* PNG is "lossless" format--if you can, make it the first file you create rather than last.
** If you create a JPG a "lossy" format then you could lose some of the beauty (like your example).
* ImageMagick has many switches you can throw--suggest you look deeper into it in the freely available manual--though its very thick.
* Often there are blah2blah programs (and many methods in ImageMagick for example) available which may help that you may be able to string together. General example:
dvips -o blah.dvi
pdf2png blah.pdf
** Maybe you can convert your file to an intermediary format and then convert it to .png
*** But again, if possible, create a PNG (.png) type file firstly since it is a "lossless" file type.