What makes a lens sharp?

If you mean resolution by "sharp", it's a complex balance of factors after all. All the side effects like distortion, vignetting or CA and the desire for resolution, nice "Bokeh" and speed (i.e. max opening) are mutually exclusive. And I'm only talking primes here.

So, every manufacturer set's his/her own goals for optimization. Some lenses may have more resolution, but a harsher Bokeh. Other may have less CA, but more vignetting and so on.

Now that technology arrived at real-time electronic correction of some factors, like distortion, vignetting and CA, manufacturers can concentrate on resolution and/or speed.
 
It's also that the perception of sharpness is affected by contrast, so the clarity of glass is also a factor. Cheaper glass, less clarity, less perceived sharpness.
 
Yes, contrast is very important so coating comes into play as well as it will control unwanted flaring that will reduce contrast.
 
I want a very, very sharp lens 1.4 or less..wide or tele. I have been mostly using my Rokinon 35mm and it's pretty nice. I always shoot wide open and I want sharper.

Any recommendations?
 
I want a very, very sharp lens 1.4 or less..wide or tele. I have been mostly using my Rokinon 35mm and it's pretty nice. I always shoot wide open and I want sharper.

Any recommendations?

I recommend for a sharper image shoot f2 not f1.4 :)
 
I know every lens has it's "sweet spot" but how would calculate what the sharpest F stop is on any given lens?

It's not really a calculation, per se. You just have to look at the image.

Take a shot with your lens at each stop. The difference will be apparent - you normally get a milky softness at the widest aperture and a cloudy blur at the smallest compared to, say, F5.6, which tends to be the sweet spot on most lenses. A higher quality lens will be sharper at its max aperture than cheaper lenses, but, like others have said, it's just not that simple - there are so many factors that affect sharpness, and sharpness is something you evaluate with your eye, not with a calculation or a tool, really.
 
Also, you will notice in most mainstream features, rarely is there a shot at max aperture, especially when it's talent coverage over an artsy insert of a prop. Usually, there is a reasonable depth of field. Part of this is a ton of money went into the production design, so the set pieces need to be visible and appreciable, but the other part is most DP's prefer to shoot around or at the sweet spot of the lens to get the sharpest image possible.
 
but if the sweet spot is not wide open, I'm only sacrificing my DOF..obviously I can create shallow dof depending on the background/foreground and the objects, but shooting open makes it much easier..
 
When I was starting my career in photography, most of us used to live and die by the camera and lens tests in the photo mags. Looking at lens resolution results were the only way to see how good the latest Nikkor or Canon lens was. We relied on lp/mm (line pairs per millimeter) resolution tests. They gave everybody a common metric to use for comparisons. You might want to seek out some of these tests. Speaking of shooting wide open vs. stopping down, I was surprised to see (on Ken Rockwells site, IIRC) showed the Nikkor 50mm f1.2 lens testing poorly wide open. If there was ever a lens that should test well wide open, you'd think this would be the one. But, most lenses really hit their stride about 2 stops down from their maximum wide-open position.
 
I know every lens has it's "sweet spot" but how would calculate what the sharpest F stop is on any given lens?

Most lenses "sweet spot" is f4-8 but stopping down a stop or two (f2 on a 1.4 or f4 on a 2.8) will usually be just as sharp as 2 or 3 stops down.
 
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