Is the field reader_field actually a Notes "Readers access" field ?
You can tell by checking the field in the Notes document properties box. You should see for that field:
Field Flags: SUMMARY READ-ACCESS NAMES
If that's the case, then the field reader_field will automatically limit who can see those documents in the view to those with the role in the field.
So your selection formula can allow everyone to view it, and the readers_field will limit it as necessary. This works for web applicaiton & Notes client.
Be sure to add a 'catch all' readers field as well as it's entirely possible to accidentally hide doecuments with a Readers field such that no-one can see them. If you add for example an [Admin] role (it can be in another field of type Readers on same doc) which only support staff have, then you have a way to see all documents, for support purposes.
If it's just a normal text field called reader_field....
If a Notes application:
About your only option is to use private views (bit too much to explain here)
If a Web application:
You can categorise the view by the reader_field and use a form to include the view with a view embedded element. Use the "Restrict To Category" setting to the user's role (if they have >1 role then you'll probably have to put some logic in to work out which one is appropriate)
Another alternative would be to display the view using an XPage, which allows you to trim the data as it's displayed.