## 1 Introduction  
Significant progresses have been made during the past few years in applying coherent X-ray diffraction imaging (CDI) and X-ray ptychography in materials sciences and soft matter materials. To introduce X-ray ptychography [1; 2; 3; 4] in short, the technique is the elegant amalgamation of scanning X-ray microscopy (STXM) with CDI, where partially overlapping illumination provides additional real-space constraint that expands the sample of interest to arbitrarily-defined region with high-resolution in both absorption and phase contrasts. In CDI, a modified algorithm that includes _ab initio_ correction of transverse partial coherence in measured data by using Lucy-Richardson (RL) deconvolution method has been shown to give better data reconstructions [5; 6]. [PERSON] and [PERSON] [7] recently demonstrated that the ptychographic method provides enough redundancy in datasets to allow high-quality reconstructions through complete recovery of X-ray illumination modes (and object's states in the case of dynamical sample). This work also opened up the exciting possibilities of information multiplexing [8] and dynamical systems imaging [9] with ptychography. Following results by [PERSON], [PERSON] et al. and [PERSON] et al. [7; 8], [PERSON] et al. [10] has recently demonstrated the feasibility of recovery of multiple sample modes by applying extra constraints into the iterative algorithms, and they discovered the inability of recovery of individual sample modes due to the mathematical equivalence in mixing the initial sample modes in multi-modal ptychography. Individual sample mode could be recovered when additional constraints on sample were applied [10].  
To understand better this for dynamical sample modes, we have simulated ptychographic data with both X-ray beam and sample modes to mimic experimental data when partially coherent X-rays are used. Implementations of both sample modes and X-ray beam modes could enable relatively higher X-ray flux on dynamical samples. This approach ultimately reduces ptychographic data acquisition time to detect dynamical sample states with few-nanometer spatial resolution in a relatively short experimental time.  
Figure 1[9] shows experimental reconstructions of X-ray orthogonal illumination modes when partially coherent X-ray illumination was adopted with a vibrating sample. Multiple sample modes due to vibration are transferred to probe modes, resulting to partially coherent illumination.  
[PERSON] et al. [10] recently successfully performed multi-modal experiments with visible lights on complex test objects with partially coherent illuminations with several orthogonal modes. Their results demonstrate the feasibility of inversion of complex wavefunctions of both object and illumination using multi-modal approach without _a priori_ information to start with. This could be trivially extended to X-rays to enable dynamical studies on condensed matter materials by adopting this technique. Figure 2 illustrates experimental work demonstrated by [PERSON] et al. [10] by using visible lights to test reconstruction quality of measured data by applying multi-modal ptychography algorithms.  
Figure 1: The first three ( \(n\) = 1, 2, 3) recovered probe modes for the cases of (**a**) a static sample; (**b**) a square wave with amplitudes 1 \(\upmu\)m and (**c**) 1.5 \(\upmu\)m; and (**d**) a sine wave with amplitudes 1 \(\upmu\)m and (**e**) 1.5 \(\upmu\)m. The bottom line also shows the square root of the summed intensity (rms, right column, linear scale) from five probe modes for the cases listed previously. The rms shows clearly how the probe forms can be manipulated using a vibrating sample. The scale bar is 1 \(\upmu\)m. The vibration frequency is selected to be 1 Hz with exposure of 6 seconds per position. Figure adapted from Ref [9], reprint permission granted, 2014 American Physical Society.