Test the fit of rate data to a Poisson process

#1
How can you test the whether a collection of rate data is consistent with a Poisson process?
I am investigating a random process which conceptually could be a Poisson process. I have a collection of rate data (counts/min), and I would like to test whether their distribution is consistent with my hypothesis of a Poisson process. However, the time intervals of each measurement are not equal (different exposures), so I convert each into a rate. For example, 2 counts/20min-> 0.1 counts/min, 6 counts/30 min= 0.2 counts/min, and so on.

I am aware of the chi square method to check goodness fit for count data, but I believe this can only be used if the time intervals are uniform.