Deep image prior plus sparsity prior: toward single-shot full-Stokes spectropolarimetric imaging with a multiple-order retarder

Abstract

Compressive full-Stokes spectropolarimetric imaging (SPI), integrating passive polarization modulator (PM) into general imaging spectrometer, is powerful to capture high-dimensional information via incomplete measurement; reconstruct algorithm is needed to recover 3D datacube (x, y, λ) for each Stokes parameter. However, existing PMs usually consist of complex elements and enslave to accurate polarization calibration, current algorithms suffer from poor imaging quality and are subject to noise perturbation. In this work, we present a single multiple-order retarder followed a polarizer to implement passive spectropolarimetric modulation for the first time. After building a unified forward imaging model for SPI, we propose a deep image prior plus sparsity prior (DIP-SP) algorithm for high-quality reconstruction. The method based on untrained network does not need training data or accurate polarization calibration, and can simultaneously reconstruct the 3D datacube and achieve self-calibration. Furthermore, as an instance, we integrate the simplest PM into our miniature snapshot imaging spectrometer to form a single-shot SPI prototype for the first time. Both simulations and experiments verify the feasibility and outperformance of our SPI scheme. It provides a novel paradigm that allows general spectral imaging systems to become passive full-Stokes SPI systems by integrating the simplest PM without changing their intrinsic mechanism. 1. INTRODUCTION High-dimensional optical information such as irradiance, spectrum, space, polarization and phase are vital for comprehensively non-invasion characterization of targets over diverse scenes [1,2]. The acquisition of maximal information using a single integrating system is highly desired in consideration of volume, weight, integration, portability and cost [3-8]. As shown in Fig. 1, spectropolarimetric imaging (SPI) integrates a polarization modulator (PM) into imaging spectrometer is a kind of such versatile integrating system [5, 9-15], which can obtain spatio-spectrally resolved 3D datacube (x, y, λ) for each of interested Stokes parameters (S 0 , S 1 , S 2 , S 3). It has aroused wide applications in the fields of aerosol detection [16], planetary exploration [17], remote sensing [18], biomedical diagnosis [19,20], etc. The design chain of SPI system involves three aspects: the PM, the imaging spectrometer, and reconstruction algorithm. It is extremely meaningful to design a kind of advanced PM and algorithm that can directly adapt to general imaging spectrometers (multispectral/hyperspectral systems) including scanning (whiskbroom, pushbroom, windowing, framing) [21] and snapshot modes [6,7]. The PM is a key component that determines the number of measurements in the polarization dimensionality. According to sampling mechanism, the PMs can be classified into two types [5,7]: well-sampled PM and under-sampled PM. For the former, the number of polarization measurements is equal to the number of interested Stokes parameters. In this case, time-sequence active scanning hardware in a single optical path or snapshot passive hardware using multiple parallel optical paths are usually employed [5]. As a result, the acquisition, storage, and processing of these measurements may result in significant time costs, power consumption, space/memory footprint, and possibly human resource costs. Meanwhile, designing and