## 1 Introduction  
Phase-only holograms can be used for 2-D [1; 2; 3; 4] or 3-D image projection [5; 6], free space optical switches [7; 8; 9; 10; 11] and optical tweezers [12; 13]. These systems generally enjoy a high efficiency due to the absence of any light absorbing element such as cross-polarizers [14]. Two-dimensional image projection is one of the most mature applications due to the simplicity of the optical systems and its high tolerance to system errors [4]. In order to form the target image, however, the phase-only hologram needs to be calculated in the first place. This is usually a computationally intensive process. Iterative Fourier transform algorithms (IFTAs) [15] including Gerchberg-Savaton (GS) [16], Fienup [17], and 'Fienup with don't-care' (FiDOC) [18; 19], are able to accelerate the calculation significantly by using the fast Fourier transform (FFT). In these algorithms, the errors in the image reconstructed from the computer-generated phase-only hologram are evaluated based on certain key image quality metrics at the end of each iteration. The iteration process is terminated until a predefined requirement is satisfied or the number of the iteration reaches the predefined threshold. Therefore, the image quality metrics used in IFTA algorithms should be able to reflect the perceived image quality [20] in the phase-only holographic projection system. It will directly affect both the quality of the reconstructed image and the speed of the algorithm.  
The choice of the image quality metrics is dependent on the specific type of errors in the reconstructed images. [PERSON] et al. [21] proposed some effective statistical methods to characterize the noise of a large number of samples and revealed that the noise usually has a Poisson or Gaussian distribution. These methods have the potential to be applied to investigate the noise characteristics in the images reconstructed from the phase-only holograms calculated by IFTAs. [PERSON] et al. [4]investigated the probability density function (PDF) for the grey-scale values in a reconstructed chessboard pattern. However, it did not identify the type of noise in the reconstructed images. This work aims to further study the noise characteristics in the images reconstructed from the phase-only holograms that are calculated by IFTAs.  
At present, the root-mean-squared error (RMSE) [22; 23] is the most widely used image quality metric in IFTAs. [PERSON] et al. proved that the RMSE would always converge towards a lower value as the iteration moved forward in IFTAs. The speed of convergence is usually quicker in Fienup algorithm than in the standard GS algorithm. However, it has been proved that RMSE was unable to reflect the perceived image quality accurately [24]. In other words, reconstructed images with similar values of RMSE might have a significantly different perceived image quality.  
Efforts have been made to establish the relationship between the objective image quality metrics and the subjective image quality. Just-noticeable difference (JND) [25] has been proposed to define the subjective image quality and it has been linked with the luminance and color characteristics of the display system [26; 27]. [PERSON] [28] proposed the square-root integral (SQRI) to evaluate the image quality. However, the calculation of SQRI is rather complicated. [PERSON] et al. [24; 29] proved that structure similarity (SSIM) is a simple and consistent image quality metric to assess the perceived quality of images. This work will investigate the suitability of SSIM as the image quality metric in the IFTAs. To authors' knowledge, it is the first time that the perceived image quality is used in the IFTAs for the phase-only hologram generation.