## Optical Setup and Image Formation Model
### Multiwavelength Object and Image Modeling
The wrapped phase is related with the true absolute phase, \(\varphi_{o}\), as \(\mu_{\lambda}\varphi_{o}=\psi_{o,\lambda}+2\pi k_{\lambda}\), where \(k_{\lambda}\) is an integer, \(\psi_{o,\lambda}\in[-\pi,\pi)\). The link between the absolute and wrapped phase conventionally is installed by the wrapping operator as follows:  
\[\psi_{o,\lambda}=\mathcal{W}(\mu_{\lambda}\varphi_{o})\equiv\text{mod}(\mu_{ \lambda}\varphi_{o}+\pi,2\pi)-\pi. \tag{3}\]  
\(\mathcal{W}(\cdot)\) is the wrapping operator, which decomposes the absolute phase \(\mu_{\lambda}\varphi_{o}\) into two parts: the fractional part \(\psi_{o,\lambda}\) and the integer part defined as \(2\pi k_{\lambda}\). The image and observation modeling is defined as  
\[u_{s,\lambda} = \mathcal{P}_{s,\lambda,d}\{u_{o,\lambda}\}, \tag{4}\] \[y_{s,\lambda} = |u_{s,\lambda}|^{2},\] (5) \[z_{s,\lambda} = \mathcal{G}\{y_{s,\lambda}\},s=1,...,S,\lambda\in\Lambda, \tag{6}\]  
where \(u_{s,\lambda}\) is a wavefront propagated to the sensor plane, \(\mathcal{P}_{s,\lambda,d}\{\}\) is an image (diffraction pattern) formation operator, i.e., the propagation operator from the object to the sensor plane, \(y_{s,\lambda}\) is the intensity of the wavefront at the sensor plane and \(z_{s,\lambda}\) are noisy observations of the intensity as defined by the generator \(\mathcal{G}\{\}\) of the random variables corresponding to \(y_{s,\lambda}\), \(S\) is a number of experiments, \(d\) is a propagation distance. The considered multiwavelength phase retrieval problem consists in reconstruction of \(\varphi_{o}\) and \(b_{o,\lambda}\) from the observations \(z_{s,\lambda}\) provided that \(\mu_{\lambda}\), \(\mathcal{P}_{s,\lambda,d}\{\}\) and \(\mathcal{G}\{\}\) are known. If the phases \(\mu_{\lambda}\varphi_{o}\in[\pi,-\pi)\), the problem becomes nearly trivial as estimates of \(\mu_{\lambda}\varphi_{o}\) and \(b_{o,\lambda}\) can be found processing data separately for each \(\lambda\) by any phase retrieval algorithm applicable for complex-valued object, in particular by the SPAR algorithm [54]. It gives for us the estimates of \(b_{o,\lambda}\) and \(\mu_{\lambda}\varphi_{o}\) directly. These estimates of \(\mu_{\lambda}\varphi_{o}(x)\) are biased as the intensities \(y_{s,\lambda}\) are insensitive with respect to invariant additive errors in \(\varphi_{o}\). We will represent these estimates in the form \(\mu_{\lambda}\varphi_{o}(x)+\delta_{\lambda}\), where \(\delta_{\lambda}\) are invariant on \(x\). The problem becomes nontrivial, much more interesting and challenging when the object phases \(\mu_{\lambda}\varphi_{o}\) go beyond the range \([\pi,-\pi)\) and the phase unwrapping is embedded in the multiwavelength phase retrieval. This paper is focused on the reconstruction of the absolute phase \(\varphi_{o}\). The light beam is formed by light sources radiating all wavelengths simultaneously and the standard RGB CMOS sensor with CFA is used for measurement registration. Then, the measurement model Equations (4)-(6) is modified to the following form:  
\[y_{s,c}(x) = |u_{s,c}(x)|^{2},\,x\in\Omega_{c}, \tag{7}\] \[z_{s,c}(x) = \mathcal{G}\{y_{s,c}(x)\},\,x\in\Omega_{c},\,c\in(R,G,B),\,s=1,...,S, \tag{8}\]  
where \(\Omega_{c},\,c\in(R,G,B)\), are the Bayer sensor areas with the corresponding RGB color filters. The index \(c\) of the measured \(z_{s,c}\) in Equation (8) is addressed to the sensor pixels with the corresponding color filters. These \(\Omega_{c}\) produce a segmentation of the sensor area \(\Omega\), such that \(\cup_{c}\Omega_{c}=\Omega\), \(\Omega_{c}\cap\Omega_{c^{\prime}}=\varnothing\). In a bit different terms, \(x\in\Omega_{c}\), \(c\in(R,G,B)\), defines a subsampling of the sensor output forming images of different colors. The sets \(\Omega_{c}\) define the structure of CFA (or mosaic filter) used in the sensor, i.e., the coordinates of the filters of the different colors. The ideal color filters would have equal sensitivity to each of the spectral components and provide a perfect separation of the three RGB sources of the corresponding wavelengths.