Design for an aberration-corrected concave grating for a mid-infrared long-slit spectrometer

A new design for an aberration-corrected concave grating for the spectral region near 10 mum is presented. It was designed for use in the ground-based astronomical medium-resolution (lambda/Dlambda ~ 100) Mid-Infrared Camera and Spectrometer (MICS). It provides a flat focal plane for a wide spectral range (7.5-13.5 mum) with small aberrations, permitting efficient long-slit observations in the mid-infrared region. It permits a simple design of the spectrometer without collimator and camera mirrors, which is quite advantageous for cryogenic instruments. The grating has variable spacing grooves to reduce aberrations. In addition, the grating surface figure is designed to be toroidal and in the direction perpendicular to the grooves, aspherical, to suppress the aberrations further over a wide spectral range. The angle of the grooves is also varied to yield better efficiency near the blaze angle. The grating was fabricated by high-quality ultraprecision machining, which made these features possible. Test observations confirmed that the designed spectral resolution was achieved.     

High-resolution, flat-field, plane-grating, f/10 spectrograph with off-axis parabolic mirrors

A high-resolution, flat-field, plane-grating, f/10 spectrometer based on the novel design proposed by Gil and Simon [Appl. Opt. 22, 152 (1983)] is demonstrated. The spectrometer design employs off-axis parabolic collimation and camera mirrors in a configuration that eliminates spherical aberrations and minimizes astigmatism, coma, and field curvature in the image plane. In accordance with theoretical analysis, the performance of this spectrometer achieves a high spatial resolution over the large detection area, which is shown to be limited only by the quality of its optics and their proper alignment within the spatial resolution of a 13 microm x 13 microm pixelated CCD detector. With a 1500 lines/mm grating in first order, the measured spectral resolving power of lambda/Dlambda = 2.5(+/-0.5) x 10(4) allows the clear resolution of the violet Ar(I) doublet at 419.07 and 419.10 nm.     

Aberrations of Spectrographs with the Correction of the Schmidt Camera Effected in the Collimator

Of the different ways to introduce the Schmidt correction of the camera in a spectrograph, the case was studied in which it is effected in the collimator. Equations which describe the form of the wave-front at one side of the grating as function of the form at the other side were found. The sixth-order terms in the correction to compensate for the deformation of the wave-front in the path from the collimator to the grating and to the mirror were also found. The aberrations for a correction which is symmetrical around the collimator axis were calculated. The limit of camera aperture for which these aberrations are tolerable is between F/D=4 and F/D=3 according to the size and number of lines of the grating.     

Broadband FUV imaging spectrometer: advanced design with a single toroidal uniform-line-space grating

Performances of a far-ultraviolet (FUV) imaging spectrometer in an advanced design are presented with a toroidal uniform-line-space (TULS) grating. It provides high spatial resolution and spectral resolution for a broadband and a wide field of view. A particular analysis for the grating aberrations, including all the high-order coefficients neglected by previous existing designs, was generated for indicating their significance. The analysis indicates that these high-order off-axis aberrations would have a remarkable influence on the design results. The transcendental equations composed of these aberration coefficients do not have analytic solutions in algebra. To solve the problem, the past designs always do some simplified calculation which only suits a narrow field of view and waveband. Thus, the optimization of the genetic algorithm is introduced to propose reasonable ranges of optical parameters. Then ZEMAX software is used to obtain the final optical system from these ranges. By comparing different design results of the same example, our advanced TULS design performs better than conventional TULS design and spherical varied-line-space grating design, and as well as the toroidal varied-line-space design. It is demonstrated that aberrations are minimized when the TULS design is operated by our method. The advanced design is low-cost, easy to fabricate, and more suitable for FUV observations.     

