Early Posting

Accepted papers to appear in an upcoming issue

Optica Publishing Group posts prepublication articles as soon as they are accepted and cleared for production. See the FAQ for additional information.

First Experimental Investigation on Backscattering Interference Cancellation for Full-duplex UOWC Based on Time-reversal Preprocessing

Weijie Liu, Shuzhe Zhang, Nuo Huang, and Zhengyuan Xu

DOI: 10.1364/JOSAA.516949 Received 27 Dec 2023; Accepted 26 Mar 2024; Posted 26 Mar 2024  View: PDF

Abstract: A co-frequency and full-duplex (FD) underwater optical wireless communication (UOWC) system hasthe potential to significantly enhance spectral efficiency, reduce complexity, and further facilitate UOWCnetworking. However, the inevitable performance degradation due to self-interference introduced bybackscattering presents a significant challenge. In this paper, we first experimentally explore the inherent characteristics of the underwater backscattering channel. Subsequently, we propose a digitaldomain backscattering interference cancellation (BIC) algorithm for FD-UOWC systems, incorporating atime-reversal preprocessing. We then experimentally investigate the communication performance of anFD-UOWC system to verify the feasibility of the proposed BIC algorithm under different channel conditions. The experimental results validate the effectiveness of the proposed method, yielding substantialenhancements in bit error rate performance across diverse scenarios.

Fluorescence Molecular Tomography Based on Online Maximum a Posteriori Estimation Algorithm

Xia Cheng, Siyu Sun, Yinglong Xiao, Wenjing Li, Jintao Li, Jingjing Yu, and Guo hongbo

DOI: 10.1364/JOSAA.519667 Received 26 Jan 2024; Accepted 25 Mar 2024; Posted 26 Mar 2024  View: PDF

Abstract: Fluorescence Molecular Tomography (FMT) is a noninvasive, radiation-free, and highly sensitive opticalmolecular imaging technique for early tumor detection.However, inadequate measurement information alongwith significant scattering of near-infrared light withinthe tissue leads to high ill-posedness in the inverseproblem of FMT. To improve the quality and efficiency ofFMT reconstruction, we build a reconstruction modelbased on Log-sum regularization and introduce an OnlineMaximum a Posteriori Estimation (OPE) algorithm tosolve the non-convex optimization problem. The OPEalgorithm approximates a stationary point by evaluatingthe gradient of the objective function at each iteration, andits notable strength lies in the remarkable speed ofconvergence. The results of simulations and experimentsdemonstrate that the OPE algorithm ensures goodreconstruction quality and exhibits outstandingperformance in terms of reconstruction efficiency.

Design of Dual Hollow Beam Optical Antenna based on Fresnel Lens-Conical Lens Combination

Yunlong Li, Liang Zhong, Shuaikang Fu, Yan Qin, Jianing Liu, Ping Jiang, and Yang Huajun

DOI: 10.1364/JOSAA.517287 Received 28 Dec 2023; Accepted 25 Mar 2024; Posted 25 Mar 2024  View: PDF

Abstract: To improve the transmission efficiency of Cassegrain antennas and enable the simultaneous transmission of signals with different wavelengths in the antenna system, this study introduces novel Fresnel lenses and conical lenses in front of the Cassegrain antenna at the transmitting end, at the receiving end, reflective mirrors and focusing lenses are introduced. A detailed description is provided of the design process for the novel Fresnel lens, as well as the impact of various parameters on the hollow radius when combined with the conical lens. Based on the laws of vector reflection and refraction, simulations are performed to track the propagation of light through the entire communication system and lens pairs, providing transmission efficiency plots of the antenna system under deflection and off-axis conditions. Taking into account practical factors such as lens chamfer, transmittance, Cassegrain antenna reflectance, and material dispersion, the transmission efficiency of the antenna system at 1550nm wavelength can still reach 93.45%. The proposed method not only improves the transmission efficiency of Cassegrain antennas but also enables the transmission of different information through the inner and outer layers of the antenna system.

