Helicoid vs. Internal Floating Group
I came into a random online question asking what would be the difference between focusing using a helicoid and focusing using the focus ring on the lens.
Well, for old vintage lenses whose focus ring moves all the elements forward and backward, adapting them onto a helicoid to achieve focus apparently will not cause any difference in resulting image. There is even an equation for that:
S = (f^2 + f D) / D
In which S is focus distance, f is focal length, and D is chassis displacement distance. For those old lenses, focus ring is moving that D, and helicoid is also moving that D.
But this will not apply for modern ultra fast lenses, zoom lenses, and telephoto lenses. For ultra fast lenses, their elements combined are too big and too heavy to be driven by motors; for zoom lenses, the focus marking will lose accuracy due to the displacement distance varies at different focal length; for telephoto lenses, the displacement distance will become too long that it quickly goes out of hand (literally). So most modern lenses use floating elements to focus, one or two decoupled groups that moves in their own.
For example, the Sigma 50mm f/1.4 ART uses 2 big groups of elements (I don’t know why I first think of this lens but I did):
At close focus, group 2 (“G2” in the image) moves forward while G1 remains still, G2B also moves slightly to G2A. In this way, only some relatively small elements need to be moved to achieve focus.
So what happens if this internal focus method is discarded and an external helicoid is adapted?
(The following simulations are created based on parameters provided in patent JP 2015-114366, example 1)
Still using the Sigma lens, this is how it looks like when focus at infinity:
And the through focus spots:
Not an ideal result, but 7 micrometers’ spot is also not horrible. The minor error is due to the patents always not representing the actual design and thus always have some deviations from the actual product.
In general, the lens seems to be sharp in the center, pretty good around the center but exhibits obvious astigmatism, as to be expected for an f/1.4 that covers full frame.
Now, moving the internal floating elements, focus at the MOD (minimum object distance):
As can be seen, the 2nd group is now moved closer to the 1st group.
The through focus spots now:
The same kind of astigmatism still persists around the corners and the image center also deteriorated a lot, with the spot increasing to 27 micrometers’ size. But this is quite common for fast normal focal length lenses at their minimum focus distance.
Let’s also take a look of the ray fan:
Same story with the through focus spots, spherical aberration in the middle, and astigmatism around the edges.
Reset the lens, and now use an virtual helicoid to increase the rear flange distance to achieve the same MOD, the layout now look like this:
Note the only difference between the current layout and when focus at infinity is that the back focal distance (distance between last element’s surface to the image plane) is increased.
And the through focus spots now:
Hmmm… the corners have such a strong coma that I can build a wave rider aircraft inside of it… also interesting to see over-corrected SA in front of focus plane and under correction behind.
Let’s see what ray fan has to say about it:
For consistency I set the plot scale to be the same with previous ray fan, apparently the coma has gone literally off the chart.
Interestingly, the very center actually have a better performance than the internal focus, as the spot diameter of external helicoid focus method is only 22 micrometers compared to the 27 micrometers of the internal focus method.
But, and this is a big but, the image immediately breaks apart as it goes to the edge. At 7 degrees the external method has a spot size of 87 micrometers and the internal one is only at 45 micrometers. Around the corners, external method reached a jaw-dropping 196 micrometers, compare to the 55 micrometers of the internal focus. Mind you a single pixel is about 4-6 micrometers for a 24MP full-frame sensor.
Using the image simulation, the internal floating element at MOD look like this:
And the external helicoid method look like this:
The helicoid one showed more vignette, image resolution almost immediately disappeared after leaving the center. This made me suspect if there are some field curvature issues, and turned out there is. For the helicoid method, the filed curvature starts at about 0.3mm at the center and goes all the way to 1mm tangentially around the corner. This means that for the internal focus method, some of the movements might be used to solve the field curvature introduced by the rather asymmetric optical design.
A closer look at the corners:
Exterior helicoid focus has inferior resolution, contrast, and illumination, there is nothing redeeming to be seen.
But we are wide open at 1.4, can things be better stopped down?
Ray fan of internal focus MOD at f/5.6:
That’s a lot of improvement.
Now let’s see the external helicoid:
While it is an improvement, it’s… not that much.
Using image simulation, compare them again at the corners:
It would appear that even when stopped down at f/5.6, external helicoid focusing is still lacking resolution. Due to the large spot size, contrast is also being negatively affected.
I guess that goes to say that lens designers didn’t put all those efforts into complicated floating elements and optomechanical designs for nothing. If a lens is using internal floating elements to focus, it’s probably better to stick with that.
