With Manage Display of image field, I set 'Link image to' to File.
so when user clicks the styled image, will link to original file, I want to change the html output of the link. How may I do so?
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The 'proper' answer to this question is: Use or make another formatter for image fields. For instance: Image URL Formatter is probably close enough for you to hack on.
If, when you're done, you feel generous... Make a sandbox project on drupal.org and share. :-)
Install the devel themer module. After enabling it you can point to whatever you want to change. It will tell you which theme method is actually called what options you have to implement your own one.