Redundant information model for Fourier ptychographic microscopy.

Fourier ptychographic microscopy (FPM) is a computational optical imaging technique that overcomes the traditional trade-off between resolution and field of view (FOV) by exploiting abundant redundant information in both spatial and frequency domains for high-quality image reconstruction. However, the redundant information in FPM remains ambiguous or abstract, which presents challenges to further enhance imaging capabilities and deepen our understanding of the FPM technique. Inspired by Shannon's information theory and extensive experimental experience in FPM, we defined the specimen complexity and reconstruction algorithm utilization rate and reported a model of redundant information for FPM to predict reconstruction results and guide the optimization of imaging parameters. The model has been validated through extensive simulations and experiments. In addition, it provides a useful tool to evaluate different algorithms, revealing a utilization rate of 24%±1% for the Gauss-Newton algorithm, LED Multiplexing, Wavelength Multiplexing, EPRY-FPM, and GS. In contrast, mPIE exhibits a lower utilization rate of 19%±1%.

Snapshot spectroscopic Mueller matrix polarimetry based on spectral modulation with increased channel bandwidth.

This paper presents a snapshot spectroscopic Mueller matrix polarimetry based on spectral modulation. The polarization state generator consists of a linear polarizer in front of two high-order retarders, and the polarization state analyzer is formed by two non-polarization beam splitters incorporated with three high-order retarder/linear analyzer pairs. It can simultaneously generate three modulated spectra used for reconstructing the 16 spectroscopic Mueller elements of the sample. Since each of the modulated spectra produces seven separate channels equally spaced in the Fourier domain, the channel bandwidth can be enhanced efficiently compared with the conventional spectrally modulated spectroscopic Mueller matrix polarimetry. The feasibility of the proposed spectroscopic Mueller matrix polarimetry is demonstrated by the experimental measurement of an achromatic quarter-wave plate.

Snapshot polarized light scattering spectroscopy using spectrally-modulated polarimetry for early gastric cancer detection.

Polarized light scattering spectroscopy (PLSS) is a promising optical technique developed for the detection of cancer, which extracts the single scattering light to infer morphological information of epithelial cells. However, traditional PLSS uses either a rotatable polarizer or two orthogonal polarizers to purify the single scattering light, which makes it complicated and challenged to build a PLSS endoscope. Herein, we propose a snapshot PLSS with a single optical path to directly get the single scattering light for the first time. The single scattering light is encoded using the spectrally-modulated polarimetry and decoded using the continuous slide iterative method. Both the polystyrene microsphere solutions and the ex vivo gastric cancer samples are used to verify the method. The experimental results of the snapshot PLSS are consistent well with that of the traditional PLSS. The proposed method has a potential for the building of snapshot PLSS endoscope systems in future.

Spectroscopic Mueller matrix polarimeter based on spectro-temporal modulation.

A spectroscopic Mueller matrix polarimeter based on spectro-temporal modulation with a compact, low-cost, and birefringent crystal-based configuration has been developed. The polarization state generator and polarization state analyzer in the system consists of a polarizer in front of two high-order retarders with equal thickness and a rotating achromatic quarter wave-plate followed by a fixed analyzer, respectively. It can acquire the 16 spectroscopic elements of the Mueller matrix in broadband with a faster measurement speed than that of the conventional spectroscopic Mueller matrix polarimeter based on a dual-rotating retarder. In addition, the spectral polarization modulation provided by the polarization state generator can produce five separate channels in the Fourier domain, which leads to a larger bandwidth of each channel than that of the existing spectral modulated spectroscopic Mueller matrix polarimeters. Experiment on the measurements of an achromatic quarter-wave plate oriented at different azimuths and SiO2 thin films deposited on silicon wafers with different thicknesses are carried out to show the feasibility of the developed spectroscopic Mueller matrix polarimeter.

Optimized design, calibration, and validation of an achromatic snapshot full-Stokes imaging polarimeter.

