How to get high resolution images from Facebook without using access tokens. Empty functions and settimeout solves a bug in IE where xdr requests are aborted randomly. See http://cypressnorth.com/programming/internet-explorer-aborting-ajax-requests-fixed/ for the full story.

gistfile1.js

// append redirect=false to the url to get json-encoded data in return

var url = "http://graph.facebook.com/712766212076612/picture?type=large&redirect=false",
    img = document.createElement('img'), 
    pre = document.createElement('pre'),
    f = document.createDocumentFragment();

f.appendChild(img);
f.appendChild(pre);
getFacebookImage(url);
document.body.appendChild(f);

function createCORSRequest(url) {
    var xhr = new XMLHttpRequest();
    if ('withCredentials' in xhr) {
        xhr.open('GET', url, true);
    } else if (typeof XDomainRequest != 'undefined') {
        xhr = new XDomainRequest();
        xhr.open('GET', url)
    } else {
        xhr = null;
    }
    return xhr;
};

function getFacebookImage(url) {
    var xhr = createCORSRequest(url);
    if (!xhr) {
        return;
    }
    xhr.onload = transferComplete;
    xhr.onerror = transferFailed;
    xhr.ontimeout = function(){};
    xhr.onprogress = function(){};
    setTimeout(function() {
        xhr.send();
    }, 0);

    function transferComplete() {
        var newurl = JSON.parse(this.responseText).data.url;
        img.setAttribute('src', newurl);        
        pre.appendChild(document.createTextNode('old url: ' + url + '\nnew url: ' + newurl));
    }
    function transferFailed() {
        console.log('transfer failed');
    }
}