There are plenty of methods for measuring the chlorophyll a and chlorophyll b contents. These methods are in two categories. In environmental research the pigment content of intact cells is preferred as a non-invasive method. After proper calibration, these methods and the equipments can give you acceptable results but you must know that the accuracy of the results remain on "environmental level", i.e. it cannot provide the same axxuracy than the spectrophotometric measurements of the extracted pigments. In this latter case, you should take the alga suspension as 20% volume and add pure acetone to get 80% acetone concentration. You can improve the extraction if you pour liquid nitrogene on the alga suspension and add the aceton to the broken algal cells. Then you should centrifuge the extracted pigment solution and measure its absorption spectrum to be sure that the baseline does not influence the absorbance values. Read the absorbance values at 663.6 and 646.6 nm, then use the equations in Porra et al. 1989, BBA 975: 384-394.
Just a little note, If you do the extraction in acetone, keep your extract in the dark as much as possible and let it extract in the cold (-20°C) overnight.
Filter the known volume of chlamy culture through 45u filterpaper and dissolve this disc in 10 ml of 90% acetone. keep the vial containing disc and acetone sealed, in dark at 4 degree C for overight and then read the absorption at 665, 645 and 630 nm.
We must be careful with both, the extraction and the in vivo measurements. In the case of extraction, a certain amount of chlorophyll remains adsorbed to the surface of the filter paper. Anyway, after, after decanting the acetone extract, it is advisable to put this filter paper into pure, fresh acetone, repeat the extraction and record the absorption spectra again. In addition, we must check the baseline and correct it, i.e. it is better to read the extinction values from the spectra. Be careful with the wavelength values, the absorption maximum of chlorophyll-a is at 663 nm in acetone. To be precise, consider the optical slits of the spectrophotometer, too.
The in vivo measurement gives semi-quantitative values because the extinction coefficients of chlorophyll-protein complexes are not known. In addition, plenty of optical problems can disturb the measurements, like baseline problems, light scattering. Even if you were satisfied with semi-quantitative results (for instance in practical works), I would suggest preparing a calibration curve via extracting the chlorophylls with acetone.
We have a discussion in different dimensions. The presence of different chlorophylls in an object can be determined spectrophotometrically in vivo. The absolute determination of a particular chlorophyll in a particular object or part of it can only be judged after careful extraction this pigments