High-order Retarders Research Articles

Widefield quantitative polarized light microscopy using spectrally encoded null polarimetry.

Quantitative polarized light microscopy enables determination of optical retardation and azimuth of birefringent specimens and is a powerful tool for label-free imaging in the fields of biology and pathology. We have recently proposed a device for fast laser-scanning birefringence microscopy based on a near-infrared wavelength-swept laser and spectral encoding of polarization, resulting in a channeled spectrum generated during the wavelength-sweep of the laser and highly sensitive to optical retardation [Opt. Lett.49, 387 (2024)10.1364/OL.507576]. In this Letter, we propose its transposition to visible widefield imaging using a white light source and a high-order retarder for spectral encoding and a hyperspectral camera to record the channeled spectrum at each point of the image in parallel. The method proposed here allows for straightforward conversion of any widefield microscope into a highly sensitive and quantitative polarized light microscope.

Full-Stokes Polarization Raman Microscope

Polarization Raman spectroscopy (PRS) can provide additional information regarding molecular orientation and symmetry compared to Raman spectroscopy, while traditional PRS only records parallel and perpendicular components of Raman scattered light. Recently, a channelled polarization Raman microscope was developed to acquire the linear-Stokes polarization Raman spectra. Since the circular polarization Raman spectra may contain important information related to molecular structure, a full-Stokes polarization Raman microscope (FPRM) is presented in this paper. A polarization modulator consisting of two high order retarder and a linear polarizer is used to modulate the full-Stokes polarization information into frequency domain, and the polarization demodulation is achieved by the Fourier transformation method. Only one camera shot is needed to acquire all polarization components of the Raman scattered light, and the feasibility of FPRM is verified by simulations.

Polarization Raman microscope based on channeled spectropolarimetry

A channeled polarization Raman microscope (CPRM) based on spectrally-modulated polarimetry is introduced. The CPRM modulates the polarization information into a spectrum by an achromatic quarter-wave plate, a high order retarder, and a linear polarizer. The linear Stokes parameters of Raman scattered light can be decoded from this spectrum by the Fourier transformation method (FTM). When compared with the traditional polarization Raman microscope, the proposed system removes the need of rotating the analyzer multiple times for the analysis of the polarization state, thus accelerating the data acquisition process. The feasibility and correctness of CPRM are validated by experiments, and the results of the instrument are shown in point and mapping spectroscopy modes. The results on polypropylene fiber and tooth samples confirm CPRM's abilities to characterize molecular orientation and enhance image contrast.

Design of channeled spectropolarimeters.

I present design and tolerancing guidelines for constructing channeled spectropolarimeter systems employing high-order retarders. The discussion includes how to select appropriate retarder thicknesses, how to accurately align the elements, how to tolerance the retarders, and how to analyze the effect of different polarizer types on the system performance.

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.

Modified snapshot spectroscopic ellipsometry based on optical frequency-domain interferometry

We propose a modified snapshot spectroscopic ellipsometry based on optical frequency-domain interferometry. The proposed system employs only one high-order retarder and a Wollaston prism to analyze the changed state of polarization of the reflected light and can provide the maximum channel bandwidth of the channeled spectroscopic ellipsometry. The spectroscopic ellipsometric parameters of isotropic samples can be accurately measured in a measurement speed of 40 ms without mechanical or active modulation devices. The feasibility of the proposed spectroscopic ellipsometry is demonstrated by experiments.

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.

Analysis of the retarders’ errors in the channeled spectropolarimeters

Channeled spectropolarimetry (CS) system is an attractive scheme with compact structure, which can acquire full spectrally resolved Stokes parameters without any internal moving or electrically controllable parts. For the CS system, retarders are the key components to extract the spectral polarization information of the targets. However, there always exist non-negligible errors brought by the retarders which would severely damage the measurement accuracy. In this paper, the effects of the retardance errors and orientation errors of the retarders on the measurement accuracy of three typical CS systems, including the dual high-order retarders system (DHRS), the single high-order retarder system (SHRS), and the linear spectropolarimetric system (LSPS), are theoretically derived and analyzed. A numerical simulation is then performed for verification. The analysis and simulation results show that the SHRS and DHRS are less sensitive to the retarders’ errors than the LSPS. Although the LSPS is only used for measurement of the linear polarization state, the measurement accuracy is affected by the circular polarization state of the input light.

Channeled compressive imaging spectropolarimeter.

