Jones Pupil Research Articles

Polarization aberrations in next-generation giant segmented mirror telescopes (GSMTs)

Context. Next-generation large segmented mirror telescopes are expected to perform direct imaging and characterization of Earth-like rocky planets, which requires contrast limits of 10−7 to 10−8 at wavelengths from I to J band. One critical aspect affecting the raw on-sky contrast are polarization aberrations (i.e., polarization-dependent phase and amplitude patterns in the pupil) arising from the reflection from the telescope’s mirror surfaces and instrument optics. These polarization aberrations induce false signals for polarimetry that can be calibrated to a certain degree, but they can also fundamentally limit the achievable contrast of coronagraphic systems. Aims. We simulate the polarization aberrations and estimate their effect on the achievable contrast for three next-generation ground-based large segmented mirror telescopes. Methods. We performed ray-tracing in Zemax® and computed the polarization aberrations and Jones pupil maps using the polarization ray-tracing algorithm. The impact of these aberrations on the contrast is estimated by propagating the Jones pupil maps through a set of idealized coronagraphs using hcipy, a physical optics-based simulation framework. Results. The optical modeling of the giant segmented mirror telescopes (GSMTs) shows that polarization aberrations create significant leakage through a coronagraphic system. The dominant aberration is retardance defocus, which originates from the steep angles on the primary and secondary mirrors. The retardance defocus limits the contrast to 10−5 to 10−4 at 1 λ/D at visible wavelengths, and 10−5 to 10−6 at infrared wavelengths. The simulations also show that the coating plays a major role in determining the strength of the aberrations. Conclusions. Polarization aberrations will need to be considered during the design of high-contrast imaging instruments for the next generation of extremely large telescopes. This can be achieved either through compensation optics, robust coronagraphs, specialized coatings, calibration, and data analysis approaches, or by incorporating polarimetry with high-contrast imaging to measure these effects.

Analysis of polarization characteristics of freeform surface optical system

Freeform surfaces are widely used in off-axis optical systems with large aperture, large field of view, and long focal length. The polarization effect caused by the non-rotationally symmetrical shape has an impact on the system’s polarization imaging quality and measurement accuracy. Based on Jones’ notation, this paper proposes a polarization aberration analysis method for fringed Zernike polynomial freeform optical systems and constructs a full-field polarisation aberration analysis model of non-rotationally symmetric freeform reflective optical systems. The light propagation vector k is added on the basis of the two-dimensional ray tracing algorithm. By tracing the full-field polarized light of the off-axis optical system in the field of view, the Jones pupil diagram is obtained. The phase aberration, diattenuation and retardance are separated by Pauli decomposition and SVD decomposition. The off-axis freeform surface optical system is designed. The analysis results show that the phase aberration of the off-axis freeform surface optical system is directly related to the surface shape of the freeform surface. The changes of the freeform surface to the diattenuation and retardance are both 56% of the diattenuation and retardance of the sistem. For deep-space telescopes and lithography systems, it is of great significance for improving system accuracy to master this change.

Comparisons between an on-axis three-mirror anastigmat telescope and an off-axis one: polarization aberrations.

Due to the ability to achieve a wide-diffraction-limited field of view, three-mirror anastigmat (TMA) telescopes are widely used in many applications that demand high imaging quality and detection accuracy, in which polarization aberrations play increasingly important roles. In this paper, polarization properties of on-axis elements and those of off-axis elements are analyzed and compared via polarization aberration theory. Then, an on-axis TMA (OTMA) telescope and an off-axis TMA (FTMA) telescope are designed and optimized to be diffraction-limited systems in parallel. Their constructional parameters and first-order parameters are set to be identical. Via polarization ray tracing, polarization aberrations of the 2 telescopes are obtained and compared in terms of diattenuation map, retardance map, Jones pupil, Pauli pupil, and amplitude response matrix. Results demonstrate that polarization aberrations are closely related to the structural features of mirrors and telescopes. The diattenuation and retardance maps of power mirrors in the OTMA telescope are rotationally symmetric, while those in the FTMA telescope are not. A Maltese cross appears in off-diagonal elements of the Jones pupil of the OTMA telescope and disappears in the FTMA telescope. Amplitude response matrices of polarization crosstalk components in the OTMA telescope are with a four-peak structure, while those in the FTMA telescope are with a two-peak structure. After quantitative comparisons, it is found that diattenuation in the OTMA telescope is smaller than that in the FTMA telescope as well as in the cases of retardance and polarization crosstalk. There are also similarities between the 2 TMA telescopes. Polarization aberrations of secondary mirrors (SM) are greater than those of both primary mirrors (PM) and tertiary mirrors (TM). What is more, polarization aberrations of TM are so small that they can be ignored safely. The numerical sum of Pauli coefficients of PM, SM, and TM is nearly identical to the cumulative Pauli coefficients. Hence, the TMA telescopes can be treated as weak polarization elements. This work compares polarization aberration performance of on- and off-axis TMA telescopes and can provide important references for designing and optimizing telescopes in which polarization aberrations matter.