Advanced Linear Axial Wavelength Spreading through Cascaded Double Hyperchromats

Lukas Werner, Hartmut Hillmer, and Robert Brunner

DOI: 10.1364/JOSAA.521502 Received 12 Feb 2024; Accepted 25 Mar 2024; Posted 25 Mar 2024  View: PDF

Abstract: This study explores the design and optimization of cascaded double-hyperchromatic optical systems (i.e. 2 x 2 lenses), focusing on achieving an extremely linear axial spectral decomposition characterized by an exceptionally low equivalent Abbe number. The investigation involves two double hyperchromats, considering both purely refractive systems and hybrid configurations that combine refractive and diffractive elements. For purely refractive systems, alternating focal lengths signs of divergent and collective lenses are crucial to achieve significant axial chromatic dispersion. In hybrid systems, the position of the Diffractive Optical Element (DOE) and the selection of focal lengths play key roles in obtaining extremely low equivalent Abbe numbers. The optimized systems demonstrate absolute equivalent Abbe numbers of 0.983 for purely refractive and 0.65 for hybrid systems—more than four times lower than the absolute Abbe number of a single diffractive element. Notably, even systems using standard materials exhibit significantly low equivalent Abbe numbers of 2.5 and 1.4 for pure refractive and hybrid configurations, respectively. These results offer promising opportunities for improving optical applications based on axial spectral decomposition, overcoming previous limitations of axial chromatic spreading.

Quaternion fast and accurate polar harmonic Fourier moments for color images analysis and object recognition

Si Yang and Ansheng Deng

DOI: 10.1364/JOSAA.514567 Received 01 Dec 2023; Accepted 24 Mar 2024; Posted 25 Mar 2024  View: PDF

Abstract: Image moments, as a kind of global feature descriptor ofimages, have become a valuable tool for pattern recognition and image analysis. However, traditional methodsare mainly used to deal with grayscale images. In thispaper, we apply quaternions to fast and accurate polarharmonic Fourier moments, proposing a kind of quaternion fast and accurate polar harmonic Fourier moments(QFAPHFMs) capable of handling color images. Furthermore, this paper provides a detailed analysis of theinvariance of QFAPHFMs under rotation, scaling, andtranslation transformations. The experimental resultsshow that QFAPHFMs exhibits excellent performance inboth image reconstruction and object recognition tasks.QFAPHFMs achieve accurate image reconstruction under noiseless and noisy conditions, and demonstrateexcellent recognition performance in the color-basedobject recognition task.

Minimizing Optical Attribute Errors for Lane Departure Warning System Using Ultra-Wide Angle Camera

Hyungtae Kim and Joonki Paik

DOI: 10.1364/JOSAA.495368 Received 11 May 2023; Accepted 23 Mar 2024; Posted 25 Mar 2024  View: PDF

Abstract: Advanced Driver Assistance Systems (ADAS) rely on Lane Departure Warning(LDW) technology to enhance safety while driving. However, the current LDW method islimited to cameras with standard angles of view, such as mono cameras and black boxes. Inrecent times, more cameras with ultra-wide-angle lenses are being used to save money andimprove accuracy. However, this has caused some problems such as fixing optical distortion,making the camera process images faster, and ensuring its performance. To effectively implementLDW, we developed three technologies: i) distortion correction using error functions based onthe projection characteristics of optical lenses, ii) automatic vanishing point estimation usinggeometric characteristics, and iii) lane tracking and lane departure detection using constraints. Theproposed technology improves system stability and convenience through automatic calculationand updating of parameters required for LDW function operation. By performing automatic distortion correction and vanishing point estimation, it has also been proven that fusion withother ADAS systems including front cameras is possible. Existing systems that use vanishingpoint information do not consider lens distortion and have slow and inaccurate vanishing pointestimation, leading to a deterioration of system performance. The proposed method enables fastand accurate vanishing point estimation, allowing for adaptive responses to changes in the roadenvironment.

Tutorial: Nonlinear Ray Tracing in Focused Fields. Part 3: Monochromatic Wavefront Aberration

qin yu and Bryan Hennelly

DOI: 10.1364/JOSAA.503924 Received 29 Aug 2023; Accepted 22 Mar 2024; Posted 26 Mar 2024  View: PDF

Abstract: Using the flux tracing algorithm developed in the previous two parts, we examine the nonlinear rays that pass through the focus of a lens containing monochromatic aberrations. Lens aberration is modeled differently in the numerical propagation algorithms relating to the thin lens and the ideal lens case. For the former, an additive phase term is applied to the transmission function of the thin lens, which describes a distortion in the thickness function of the lens, and for the latter an additive phase term is added to the pupil function of the lens (the Fourier transform of the image plane). In both cases, the Zernike polynomials are applied to model various aberrations including spherical, defocus, comatic, astigmatism, trefoil, and quadrafoil. Despite the different methods of modelling aberration for the two types of lens, remarkably similar results are obtained for both cases. A discussion is also provided on the relation ship between classical wavefront aberration theory and nonlinear tracing. This paper demonstrates the extraordinary potential of nonlinear ray tracing to gain insights into complex optical phenomena.

