This is a civil war era photograph, depicting members of the 23rd New York Infantry in camp. The photograph dates from between 1861 and 1865.
Note the axe on the ground in front of the soldiers. It appears to be a Dayton pattern boy’s axe with a curved handle. So far all the poll axes I have seen from the Civil War have had well made curved handles. This leads me to believe that by this time the curved handle was predominant.
It is often said that the curved handle came into use around the 1850. Either it made very significant gains in the market over the ten year period before the Civil War, or the introduction was more gradual and started earlier. Of course this is all speculation.