PictureBox使用GDI绘图保存为空的问题

直接用GDI绘图保存时picturebox.image为空，下面是解决方法！

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Text;
using System.Windows.Forms;
using System.Drawing.Drawing2D;

namespace 算法验证图像生成
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }

        private void Form1_Load(object sender, EventArgs e)
        {
            pictureBox1.Width = 512;
            pictureBox1.Height = 256;
            pictureBox1.Top = 32;
            pictureBox1.Left =32;

            pictureBox2.Top = pictureBox1.Height + pictureBox1.Top;
        }

        private void pictureBox1_Paint(object sender, PaintEventArgs e)
        {
             Bitmap bmp = new Bitmap(pictureBox1.ClientSize.Width, pictureBox1.ClientSize.Height);
             Graphics g = Graphics.FromImage((Image)bmp);
             g.FillRectangle(new SolidBrush(Color.Gainsboro), 0, 0, 512,256);                
             pictureBox1.Image = (Image)bmp;
        }

        private void 保存ToolStripMenuItem_Click(object sender, EventArgs e)
        {
            //pictureBox1.Image.Save("111.bmp");
            SaveFileDialog dlg = new SaveFileDialog();
            dlg.Title = "保存图片";
            dlg.OverwritePrompt = true;
            dlg.InitialDirectory = "c:\\pic\\";
            dlg.Filter = "*.bmp|*.bmp";
            dlg.FilterIndex = 2;

            if (dlg.ShowDialog() == DialogResult.OK)
            {
                string temp = dlg.FileName ;
                pictureBox1.Image.Save(temp);
            }
        }
    }
} 

感谢zxcayumi() 无私的帮助，十分感激！

希望看过的朋友能给出更好的解决方案！