In acoustic-resolution photoacoustic microscopy (AR-PAM) systems, the lateral resolution in the focal zone of the ultrasound (US) transducer is determined by the numerical aperture (NA) of the transducer. To have a high lateral resolution, a large NA is used. However, the larger the NA, the smaller the depth of focus [DOF]. As a result, the lateral resolution is deteriorated at depths out of the focal region. The synthetic aperture focusing technique (SAFT) along with a beamformer can be used to improve the resolution outside the focal region. In this work, for image formation in AR-PAM, we propose the double-stage delay-multiply-and-sum (DS_DMAS) algorithm to be combined with SAFT. The proposed method is evaluated experimentally using hair targets and in vivo vasculature imaging. It is shown that DS_DMAS provides a higher resolution and contrast compared to other methods. For the B-mode images obtained using the hair phantom, the proposed method reduces the average noise level for all the depths by about 134%, 57% and 23%, compared to the original low- resolution, SAFT+DAS and SAFT+DMAS methods, respectively. All the results indicate that the proposed method can be an appropriate algorithm for image formation in AR-PAM systems.