In this paper, a phase retrieval method based on deep learning is proposed and applied to the phase-modulated holographic storage system. The phase-modulated holographic storage system has become a research hotspot because of its higher encoding rate and higher signal-to-noise ratio (SNR). Since the phase data cannot be detected directly by the detector, the intensity image is used to retrieve the phase. The traditional interferometric phase retrieval method is not suitable for the storage system because its optical system is complex and is easily affected by environmental disturbances. The non-interferometric phase modulation storage system uses iterative methods to solve the phase data, and the number of iterations will affect the data transmission rate in the holographic data system. In this paper, a simulated non-interferometric phase retrieval system based on deep learning is established, which uses a convolutional neural network to directly establish the relationship between phase and intensity images captured by CCD. The neural network is trained by learning the dataset of intensity images and phase data images. After training, the phase can be obtained by a single calculation, which greatly improves the data transmission speed. In the process of deep learning training, we introduced embedded data to improve the precision of phase reconstruction and reduce the bit error rate. According to our investigation, this is the first application of deep learning in phase retrieval of optical holographic storage.
The single-shot iterative Fourier transform algorithm as a common non-interferometric phase retrieval algorithm is very suitable for phase-modulated holographic data storage due to its fast, simple and stable properties. It retrieves the phase in the object domain iteratively from the intensity image in the Fourier domain captured by the detector. Because of the effects by complex noises of the experimental system, there is always an intensity image degradation which increases the phase decoding bit error rate. This paper proposed a denoising method based on end-to-end convolutional neural networks by learning the relationship between the captured intensity images and the simulation results to improve image quality significantly. Then the denoised intensity image was used in the phase retrieval. The experiment results showed that the bit error rate can be reduced by 6.7 times using the denoised image, which proved the feasibility of the neural network denoising method in the phase-modulated holographic data storage system.
A single-shot non-interferometric phase retrieval method in holographic data storage is proposed to solve the problems that undetectability for phase by detector directly and unstability caused by interferometric detection. Embedded data are inserted in iterative Fourier transform algorithm to shorten iterations sharply. For avoiding embedded data occupying the code rate, we propose a collinear system to refer to the reference beam, which is always known, as the embedded data. Finally, fast stable phase information reading is realized because of single-shot non-interferometric detection and fast phase retrieval within only several iterations.
We present single-shot fast phase information retrieval without interferometry in the holographic data storage. Noninterferometry systems are more compact and stable than interferometric ones. Only single-shot of the intensity distribution on the Fourier plane is required to retrieve the phase information. Enhanced iterative Fourier transform algorithm (IFTA) was developed by applying embedded known phase data and phase only modulation as the prior constraints, which can be provided easily as the code rule in holographic data storage system. Strong intensity distribution on the Fourier plane reduces the requirement of high-power laser and high material diffractive efficiency. The bit-errorrate (BER) can be decreased to 0 in the simulation study. We realized BER without check code in the order of 10-2 for 4 level phase retrieval experimentally. The code rate is increased by 2.8 times using 4 level phase code compared to with amplitude code.
A non-interferometric phase retrieval method in collinear holographic data storage (HDS) is proposed. Noninterferometric system is stable which is suitable for phase-modulated HDS but non-interferometric phase retrieval algorithm replies on strong constraint to shorten iteration number. Embedded data can provide strong constraint. However, in off-axis system, embedded data have to be in the signal part which sacrifice code rate. Our proposed collinear system considers the reference beam as embedded data to increase the code rate by about 2 times.
In this paper, we propose a frequency expanded method based on non-interferometric phase retrieval which can retrieve complex multi-level phase image by using only 1 times Nyquist frequency. Our proposed method utilizes the property of frequency spectrum periodicity and is the unique method with non-interferometry due to the intensity detection directly on the Fourier domain. For a regular phase image, same spacial frequency means same spectrum width. We choose a rectangular window with the same spacial frequency to the phase image and consider normalized Fourier intensity distribution of the rectangular window as the envelope of that of the phase image. After normalizing the spectrum of the phase image, we can expand its Fourier frequency with 1 times Nyquist size to other higher order frequency positions. Therefore, we can generate high-order frequencies artificially from low-order frequency which help us to retrieve phase image accurately and quickly.
Non-interferometric phase retrieval is a fundamental technique for phase-modulated holographic data storage due to its advantages of easy implementation, simple system setup, and robust noise tolerance. Usually, the iterative algorithm of non-interferometry needs hundreds of iteration numbers to retrieve phase accurately, which decreased the data transfer rate severely. Strong constraint conditions, such as embedded data, can be used on the phase data page to reduce the iteration numbers. However, introducing embedded data will reduce the code rate of the system. We proposed a method that combined the single-shot interferometric method with the non-interferometric iterative Fourier transform algorithm method. We used the phase decoding result by single-shot interferometry as the embedded data in the process of non-interferometry. Therefore, no extra embedded data are needed in the signal code. We realized the code rate improvement as well as keeping fast data transfer rate. In the demonstration, we recorded a four-level phase pattern and retrieved the phase correctly. The bit error rate of phase retrieval is less than 1% within 20 iterations, which proves our approach is practical. In our case, the code rate is increased by two times.
A non-interferometric phase retrieval method in the phase-modulated holographic data storage system is proposed. This method can not only avoid phase ambiguity issue with interferometric, but also increase the capacity by reducing media consumption. Iterative Fourier transform (IFT) algorithm is one of easiest non-interferometry methods. We choose to use IFT algorithm due to its compact and stable realized system and simple single-shot operation. Strong constraint conditions such as phase-only and embedded data which are known phase values of the certain positions on the encoded data page are provided to realize accurate and quick phase retrieval in the holographic data storage system.
We demonstrated the phase retrieval process of the recorded 4-level phase pattern in the media experimentally. Besides, we can realize one-time Nyquist frequency recording which is the limitation of recording area by using the non-interferometric phase retrieval method and the periodicity of Fourier frequency spectrum. Therefore, the media consumption can be reduced by 35%. Eventually, we can increase storage capacity by at least 1.5 times.
Data driven bidirectional reflectance distribution function (BRDF) models have been widely used in computer graphics in
recent years to get highly realistic illuminating appearance. Data driven BRDF model needs many sample data under
varying lighting and viewing directions and it is infeasible to deal with such massive datasets directly. This paper proposes
a Gaussian process regression framework to describe the BRDF model of a desired material. Gaussian process (GP), which
is derived from machine learning, builds a nonlinear regression as a linear combination of data mapped to a highdimensional
space. Theoretical analysis and experimental results show that the proposed GP method provides high
prediction accuracy and can be used to describe the model for the surface reflectance of a material.