How to create and get Field Choice in SharePoint 2013 by REST

gistfile1.txt

GetFieldsFromCollectionREST = function (restUrl, properties) {
    var values = [];
    select = "$select="
    if (properties.length > 1) 
        select += _(properties.slice(1)).reduce(function (memo, item) { return memo + "," + item }, properties[0]);
    else 
        select += properties[0];
    if (restUrl.indexOf('?') > -1) 
        restUrl = restUrl + "&" + select;
    else 
        restUrl = restUrl + "?" + select;

    $.ajax({
        url: restUrl,
        type: "GET",
        async: false,
        headers: {
            "accept": "application/json;odata=verbose",
        },
        success: function (data) {
            if (data.d && data.d.results) {
                _(data.d.results).each(function (res) {
                    var value = {};
                    _(properties).each(function (fst) {
                        value[fst] = res[fst];
                    });
                    values.push(value);
                });
            }
        },
        error: function (err) {}
    });
    return values;
};

PostCreateByREST = function (restUrl, data) {
    var result;
    $.ajax({
        url: restUrl,
        async: false,
        type: "POST",
        data: data,
        contentType: "application/json;charset=utf-8;odata=verbose",
        headers: {
            "accept": "application/json;odata=verbose",
            "X-RequestDigest": $("#__REQUESTDIGEST").val(),
            "IF-MATCH": "*",
        },
        success: function (data) {
            result = true;
        },
        error: function (err) {
            result = false;
        }
    });
    return result;
};

//usage
var choiceFieldValue = GetFieldsFromCollectionREST("<siteUrl>/_api/Web/Lists/GetByTitle('<listName>')/fields?$filter=TypeAsString eq 'Choice'", ["Title", "Choices"]);
var choices = choiceFieldValue.results;

var dataFieldCreation = "{ '__metadata': { 'type': 'SP.FieldChoice' }, 'Title': 'New choice Field', 'FieldTypeKind': 6,'Required': 'false',  'Choices': { 'results': ['Choice1', 'Choice2', 'Choice3'] } }";
var success = PostCreateByREST("<siteUrl>_api/Web/Lists/GetByTitle('<listName>')/fields", dataFieldCreation);