Post image with raw json? Using Content Type: application/json I tried like:

EDIT:

{
 "type": "article",
 "title": "Test article with image1",
 "body": {
 "und": [{
     "value": "test body!"
   }]
  },
 "field_image":{
 "und":[{
  "fid":{
  "filename": "bar.jpg",
  "target_uri": "sites/default/files/styles/large/public/field/image/bar.jpg",
  "filemime": "image/jpeg",
  "file":        "iVBORw0KGgoAAAANSUhEUgAAAKQAAAFzBAMAAABC179RAAAAD1BMVEUYooorZrPZwVO3Sd0M9BOSfwC2VwFIl7c9aAAAAABJRU5ErkJggg==",
   "filesize": "12345"
       }
     }]
    },

  "language": "und"
 }


Problem: Image is not created.
You need to use the file resource to upload the file first; that will provide you with a fid (file ID), which gets attached to the field on the node. The payload for that request might look something like:

{
    "filename": "foo.jpg",
    "target_uri": "bar/foo.jpg",
    "filemime": "image/jpeg",
    "file": "iVBORw0KGgoAAAANSUhEUgAAAKQAAAFzBAMAAABC179RAAAAD",
    "filesize": "12345"
}


And then to attach it the field your existing code will change to something like:

"field_image":{
  "und": [{
    "fid": [FILE ID RECEIVED FROM FILE SERVICE HERE]
   }],
}