Radio frequency fingerprint (RFF) identification has emerged as a promising technique for physical-layer identity authentication. However, most RFF identification schemes tend to make the restrictive closed-set assumptions and focus solely on RFF classification. In this paper, we propose a novel open-set RFF identification scheme, with both device classification and rogue device detection capability. Moreover, to reduce the open space risks and mitigate the impact of channel noise, an RFF extraction scheme based on Fourier-based synchrosqueezing transform (FSST) and supervised contrastive learning (SCL) is proposed to acquire more concentrated and distinctive features. The performance of the proposed scheme is experimentally demonstrated using the datasets from 11 commercial wireless network interface controllers (WNICs) as well as open-source datasets. The results verify the significant improvements in high-openness and low-SNR scenarios, with high identification accuracy of 82 %, at a low SNR of 5 dB, while the openness can be as high as 21 %, and an accuracy of approximately 100 % when SNR>20 dB.