Polarization aberrations corrections and polarization-dependent imaging quality analysis in polarization lidars

The polarization aberration in lidar system can reduce the imaging quality and causes the atmospheric polarization measurement error. In order to accurate polarization signal measurement, the polarization aberration correction of system is necessary. In this paper, the physical properties of Jones pupil function are analyzed and the polarization-dependent point spread function is derived for the polarization lidar. A high-reflection dielectric multilayer coating with low polarization effect is designed to correct the polarization aberration of Cassegrain telescope in lidar. The simulation shows that the polarization aberration of telescope coated with multilayer coatings are significantly smaller than that coated with aluminum coating. Furthermore, the imaging quality performance of telescope coated with multilayer coatings is analyzed, and the relative error of atmosphere parameter is calibrated based on the imaging information of two receiver channels in linear or circular polarization lidar. The correction method can reduce the polarization aberration and improve the measurement accuracy in polarization lidar.

Jones pupil decomposition and its lithographic imaging impacts.

The Jones pupil is a full description of imaging properties of projection lenses in optical lithography. The decomposition of the Jones pupil into components with clear physical meanings was studied previously; however, the decomposition method has not been studied systematically. To generalize the existing decomposition method, this work is aimed at finding all the decomposition methods and analyzing the lithographic imaging impacts. In this work, six decomposition methods are proposed, and the lithographic imaging impacts of the Jones components are studied and compared for all the decomposition methods. The results demonstrate that, although the decomposition methods are different, their lithographic impacts are identical. To be specific, apodization has a dominant impact on the critical dimension with a magnitude of 1.3 nm, and the impact of diattenuation is 0.3 nm. In contrast, the impacts of the other Jones components of aberration, birefringence, rotator, and ellipticity are negligible. This work gives a complete understanding of the imaging impacts of the Jones pupil.

Effects of polarization aberrations in an unobscured off-axis space telescope on its PSF ellipticity

Polarization aberrations exist in almost all astronomical telescopes. Polarization aberrations would bring about asymmetric apodization in the exit pupil, leading to asymmetric PSFs. The shape of PSFs is critical to telescopes that are used to detect weak gravitational lensing (WGL) in the universe. In this paper, polarization aberrations and their connections with PSF ellipticity in an unobscured off-axis space telescope are analyzed. Together with the Jones pupil, cumulative diattenuation and retardance maps of the telescope are obtained via polarization ray tracing. Due to asymmetric apodization caused by polarization aberrations, the ellipticities of all four PSF components are found to be greater than zero. The PSF ellipticity of the telescope over the full FOV is obtained. Results show that polarization aberrations change PSF ellipticity in different degrees at different FOVs. The maximum variance of PSF ellipticity induced by polarization aberrations is 7.5e-3 and the average value is 2.7e-3. In addition, interpolation errors of PSF ellipticity would also be affected by polarization aberrations. It is found that there are 405 FOV points (about 4% of all FOV points involved in the calculations) whose variances of interpolation errors caused by polarization aberrations are greater than 1.4e-4. According to the results shown in this paper, polarization aberrations of telescopes play a significant role in WGL measurements.

Jones pupil metrology of lithographic projection lens and its optimal configuration in the presence of error sources.

Mueller matrix imaging polarimeter (MMIP) can be used to measure the polarization aberration (PA) of a lithographic projector in the form of the Mueller pupil, while the Jones pupil is required for lithographic imaging simulations, projection lens design and PA evaluation. In this paper, a Jones pupil measurement method of lithographic projection lens is proposed. The measurement device of the method is the same as an MMIP, but a new polarimetric measurement equation is derived to solve the Jones pupil directly from the Kronecker product of the Jones matrix and the measured intensities. Two new polarimeter configurations with the minimum condition number are designed to further improve the accuracy in the presence of error sources. The performance of the method is evaluated by measurement errors of a typical Jones pupil in the presence of error sources. Comparisons between the proposed method and the conventional method, in which the Jones pupil is converted from the Mueller pupil measured by MMIP, are given. The results validate that the measurement accuracy of the Jones pupil is significantly improved without increasing the complexity of existing measurement systems.

Polarization aberration analysis in lithographic tools

Hypernumerical aperture and polarized illumination are the key technologies of resolution enhancement of lithography. When the numerical aperture reaches 0.85 and above, especially in the immersion lithography, polarization effect must be taken into consideration. The performance of the projection lens needs to be characterized by rigorous polarization aberration. The vector polarization imaging system that is suitable for hypernumerical aperture is established, and the distortion effects introduced by polarization aberration are analyzed. Orientation Zernike polynomials-based method and Pauli–Zernike polynomials-based method are adopted to parameterize the polarization aberration represented by Jones pupil. Critical dimension error, placement error, and normal int. log slope index are introduced as the index to value imaging distortion. The proposed method and analysis conclusion would provide meaningful guidance for projection lens design of lithographic tools.

