It is necessary to identify the latest and newest techniques that proposed in order to fulfill the specific requirements and use it in the field of information security. There are some chaos techniques in image encryption and phase modulation encryption technique have been suggested. In the present paper the discrete Fourier transform was used to create phase modulation for a grayscale image. The image to encrypt is placed by one of chaos maps, Baker and Arnold cat maps, then combined with two random phase modulation based on the discrete Fourier transform. However, to decrypt the encrypted image required to have three keys, one for chaotic map and other two keys for removing phase modulation. The use of the discrete Fourier transform, phase modulation and chaos in image encryption add much more complexity to the decryption of the image for unauthorized person. The main contribution of this paper to compare between our two proposed in performance and efficiency. Numerical simulation results by Matlab have been executed to validate the two proposals. Furthermore, second proposal which implements by Arnold cat map and phase modulation achieved good test results in encryption quality metrics and noise immunity which is most optimal.