Aberration measurement of projection optics in lithographic tools by use of an alternating phase-shifting mask

As a critical dimension shrinks, the degradation in image quality caused by wavefront aberrations of projection optics in lithographic tools becomes a serious problem. It is necessary to establish a technique for a fast and accurate in situ aberration measurement. We introduce what we believe to be a novel technique for characterizing the aberrations of projection optics by using an alternating phase-shifting mask. The even aberrations, such as spherical aberration and astigmatism, and the odd aberrations, such as coma, are extracted from focus shifts and image displacements of the phase-shifted pattern, respectively. The focus shifts and the image displacements are measured by a transmission image sensor. The simulation results show that, compared with the accuracy of the previous straightforward measurement technique, the accuracy of the coma measurement increases by more than 30% and the accuracy of the spherical-aberration measurement increases by approximately 20%.     

Selective edge enhancement using anisotropic vortex filter

In optical image processing, selective edge enhancement is important when it is preferable to emphasize some edges of an object more than others. We propose a new method for selective edge enhancement of amplitude objects using the anisotropic vortex phase mask by introducing anisotropy in a conventional vortex mask with the help of the sine function. The anisotropy is capable of edge enhancement in the selective region and in the required direction by changing the power and offset angle, respectively, of the sine function.     

Effect of defocus on on-axis wave aberration of a centered optical system

We derive equations for defocus and primary spherical wave aberration coefficients caused by a shift in image plane of a perfect optical system. The spherical aberration equation is accurate at describing changes in the spherical aberration of an aberrated schematic eye.     

Large‐Field‐of‐View Wide‐Spectrum Artificial Reflecting Superposition Compound Eyes

In nature, reflecting superposition compound eyes (RSCEs) found in shrimps, lobsters and some other decapods are extraordinary imaging systems with numerous optical features such as minimum chromatic aberration, wide‐angle field of view (FOV), high sensitivity to light and superb acuity to motion. Here, we present life‐sized, large‐FOV, wide‐spectrum artificial RSCEs as optical imaging devices inspired by the unique designs of their natural counterparts. Our devices can form real, clear images based on reflection rather than refraction, hence avoiding chromatic aberration due to dispersion by the optical materials. Compared to imaging at visible wavelengths using conventional refractive lenses of comparable size, our artificial RSCEs demonstrate minimum chromatic aberration, exceptional FOV up to 165° without distortion, modest aberrations and comparable imaging quality without any post‐image processing. Together with an augmenting cruciform pattern surrounding each focused image, our large‐FOV, wide‐spectrum artificial RSCEs possess enhanced motion‐tracking capability ideal for diverse applications in military, security, medical imaging and astronomy.     

A Configuration of the Optical System for a 5 m Telescope

A configuration of the optical system for a 5 m telescope is described Its salient features are: (1) A common secondary mirror is used for all foci. (2) While used for each focus, the secondary mirror should be moved to a proper corresponding position. Thus the image quality at each focus can be obviously improved. (3) A specific ‘prime’ focus system has been developed. (4) A specific Nasmyth system has been developed. In this configuration the Cassegrain system is the Ritchey-Chrétien system. The spherical aberration and coma at each focus are eliminated simultaneously. At ‘prime’ focus the astigmatism is also eliminated simultaneously.     

相移掩模和离轴照明在ArF浸没式光刻中对工艺窗口的影响

研究了交替型相移掩模及离轴照明对65nm分辨率ArF浸没式光刻的影响,在3／4环形照明和3／4四极照明方式下,分别选用传统掩模和交替型相移掩模,研究65nm线宽的密集线条、半密集线条、孤立线条在较大的曝光系统参数范围内,对光刻工艺窗口的改善。并对在不同的照明方式、掩模结构下获得的工艺窗口进行了比较,结果表明：①在较大焦深(DOF)范围内,满足光刻性能要求可以有较大范围的曝光系统参数配置;②相时于传统照明和传统掩模,采用交替型相移掩模或者离轴照明,焦深均可提高100％-150％。     

Implementation of multilens micro-optical systems with large numerical aperture by stacking of microlenses

In the field of micro-optics there is a demand for objectives with large numerical aperture (NA). One example is optical storage in which a NA greater than 0.5 is required. For planar microlenses the NA is determined by means of the maximal index difference and the degree of exchange and reaches typical values of 0.13-0.2. Thus stacking is needed to build high NA objectives from planar microlenses. An additional benefit of stacking lenses is the possibility to correct for different types of aberrations. We realized two stacked systems: an array of micro-objectives with a NA of 0.45 from three microlens arrays and a confocal sensor head from four microlens arrays and one pinhole array mask.     

