Polarization aberration of projection optics should be measured, controlled and compensated accurately in high numericalaperture image optical system, such as lithography tools for technical node of 14-5 nm. In this paper, we develop a threestep eigenvalue calibration method for polarization aberration measurement in-situ accurately. The whole system and subsystems can be calibrated by using the wide-view-angle quarter-wave plate as one of the reference samples. In addition, an experimental tool is developed to implement the proposed method, which is of significant importance to quantify and improve the properties of the projection optics in lithography.
An efficient method that allows spectral calibration for a Stokes polarimeter is presented in this paper. The calibration procedure only uses a reference polarizer to generate an arbitrary linear polarization state. The reference polarizer could also be calibrated while calibrating the Stokes polarimeter. In addition, this method does not involve the small-angle approximation and could avoid the influence of the initial azimuth error of the retarder and the reference polarizer. The experiment was carried out by a spectroscopy and a polarization state analyzer with a rotating wave plate. Experimental results show that the alignments of axis as well as the true retardation at a specific wavelength of the retarder are obtained.
Mueller polarization imaging technology can fully reflect the polarization characteristics of the sample, and can be used
as a method for imaging thin pathological sections of collagen tissue samples. So far, there has been no actual publication
about the detection of transplanted tendons using Mueller matrix imaging technology. In this paper, we apply the Mueller
imaging polarimeter for quantitative detection of rabbit transplanted tendon samples with or without tenocytes. The polar
decomposition parameters of the Mueller matrix of the rabbit tendon tissues are calculated and analyzed. Quantitative
analysis showed that tenocytes caused the decrease of tendon fibers retardance and the increase of standard deviation of
tendon fibers orientation. The experimental results indicate that the retardance and the orientation angle parameters of the
Mueller matrix can be used as quantitative indicators to distinguish rabbit tendon tissues with or without tenocytes and
can reveal the structural characteristics of collagen fiber bundles, which may provide more useful information for the
evaluation of tendon transplantation.
Mueller matrix polarization imaging system (MMPIS) is one of the most prospective tools that can provide a highresolution image of polarization properties for samples or systems. The MMPIS is composed of a laser source, polarization state generator (PSG), the sample, polarization state analyzer (PSA), a high-resolution imaging optics, collimating optics, and a CCD camera. Usually, the traditional eigenvalue calibration method (ECM) can be used to calibrate PSG and PSA. However, the imaging and collimating optics are not calibrated in MMPIS. For the highnumerical-aperture imaging system, the imaging and collimating optics can behave as polarization aberration modifying the tested sample’s polarization properties leading to the erroneous judgment which affects the measurement accuracy of the MMPIS. In this paper, the multi-step eigenvalue calibration method (MECM) is explored to calibrate MMPIS. For the MECM applied to calibrate MMPIS, the calibration samples are required to place in different positions of the light path and the ECM is adopted in each position. In this way, the Mueller matrices of PSG and PSA, as well as the Mueller matrices of imaging optics and collimating optics can be obtained through calculation. To evaluate the measurement accuracy of MMPIS, the sample with known polarization properties such as air is measured. The experimental results show that before calibrating the imaging optics and collimating optics the measurement accuracy of MMPIS is 0.0124, while after the measurement accuracy has been improved to 0.0046, which is 62.90% better than before. The MECM can be used for the requirements of high accuracy measurement.
Mueller matrix images(MMI) contain complete polarization information of the media. Mueller matrix decomposition technique, where Mueller matrix polar decomposition(MMPD) and differential decomposition(MMDD) are widely used to decompose MMI, is the key to extract intrinsic polarimetry characteristics of biological tissues. For the decomposition of biological tissue MMI, Satish et al. expressed that MMDD was more suitable for Mueller matrix polarimetric analysis of tissues, while Alali et al. pointed out that MMDD did not offer a great advantage over MMPD. To deal with this problem, we explore how to choose the appropriate decomposition method to accurately extract the polarization information in biological tissues. The experimental results indicate that the linear retardance and optical rotation images obtained from two decomposition methods are different if tissues exhibit significant linear retardance and optical rotation effects simultaneously. According to the physical model of MMDD that the occurrence of polarization effects is orderindependent, MMDD should be applied to MMI of tissues to obtain accurate polarization characteristics in this situation. The biological tissue has low optical rotation in most cases in which the polarimetric images extracted from two decomposition methods are nearly identical, so MMPD and MMDD both can accurately acquire the polarimetric properties of tissues. Meanwhile, comparing the runtime of two decomposition methods to process MMI, we find the processing speed of MMDD is much faster than MMPD. Thus, we summarize that MMDD method is more suitable for the decomposition of the biological tissue MMI, with the advantages of both fast and accurate, which is significant in diagnosis of clinical.
Recently, micro-retarder arrays consisting of patterned liquid crystal polymer or sub-wavelength grating arrays with four different orientations are widely used in division of focal plane(DOFP)Stokes polarimeters. However, due to thermal sensitivity of liquid crystal, real-time calibration of the instruments is required to achieve high-precision detection under non-isothermal conditions. Sub-wavelength grating arrays require sophisticated process, and the study of the influence of grating structure errors on measurement accuracy has been rarely reported. To overcome these limitations, we design a quartz crystal micro-retarder array for DOFP full-Stokes polarimeter, which is composed of identical units with different retardances at four neighboring pixels. The retardance errors introduced by the errors of the substrate thickness (t) and etching depth (d) of the micro-retarder array are analyzed. Furthermore, the relationship among the measurement error, the instrument matrix error of Stokes polarimeter, and polarization state of incident light is established. Hereby, the influence of retardance error on the measurement error corresponding to incident light of different polarization state is analyzed. To reduce the measurement error of Stokes parameters to less than 0.02, the tolerances of t and d should be less than 0.11 μm and 0.09 μm, respectively. The micro-retarder array on quartz crystal is fabricated according to our design and tolerances analysis. Finally, the retardance characteristics of the micro-retarder arrays are characterized by the high accuracy (0.1%) Mueller polarimeter developed in house.