Tutorial: Nonlinear Ray Tracing in Focused Fields. Part 2: Tracing the Flux.

Bryan Hennelly and qin yu

DOI: 10.1364/JOSAA.503925 Received 29 Aug 2023; Accepted 22 Mar 2024; Posted 26 Mar 2024  View: PDF

Abstract: In this three part paper, we develop a method to trace the lines of flux through a three-dimensional wavefield by following a direction that is governed by the derivative of the phase at each point, a process that is best described as flux tracing but which we interchangeably name as 'nonlinear ray tracing'. In the first part we focused on the high-speed calculation of focused three-dimensional complex wavefields in the paraxial approximation for TEM00 and TEM01 laser modes. The algorithms developed in the first paper are first used to generate the three-dimensional grid of samples of the complex wavefield in the focal region. In this second part, we focus on tracing a flux through this three-dimensional point cloud. For a given 'ray' at an arbitrary position in the 3D volume, interpolation of the three-dimensional samples is applied to determine the derivative of the phase (normal to the direction of propagation) at the ray position, which is then used to direct the ray as it 'propagates' forward in a straight line over a short distance to a subsequent plane; the process is repeated between consecutive planes. The initial origin of the ray can be chosen arbitrarily at any point and the ray can be then be traced through the volume with appropriate interpolation. Results are demonstrated for focused wavefields in the absence of aberrations, corresponding to the cases highlighted in the first paper. Some of the most interesting results relate to focused Laguerre-Gaussian beams, for which the rays are found to spiral at different rates of curvature. In the third paper we extend the application of this algorithm to the investigation of lens aberration.

Tutorial: Nonlinear Ray Tracing in Focused Fields. Part 1: Calculating 3D Complex Wavefields.

qin yu and Bryan Hennelly

DOI: 10.1364/JOSAA.503926 Received 30 Aug 2023; Accepted 22 Mar 2024; Posted 26 Mar 2024  View: PDF

Abstract: In this three part paper, we develop a method to trace the lines of flux through a three-dimensional wavefield by following a direction that is governed by the derivative of the phase at each point, a process that is best described as flux tracing but which we interchangeably name as ’nonlinear ray tracing’. In this first part, we focus on the high-speed calculation of three-dimensional complex wavefields, which is a necessary precursor to flux tracing. The basis of this calculation is the Angular Spectrum method, a well known numerical algorithm that can be used to efficiently and accurately calculate diffracted fields for numerical apertures <0.7. It is known that this approach yields identical predictions to the first Rayleigh-Sommerfeld solution. We employ the Angular Spectrum method to develop two algorithms that generate the 3D complex wavefield in the region of focus of a lens. The first algorithm is based on the thin lens approximation and the second is based on the concept of an ideal lens, which can be modelled using an optical Fourier transform. Both algorithms are investigated to calculate focused laser beams with TEM00 and TEM01 laser profiles. The three-dimensional sampling requirements of the focused field are investigated in addition to the computational and memory efficiency of the two algorithms. These two algorithms generate the 3D scaffold for the flux tracing method developed in the second paper and in the third paper we highlight the application of the method to understanding monochromatic lens aberration. Disregarding the second and third papers, the two algorithms developed in this paper are interesting for anyone seeking to compute focused fields in three-dimensions.

Relationship between Turbulent Image Variance and Average Image Gradient

Guy Potvin

DOI: 10.1364/JOSAA.516238 Received 18 Dec 2023; Accepted 21 Mar 2024; Posted 21 Mar 2024  View: PDF

Abstract: Optical turbulence can cause substantial distortions in imaging over long horizontal paths.For Lambertian objects, these distortions are only seen where there is a gradient in the object's radiance.It is possible to establish a relationship between the intensity variance of a turbulent image and the average image's gradient squared.We test the validity of a linear relationship between these quantities using turbulent imaging data.We find that it performs reasonably well for weak and intermediate optical turbulence regimes, but that some discrepancies remain to be explained.The linear relationship may permit the determination of turbulence parameters using imaging data.

