were to replace this lens with another (and I need one with a long focal length for sports filming), would you recommend going for a cheaper HD lens or going for a high-end ENG variety?

ENG lenses come in both SD and HD varieties. An HD lens will almost certainly be better than an SD lens, but the difference may not be big.

Thanks for your information Alister. You are a real asset to this forum. Nothing can replace true knowledge on a subject.

Thanks, Alister. At last I know why it is that video lenses are so expensive. I also noticed that the 'cheaper' ones suffer from 'breathing'. Having read your explanation, I suppose breathing is a compromise to keep focus over the entire zoom range, but with a slight change of the field of view due to less complicated correction measures, in order to keep the price down. Or am I mistaken?

Even expensive zoom lenses can suffer from breathing. It's usually the wide angle broadcast zooms that tend to have the breathing corrected (although if you look hard enough you can spot it), it's something you have to test when selecting a lens. How important it is really depends on the purpose the lens is designed for.

Modern high end cine zoom lenses now have a lot of effort put into correcting the breathing and they are expensive.

I might get shot down for this, but I like a little bit of breathing. I used some very nice (and very expensive) CineXenarII lenses recently that have absolutely zero breathing and focus pulls looked weird as the focus shifted but nothing else changed. In some cases the focus pull just didn't really work as it just looked odd as the focus shifted. A small amount of breathing helps for focus pulls, in my opinion at least. However when your trying to find focus mid shot, you don't want breathing.

Again, it really comes down to what you are shooting and how you want it to look.
If you are integrating large focus 'pulls' from one person or object to another for emphasis, the breathing may be a nice visual addition to the shot.
However, if your are sitting on a medium wide lockoff shot and your talent is pacing closer to and further from the camera, breathing from the focus adjustment to maintain proper focus on the actor can easily look like s alight zoom, probably the last thing you want in this situation.