Channeled spectropolarimeter (CSP) measures the spectrally resolved Stokes vector of light from only one single spectral acquisition, which makes it possible to accurately measure dynamic events. The accurate reconstruction of Stokes vector plays a key role in this snapshot technique shifting the main burden of measurement to computational work. The state-ofthe-art algorithm runs the Fourier transform of the channeled spectrum or linear operator model of the system and its pseudo-inverse to reconstruct Stokes vector. However, they may suffer from the lack of signal-to-noise ratio (SNR) then reduce the accuracy of reconstruction. To accurately reconstruct Stokes vector from noise-contaminated data, we propose an effective method called fast compressed channeled spectropolarimeter (FCCSP). In our FCCSP method, the spectrum from spectrometer is seen as the compressive representation of Stokes vector, thus the FCCSP algorithm is to solve an underdetermined problem, where we reconstruct the 4N×1 Stokes vector from only N×1 spectral data acquisition points. Simulation results show that our FCCSP method is more accurate to reconstruct Stokes vector changing gradually with wavelength from noise-contaminated spectrum than Fourier and linear operator methods. Besides, it is faster and more memory and computation-friendly than other compressed CSP method.
Vortex beams have drawn much attention for their distinct properties. When vortex beams propagate along optical axis, they exhibit complicated physical phenomena. Under tight focusing condition, we investigate the defocusing behavior of two superposed vortex beams with opposite but arbitrary topological charge. The results reveal that the intensity distribution of the focus will be petal-shaped if the two topological charges have opposite sign, where the number of intensity lobes in the focal plane is |m− n + 2| . Meanwhile, we find that the focusing intensity of topological charge m = −n would not appear the helical structure when a defocusing occurs. Otherwise, the defocusing would result in the helical structure of intensity when m ≠ −n , and the rotation of helical structure depends on the sign of m + n . Of which clockwise rotation of defocus intensity is related to the negative m + n , and anti-clockwise direction corresponds to the positive m + n . Furthermore, the helical degree of the helical intensity also depends on the magnitude of m + n . The interesting results obtained in this paper will lead to further advances in the field of optical vortices.
Measurement of the probability density of polarization state need specific phase modulator.However, the existence of mechanic processing error results in the error of the polarization property of modulator. Meanwhile, the error of the measurement system’s alignment is also existing. All of this errors need to calibrate to ensure the accuracy of measurement. In this paper, We present a self-calibration method based on the theory of the probability density of polarization state which is represented in Mueller formalism. After measuring the probability density of polarization state, we can extract the Stokes parameters of a light field of unknown polarization in a single irradiance measurement, by finding the maximum of the probability density of polarization state.
Optical vortices have been applied in many fields for their distinct properties. In this paper, we explore the focusing intensity distribution of the radially and azimuthally polarized vortex beam (VB) with varying beam waist parameter. The results reveal that low beam waist parameter is beneficial to form a super-resolution spot. In the condition of the high beam waist parameter, the focusing intensity of radially and azimuthally polarized VB along the longitudinal direction would split to multi-spots. Meanwhile, the focal plane intensity distribution become non-symmetrical as well as expansion when the beam waist parameter increase. Therefore, appropriate beam waist must be chosen for the two kind beam in actually application. Furthermore, we also investigate the focal properties affected with helical phase TC. The results reveal that the focal spot size of radially polarized VB along the longitudinal gradually increases with the order of helical phase. The peak intensity ratio of the longitudinal and transverse field of radially polarized VB holds a maximum value when helical phase order l = 0 and becomes to minimum when l =1 , then gradually increases with the order of helical phase. For the azimuthally polarized VB, when l =1 , the focal intensity would exhibit an excellent small solid spot. The results obtained in this paper are useful for application of radially and azimuthally polarized VB.
An imaging polarimeter is developed for measuring polarization properties of hyper number aperture (NA) lithography tools, which can be represented by stokes entrance-pupil, stokes exit-pupil and mueller pupil of projection optics. This imaging polarimeter is optimized from the following three aspects. Firstly, a new method is proposed to measure stokes entrance-pupil of projection optics. It employs a rotating-waveplate and a fixed-polarizer as polarization state analyzer (PSA). Compared to the method proposed by Nomura, the number of measurements is reduced from 16 to 4 times. Additionally, the large incident angle in the mask plane leads to unacceptable retardation error of conventional waveplate, which terribly influent the measurement accuracy of the imaging polarimeter. Therefore, the imaging polarimeter can be optimized by employing a wide-view-angle (WVA) waveplate composed of quartz and sapphire plates. An example of 632.8nm WVA λ/4 waveplate is designed based on least square algorithm, which is firstly introduced to calculate the thicknesses of four crystal plates. Simulation result shows that the retardation error is less than 0.3° for incident angle within 20°. Thirdly, the WVA waveplate is successfully fabricated and its retardation is calibrated by senarmont method. Measurement data is contributed to eliminate the uncertainty of retardation and thus improves the performance of the imaging polarimeter. Because of the lack of lithography equipment, the imaging polarimeter is preliminarily tested in the visible optical system with a He-Ne laser. Stokes entrance-pupil, stokes exit-pupil and mueller pupil of projection optics are all measured with quite enough measurement repeatability.
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