光刻投影物镜的琼斯光瞳检测方法

光刻投影物镜的琼斯光瞳检测方法

A nonlinear measurement method of polarization aberration in immersion projection optics by spectrum analysis of aerial image.

Polarization aberrations (PA) can be presented by Jones pupil and can also impact the imaging performance of immersion projection optics significantly. Precise PA measurement is most important for resolution enhancement technology and holistic lithography at 7nm node and below, in order to improve the pattern fidelity and processing stability. However, the current imaging-based measurement method of PA by linear approximation has not taken the coupling effect of the PA coefficients into account. This paper proposes a nonlinear measurement method of PA based on a rigorous nonlinear model to improve the measurement accuracy significantly. In this invention, the new spectrum modulation theory is developed to establish a rigorous quadratic form of PA and aerial image spectrum. A hybrid genetic algorithm is developed to solve the quadratic form inversely to obtain the PA accurately. An overall simulation validates that this method provides a superior quality of PA measurement with very high precision of 10-4λ.

Polarization Aberrations in Astronomical Telescopes: The Point Spread Function

Detailed knowledge of the image of the point spread function (PSF) is necessary to optimize astronomical coronagraph masks and to understand potential sources of errors in astrometric measurements. The PSF for astronomical telescopes and instruments depends not only on geometric aberrations and scalar wave diffraction but also on those wavefront errors introduced by the physical optics and the polarization properties of reflecting and transmitting surfaces within the optical system. These vector wave aberrations, called polarization aberrations, result from two sources: (1) the mirror coatings necessary to make the highly reflecting mirror surfaces, and (2) the optical prescription with its inevitable non-normal incidence of rays on reflecting surfaces. The purpose of this article is to characterize the importance of polarization aberrations, to describe the analytical tools to calculate the PSF image, and to provide the background to understand how astronomical image data may be affected. To show the order of magnitude of the effects of polarization aberrations on astronomical images, a generic astronomical telescope configuration is analyzed here by modeling a fast Cassegrain telescope followed by a single 90° deviation fold mirror. All mirrors in this example use bare aluminum reflective coatings and the illumination wavelength is 800 nm. Our findings for this example telescope are: (1) The image plane irradiance distribution is the linear superposition of four PSF images: one for each of the two orthogonal polarizations and one for each of two cross-coupled polarization terms. (2) The PSF image is brighter by 9% for one polarization component compared to its orthogonal state. (3) The PSF images for two orthogonal linearly polarization components are shifted with respect to each other, causing the PSF image for unpolarized point sources to become slightly elongated (elliptical) with a centroid separation of about 0.6 mas. This is important for both astrometry and coronagraph applications. (4) Part of the aberration is a polarization-dependent astigmatism, with a magnitude of 22 milliwaves, which enlarges the PSF image. (5) The orthogonally polarized components of unpolarized sources contain different wavefront aberrations, which differ by approximately 32 milliwaves. This implies that a wavefront correction system cannot optimally correct the aberrations for all polarizations simultaneously. (6) The polarization aberrations couple small parts of each polarization component of the light (∼10-4) into the orthogonal polarization where these components cause highly distorted secondary, or “ghost” PSF images. (7) The radius of the spatial extent of the 90% encircled energy of these two ghost PSF image is twice as large as the radius of the Airy diffraction pattern. Coronagraphs for terrestrial exoplanet science are expected to image objects 10-10, or 6 orders of magnitude less than the intensity of the instrument-induced “ghost” PSF image, which will interfere with exoplanet measurements. A polarization aberration expansion which approximates the Jones pupil of the example telescope in six polarization terms is presented in the appendix. Individual terms can be associated with particular polarization defects. The dependence of these terms on angles of incidence, numerical aperture, and the Taylor series representation of the Fresnel equations lead to algebraic relations between these parameters and the scaling of the polarization aberrations. These “design rules” applicable to the example telescope are collected in § . Currently, exoplanet coronagraph masks are designed and optimized for scalar diffraction in optical systems. Radiation from the “ghost” PSF image leaks around currently designed image plane masks. Here, we show a vector-wave or polarization optimization is recommended. These effects follow from a natural description of the optical system in terms of the Jones matrices associated with each ray path of interest. The importance of these effects varies by orders of magnitude between different optical systems, depending on the optical design and coatings selected. Some of these effects can be calibrated while others are more problematic. Polarization aberration mitigation methods and technologies to minimize these effects are discussed. These effects have important implications for high-contrast imaging, coronagraphy, and astrometry with their stringent PSF image symmetry and scattered light requirements.

