What is the best lens to take an accurate photo of the face with no distortion?

DOF, bokeh and background blur have nothing to do with rendering facial features proportionally correct.
I guess you haven't looked at it, either. I only offered it as a possibility, as I read that it can show how the proportions of the face change between close up and distance. If that is indeed a fact, I think it could be of some use to bossman.
 
I have to agree with those who said 85mm-105mm. I always carried a 105. A 50mm or even wider is fine for backing off and including more background and environment, but they can be very unflattering up close. And also distorted which is what you're trying to avoid.
 
Why do you say that ... based on the OP's first post?
i thought it obvious that comment had no connection with the OP's first post.
 
@dxqcanada a 100mm macro lens are great for rendering some of the sharpest detail, with a crispness that other lenses can't produce if you catch focus on the money. They're also great if you're looking to "fill the frame" with a head shot, as they generally have a very small minimum focus distance. By comparison my 70-200 f2.8 has a minimum focus distance of 3.9 ft. The inherent capability to render details can also be a deterrent in portrait photography if your looking for softness to hide skin blemishes, and brokeh isn't as creamy as a prime in equal FL.

In the case of the OP's question he's looking for an option to minimize facial proportion distortion. As I mentioned in an earlier comment, there are three types of distortion to contend with Barrel distortion (lens design inherent), Pin Cushion (focal length dependent) and Perspective Distortion (dependent on distance to subject). So lens choice becomes a matter of matching your photo requirements to your equipment.

In the case of the OP a focal length in the range of 85 to 135mm will give the most realistic rendering of the facial proprotions, assuming he adjusts his distance to subject accordingly.
 
In the studio I prefer a 50mm for the full shots on a FF camera and a 100mm for the close-ups. As mentioned by so many, achieving what is desired will be precise distance measurements based on the lens. Absent that, anything perceived may not work due to the precision desired. Time to put an engineering or mathematical background to the test LOL! Also, in printing one would need an accurate size print if the aim is physical size accuracy. That would require the user to measure the size of the head of the individual in question and print the image to that life size. As long as it is done via a straight digital printer, all should be accurate. But the minute another lens is involved...
 

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