title: How to re-scaling signal intensity in image in relation to their spatial position?
body: <p>Hi I have a 1D radial profile of a sample across a pipe (fig_1). One data point (along the orange straight line) is acquired at each "band" from the image. The resolution (x,y,z) of each data point is 100um x 100um x 1000um.</p>
  
  <p><img src="https://i.stack.imgur.com/lqHqu.jpg" alt="fig_1 ">
  (fig_1)</p>
  
  <p>However in order to produce a quantitative image, each data point in the 1D profile must be re-scaled by multiplying with a constant C. Where C is:</p>
  
  <p><img src="https://i.stack.imgur.com/Q7P9Q.png" alt="fig_2">
  (fig_2)</p>
  
  <p>Where, phi0 = 0.35, A = cross-section A of a circular pipe, v = velocity across a pipe cross-section. S = signal (data points). At the end they produce a 1D profile as such.</p>
  
  <p><img src="https://i.stack.imgur.com/R9gEY.png" alt="fig_3">
  (fig_3)</p>
  
  <p><strong>My question is, how do I calculate the integral over the area (highlighted in red box, fig_2)?</strong></p>
  
  <p>In case I have missed any details I have provided the <a href="https://i.stack.imgur.com/YvIis.png" rel="nofollow noreferrer">snippet of the text</a>.</p>
  
  <p>Comparison of radially averaged profile from a quantitative 2D image and 1D image is: </p>
  
  <p><a href="https://i.stack.imgur.com/CaXzE.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/CaXzE.png" alt="enter image description here"></a></p>
  
  <p>Ps: I have gotten around this problem by acquiring a 2D image from which I have calculated a 1D radially averaged intensity profile. 2D profile is quantitative and works fine, however I would like to know how I can make my 1D data quantitative as well.</p>