Pellicle contribution to optical proximity and critical dimension uniformity for 1.35 numerical aperture immersion ArF lithography

Pellicles are mounted on the masks used in ArF lithography for integrated circuit manufacturing to ensure defect-free printing. The pellicle, a thin transparent polymer film, protects the reticle from dust. But, as the light transmittance through the pellicle has an angular dependency, the pellicle also acts as an apodization filter. In the current work, we present both experimental and simulation results at 1.35 numerical aperture immersion ArF lithography showing the influence of two types of pellicles on proximity and intra-die critical dimension uniformity (CDU). To do so, we mounted and dismounted the different pellicle types on one and the same mask. The considered structures on wafer are compatible with the 32-nm logic node for poly and metal. For the standard ArF pellicle (thickness 830 nm), we experimentally observe a distinct effect of several nm due to the pellicle presence on both the proximity and the intra-die CDU. For the more advanced pellicle (thickness 280 nm), no signature of the pellicle on proximity or CDU could be found. By modeling the pellicle's optical properties as a Jones Pupil, we are able to simulate the pellicle effects with good accuracy. These results indicate that for the 32-nm node, it is recommended to take the pellicle properties into account in the optical proximity correction calculation when using a standard pellicle. In addition, simulations also indicate that a local dose correction can compensate to a large extent for the intra-die pellicle effect. When using the more advanced thin pellicle (280 nm), no such corrections are needed.

John Webb, William Samwell and the Grange

AbstractThe Grange at Northington, Hampshire, originally a great house of the 17th century by William Samwell, but clad in Greek dress by William Wilkins in 1809, has recently been reconstructed on paper to show the complexity of its planning. This article sets out the arguments for the reconstruction, and resolves the question of the original roof in favour of an eaves cornice. The physical reinstatement of the 19th-century staircase is also assessed for what it tells us about the history and design of both this and the original staircase. The author then examines the antecedents of the overall design, finding many connexions between Samwell and Inigo Jones's pupil and heir, John Webb. A surviving design drawing for the Grange, which differs from what was actually built, is shown to reveal much about Samwell's distinctive thoroughness in building the house. Finally, the place of the Grange in Samwell's oeuvre is considered, particularly in relation to Bushy House, his other complete surviving house.

Polarization influence on imaging

We give a general introduction into polarized imaging and report on a Jones pupil approach for a complete evaluation of the resulting optical performance. The Jones pupil assigns a Jones matrix to each point of the exit pupil, describing the impact of both the global phase and the polarization on imaging. While we already can learn much about the optical system by taking a close look at the Jones pupil-and starting imaging simulations from it-a quantitative assessment is necessary for a complete evaluation of imaging. To do this, we generalize the concept of scalar Zernike aberrations to Jones-Zernike aberrations by expansion of the Jones pupil into vector polynomials. The resulting method is nonparaxial, i.e., the effect of the polarization-dependent contrast loss for high numerical apertures is included. The aberrations of the Jones matrix pupil are a suitable tool to identify the main drivers determining polarization performance. Furthermore, they enable us to compare the polarized and unpolarized performance of such a characterized lithographic system.

Polarization effects associated with hyper-numerical-aperture <inline-formula><math display="inline" altimg="none" overflow="scroll"><mrow><mo>(</mo><mo>></mo><mn>1</mn><mo>)</mo></mrow></math></inline-formula> lithography

The use of immersion technology will extend the lifetime of 193-nm technology by enabling numerical apertures (NAs) much greater than 1.0. The ultimate limits of NA are explored by analysis of polarization effects at the reticle and imaging effects at the wafer. The effect of reticle birefringence with polarized illumination is explored. The effects on critical dimension (CD) uniformity are mitigated if the maximum birefringence is <5 nm/cm. Hertzian or micropolarization due to the size of the reticle structures is examined through rigorous simulation. For the regime of interest, 20- to 50-nm imaging, it is found that dense features on a Cr binary reticle will polarize the light into the TE component upward of 15%. Below this regime, the light becomes polarized in the TM direction. The use of polarization in the illuminator for imaging will result in substantial gains in exposure latitude and mask error factor (MEF) when the NA~1.3 with 45-nm lines at 193 nm, with overall polarization effects increasing with decreasing k1. The end-of-line pullback for 2-D patterns is reduced by the use of TE polarization in the illuminator. The interaction between the reticle-induced polarization and the illumination polarization is shown to be significant when an analysis is done using rigorous mask simulation instead of the more common Kirchhoff approximation. The impact of birefringence in the lens is analyzed using Jones pupil matrices to create a local polarization error in the pupil. The photoresist process is shown to interact with polarization. Different photoresists will show varying degrees of sensitivity to polarization variation.