Get author custom image field URL to display on post page?

From codex:

The the_author_meta Template Tag displays the desired meta data for a
user. If this tag is used within The Loop, the user ID value need not
be specified, and the displayed data is that of the current post
author. A user ID can be specified if this tag is used outside The
Loop.

If the meta field does not exist, nothing is printed.

NOTE: Use get_the_author_meta() if you need to return (not display)
the information.

So, replace the_author_meta() with get_the_author_meta(). You can then use wp_get_attachment_image() to get an image element ready for outputting to the page.

<?php 
$id = get_the_author_meta('author_logo');
if ($id) {
    echo wp_get_attachment_image($id);
}
?>