Order of Image Processing for Arithmetic operations such as subtraction and division

Question

I am processing an image taken from laser diagnostics such as laser induced fluorescence. This image requires correction for background noise laser sheet non uniformity. Laser non uniformity correction is applied by imaging a homogenous source often referred as flatfield. Now my question is in which order should I apply these corrections ?

1. if I should subtract background first and divide image by flatfield

• or

2. Divide the image by flatfield and then subtract background ?

For example lets say we have an 3X3 array of

signal = [[4,5,6],[5,5,4],[4,6,4]]
background = [[2,2,2.5],[1.8,2,2],[3,1,5,2]]
flatfeild = [[0.98,0.98,0.87],[1,0.98,1],[1,1,1]]