因为你想将Panel的内容渲染为Bitmap（它是一个外部应用程序），所以你不能使用Control.DrawToBitmap()：将不会打印托管应用程序的内容，父级调用SetParent()。
由于您还希望从渲染中排除可能悬停在Panel上方的任何其他窗口，因此可以使用PrintWindow函数，传递Panel父窗体的句柄。
表单将接收WM_PRINT或WM_PRINTCLIENT消息，并将自身打印到指定的设备上下文：在本例中，它是从位图生成的。
这不是截图：Windows将其自身及其内容绘制到DC，因此其他Windows是否悬停/部分或完全重叠它并不重要，结果都是一样的。
我使用DwmGetWindowAttribute，设置DWMWA_EXTENDED_FRAME_BOUNDS，获取要打印的窗口的边界。这可能看起来是“多余的”，但是，如果您的应用不是DpiAware，并且您有一个High-Dpi屏幕，那么在这种情况下它将显得不那么多余。最好有它，IMO。
这个函数比GetWindowRect或GetClientRect更可靠，它将在可变DPI上下文中返回正确的度量值。
你不能将子窗口的句柄传递给这个函数，所以我使用父窗体的句柄来生成位图，然后选择Panel所在的部分。这取决于：
[ParentForm].RectangleToClient([Child].RectangleToScreen([Child].ClientRectangle))
启动Panel控件的Process和父Notepad窗口：

private void Notepad_Button_Click(object sender, EventArgs e)
{
    var psi = new ProcessStartInfo(@"notepad.exe") { WindowStyle = ProcessWindowStyle.Minimized };
    using (var p = Process.Start(psi)) {
        p.WaitForInputIdle();
        var handle = p.MainWindowHandle;
        if (handle != IntPtr.Zero) {
            SetParent(handle, panel1.Handle);
            MoveWindow(handle, 0, 0, panel1.Width, panel1.Height, true);
        }
    }
}

现在，无论何时你想将面板所在的窗体部分渲染到Bitmap，调用RenderWindow并获取你感兴趣的部分：面板的ClientRectangle。

using (var image = RenderWindow(this.Handle, true, false)) {
    if (image is null) return;
    if (WindowState == FormWindowState.Minimized) return;
    var panelRect = RectangleToClient(panel1.RectangleToScreen(panel1.ClientRectangle));
    pictureBox1.Image?.Dispose();
    pictureBox1.Image = image.Clone(panelRect, PixelFormat.Format32bppArgb);
}

// [...]

public static Bitmap RenderWindow(IntPtr hWnd, bool clientAreaOnly, bool tryGetFullContent = false)
{
    var printOption = clientAreaOnly ? PrintWindowOptions.PW_CLIENTONLY : PrintWindowOptions.PW_DEFAULT;
    printOption = tryGetFullContent ? PrintWindowOptions.PW_RENDERFULLCONTENT : printOption;
    var hResult = DwmGetWindowAttribute(hWnd, DWMWINDOWATTRIBUTE.DWMWA_EXTENDED_FRAME_BOUNDS, out Rectangle dwmRect, Marshal.SizeOf<Rectangle>());
    if (hResult < 0) {
        Marshal.ThrowExceptionForHR(hResult);
        return null;
    }

    if (dwmRect.Width <= 0 || dwmRect.Height <= 0) return null;

    var bmp = new Bitmap(dwmRect.Width, dwmRect.Height);
    using (var g = Graphics.FromImage(bmp)) {
        var hDC = g.GetHdc();
        try {
            var success = PrintWindow(hWnd, hDC, printOption);
            if (!success) {
                // Failed, see what happened
                var win32Error = Marshal.GetLastWin32Error();
                return null;
            }
            return bmp;
        }
        finally {
            g.ReleaseHdc(hDC);
        }
    }
}

Win32声明：

[DllImport("user32.dll", SetLastError = true)]
static extern IntPtr SetParent(IntPtr hWndChild, IntPtr hWndNewParent);

[DllImport("user32.dll", SetLastError = true)]
static extern bool MoveWindow(IntPtr hWnd, int x, int y, int nWidth, int nHeight, bool bRepaint);

public enum PrintWindowOptions : uint
{
    PW_DEFAULT = 0,
    PW_CLIENTONLY = 1,
    PW_RENDERFULLCONTENT = 2  // Undocumented. Use, e.g., with a WebBrowser
}

[DllImport("user32.dll", SetLastError = true)]
static extern internal bool PrintWindow(IntPtr hwnd, IntPtr hDC, PrintWindowOptions nFlags);

public enum DWMWINDOWATTRIBUTE : uint
{
    DWMWA_NCRENDERING_ENABLED = 1,      // [get] Is non-client rendering enabled/disabled
    DWMWA_NCRENDERING_POLICY,           // [set] DWMNCRENDERINGPOLICY - Non-client rendering policy - Enable or disable non-client rendering
    DWMWA_TRANSITIONS_FORCEDISABLED,    // [set] Potentially enable/forcibly disable transitions
    DWMWA_ALLOW_NCPAINT,                // [set] Allow contents rendered In the non-client area To be visible On the DWM-drawn frame.
    DWMWA_CAPTION_BUTTON_BOUNDS,        // [get] Bounds Of the caption button area In window-relative space.
    DWMWA_NONCLIENT_RTL_LAYOUT,         // [set] Is non-client content RTL mirrored
    DWMWA_FORCE_ICONIC_REPRESENTATION,  // [set] Force this window To display iconic thumbnails.
    DWMWA_FLIP3D_POLICY,                // [set] Designates how Flip3D will treat the window.
    DWMWA_EXTENDED_FRAME_BOUNDS,        // [get] Gets the extended frame bounds rectangle In screen space
    DWMWA_HAS_ICONIC_BITMAP,            // [set] Indicates an available bitmap When there Is no better thumbnail representation.
    DWMWA_DISALLOW_PEEK,                // [set] Don't invoke Peek on the window.
    DWMWA_EXCLUDED_FROM_PEEK,           // [set] LivePreview exclusion information
    DWMWA_CLOAK,                        // [set] Cloak Or uncloak the window
    DWMWA_CLOAKED,                      // [get] Gets the cloaked state Of the window. Returns a DWMCLOACKEDREASON object
    DWMWA_FREEZE_REPRESENTATION,        // [set] BOOL, Force this window To freeze the thumbnail without live update
    PlaceHolder1,
    PlaceHolder2,
    PlaceHolder3,
    DWMWA_ACCENTPOLICY = 19
}

[DllImport("dwmapi.dll", SetLastError = true)]
static extern internal int DwmGetWindowAttribute(IntPtr hwnd, DWMWINDOWATTRIBUTE dwAttribute, out Rectangle pvAttribute, int cbAttribute);