Ultra-high order mode-assisted optical differentiator for edge detection with high tunability

Chengyu Wu, Yanbin Tang, J Shi, Cuicui Li, Wenli He, Gangyun Xu, Jian Wu, and Xianping Wang

DOI: 10.1364/JOSAA.520871 Received 05 Feb 2024; Accepted 21 Mar 2024; Posted 21 Mar 2024  View: PDF

Abstract: An optical spatial differentiator based on the photonic spin Hall effect (PSHE) with hightunability is presented. By utilizing the characteristics of ultra-high order modes in the symmetricalmetal cladding waveguide, the Fresnel reflection coefficient spectrum exhibits a narrow peak widthand low trough at the resonant incident angles, resulting in high sensitivity to changes in incidentangle-induced spatial shift caused by PSHE (the highest ∂(|r𝑠/r𝑝|) ∂𝜃 value can reach 107). Afterpolarization transformation and extinction, the output field demonstrates differential operation withrespect to the input field. When applied to edge detection, our differentiator can achieve tunableresolution edge images by adjusting the incident angle. Our proposed edge detection scheme haspotential applications for cellular and molecular imaging through two-dimensional extension via thetarget rotation.

Effect of Surface Anchoring Energy on Liquid Crystal Optical Waveguide-Based Polarization Rotator

Zheng Tao ZHA

DOI: 10.1364/JOSAA.520908 Received 05 Feb 2024; Accepted 20 Mar 2024; Posted 21 Mar 2024  View: PDF

Abstract: This study reports the effect of the surface anchoring energy of the liquid crystal (LC) cell on the performance of the liquid crystal optical waveguide polarization rotator (LCOW-PR) with the purpose of providing a theoretical reference for their practical preparation. Firstly, the expression for the deflection angle of the director at the boundary of the LC cell is derived so that the distributions of director and dielectric tensor of the LC can be accurately solved under any anchoring energy. On this basis, the correlation between crucial indicators such as polarization conversion length (PCL) together with polarization conversion efficiency (PCE) of the LCOW-PR and the anchoring effect strength is constructed by combining with the existing numerical algorithms. The numerical results show that the maximum variation of the PCL is lower than 0.1 μm as the anchoring effect strength increases from 1×10-6 J/m2 to 1×10-3 J/m2, while the PCE decreases from 99.72% to 78.33%. This implies that the PCL of the LCOW-PR does not depend on the surface anchoring energy, but the anchoring effect strength of the orientational layer must be controlled to the order of 10-6 J/m2 or even lower to achieve high-performance conversion between polarization modes. Simultaneously, the effectiveness of the calculations in this work is verified with the help of coupled mode theory as well as a comparison with previous reports.

Virtually Measuring Layered Material Appearance

Kewei XU, Arthur cavalier, Benjamin Bringier, Mickaël Ribardière, and Daniel Meneveaux

DOI: 10.1364/JOSAA.514604 Received 30 Nov 2023; Accepted 17 Mar 2024; Posted 18 Mar 2024  View: PDF

Abstract: This paper describes the design and the implementation of a virtual gonioradiometer dedicated to theanalysis of layered materials BSDF. For a given material sample, interfaces between layers are representedby geometric meshes, associated with elementary reflectances. Light scattering is performed using pathtracing. Our system is composed of 5 hemispherical sensors, which cells have uniform solid angles, anda close-to-uniform geometry. The upper hemisphere captures the reflected radiance distribution, whilethe other 4 collect the light energy lost by the sample sides. Sensor resolutions can be set to gather veryfine details of the BSDF. With the proposed system, any type of virtual surface reflection and transmissioncan be simulated, with several controllable surface layers, and with any type of reflection configuration,including direct reflections, two bounces of reflection, or all contributions. A series of results are providedwith several types of layered materials, as well as discussion and analysis concerning the assumptionsmade with analytical layered BSDF models. We also propose an in-depth study of the side effects thatinevitably appear when measuring such (real) material configurations. Finally, our system will be freelyavailable to the community (open source dissemination). ©

Dynamic iterative correction algorithm for designing diffractiveoptical elements

Hu Chi, zhang jin, jiang shilei, and sun guobin

DOI: 10.1364/JOSAA.516657 Received 21 Dec 2023; Accepted 12 Mar 2024; Posted 12 Mar 2024  View: PDF

