The doping-induced ferroelectric phase transition in Ca-doped ${\text{SrTiO}}_{3}$ is investigated by observing the birefringence and coherent phonons. The structural phase-transition temperature is determined by the birefringence measurement. Coherent phonons of the soft modes are studied by using ultrafast polarization spectroscopy. Two phonon modes are observed to be softened toward the ferroelectric phase-transition point at 28 K and other two phonon modes are observed to be softened toward the structural phase-transition point at 180 K. Another structural deformation at 25 K is found below the ferroelectric phase-transition temperature. From the temperature dependence of phonon frequencies under an ultraviolet (UV) illumination, a shift of the ferroelectric phase-transition point toward the lower temperature side is found. A decrease in phonon frequencies after the UV illumination is also found.