Feedback form sends empty emails

would you please take a look at my code and answer the question: why am I getting empty e-mails? I've tried doing a lot of things, but nothing seems to have helped :)

    <?php 
mb_internal_encoding('UTF-8');
mb_http_output('UTF-8');
mb_http_input('UTF-8');
mb_language('uni');
mb_regex_encoding('UTF-8');
ob_start('mb_output_handler');
$field_name = $_POST['cf_name'];
$field_email = $_POST['cf_email'];
$field_message = $_POST['cf_message'];

$mail_to = 'radik.mcphilimy@gmail.com';
$subject = 'Сообщение от посетителя сайта '.$field_name;

$body_message = 'От: '.$field_name."\n";
$body_message .= 'Электронный ящик: '.$field_email."\n";
$body_message .= 'Сообщение: '.$field_message;

$headers = 'From: '.$field_email."\r\n";
$headers .= 'Reply-To: '.$field_email."\r\n";

$mail_status = mail($mail_to, $subject, $body_message, $headers);

if ($mail_status) { ?>
    <script language="javascript" type="text/javascript">
        alert('the message was sent.');
        window.location = 'contact.html';
    </script>
<?php
}
else { ?>
    <script language="javascript" type="text/javascript">
        alert('the message was not sent.');
        window.location = 'contact.html';
    </script>
<?php
}
?>

and here's the html:

<form action="contact.php" method="post">
                  <div class="templatemo_form">
    <input name="cf_name" type="text" class="form-control" id="cf_name" placeholder="your name" maxlength="40">
</div>
<div class="templatemo_form">
    <input name="field_email" type="text" class="form-control" id="field_email" placeholder="your e-mail" maxlength="40">
</div>
<div class="templatemo_form">
    <textarea name="field_message" rows="10" class="form-control" id="field_message" placeholder="Message"></textarea>
</div>
<div class="templatemo_form"><button type="submit" value="Send" class="btn btn-primary">Send</button></div>

Thanks a lot. Radik