## 1 Introduction  
DLS is a widely used technique for measuring the PSD of ultrafine particles in suspension [1; 2; 3; 4]. The principle of DLS is based on the Brownian motion of particles in suspension, which leads to the fluctuation of scattered light. This fluctuation contains particle size information. DLS technology obtains PSD by measuring the autocorrelation function (ACF) of scattered light intensity [5; 6]. Retrieving the PSD information from ACF (measurements data) is known as a highly ill-posed problem. The small disturbances in the measurement data may lead to serious deviation in PSD. In order to deal with this problem, the numerous inversion approaches have been proposed to estimate the PSD from DLS data, such as the cumulants method [7; 8], constrained regularization method (CONTIN) [9; 10], Laplace transform method [11], the nonnegative leastsquares method (NNLS) [12], maximum likelihood method [13], exponential sampling method [14], nonnegative TSVD method [15], Bayesian inversion method [16; 17; 18], the maximum entropy method [19], and the various intelligences methods [20; 21; 22; 23; 24; 25]. In addition, various improved algorithms have constantly emerged [26; 27; 28; 29]. Each of these algorithms has its own advantages and limitations. In general, these approaches solve the problem in a single-scale space and a fixed inversion range. The inversion range has been fixed during the solution. In fact, the inversion range is related to the inversion accuracy of PSD. The appropriate inversion range is the precondition for the various inversion methods mentioned above to obtain a good PSD. The inappropriate inversion range is likely to get lower accuracy or even wrong inversion results. In practice, the inversion range can be manually adjusted based on the repeated inversions. However, in many cases, the manual method is not feasible, for example, polymeric materials study and biological analysis [30; 31]. The former inversion results have been no longer applicable for the latter inversion. Thus, the inversion approach with fixed inversion range is difficult to give the accurate inversion PSD.  
WRIM is an effective method for obtaining the optimal PSD in preselecting a large inversion range. The method gradually approaches the true particle size range by adaptive adjustment of the inversion range and has high inversion accuracy [32]. In WRIM, maximum scale of wavelet decomposition is called as initial decomposition scale (IDS). For convenience of expression, IDS N indicates that the initial decomposition scale is N. WRIM only uses IDS 4 in Reference [32]. However, in the application, IDS has great effect on the inversion accuracy. PSD obtained from unsuitable IDS is not optimal. Sometimes, the recovery PSD is even worse than the recovery PSD of the traditional single-scale method. Therefore, the scale effect of WRIM is carried on further studies in this paper. Besides, considering the application, an improved WRIM with the optimal IDS is proposed in this paper. By the improved algorithm, the high-accuracy inversion PSD is obtained from DLS data. Finally, the effectiveness of the algorithm is demonstrated by the simulated and experimental data. This study has a very important role for improving the measurement accuracy of DLS data.