Stigmatic spectrometers for extended sources: design with toroidal varied-line-space gratings

Performances are presented of three classes of imaging slit spectrometers for extended sources with aberration-corrected gratings. A general analytical expression for minimizing off-axis grating aberrations is obtained, and it is demonstrated that these aberrations are minimized when the spectrometer is operated at a magnification higher than unity. Classical designs with toroidal uniform-line-spaced (TULS) or spherical varied-line-space (SVLS) gratings are compared with a new class of designs that utilize toroidal varied-line-space (TVLS) gratings. Although TULS and SVLS designs with two stigmatic points can be designed to operate at near-unity magnification with excellent on-axis spectral and spatial resolutions, they cannot be made to satisfy the general off-axis condition, and so their off-axis performances are not optimum. On the contrary TVLS designs with two stigmatic points can be operated at almost any magnification, thus satisfying the off-axis condition perfectly. Such designs are suitable for imaging spectrometer observations that require an extended field of view.     

Two-channel tunable monochromatic illuminator with a concave diffraction grating and an original scanning system

A two-channel monochromatic illuminator with only one diffraction grating and an original scanning system has been designed for multiple applications. This scanning system consists of two rotational plane mirrors that reflect light diffracted by a concave diffraction grating to the ?1 orders of the spectrum. The light reflected by the mirrors goes to two exit slits that correspond to two channels of the device. The positions of the centers of rotation of the mirrors are selected to produce minimal deviation of the direction of the light reflected during the scanning. The aberration characteristics of some variations in the optical mounting of the device made by use of spherical and toroidal holographic diffraction gratings recorded in stigmatic and astigmatic beams, the possibilities for application of the device for measuring the color sensitivity of the human eye, and the possibilities for measuring the efficiency of concave diffraction gratings, are also discussed.     

Geometrical theory of aberrations near the axis in classical off-axis reflecting telescopes

A geometrical theory of aberrations for the vicinity of the focus of arbitrary off-axis sections of conic mirrors is derived. It is shown that an off-axis conic mirror introduces linear astigmatism in the image. However, in classical two-mirror telescopes this aberration can be eliminated by tilting the secondary parent mirror axis. It is also shown that the practical geometrical-optics performance of a classical off-axis two-mirror telescope with no linear astigmatism is equivalent to the performance of an on-axis system, proving that both systems have identical third-order coma. To demonstrate the applicability of the theory developed in a practical system, a fast (i.e., f/2), compact, obstruction-free classical off-axis Cassegrain telescope is designed.     

Aberrations of Plane Grating Monochromators with Off-axis Paraboloidal Mirrors

Aberrations of plane grating monochromators with off-axis paraboloidal mirrors are studied analytically by the use of the light-path function and the Burch plate diagram extended to off-axis systems. Residual wave aberration of the third order becomes vanishingly small by compensation of two aberration terms in the U configuration, but remains fairly large by accumulation in the Z configuration. This explains an excellent image quality of the U configuration. It is shown that exact slit-image-curvature invariance with wavelength exists in the Z configuration but does not in the U configuration. A suitable value of the distance between the grating and off-axis paraboloidal mirror can be determined to eliminate certain residual aberration terms of the fourth order.     

Optimization method for ultra-wide-angle and panoramic optical systems

To an ultra-wide-angle and panoramic optical system, the aberrations of point object at any field angle are separated into two types: the aperture-ray aberrations of off-axis point object and the chief-ray aberrations. A simple form of the triangular formulae of tracing an oblique-incidence ray is derived to calculate the chief-ray parameters and their aberrations; moreover, the aperture-ray aberrations of an off-axis point object are analyzed with the plane-symmetric aberration theory. Based on the two types of aberrations, we present a merit function for ultra-wide-angle and panoramic optical systems; the optimization program with the differential-evolution algorithm is then developed. To validate the optimization method we finally optimize a fish-eye lens and a catadioptric omnidirectional imaging system.     