An achromatic snapshot full-Stokes imaging polarimeter (ASSIP) that enables the acquisition of 2D-spatial full Stokes parameters from a single exposure is presented. It is based on the division-of-aperture polarimetry using an array of four-quadrant achromatic elliptical analyzers as polarization state analyzer (PSA). The optimization of PSA is addressed for achieving immunity of Gaussian and Poisson noises. An extended eigenvalue calibration method (ECM) is proposed to calibrate the system, which considers the imperfectness of retarder and polarizer samples and the intensity attenuation of polarizer sample. A compact prototype of ASSIP operating over the waveband of 450-650 nm and an optimized calibration setup are developed. The achromatic performance is evaluated at three bandwidths of 10, 25, and 200 nm, respectively. The results show that the prototype with an uncooled CMOS camera works well at each bandwidth. The instrument matrix determined at the narrower bandwidth is more applicable to the wider one. The uncertainties of the calibrated instrument matrices and reconstructed Stokes parameters are improved by using the extended EMC at each bandwidth. To speed up the acquisition of high-contrast images, wide bandwidth along with short exposure time is preferable. The snapshot capability was verified via capturing dynamic scenes.

Compact snapshot optically replicating and remapping imaging spectrometer (ORRIS) using a focal plane continuous variable filter.

In this Letter, a novel snapshot spectral imaging technique, optically replicating and remapping imaging spectrometer, is presented. It is based on the combination of shifting subimages by a specially designed lenslet array (LA) and filtering subimages by a focal plane continuous variable filter (CVF). The 3D datacube is recovered by just using a simple image remapping process. The use of the LA and the focal plane CVF makes the system compact and low in cost. A handheld proof-of-principle prototype has been built and demonstrated; it covers a wavelength range of 380-860 nm with 80 spectral channels with a spatial resolution of 400×400 pixels.

Stokes imaging spectropolarimeter based on channeled polarimetry with full-resolution spectra and aliasing reduction.

A Stokes channeled interference imaging spectropolarimeter with full-resolution spectra and aliasing reduction is presented. The sensor uses a Wollaston prism, a Savart polariscope, and a linear analyzer as a birefringent interferometer, along with two high-order retarders to incorporate channeled polarimetry employing a tempo-spatially mixed modulated mode with no internal moving parts and offering a robust system. The performance of the system is verified through laboratory tests. Compared with the previous sensors, the most significant advantage of the described instrument is that the reconstructed spectra retain the resolution of the interferometer, and the errors in the reconstructed spectral resolved polarization state caused by aliasing between the interference channels are suppressed effectively. Additionally, the advantages of the interferometer are maintained, such as compact structure and high optical throughput.

Stokes polarimeter performance: general noise model and analysis: erratum.

We correct two errors in Appl. Opt.57, 4283 (2018)APOPAI0003-693510.1364/AO.57.004283.

Snapshot linear-Stokes imaging spectropolarimeter using division-of-focal-plane polarimetry and integral field spectroscopy.

In this paper, the design and experimental demonstration of a snapshot linear-Stokes imaging spectropolarimeter (SLSIS) is presented. The SLSIS, which is based on division-of-focal-plane polarimetry with four parallel linear polarization channels and integral field spectroscopy with numerous slit dispersive paths, has no moving parts and provides video-rate Stokes-vector hyperspectral datacubes. It does not need any scanning in the spectral, spatial or polarization dimension and offers significant advantages of rapid reconstruction without heavy computation during post-processing. The principle and the experimental setup of the SLSIS are described in detail. The image registration, Stokes spectral reconstruction and calibration procedures are included, and the system is validated using measurements of tungsten light and a static scene. The SLSIS's snapshot ability to resolve polarization spectral signatures is demonstrated using measurements of a dynamic scene.

High throughput static channeled interference imaging spectropolarimeter based on a Savart polariscope.

