Admittedly with single diffusion softbox, there is a hot pattern + visible, with double diffusion the hot pattern disappears.
Just 'for grins' I'll put my bare bulb Dynalite 4040 into the same softbox with only single diffusion, and shoot the softbox for comparison, and also measure evenness of illumination using incident meter at center and four sides, both with Metz 45CL and with Dynalite bare bulb head.
I just repeated the test with the same softbox with double diffusion panel removed, with a Dynalite 4040 bare tube head in place. Interestingly, there is a + pattern visible even with this head, so that phenomenon is not related to a flash lens distribution vs. bare tube configuration.
And just to have the 45CL flash head image to conveniently compare to the above bare tube pattern...
As for intensity uniformity across the single diffusion softbox, I measured in center, then 6" in from each edge of the softbox...
With the 4040 bare tube head, I measured sides down -0.5EV from center, and the top/bottom down -0.3EV from center
With the 45CL and 24mm wide angle setting, I measured sides down -1.2EV from center and the top/bottom down -0.7EV from center
So the bare tube head is much more uniform than the speedlight lens, even without the double diffusion panel in place.



