In this paper the robustness of a recently proposed image watermarking scheme is investigated, namely the Double Random Phase Encoding spread-space spread-spectrum watermarking (DRPE SS-SS) technique. In the DRPE SS-SS method, the watermark is in the form of a digital barcode image which is numerically encrypted using a simulation of the optical DRPE process. This produces a random complex image, which is then processed to form a real valued random image with a low number of quantization levels. This signal is added to the host image. Extraction of the barcode, involves applying an inverse DRPE process to the watermarked image followed by a low pass filter. This algorithm is designed to utilize the capability of the DRPE to reversibly spread the energy of the watermarking information in both the space and spatial frequency domains, and the energy of the watermark in any spatial or spatial frequency bin is very small. The common geometric transformations and signal processing operations are performed using both the informed and the blind detections for different barcode widths and different quantization levels. The results presented indicate that the DRPE SS-SS method is robust to scaling, JPEG compression distortion, cropping, low pass and high pass filtering. It is also demonstrated that the bigger the barcode width is, the lower the false positive rate will be.