Design and performance of a throughput-matched, zero-geometric-loss, modified three objective multipass matrix system for FTIR spectrometry

The design of and initial results obtained from a multipass matrix system (MMS) for mid-infrared spectroscopy that operates in the Highly Instrumented Reactor for Atmospheric Chemistry (HIRAC) recently constructed in the School of Chemistry at the University of Leeds, is described. HIRAC is an evacuable, temperature variable, photochemical atmospheric reaction chamber. The MMS design is a modified Chernin cell, utilizing three objective mirrors and two field mirrors. In addition to providing the paraxial equations required for design of a throughput matched multipass cell and throughput matched transfer optics, advanced ray tracing simulations have been performed for the Chernin design described herein. The simulations indicate that, for this MMS, which features small off-axis angles and preserves perfectly the focal properties of the original White design, the paraxial equations are nearly exact, throughput losses due to astigmatism are insignificant, and the system has zero theoretical geometric loss. Measurements of the signal incident on the detector at different matrix arrangements confirm the ray trace results, suggesting that geometric loss in this system is insignificant. The MMS described herein provides adequate stability to permit measurements while the chamber mixing fans are on, gives very good detection limits for some representative species, and is easy to align.     

Asymmetric white-pupil collimators for high-resolution spectrographs

We present the optical principle of a white-pupil collimator made up of two mirrors with unequal focal lengths. Analytic formulas for third-order aberrations are derived and compared with the results of ray-tracing experiments. It is shown that the image quality is good if the second mirror has a suitable conic coefficient and the F ratio is not too small. Furthermore, third-order coma and astigmatism can be zeroed simultaneously if the angles are also appropriately selected. When implemented in high-resolution echelle spectrographs, this design permits smaller cross dispersers and cameras, with considerable savings in cost.     

The design of a triplet with a shape-dependent third-order aberration optimization technique

Abstract

We have derived a series of shape-dependent third-order aberration equations involving lens thickness. These equations are used in a simple and direct method to correct real aberrations and to find the minimum aberration for triple design that has been proposed. These calculated third-order aberrations can exactly meet the target values for each stage by means of the damped least-squares method. The shape of the three elements permits the control of three third-order aberrations: spherical aberration, coma and astigmatism. The spherical aberration is targeted first. The minimal value of the real on-axis aberration is obtained. Similarly, the coma and astigmatism target values are adjusted so as to force the full field angle real off-axis aberrations down to a minimum. Finally, the manual adjustment of the lens thickness and air spacing is used to attain the minimum aberration at the 0.7 field angle. To verify the method, two triplet design examples are presented.     

Parallel two-step phase-shifting digital holograph microscopy based on a grating pair

An optical configuration for parallel two-step phase-shifting digital holographic microscopy (DHM) based on a grating pair is proposed for the purpose of real-time phase microscopy. Orthogonally circularly polarized object and reference waves are diffracted twice by a pair of gratings, and two parallel copies for each beams come into being. Combined with polarization elements, parallel two-step phase-shifting holograms are obtained. Based on the proposed configuration, two schemes of DHM, i.e., slightly off-axis and on-axis DHM, have been implemented. The slightly off-axis DHM suppresses the dc term by subtracting the two phase-shifting holograms from each other, thus the requirement on the off-axis angle and sampling power of the CCD camera is reduced greatly. The on-axis DHM has the least requirement on the resolving power of the CCD camera, while it requires that the reference wave is premeasured and its intensity is no less than 2 times the maximal intensity of the object wave.     

Configuration of an off-axis three-mirror system focused on compactness and brightness

We propose a configuration of an off-axis three-mirror system for maximum compactness and brightness. The chief ray is arranged to cross three times inside the system, and the system has a round configuration for compactness. We introduced into the design a ray triangle formed by the reflection points of the chief rays at the mirrors. The ray triangle indicates the size and the brightness of the system. Based on the proposed configuration, a design example of a 4 degrees x 4 degrees field of view is shown. The F-number of the system is 2.2, in close agreement with the estimation from the ray triangle.     