Abstract: When utilizing the Gerchberg-Saxton (GS) algorithm to design diffractive opticalelements, correction coefficients are introduced to improve the quality of the design results. Themain design idea is to correct the target information dynamically during the iterative calculationprocess. The effectiveness of the proposed method is demonstrated through the verification of beamshaping and phase-type hologram designs. Compared to the traditional GS algorithm, the results ofbeam shaping show that the light intensity nonuniformity and the RMSE (root-mean-square error)of the shaped spot are reduced by an order of magnitude. The results of phase-type holograms showthat the reconstructed image’s PSNR (peak signal-to-noise ratio) is improved by about 12dB. Finally,the paper also discusses the selection of correction coefficients, providing insights into the selectionof optimal design correction coefficients. The simulation and experimental results show that theimproved algorithm proposed in this paper is not only simple in design but also highly efficient inobtaining high-quality phase structure, which is of great help in designing high-quality diffractiveoptical elements.

Res-U2Net: Untrained Deep Learning for PhaseRetrieval and Image Reconstruction

Carlos Osorio Quero, Daniel Leykam, and Irving Rondon Ojeda

DOI: 10.1364/JOSAA.511074 Received 03 Nov 2023; Accepted 12 Mar 2024; Posted 12 Mar 2024  View: PDF

Abstract: Conventional deep learning-based image reconstruction methods require a large amount of training datawhich can be hard to obtain in practice. Untrained deep learning methods overcome this limitation bytraining a network to invert a physical model of the image formation process. Here we present a noveluntrained Res-U2Net model for phase retrieval. We use the extracted phase information to determinechanges in an object’s surface and generate a mesh representation of its 3D structure. We compare theperformance of Res-U2Net phase retrieval against UNet and U2Net using images from the GDXRAYdataset.

Simulating a turbulent video affected byspatiotemporally-varying blur and tilt usingtemporal cross-correlation of intermodal Zernikecoefficients

Or Maor and Yitzhak Yitzhaky

DOI: 10.1364/JOSAA.514892 Received 01 Dec 2023; Accepted 12 Mar 2024; Posted 12 Mar 2024  View: PDF

Abstract: Videos captured in long-distance horizontal imaging through the atmosphere, suffer fromdynamic spatiotemporal movements and blur caused by the air turbulence. Simulations of atmosphericturbulence in such videos, which have been conducted in the past, are difficult to compute. Our goal inthis research is to develop an effective simulation algorithm of videos affected by atmospheric turbulencecharacterized by spatiotemporally-varying blur and tilt, when supplied with a given image. Weaccomplish this via extending an already-established way that simulates atmospheric turbulence in asingle image, by incorporating turbulence properties in the time domain that include both the tilts andblurring effects. This study also extends our previous work that simulated turbulence, but did not considerthe space-varying property of the blur. This is done by employing the relationship between turbulenceimage distortions and the intermodal correlations of the Zernike coefficients in time and space, and alsovia analyzing the spatiotemporal matrix that represents the spatial correlation of movements betweendifferent frames. The proposed method can facilitate the production of simulations, given turbulenceproperties that include turbulence strength, object distance, and height. The simulation is applied tovideos with low and high frame-rates, and the differences between them are analyzed. The proposedmethod can prove useful when generating machine-learning algorithms that apply to videos affected byatmospheric turbulence, which require large labeled video datasets (with controlled turbulence andimaging parameters) for training.

EFNet: Enhancing feature information for 3D object detection in LiDAR point clouds

xin meng, Yuan Zhou, Kaiyue DU, Jun Ma, Jin Meng, Aakash Kumar, Jiahang Lv, JONGHYUK kim, and Shifeng Wang

DOI: 10.1364/JOSAA.511948 Received 09 Nov 2023; Accepted 10 Mar 2024; Posted 12 Mar 2024  View: PDF

Abstract: With the development of autonomous driving, there has been considerable attentionon 3D object detection using LiDAR. Pillar-based LiDAR point cloud detection algorithms areextensively employed in the industry due to their simple structure and high real-timeperformance. Nevertheless, the pillar-based detection network suffers from significant loss of3D coordinate information during the feature degradation and extraction process. In the paper,we introduce a novel framework with high performance, termed EFNet. The EFNet uses theEnhancing Pillar Feature Module (EPFM) to provide more accurate representations of featuresfrom two directions: pillar internal space and pillar external space. Additionally, the Head UpModule (HUM) is utilized in the detection head to integrate multi-scale information andenhance the network's information perception ability. The EFNet achieves impressive resultson the nuScenes datasets, namely 53.3% NDS and 42.4% mAP. Compared to the baselinePointPillars, EFNet improves 8% NDS and 11.9% mAP. The results demonstrate that theproposed framework can effectively improve the network's accuracy while ensuringdeployability.

