What type of improvement are you talking about? So some company has come up with a lens with more elements but what is the purpose of these extra elements or group? Your the expert. Let us know what is going to be the improvement.
Generally speaking, the more surfaces in a lens, the better the performance potential, given a good design to start with. Of course, on the other hand, you can have a crappy design with 20 surfaces that doesn't perform as well as a great design with only 6 surfaces. Over-engineering is always something that needs to be kept in mind as a pitfall.
This "other" lens (as I understand it) has an optimization that favours flatter, hence cheaper screens. Geometric distortion is reduced, but not to such an extent that it adversely affects curved screen performance either (if that's the way the user wants to go... more
money!). What this reduction in geometric distortion means is that grid squares are more evenly sized right across the screen. Traditional 4-element designs tend to have side-to-center distortions upwards of 5%. The shorter the TR the bigger the distortion. In this, the simpler 4-element designs are similar in distortion metrics to prism lenses. Both of these types of designs go back to the 1920s when, during design, every ray had to be traced through them by hand (and log tables). Today, using modern software, you can trace 10,000 rays a second, automatically, so you can be a little bit more adventurous with a design, making it more complex.
Simpler designs are more suited to larger TRs (3.0+), where they perform OK. Most (not all though) commercial cinemas have these long TRs, so the limitations of the simpler designs aren't apparent until you use them with the short TRs typical of Home Theater.
Additionally, the more surfaces you have available for curving the more you can "condition" or "massage" the beam as it passes through the lens. Take a simple convex lens. You can use it as a projector lens - it inverts and focuses at a distant point - but you'll have astigmatism, color aberration, possible coma and so on. So you add elements (extra surfaces) that get rid of these aberrations. If you look at a projector lens it contains many such elements, each one gradually adding its own little piece of quality to the overall image, making sure the beam isn't too "bent" in any one place along the light path.
Now consider an anamorphic design. If designed as an add-on adapter, especially in Home Theater usage, the diameters of the lenses have to be huge. This makes them very heavy and very expensive to fabricate to exacting standards. So you can't use too many or else you might end up with a great image at a prohibitive cost to the customer. There has to be a compromise position somewhere. Add some surfaces, but not so many that the design prices itself out of the market.
Benefits of added surfaces are that you can tweak the image to be better over a wider range of applications.
For example, a 4-element design that has only 4 outer (glass-air) surfaces (two per individual element in the lens) might have a couple of them flat (plano) to aid in manufacture and assembly. But this leaves only two surfaces that can be curved, necesitating extra-steep curvature on those remaining available surfaces to achieve the desired anamorphic effect.
By contrast, if all four
surfaces were curved then the light wouldn't have to be bent as much on each curved surface as it passes through the lens. Having more curved surfaces allows each of them to "share the load" of conditioning the beam. Reducing
the number of curved surfaces in a lens (consequently "crowding" the light-bending potential of the lens into less surfaces) makes it more susceptible to aberrations at the margins. It requires more exact placement of the lens in the light path, down to a millimetre or so. Outside these boundaries, lens performance can suffer at the edges.
Lenses with reduced numbers of curved surfaces tend to work well only within a more limited throw range, and throw ratio range. For example, they might be superbly sharp and contrasty at TRs of 2 and up, at throws of 4 to 8 metres, but outside that envelope they tend to lose performance edge. To work outside the envelope you require a new design, optimized for that new envelope.
Now, a design with more surfaces can still use a couple of plano surfaces for ease of manufacture, but can also
have a significant number of curved surfaces to do the optical work, simply because there is a greater degree of freedom in the design, due to the extra surfaces. With more surfaces, the designer (and the customer) can have his cake and eat it too.
For example, a 6-element design with two plano surfaces still has 4 surfaces that can be curved. It can have the manufacturing flexibility of plano surfaces, and the optical flexibility of the remaining surfaces being eligible to be curved.
Other advantages of lenses with lots of curved surfaces could be in areas such as ghost imaging. "Ghost" images are the result of reflective interactions of the anamorphic adapter both with the projector lens and with its own internal elements. AR coating is important. There are cheap single AR coatings and more expnsive "multi-coatings". These serve to reduce internal reflection and increase transmission, paying off in brightness and contrast performance. Occasionally, despite AR coating, reflections will conspire to present a focused (or somewhat focused) "ghost" image right onto the screen, particularly during end credits and dark scenes with bright highlights, where contrast is usally at its highest (white characters, fires, flames, torchlights, city lights etc. on a black background). Intuitively you might think that the more surfaces in the lens the more potential for stray reflections, but this is not necessarilty the case. If the designer is careful, by using more curved surfaces he can reduce
the chance of ghost images by interfering with the reflection potential inside the lens, presenting too many surfaces for a patent image to escape and form on the screen, making the chances of ghosts actually less
than with simpler designs.
In summary, it's simple: the more surfaces you have, given a decent design, the more you can do good things with the light that passes through them.
P.S. This other news lens is not called "Horizon" and bears only a faint similarity to that design.