Grazing-incidence telescope-spectrograph for space solar-imaging spectroscopy

The design of a stigmatic grazing-incidence instrument for space applications to solar-imaging spectroscopy is presented. It consists of a double telescope and a spectrograph: Telescope I consists of a single cylindrical mirror with parabolic section, focusing the radiation on the entrance slit of the spectrograph in the spectral dispersion plane; telescope II consists of two cylindrical mirrors with aspherical section in a Wolter configuration, focusing the radiation on the spectrograph focal plane in the direction perpendicular to the spectral dispersion plane. The spectrograph consists of a grazing-incidence spherical variable-line-spaced grating with flat-field properties. Telescope II is crossed with respect to the grating and telescope I; i.e., it is mounted with its tangential planes coincident with the grating equatorial plane. The spectrum is acquired by a detector mounted at near-normal incidence with respect to the direction of the exit beam. The spectral resolution is also preserved for off-axis angles. The effective collecting area of the instrument can be preserved by adoption of a nested configuration for telescope II without degradation of the spectral resolution.     

Imaging characteristics of a wavefront coding system with off-axis aberrations

Imaging characteristics are analyzed for a wavefront coding system suffering from off-axis aberrations such as primary astigmatism and primary coma. Some analytical expressions for the optical transfer function are obtained by using the stationary-phase method. These expressions give the relationship between the optical transfer function and the off-axis aberrations. Some cases are computed and illustrated graphically. It is shown that the wavefront coding system has a high tolerance to primary astigmatism and a low sensitivity to primary coma.     

用于低能X射线段的掠入射光栅摄谱仪

介绍一种新颖的用于研究激光等离子体的掠入射光栅摄谱仪。掠入射光栅摄谱系统由三部分组成：掠入射光栅摄谱仪、四维精密微调装置和一个含光纤传象束、摄象机、监示器和激光准直仪等构成的瞄准系统。文中论述了掠入射光栅摄谱仪的光路设计、机械设计特点和性能实验结果。     

Off-axis pivot mounting for aberration-corrected concave gratings at normal incidence

The off-axis pivot-point mounting for toroidal uniform line-space (TULS) gratings and spherical varied line-space (SVLS) is presented: One scans the spectrum by rotating the grating about the pivot point. The best choice for the location of the point is discussed: For a monochromator the location is chosen such that the grating is moved approximately along the bisector of the subtended angle; for a spectrometer, it is chosen such that the grating is moved approximately along the direction of the incident ray. Minimizing the spectral defocusing caused by the rotation of the grating determines the optimum length of the pivot arm. The pivot points for TULS and SVLS gratings are found to be located on opposite sides with respect to the normal to the grating. In a comparison of the optical performance, the spectral focusing is similar, but the spatial aberrations can be fewer for a SVLS grating.     

Aberration measurement from specific photolithographic images: a different approach

Techniques for measurement of higher-order aberrations of a projection optical system in photolithographic exposure tools have been established. Even-type and odd-type aberrations are independently obtained from printed grating patterns on a wafer by three-beam interference under highly coherent illumination. Even-type aberrations, i.e., spherical aberration and astigmatism, are derived from the best focus positions of vertical, horizontal, and oblique grating patterns by an optical microscope. Odd-type aberrations, i.e., coma and three-foil, are obtained by detection of relative shifts of a fine grating pattern to a large pattern by an overlay inspection tool. Quantitative diagnosis of lens aberrations with a krypton fluoride (KrF) excimer laser scanner is demonstrated.     

Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization

A rigorous modal theory for the diffraction of Gaussian beams from N equally spaced slits (finite grating) in a planar perfectly conducting thin screen is presented. The case of normal incidence and TE polarization state is considered; i.e., the electric field is parallel to the slits. The characteristics of the far-field diffraction patterns, the transmission coefficient, and the normally diffracted energy as a function of several optogeometrical parameters are analyzed within the so-called vectorial region, where the polarization effects are important. The diffraction pattern of an aperiodic grating is also considered. In addition, one diffraction property known to be valid in the scalar region is generalized to the vectorial region: the existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits. The classical grating equation is tested for incident Gaussian beams under several conditions.