以下是通过PayPal Rest API实现授权并捕获PayPal订单的示例代码：

$ch = curl_init();

$headers = array(
    'Content-Type: application/json',
    'Authorization: Bearer ' . $access_token,
);

// Set the url
curl_setopt($ch, CURLOPT_URL, 'https://api.paypal.com/v2/checkout/orders/' . $order_id . '/authorize');

// Set the headers
curl_setopt($ch, CURLOPT_HTTPHEADER, $headers);

// Set the request method
curl_setopt($ch, CURLOPT_CUSTOMREQUEST, 'POST');

// Set the request data
$post_data = array(
    'amount' => array(
        'currency_code' => 'USD',
        'value' => '10.00',
    ),
);
curl_setopt($ch, CURLOPT_POSTFIELDS, json_encode($post_data));

// Return response as a string
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);

// Execute the request
$response = curl_exec($ch);

// Check for errors
if (curl_errno($ch)) {
    $error_msg = curl_error($ch);
}

// Close the curl session
curl_close($ch);

// Handle response
if (isset($response)) {
    $result = json_decode($response);
    $authorization_id = $result->id;
}

$ch = curl_init();

$headers = array(
    'Content-Type: application/json',
    'Authorization: Bearer ' . $access_token,
);

// Set the url
curl_setopt($ch, CURLOPT_URL, 'https://api.paypal.com/v2/checkout/orders/' . $order_id . '/capture');

// Set the headers
curl_setopt($ch, CURLOPT_HTTPHEADER, $headers);

// Set the request method
curl_setopt($ch, CURLOPT_CUSTOMREQUEST, 'POST');

// Set the request data
$post_data = array(
    'amount' => array(
        'currency_code' => 'USD',
        'value' => '10.00',
    ),
    'final_capture' => true,
    'note_to_payer' => 'Thank you for your order!',
    'invoice_id' => '12345',
    'custom_id' => '67890',
);
curl_setopt($ch, CURLOPT_POSTFIELDS, json