A high throughput static channeled interference imaging spectropolarimeter (CIISP) over 480-960nm spectral range is presented. The CIISP system includes two birefringent retarders and a Savart interferometer employing tempo-spatially mixed modulated mode with no internal moving parts, and offers a robust system and a high optical throughput to resist the instrument noise. The optical layout and operation of the CIISP sensor are presented in addition to the radiometric, spectral and improved polarimetric calibration techniques used with the system. The performance of the system is verified through laboratory tests, and the outdoor measurement demonstrates the sensor's ability for target identification, color measurement, and agriculture monitoring applications.

Generation of a controllable multifocal array from a modulated azimuthally polarized beam.

In this Letter, the focal spot areas of an azimuthally polarized beam modulated with a vortex-0-2π-phase plate or a π-phase-step plate are numerically found to be smaller than a radially polarized beam for three pupil functions with uniform, Gaussian, and Bessel-Gauss profiles. Several types of multizone phase plates are theoretically designed and numerically simulated for generating tight multifocal arrays from the azimuthally polarized beams for what we believe is the first time. The positions and polarization states of the multifocal arrays can be controlled simply by varying the pattern of the multizone plates. The produced multifocal array with controllable position and polarization is beneficial to parallel optical recording and parallel optical imaging.

Optimal design and performance metric of broadband full-Stokes polarimeters with immunity to Poisson and Gaussian noise.

In this paper, the design, optimization and analysis of broadband full-Stokes polarimeters with immunity to both Poisson and Gaussian noise are presented. Different from the commonly-used optimization metrics such as, the condition number (CN), the equally weighted variance (EWV), or the polarimetric modulation efficiency (PME) for Gaussian noise, the optimally balanced condition for Poisson noise (BCPN) is, for the first time, proposed and used as a metric for the optimization of polarimeters. The numerical results show that the polarimeters optimized with the BCPN have immunity to both Poisson and Gaussian noise. The broadband polarimeters optimized from the BCPN are achromatic and have similar polarimetric modulation properties over the waveband, in contrast to the polychromatic polarimeters optimized from the CN, EWV and PME, whose polarimetric modulation properties vary with wavelength.

Achromatization of waveplate for broadband polarimetric system.

A broadband polarimetric system with enhanced performance is highly desired in many applications, such as remote sensing. To achromatize a waveplate by combining a stack of retardance plates made of same material with different azimuths, two merit functions are presented in this Letter. The first merit function based on the Jones theorem directly accounts for the equivalent retardance and azimuthal angles of the combined plates. The second one can search for the optimal equivalent azimuthal angles automatically by using the condition number κ2 based on 2-norm or the equally weighted variance EWV, two figures of merit for the full-Stokes polarimeters, as the objective function. Our study within the framework of the simplest full-Stokes polarimeter shows that, for the super-achromatic 131.8° waveplate consisting of seven quartz plates, the root-mean-square errors of the κ2 and EWV are about 0.49% and 0.07%, and the maximum deviations of the equivalent retardance and azimuthal angle are approximately 0.42° and 0.59°, respectively, over the waveband of 0.4-0.7 µm. For the super-achromatic quarter-wave plate comprising seven quartz plates, the maximum deviations of the equivalent retardance and azimuthal angle are only 0.18° and 0.7°, respectively.

Error analysis of single-snapshot full-Stokes division-of-aperture imaging polarimeters.

Single-snapshot full-Stokes imaging polarimetry is a powerful tool for the acquisition of the spatial polarization information in real time. According to the general linear model of a polarimeter, to recover full Stokes parameters at least four polarimetric intensities should be measured. In this paper, four types of single-snapshot full-Stokes division-of-aperture imaging polarimeter with four subapertures are presented and compared, with maximum spatial resolution for each polarimetric image on a single area-array detector. By using the error propagation theories for different incident states of polarization, the performance of four polarimeters are evaluated for several main sources of error, including retardance error, alignment error of retarders, and noise perturbation. The results show that the configuration of four 132° retarders with angular positions of ( ± 51.7°, ± 15.1°) is an optimal choice for the configuration of four subaperture single-snapshot full-Stokes imaging polarimeter. The tolerance and uncertainty of this configuration are analyzed.

Achromatic Savart polariscope: choice of materials.

