## 4 Numerical Experiments  
### Setup of Experiments  
In numerical experiments, we model the lensless optical system (Figure 1a), where a thin transparent phase object is illuminated by monochromatic three color (RGB) coherent light beams from lasers. The wavelengths are \(\Lambda=[417,\,532,\,633]\) nm with the corresponding refractive indexes [1.528, 1.519, 1.515] as taken for BK7 optical glass. The reference wavelength is \(\lambda^{\prime}=633\) nm, then the relative wavelengths are \(\mu_{\lambda}=[1.48,\,\,1.17,\,\,1]\). The pixel sizes of CMOS camera and SLM are 1.4 and 5.6 \(\upmu\)m, respectively. The distance \(d\) between the object and CMOS camera is equal to 5 mm. Figure 1b illustrates arrangement for each color channel of the CMOS camera [64].  
A free propagation of the wavefronts from the object to the sensor is given by the Rayleigh-Sommerfeld model with the transfer function defined through the angular spectrum (AS) [65].  
For the proper numerical AS propagation without aliasing effects, we introduce a zero-padding in the object plane of the size obtained from the inequality:  
\[d\leq\frac{N\Delta x^{2}}{\lambda}, \tag{23}\]  
which binds the propagation distance \(d\), the number of pixels \(N\) in one dimension of the zero-padded object and the pixel size of the sensor \(\Delta x\)[66]. For the distance \(d=5\) mm and the object \(100\times 100\) pixels, the zero-padded object has as a support \(1700\times 1700\) pixels.  
The intensities of the light beams registered on the sensor are calculated as \(z_{s,\lambda}=\mathcal{G}\{|\mathcal{AS}_{\lambda,d}\{M_{\mathrm{s}}\circ u_{ \lambda,\lambda}\}|^{2}\}\), \(s=1,...,S\), \(\lambda\subset\Lambda\).  
Here \(\mathcal{AS}_{\lambda,d}\) denotes the AS propagation operator and \(M_{\mathrm{s}}\) are the modulation phase masks inserted before the object and pixelated as the object, \({}^{\prime}\circ^{\prime}\) stands for pixel-wise multiplication of the object and phase masks. These phase masks enable strong diffraction of the wavefield introduced in order to achieve the phase diversity sufficient for reconstruction of the complex-valued object from intensity measurements. As it was described in [34], we use the Gaussian random phase masks. These phase masks are implemented on SLM. It follows that the pixels of these masks and SLM have the same size.  
Thus, in our experiments the propagation operator \(\mathcal{P}_{s,\lambda,d}\) in Equation (4) is implemented as a combination of the angular spectrum propagation \(\mathcal{AS}_{\lambda,d}\) and the modulation phase mask \(M_{\mathrm{s}}\).  
To produce multiwavelength color images we need the three color components at each pixel location. It can be achieved by three sensors, each of which registers a light of the specific color  
Figure 1: (**a**) Optical setup. \(\lambda_{1}=417\) nm, \(\lambda_{2}=532\) nm, \(\lambda_{3}=633\) nm are wavelengths of the blue, green, and red light sources, M are mirrors, BS are beam-splitters, SLM stands for Spatial Light Modulator, O is the object, CMOS+CFA is a registration camera with CFA; (**b**) Color filter array. BGGR CFA is a blue-green-green-red disposed CFA; Blue, Green and Red are separate color channels.  
This optical setup for absolute phase retrieval from multiwavelength observations has been studied in our paper [52].  
To reduce the complexity and the cost, most digital cameras use a single sensor covered by CFAs. In our simulation we assume that the popular RGB Bayer CFA pattern is used. The corresponding sampled color values are termed mosaic images, Figure 1. To render a full-color pattern at the sensor plane from these CFA samples, an image reconstruction process is applied as defined by Equation (15).