A compressive imaging spectropolarimeter is proposed in this paper, capable of simultaneously acquiring full polarization, spatial and spectral information of the object scene. The spectral and polarization information is modulated through a combination of high-order retarders, a dispersion prism and a polarizer filter wheel. Using a random coded aperture, compressive sensing is applied to eliminate the channel crosstalk and resolution limitation of traditional channeled spectropolarimeters. The forward sensing model and inverse problem are developed. Computer simulation results are reported, followed by experimental demonstrations.

Channeled spectropolarimetry with increased bandwidth and aliasing reduction

A channeled spectropolarimetry with increased bandwidth and aliasing reduction that consists of a high order retarder and a Wollaston prism is presented. It has the advantages of compact, low-cost, static and a measurement speed of the complete spectrally resolved Stokes vector [S0(σ) S1(σ) S2(σ) S3(σ)]T around 30 ms. Compared with the conventional channeled spectropolarimetry, it can acquire full resolution S0(σ) reconstruction and S1(σ), S2(σ) and S3(σ) reconstruction without errors caused by dominant aliasing between the channels. Besides, the bandwidth of each channel increases by 7/3 times than that of conventional channeled spectropolarimetry. The feasibility of the proposed method is demonstrated by both simulation and laboratory experiments.

Easily implemented approach for the calibration of alignment and retardation errors in a channeled spectropolarimeter.

Calibration of the channeled spectropolarimeter is significant for the quantitative application of this instrument. In current calibration methods for a channeled spectropolarimeter, an absolute angle between the coordinate system of an auxiliary polarizer and the global coordinate system of the instrument is usually indispensable. The effectiveness of calibration depends on the precision of the absolute angle, while it is usually difficult to achieve in a practical calibration process. This paper presents an easily implemented method to simultaneously calibrate the alignment and retardation errors of high-order retarders for a channeled spectropolarimeter. In the presented method, the requirement of an absolute angle between the coordinate system of an auxiliary polarizer and the global coordinate system of the instrument is replaced by only rotating a relative angle in the coordinate system of the auxiliary polarizer itself. First, we theoretically derive the modified reconstruction model considering the alignment errors of high-order retarders. By analyzing and summarizing the modified reconstruction model, the calibration and compensation models of the alignment and retardation errors are further proposed. Then, two linearly polarized beams with a relative angle of 45° between them are utilized to determine the alignment and retardation errors. Based on these results, the alignment and retardation errors can be compensated by a software correction algorithm without any precise mechanical adjustments. The effectiveness and feasibility of the presented method are verified by numerical simulations and experiments. The advantage of easy implementation makes this calibration method more suitable to apply in the laboratory and to be on track for correcting the channeled spectropolarimeter.

Adaptive correction of retardations with immunity to alignment errors for a channeled spectropolarimeter.

Retardation errors of high-order retarders will decrease the accuracy of a channeled spectropolarimeter. Taniguchi et al. have proposed a self-calibration method to calibrate the retardations [Opt. Lett.31, 3279 (2006)OPLEDP0146-959210.1364/OL.31.003279]; however, they do not take into account the inevitable alignment errors of high-order retarders. In this paper, an adaptive correction method with immunity to alignment errors is proposed to reduce the effects of temperature variation on retardations. By separating and analyzing the amplitude terms and phase terms contained in the measurement data, the phase terms are utilized to correct the retardations, which makes the effectiveness of this adaptive correction method immune to the inevitable alignment errors of high-order retarders. The adaptive correction process can be accomplished in parallel to the measurement process without any auxiliary resources. The effectiveness and feasibility of this method is verified by simulations and experiments. The convenience and simplicity of the presented method make it extremely suitable for application on track.

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.

Full linearly stokes interference imaging spectropolarimeter based on channeled polarimetric technique with high optical throughput

A static full linearly Stokes interference imaging spectrpolarimeter (FLCIISP) over 400–800 nm spectral range is presented. The FLCIISP system includes an achromatic quarter wave plate, a high order retarder and a Savart interferometer. The instrument employs tempo-spatially mixed modulated mode without internal moving parts, offers a robust system and a high optical throughput to resist the instrument noise. The feasibility of the system was verified by simulation and laboratory experiments. Compare with the conventional channeled interference imaging spectropolarimeter, the resolution of the reconstructed spectrum is remarkably improved and the errors in reconstructed spectral Stokes parameters caused by aliasing are suppressed effectively.