This paper presents the achromatization of Savart Polariscope to decrease the lateral-shear dispersion in the lateral displacement. The achromatic Savart Polariscope can be made from two different birefringent crystal materials. The achromatic model for the choices of material is presented. The achievements and performances of different achromatic Savart Polariscopes are demonstrated with numerical simulations and ray tracing program. The chromatic variation in lateral displacement can be reduced by an order of magnitude across the spectral range 0.4µm to 0.9µm.

Precise spectrum reconstruction of the Fourier transforms imaging spectrometer based on polarization beam splitters.

A method was proposed to precisely reconstruct the spectrum from the interferogram taken by the Fourier transform imaging spectrometer (FTIS) based on the polarization beam splitters. Taken the FTISs based on the Savart polariscope and Wollaston prism as examples, the distorted spectrums were corrected via the proposed method effectively. The feasibility of the method was verified via simulation. The distorted spectrum, recovered from the interferogram taken by the polarization imaging spectrometer developed by us, was corrected.

Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer.

Based on empirical mode decomposition (EMD), the background removal and de-noising procedures of the data taken by polarization interference imaging interferometer (PIIS) are implemented. Through numerical simulation, it is discovered that the data processing methods are effective. The assumption that the noise mostly exists in the first intrinsic mode function is verified, and the parameters in the EMD thresholding de-noising methods is determined. In comparison, the wavelet and windowed Fourier transform based thresholding de-noising methods are introduced. The de-noised results are evaluated by the SNR, spectral resolution and peak value of the de-noised spectrums. All the methods are used to suppress the effect from the Gaussian and Poisson noise. The de-noising efficiency is higher for the spectrum contaminated by Gaussian noise. The interferogram obtained by the PIIS is processed by the proposed methods. Both the interferogram without background and noise free spectrum are obtained effectively. The adaptive and robust EMD based methods are effective to the background removal and de-noising in PIIS.

Static hyperspectral imaging polarimeter for full linear Stokes parameters.

A compact, static hyperspectral imaging linear polarimeter (HILP) based on a Savart interferometer (SI) is conceptually described. It improves the existing SI by replacing front polarizer with two Wollaston prisms, and can simultaneously acquire four interferograms corresponding to four linearly polarized lights on a single CCD. The spectral dependence of linear Stokes parameters can be recovered with Fourier transformation. Since there is no rotating or moving parts, the system is relatively robust. The interference model of the HILP is proved. The performance of the system is demonstrated through a numerical simulation, and the methods for compensating the imperfection of the polarization elements are described.

Static polarization-difference interference imaging spectrometer.

A static polarization-difference imaging spectrometer is conceptually described and demonstrated through experiment. It consists of a Wollaston prism, a Savart polariscope, a linear analyzer, and a CCD camera. This design improves the existing polarization-difference system by eliminating its moving parts and obtaining the spectral variation of the polarization state, and making the system more compact and robust. After simultaneously acquiring two sequential interference images corresponding to two orthogonal polarization states, the hyperspectral images of the states can be reconstructed, respectively. The use of uniaxial birefringent crystal can widen the detectable spectral region.

Spectrum reconstruction based on the constrained optimal linear inverse methods.

The dispersion effect of birefringent material results in spectrally varying Nyquist frequency for the Fourier transform spectrometer based on birefringent prism. Correct spectral information cannot be retrieved from the observed interferogram if the dispersion effect is not appropriately compensated. Some methods, such as nonuniform fast Fourier transforms and compensation method, were proposed to reconstruct the spectrum. In this Letter, an alternative constrained spectrum reconstruction method is suggested for the stationary polarization interference imaging spectrometer (SPIIS) based on the Savart polariscope. In the theoretical model of the interferogram, the noise and the total measurement error are included, and the spectrum reconstruction is performed by using the constrained optimal linear inverse methods. From numerical simulation, it is found that the proposed method is much more effective and robust than the nonconstrained spectrum reconstruction method proposed by Jian, and provides a useful spectrum reconstruction approach for the SPIIS.