You basic answer is you need to do a HTTP GET request with the correct query params. Not totally sure how you are trying to do this based on your question, so here are two options.
If you are trying to do this from javascript you can look at this question. It has a bunch of answers that show how to perform AJAX GETs with the built in XMLHttpRequest
or with jQuery
.
If you are trying to download the page from a java application, this really doesn't involve AJAX at all. You'll still need to do a GET request but now you can look at this other question for some ideas.
Whether you are using javascript or java, the hard part is going to be figuring out the right URLs to query. If you are trying to scrape someone else's site you will have to see what URLs your browser is requesting when you filter the results. One of the easiest ways to see that info is in Firefox with the Web Console
found at Tools
->Web Developer
->Web Console
. You could also download something like Wireshark which is a good tool to have around, but probably overkill for what you need.
EDIT
For example, when I clicked the "rectangle frames" option at zenni optical, this is the query that fired off in the Web Console
:
[16:34:06.976] GET http://www.zennioptical.com/?prescription_type=single&frm_shape%5B%5D=724&nav_cat_id=2&isAjax=true&makeAjaxSearch=true [HTTP/1.1 200 OK 2328ms]
You'll have to do a sufficient number of these to figure out how to generate the URLs to get the results you want.
DISCLAIMER
If you are downloading someone's else data, it would be best to check with them first. The owner of the server may not appreciate what they might consider stealing their data/work. And then depending on how you use the data you pull down, you could be venturing into all sorts of ethical issues... Then again, if you are downloading from your own site, go for it.