Post processing is the work that is done to photo after it has been taken, such as adjusting the contrast, exposure, and color balance. It's easy to spontaneously set up a computer and start working without thinking about the lighting in the room, but that may make the color correction more difficult than necessary.
If possible, it's best to make adjustments to the photograph while comparing what you see on the computer display to the actual painting. I set small paintings up on a table top easel in front of my computer. There may be situations where this isn't possible such as if you sold the painting, or if it's an outdoor mural. In these cases you would have to make color adjustments based upon your memory which is generally unreliable.
Most computer monitors have a color temperature of around 6500K, which is biased towards blue and similar to daylight. If the lighting in the room has a different color temperature than the computer monitor you will have difficulty determining if the photograph accurately represents the colors in the painting. For example, if the room has incandescent lighting then that's going to clash with the color temperature of the computer monitor. Incandescent lighting has a color temperature of approximately 3200K which is warmer than the computer display. One light source will have a cool color cast and the other light source will have a warm color cast. This is the same problem as photographing a painting using mixed light sources. The solution is to use a "Daylight" light bulb or take advantage of the afternoon sunlight from a nearby window. I use the light bulbs because they provide consistent light.
I demonstrated this principle in the photographs below. In the first photograph I have a painting on a table top easel in front of my computer. The computer display has a color temperature of 6500K. The light is a regular incandescent light bulb. I used the "Daylight" white balance setting on my camera to take a picture of the painting in front of the computer. Notice how it's impossible to compare the colors in the painting with the image on the computer screen because of the orange color cast the incandescent light creates. The colors won't look that orange to the eye but there will enough of difference to make it difficult to colors on the computer screen with the original painting.
|Computer monitor: 6500K|
Tungsten light bulb: 3200K
“Daylight” white balance setting on the camera
RESULT: The difference in color temperature between the
lamp and the monitor make it difficult to judge colors.
|Computer monitor 6500K|
Daylight CFL 5500K
“Daylight” white balance setting on my camera
RESULT: The color temperature of the monitor
and lighting are similar enough to make
it easier to judge colors.