Simple parallax without empty spaces on background

function axelerateBackground(bgWrapperHeight) {
    var $bgWrapper = $('.bg_wrapper'); //parallax block inside body with position fixed and css background

    $(document).on('scroll', function() {
        var dHeight = $(document).height(),
            wHeight = $(window).height(),
            imgHeight = bgWrapperHeight ? bgWrapperHeight : $bgWrapper.height(), //height of parallax block
            coeff = (imgHeight - wHeight) / (dHeight - wHeight); //coefficient to avoid empty spaces on background

        var shift = -1 * ($(window).scrollTop() * coeff); //size of shift on the top

        if (dHeight - wHeight > 20) $bgWrapper.css('top', shift + "px");
    });
}