Aberrations and convergence characteristics of a concentric-circular focusing grating coupler: analysis

The convergence characteristics of the previously proposed concentric-circular focusing grating coupler (CFGC) are analyzed, and aberration functions for such typical errors as wavelength errors, effective index errors, grating pattern distortion, and CFGC eccentricity are derived for evaluation of their allowances. The analyzed results prove that the Strehl intensity deterioration caused by a wavelength error and an effective index offset can be minimized by optimization of the annular aperture of the CFGC. In the case of Marechal's criterion, a wavelength error of ±8.6% at the annular aperture of NA = 0.440-0.607 and an effective index error of ±20.4% at NA = 0.500-0.652 are permissible, and these values are ～100 times greater than those that are seen in a conventional focusing grating coupler that has a rotationally asymmetrical structure with respect to its optical axis.     

Dependence of Strehl ratio on f-number of optical system

Formulas for a minimum of wave aberration variance and a maximum of the Strehl ratio in the optimal image point are derived using the third- and fifth-order aberration theory. Moreover, relations for the calculation of the optimal value of f-number of the optical system were derived, which enabled us to theoretically analyze real optical systems and their image quality. The optimal f-number corresponds to such a value of f-number when the image quality of a real optical system is comparable to an aberration-free optical system. This value may also serve as an auxiliary criterion of the image quality of the optical system, for example, in photography.     

The Fabry-Perot Interferometer. History,Theory, Practice and Applications

Abstract

A simple algebraic algorithm is proposed as a computational tool for the thin-lens design of a triplet which consists of a singlet and a cemented doublet. The triplet is required to yield specified amounts of lens power, primary spherical aberration, central coma, longitudinal chromatic aberration and secondary spectrum. The three element powers of the triplet are first obtained by solving the simultaneous linear equations of the total lens power, longitudinal chromatic aberration and secondary spectrum. A quadratic equation is obtained by combining the equations of spherical aberration and central coma, and the lens shapes are then obtained by solving this quadratic equation. The solving process is purely algebraic and is therefore easy to calculate and guarantees that all the solutions can be found.     

Influence of the mask magnification on imaging in hyper-NA lithography

Argon fluoride laser (ArF) lithography using immersion technology has the potential to extend the application of optical lithography to 45 nm half-pitch and possibly beyond. By keeping the same 4x magnification factor, the dimensions of the structures on masks are becoming comparable to the exposure wavelength or even smaller. The polarization effect induced by mask features is, however, an issue. The introduction of a larger mask magnification should be strongly considered when poor diffraction efficiencies from subwavelength mask features and the resulting image degradation would be encountered in hyper-NA lithography. The dependence of the diffraction efficiencies on mask pitch and illuminating angle are evaluated. The near-field intensity and phase distributions from the mask are calculated. The imaging performance of 4x and 8x masks for the sub-45 nm node are explored. A rigorous coupled-wave analysis is developed and employed to analyze the optical diffraction from the 3D topographic periodic features.     

Enhanced optical microlithography with a Fabry-Perot-based spatial filtering technique

A coherent multiple imaging technique for use in optical microlithography was studied. The technique involves placing a thin Fabry-Perot etalon between the mask and the projection lens of an optical stepper. An optical lithographic computer simulation tool, Prolith/2, was used to evaluate the aerial image profile obtained for extended mask structures such as typical contact hole arrays and line-space patterns used in integrated circuit fabrication. Additionally, a set of experimental studies were performed to validate the simulation results. Enhancement of both resolution and depth of focus can be obtained simultaneously with appropriate etalon parameters.     

Inverse scattering for frequency-scanned full-field optical coherence tomography

Full-field optical coherence tomography (OCT) is able to image an entire en face plane of scatterers simultaneously, but typically the focus is scanned through the volume to acquire three-dimensional structure. By solving the inverse scattering problem for full-field OCT, we show it is possible to computationally reconstruct a three-dimensional volume while the focus is fixed at one plane inside the sample. While a low-numerical-aperture (NA) OCT system can tolerate defocus because the depth of field is large, for high NA it is critical to correct for defocus. By deriving a solution to the inverse scattering problem for full-field OCT, we propose and simulate an algorithm that recovers object structure both inside and outside the depth of field, so that even for high NA the focus can be fixed at a particular plane within the sample without compromising resolution away from the focal plane.     

Image formation by use of the geometrical theory of diffraction

A deeper understanding of imaging behavior is needed with the widespread adoption of optical proximity correction in advanced lithography processes. To gain insight into the printing behavior of different mask pattern configurations, we derive edge-based and vertex-based image models by combining concepts contained in the geometrical theory of diffraction and Hopkins's image model. The models are scalar models and apply to planar, perfectly conducting mask objects.     

