Create a new image, 800x800 pixels.
Go to the Channels window, create a new channel
,
and select the Rectangular Marquee Tool.
Holding down Shift, draw a selection about 25x25 pixels.
To see how big your selection is, open the Info Palette, by going Window > Show Info.
Press D to select White as the foreground color, and then fill the selection by pressing Alt+Backspace.
In the menu, go:
Select > Modify > Contract... 2 pixels
Press Delete to clear the selection, and then use the arrow keys on your keyboard to nudge the selection up and to the left by 2 pixels.
Edit > Define Pattern
Create a new channel
,
select the Paint Bucket Tool
.
Then, go to the Options palette.
Window > Show Options
Change the Contents dropdown to Pattern, and then click inside the new channel to fill it with the grid pattern.
In the Channels window, click on the Load Channel as Selection button.
Go back to the Layers window, and create a new layer.
Press D on the keyboard to select Black as the foreground color, and then press Alt+Backspace to fill the selection.
Ctrl+D to deselect.
Click and hold down the Rectangular Marquee Tool button, and select the Elliptical Marquee Tool
Holding down Shift, make a circular selection filling up most of the image.
Filter > Distort > Sphereize... Amount 100
Select > Inverse
Edit > Clear
Ctrl+D to deselect.
To get rid of the jagged edges, resize the image to 400x400 pixels,
Image > Image Size...