Optimized Stokes imaging for highly resolved optical speckle fields, part III: Topological analysis of polarimetric states distributions with optimized data representations

Jonathan Staes and Julien Fade

DOI: 10.1364/JOSAA.516717 Received 21 Dec 2023; Accepted 09 Mar 2024; Posted 11 Mar 2024  View: PDF

Abstract: In this last article of a three-paper series focusing on Stokes polarimetry of opticalspeckle fields resolved at the individual speckle grain scale, experimental results are provided ontest samples of varying nature and polarization properties, and are analyzed extensively. Forthis purpose, a review of the classical ways of displaying Stokes polarimetric information isprovided. Then, some original alternative graphical representations are introduced that ensureoptimal readability and interpretability of the Stokes imaging data in the context of speckle fieldpolarimetry, and it is shown how they can be adapted to various observation scales. Finally, thesetools are implemented in order to provide a topological analysis of the distribution of the states ofpolarization across a speckle pattern, and in the vicinity of polarimetric singularities of the field.

Optimized Stokes imaging for highly resolved optical speckle fields, part II: Optimal acquisition & estimation strategies

Jonathan Staes and Julien Fade

DOI: 10.1364/JOSAA.516702 Received 21 Dec 2023; Accepted 09 Mar 2024; Posted 14 Mar 2024  View: PDF

Abstract: In this second article of a three-paper series focusing on Stokes polarimetry ofoptical speckle fields resolved at the individual speckle grain scale, a theoretical study basedon numerical simulations is presented in order to establish the optimum sensing, estimationand processing strategies that guarantee the best precision, accuracy and robustness for Stokespolarimetry in this specific context. In particular, it is demonstrated that the so-called StateOf Polarization Analysis by Full Projection on the Poincaré space (SOPAFP) approach can beoptimized in order to ensure best estimation performance. These numerical simulations also makeit possible to establish that the SOPAFP approach provides better results in terms of robustness toresidual experimental imperfections of the setup when compared to classical Stokes polarimetryapproaches.

Optimized Stokes imaging for highly resolved optical speckle fields, part I: Optimized experimental setup

Jonathan Staes and Julien Fade

DOI: 10.1364/JOSAA.516693 Received 21 Dec 2023; Accepted 27 Feb 2024; Posted 27 Feb 2024  View: PDF

Abstract: In this first article of a three-paper series focusing on Stokes polarimetry of optical speckle fields resolved at the individual speckle grain scale, a review of the state of the art techniques for such experimental investigations is first provided. An optimized experimental setup is then extensively described which allows polarimetric Stokes measurements on such complex interference patterns to be carried out at each location of the speckle field without disturbing the wavefront. Specific calibration procedures are also described in order to provide the estimation of trustful polarimetric properties of light across a resolved speckle field.

Matrix-based integral transformations for Stokesimaging with partially polarized and partially coherentlight

Wei Wang and Mitsuo Takeda

DOI: 10.1364/JOSAA.517693 Received 03 Jan 2024; Accepted 22 Feb 2024; Posted 27 Feb 2024  View: PDF

Abstract: With the aid of the matrix-based integral transforms, called matrix convolution and matrix direct correlation, weprovide a simplified expression for the space-domain and frequency-domain calculations of polarization imagingwith partially polarized and partially coherent light. As an example of practical interest, a formula for Stokesimaging, based on the generalized Stokes parameters, is presented, in which a hypermatrix-based transmissioncross-coefficient matrix is introduced to represent the combined effects of diffraction and aberrations of apolarization-dependent imaging system and a partially-polarized and partially-coherent illumination system. Thecoherent limit and the incoherent limit in Stokes imaging are discussed with the optical transfer matrix, alongwith its frequency response for a diffraction-limited incoherent polarization imaging system. A generalizedconcept of the apparent transfer matrix is introduced to deal with the nonlinearity inherent in the polarizationimaging system under partially coherent illumination.