Aberration Tolerances Based on the Line Spread Function

Abstract

Approximate formulae are obtained for the influence of aberration on the image of an incoherent line, by a method corresponding to that used by Maréchal for the image of a point. The best forms of correction in the presence of higher-order aberrations, and the best focal planes, may be easily determined using tables of coefficients that are provided. For the case of asymmetric aberrations, the image shift to the diffraction focus is also simply found. This, and the tolerance formulae, also apply to the gradient of intensity in the image of an edge.     

Polarization Aberration Effects Propagated in Optical Systems

Abstract

The propagation and imaging of polarized light through optical systems described by a polarization aberration expansion is treated by combining a scalar operator calculus with the Jones calculus. The martrix-operator framework provides a means for handling diffraction and propagation in optical systems containing polarization aberrations. An expansion for the polarization aberration function of an optical system, similar to the expansion of the wavefront aberration function into defocus, tilt, piston, and higher-order terms, is analysed. These polarization aberration terms introduce phase changes in the diffraction image proportional to the first and second derivatives of the non-polarization aberrated image structure.     

Exact ray-trace beam for an off-axis paraboloid surface

When an off-axis paraboloidal mirror focuses a parallel beam, the image is formed on one side of the optical axis. For a tilted beam focused by an off-axis paraboloidal mirror, the focus is no longer pointlike (not considering the diffraction effect); rather, it is a distorted spot. This is due to the inherent aberrations of the surface. In addition, there is a change in the focus position. We calculate by exact ray-trace equations the modified wave-front aberration and express it in power series. Our formulation uses the optical path variation along a defined principal ray that we relate to the parameter that describe the surface and the beam angle of incidence. We designate this ray as that reflected by the center of the entrance pupil and field of view. We employ the direction cosines of the principal ray to compute the wave-front aberration function of a beam reflected by an off-axis paraboloid.     

Mask optimization approaches in optical lithography based on a vector imaging model

Recently, a set of gradient-based optical proximity correction (OPC) and phase-shifting mask (PSM) optimization methods has been developed to solve for the inverse lithography problem under scalar imaging models, which are only accurate for numerical apertures (NAs) of less than approximately 0.4. However, as lithography technology enters the 45 nm realm, immersion lithography systems with hyper-NA (NA>1) are now extensively used in the semiconductor industry. For the hyper-NA lithography systems, the vector nature of the electromagnetic field must be taken into account, leading to the vector imaging models. Thus, the OPC and PSM optimization approaches developed under the scalar imaging models are inadequate to enhance the resolution in immersion lithography systems. This paper focuses on developing pixelated gradient-based OPC and PSM optimization algorithms under a vector imaging model. We first formulate the mask optimization framework, in which the imaging process of the optical lithography system is represented by an integrative and analytic vector imaging model. A gradient-based algorithm is then used to optimize the mask iteratively. Subsequently, a generalized wavelet penalty is proposed to keep a balance between the mask complexity and convergence errors. Finally, a set of methods is exploited to speed up the proposed algorithms.     

Four-plane space-variant Fresnel-transform optical processor with a random phase encoder

We introduce a four-plane Fresnel-transform space-variant optical processor consisting of an input plane and two filter planes. One filter mask is programmable with a spatial light modulator. The second filter mask is a fixed random binary phase array with a known pseudorandom distribution of pixels. The order of the masks can be interchanged, giving different output characteristics. In one case the Horner efficiency of the correlator increases dramatically. In the other case the edge enhancement of the output image is removed. We discuss the theory for this general processor and its implementation with phase-only masks. We present experimental results when a binary magneto-optic spatial light modulator was used.     

Apodization by the Stiles-Crawford effect moderates the visual impact of retinal image defocus

Previous optical modeling of the human eye with large pupils has predicted a larger impact of defocus on the human contrast sensitivity function and modulation transfer function than is observed experimentally. Theory predicts that aberrations and the Stiles-Crawford effect (SCE) should both lead to increased depth of focus, resulting in higher contrast sensitivities and veridical (not phase-reversed) perception over a larger range of spatial frequencies in defocused retinal images. Using a wave optics model, we examine these predictions quantitatively and compare them with psychophysical experiments that measure the effect of defocus on contrast sensitivity and perceived phase reversals. We find that SCE apodization has its biggest effect on defocused image quality when defocus and spherical aberration have the same sign. A model including typical amounts of spherical aberration and pupil apodization provides a dramatically improved prediction of the effects of defocus on contrast sensitivity with large pupils. The SCE can significantly improve defocused image quality and defocused vision, particularly for tasks that require veridical phase perception.