What steps can be taken to optimize a PHP script that is experiencing issues with displaying content in the browser while still processing data in the background?

The issue of slow content display in the browser while processing data in the background can be optimized by implementing asynchronous processing using AJAX. By sending requests to the server in the background and updating the content dynamically, the user experience can be improved.

```php
// PHP script to handle AJAX requests for processing data in the background

if ($_SERVER['REQUEST_METHOD'] === 'POST' && isset($_POST['data'])) {
    // Process the data in the background
    // This could be a time-consuming task
    $processedData = processData($_POST['data']);
    
    // Send the processed data back to the client
    echo json_encode($processedData);
    exit;
}

function processData($data) {
    // Simulate a time-consuming task
    sleep(5);
    
    // Return processed data
    return 'Processed: ' . $data;
}
```

In this code snippet, we handle AJAX POST requests to process data in the background using the `processData` function. The function simulates a time-consuming task using `sleep(5)` to demonstrate the concept. The processed data is then sent back to the client using `json_encode`. This approach allows the PHP script to continue processing data in the background while updating the content dynamically in the browser.