hello, for the 77mm nd filter ,the lens hood size should be 82mm for the 72mm nd filter , the lens hood size should be 77mm. by the way, when you use a nd filter , you better not add a lend hood ,the lend hood should move. 

the new version of this ND filter is double-side multilayer blue coating 

If you rotate your ND filter past the ‘Max’ mark on the filter rim, it can cause an x-pattern, so ensure you’re not over-rotating. Variable ND filters also have limited application with wide angle lenses (they can only be used to about the halfway mark of Min and Max markings because the field of view is so broad). For a wide-angle lens, we suggest using fixed ND filters or ND2-32 or ND8-128. You can also try adjusting your focal length and reducing the density (rotating back towards the ‘Min’ mark) until the colour shift disappears. 

the lens cap should one size bigger than the filter. so the lens cap should be 55mm when using the 52mm lens filter.