Then, people measure the net exchange in the dark (another incubation), to obtain respiration, and then, by difference, calculate photosynthesis (or gross primary production) in the light. However, nobody really knows whether respiration in the dark is the same as that in the light, and thus this procedure can be erroneous.
Another way to measure photosynthesis is to add ¹⁴C to water and measure how much accumulates in the cells (represneted below by blue cells appearing):

The problem with the ¹⁴C method is that no one knows whether sometimes ¹⁴C instead of ¹²C goes back to water during respiration. I other words, it is not possible to know whether net or gross production is being measured.
I am working on a solution for this problem and will try to publish a paper about that soon.

Other interests: Fractionation / discrimination of carbon stable isotopes in photosynthesis and respiration by algae

In photosynthesis, ¹²C is absorbed faster than ¹³C. This difference in absorption speed is called isotopic fractionation.
My study has shown that when photosynthesis is stronger, the difference in the velocity of absorption of different C isotopes (isotopic fractionation) diminishes, as shown below:

Notice that in slower photosynthesis the proportion ¹²C/¹³C entering the cell is 5/1, while in the faster photosynthesis it is 3/1. In other words, proportionally more ¹³C enters the cell when photosynthesis is faster.
I have also tested the influence of temperature on fractionation in photosynthesis, and found that for a same photosynthetic rate fractionation increased with temperature:


Look that the proportion of ¹³C absorbed is higher at the lower temperature. The photosynthetic rates are the same for both temperatures (look carefully, counting the atoms being absorbed, and you will see!).

Overall, my results can be explained based on a demand-supply control of fractionation. When there is more carbon available (carbon supply), it becomes easier for ¹²C to react faster, and thus fractionation values go up (towards 3%). The opposite is true when carbon is not very available. Hence, when photosynthesis is strong, carbon is less available, and fractionation values go down, as in the results obtained in my research. When temperature increases, diffusion rates of molecules also increase, making carbon more available, which increases fractionation, also as in the results of my research.

More recently, I investigated about the fractionation that happens in respiration by seaweeds. I found that the overall fractionation was in average small (0.3%), and variation could be somewhat explained by the consumption of different organic substrates (lipids or carbohydrates).