Full linearly Stokes channeled polarimetric technique with low reconstruction errors

A novel full linearly Stokes channeled polarimetric technique is presented. The system includes an achromatic quarter wave plate, a high order retarder and interference imaging spectrometer. The principle of the system is verified by simulation. Compare with the conventional channeled polarimetric technique, the resolution of the reconstructed spectrum is remarkably improved and the errors in reconstructed spectral Stokes parameters caused by crosstalk are suppressed effectively. A compensation procedure is proposed to account for the alignment errors. An analytical treatment is given, followed by a numerical example to demonstrate the effectiveness of the compensation method.

Reduction of the effects of angle errors for a channeled spectropolarimeter.

Angle errors of high-order retarders will decrease the accuracy of a channeled spectropolarimeter. This paper presents an easily implemented and widely applicable method for reducing the effects of the angle errors. First, we theoretically derive a modified reconstruction model to express and analyze the effects of the angle errors. Based on the modified reconstruction model and current reference beam calibration technique, we put forward the modified reference beam calibration technique to reduce the effects of the angle errors. This method can calculate the angle errors by employing the amplitude terms, which have been ignored in the results of the current reference beam calibration. The effectiveness of the presented method is verified by numerical simulations, which show that the demodulated deviations of polarization parameters have been reduced by one order of magnitude. Experiments are further implemented to validate the proposed method. The convenience and wide applicability of the presented method make it suitable for regular correction of the instrument, especially for the case on track.

Methods of polarimetric calibration and reconstruction for a fieldable channeled dispersive imaging spectropolarimeter.

Polarimetric calibration and reconstruction methods for a fieldable channeled dispersive imaging spectropolarimeter (CDISP) are presented. A theoretical model for the polarimetric calibration is derived first. In the polarimetric calibration for the CDISP, the alignment errors of the polarimetric spectral intensity modulation module, and the polarization effects of the optical system and phase factors of the high-order retarders at different viewing angles, are considered and determined independently. Based on the results of the polarimetric calibration, the Stokes vector of the target is reconstructed through the derived reconstruction model. Simulation results with a fieldable CDISP designed for airborne remote sensing indicate that by using the presented polarimetric calibration and reconstruction methods, the measurement accuracy at each viewing angle of the fieldable CDISP can be improved. Experimental results are summarized and analyzed to demonstrate the effectiveness of the presented methods.

Dual Visual Cryptography Using the Interference Color of Birefringent Material

Visual cryptography is a method of encrypting an image into several encrypted images. Conventional visual cryptography can display only monochrome images. We previously proposed a color visual cryptography method that uses the interference color of high-order retarder films and encrypts one secret image into two encrypted images. In other words, this method can only encrypt one image at a time. In this paper, we propose a new method that encrypts two color images using interference color.

Alignment errors calibration for a channeled spectropolarimeter.

This paper presents a method to calibrate alignment errors for a channeled spectropolarimeter. A calibration model, including an alignment errors determination model and an alignment errors compensation model, is derived firstly. To determine the exact alignment errors of the high-order retarders and polarizer included in the spectropolarimeter, an auxiliary high-order retarder and a reference beam are used. The auxiliary high-order retarder does not affect the normal use of the spectropolarimeter and the polarization state of the reference beam needs not to be controlled accurately. Based on the determination results, the alignment errors are compensated by using a correction algorithm without any precise mechanical adjustments. Simulation results show that the alignment errors can be determined accurately and the errors of the reconstructed Stokes parameters due to the alignment errors are reduced effectively by the presented method. Finally, experimental results are summarized and analyzed to demonstrate the effectiveness of the calibration method.

Polarization state demodulation of channeled imaging spectropolarimeter by phase rearrangement calibration method

The basic principle of channeled Fourier-transform imaging spectropolarimeter (CFTISP) is outlined. The two mainstream techniques existing for performing polarization state demodulation are analyzed, which show uncertainty that may not be suitable for CFTISP based on lateral shear interferometer. A modified demodulation method for Stokes parameters is described. The method separate the phase of the sign and the high-order retarders’ retardations from the total phase acquired from the fast Fourier transform of the interferogram, which will not cause the amplitude error from the reference beam. Furthermore, the retardations and the residual phase error in each band introduced by instrument can be seen directly in this method. The effectiveness of this method is experimentally demonstrated with four known input states of polarization, and the results are satisfactory. The RMS error of each Stokes parameters is also presented, which demonstrates that the low spectral signal-to-noise ratio can increase the RMS error by nearly a factor of 2–5 for the individual Stokes parameters. The comparison of reconstructed results by four methods further demonstrates the effectiveness of the proposed method.