How to extract values of some parameter along defined straight line(start lat/lon pts and end lat/lon pts) from a uniformly gridded data set and plot vertical profile of the same along that straight line?

I have uniformly spaced gridded model output data set. I want to extract data of a meteorological variable named Aeorosol Optical Depth (AOD) along a straight line defined by its start Latitude/Longitude points and end Latitude/Longitude points (both lat & lon is varying simultaneously). Then I want to plot vertical profile of that parameter along that straight line. (Basically that straight line is nothing but CALIPSO Satellite swath and its shown in the given figure for illustration )