We investigate the saturation effect, which describes the violation of the linearity between the measured photoacoustic amplitude and the object's optical absorption coefficient in functional photoacoustic imaging when the optical absorption in the object increases. We model the optical energy deposition and photoacoustic signal generation and detection in a semi-infinite optical absorbing object. Experiments are carried out by measuring photoacoustic signals generated from an ink-filled plastic tube. The saturation effect is studied by varying the optical absorption coefficient in the model and the ink concentration in the photoacoustic experiments. By changing the center frequency of the ultrasonic detector, the requirement to minimize the saturation effect in functional photoacoustic imaging is established.