which factors (light, nutrient level, CNP ratio) are critical in determining the initiation of cell division in microalgae
Growing algae will increase their size with a rate depending on light amount and quality, temperature and amount of nutrients available. When they reach so called treshold size they will become able to undergo cell division, a process called attainment of commmitment point, but it will take some time before they actually divide. So the treshold size at commitment point is different from actual size at cell division if the cells are grown on light while it will be similar if they are moved into dark at the moment of commitment point. If you want to measure a treshold cell size at commitment (which is usually not affected by light or nutrients but is affected by temperature) you can simply grow the cells on continuous ligth until certain cell density is reached, then treat them with prolonged dark (24 hours) and then measure cell size by for example Coulter counter. The maximum cell size reached by these cell is a rough estimate of commitment treshold cell size since all the cells above the treshold size will divide in dark. There are more precise measurements but this estimate is usually very good and sufficient.
It is easy to determine the average cell size as well as cell number using coulter counter. At the following link you can find more information;
https://en.wikipedia.org/wiki/Coulter_counter
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