I am trying to retrieve data from salesforce using the REST api and CURL in PHP.

I perform the authentication request and recieve an 'instance_url' and 'access_token' but after performing a query request using those, i receive an "INVALID_SESSION_ID" error.

my authentication request code:

function get_sf_auth_data() {

	$post_data = array(
        'grant_type'    => 'password',
        'client_id'     => 'xxxxxxxxxxxxxxxxxxxxxx', //My client id (xxx... for this example)
        'client_secret' => '111111111111', // My client secret (111... for this example)
        'username'      => 'my_user_name',
        'password'      => 'my_user_password'
	);
	
	$headers = array(
    	'Content-type' => 'application/x-www-form-urlencoded;charset=UTF-8'
	);

	$curl = curl_init('https://login.salesforce.com/services/oauth2/token');
	curl_setopt($curl, CURLOPT_HTTPHEADER, $headers);
	curl_setopt($curl, CURLOPT_RETURNTRANSFER, true);
	curl_setopt($curl, CURLOPT_POST, true);
	curl_setopt($curl, CURLOPT_POSTFIELDS, $post_data);

	$response = curl_exec($curl);
	curl_close($curl);

    // Retrieve and parse response body
    $sf_access_data = json_decode($response, true);
    
    echo '*********' . $sf_response_data['instance_url'] . '********';
    echo '*********' . $sf_response_data['access_token'] . '********';

    return $sf_access_data;
}

function get_user_sfid($sf_access_data, $user_id_number){

	$sql = "SELECT Id, Name 
			FROM Account 
			WHERE ID__c = '$user_id_number'";

	$url = $sf_access_data['instance_url'] . '/services/data/v20.0/query/?q=' . urlencode($sql);

	$headers = array(
		'Authorization' => 'OAuth ' . $sf_access_data['access_token']
	);

	$curl = curl_init($url);
	curl_setopt($curl, CURLOPT_HEADER, false);
	curl_setopt($curl, CURLOPT_RETURNTRANSFER, true);
	curl_setopt($curl, CURLOPT_HTTPHEADER, $headers);

	$json_response = curl_exec($curl);
	curl_close($curl);

	var_dump($json_response); // This prints out the response where i got the error

	$response = json_decode($json_response);

	return $response['id'];
}

[{"message":"Session expired or invalid","errorCode":"INVALID_SESSION_ID"}]