Theory and computation of three cosmic origin spectrograph aspheric gratings recorded with a multimode deformable mirror

The theory of three Cosmic Origin Spectrograph holographic gratings recorded with a deformable plane mirror is presented. Their working conditions are severe, since they have to correct the strong spherical aberration and the field astigmatism of the Hubble Space Telescope. Recorded on aspherized substrates, the gratings produce images that are diffraction limited with regard to spectral resolution.     

Grazing-incidence hyperboloid-hyperboloid designs for wide-field x-ray imaging applications

The classical Wolter type I grazing-incidence x-ray telescope consists of a paraboloidal primary mirror and a confocal hyperboloidal secondary mirror. This design exhibits stigmatic imaging on-axis but suffers from coma, astigmatism, field curvature, and higher-order aberrations such as oblique spherical aberration. Wolter-Schwarzschild designs have been developed that strictly satisfy the Abbe sine condition and thus exhibit no spherical aberration or coma. However, for wide-field applications such as the solar x-ray imager (SXI), there is little merit in a design with stigmatic imaging on-axis. Instead, one needs to optimize some area-weighted-average measure of resolution over the desired operational field of view. This has traditionally been accomplished by mere despacing of the focal plane of the classical Wolter type I telescope. Here we present and evaluate in detail a family of hyperboloid-hyperboloid grazing-incidence x-ray telescope designs whose wide-field performance is much improved over that of an optimally despaced Wolter type I and even somewhat improved over that of an optimally despaced Wolter-Schwarzschild design.     

Parabolic liquid mirrors in optical shop testing

A parabolic liquid mirror obtained by the rotation of a mercury bath around a vertical axis has been built and its optical surface characteristics measured to demonstrate that it can be used in optical shop testing as a reference surface. A linear Hartmann test allowed us to check that the focal length is well related to the rotation velocity, following the theory, and that no spherical aberration is present, as assumed by previous authors. The spherical aberration has been found to be smaller than λ/50 at 633 nm. An interferometric test of the mirror compared with a null lens gave information about the quality of the optical surface for which the rms wave-front error, when the random errors are averaged, is ~λ/25. Because modifying the mirror diameter is cheap and fast and adjusting its focal length within a large range is straightforward, the parabolic liquid mirror can become a highly adaptable tool in optical metrology. In particular, it can be used in optical shop testing as a reference surface to test null correctors, to check any system developed to control the shape of large parabolic or quasiparabolic top-quality solid-state mirrors, or to make holographic references of such surfaces.     

Low-order adaptive deformable mirror

We report the main parameters of a nine-electrode bimorph piezoelectric adaptive mirror designed to correct low-order aberrations. We describe measurements of the control coefficients for defocus, astigmatism, pure coma, and spherical aberration of this mirror and the temperature stability of its profile. The performance of a simple adaptive optical system for imaging through laboratory-generated turbulence is investigated. This low-order device is suitable for small (<1-m-diameter) telescopes and for nonastronomical applications of adaptive optics.     

Diffraction patterns formed by an off-axis paraboloid surface

We derive a general, closed-form expression for the diffraction patterns including the aberrations that are due to off-axis alignment and positioning, of a paraboloid mirror. The diffraction patterns obtained in the focal plane of an off-axis paraboloidal mirror suffer modifications by the aberrations that are inherent in these surfaces: astigmatism and coma. Different magnifications in two perpendicular spatial directions indicate astigmatism. The Airy function, which affects a single spatial coordinate, describes the coma aberration. We identified the coma by the increased number of intensity zeros within adjacent lobules.     

An Analytical Determination of the Flexure of the 3·5 m Primary and 1 m Test Mirror of the ESO's New Technology Telescope for Passive Support and Active Control

Abstract

The active optics control concept of the ESOs 3·5 m New Technology Telescope (NTT) is based on the correction of aberrations by pre-calibrated changes of the axial forces that provide passive astatic support of the primary. The corrected aberrations are the basic orders of spherical aberration, ordinary astigmatism, triangular and quadratic astigmatism, and furthermore, coma up to the fifth order. This paper is concerned with the analytical determination of the force changes necessary, in either certain groups or the entirety of the supports, to produce any one of these aberration modes. The calibration is derived for two meniscus-shaped mirrors, the NTT primary of aspect ratio 1 : 15 and a thin test mirror of 1 m diameter and aspect ratio 1 : 56, designed to prove the control principle. The theoretical approaches used are adapted to the different stress distributions resulting from the different mirror shapes. Realized as flexural Fourier modes, the generated aberrations are orthogonal to each other and therefore exclude operative interference. The deviations from the desired radial laws amount to very few percent at most. Preparatory to this analysis, the paper treats both the passive axial supports and the radial edge support of the primary. A novel solution for the latter restricts the unavoidable flexural coma to low orders that are readily correctable by active control. Wherever possible, the analytical results are compared with related finite-element results obtained by other authors.     

Highly efficient and aberration-corrected spectrometer for advanced Raman spectroscopy

We designed an asymmetric Czerny-Turner-type spectrometer with a spectral resolution of approximately 1 cm(-1) and a focal length of 500 mm (F/4.1) to improve the aberration properties: (1) coma aberration was corrected by use of a particular incident angle for a condensing mirror based onShafer's equation, (2) astigmatism was corrected by use of a toroidal condensing mirror, (3) the optimum distance was found between a grating and condensing mirror so that the centered light and marginal light at the detector possess the same incident angles to the condensing mirror (the aberration is therefore excellently corrected over the whole detector surfaces), and (4) these optimal configurations are ensured in a wide wavelength between 400 and 800 nm by use of gratings with different grooves. Then the spectrometer was constructed, and the excellent optical properties were confirmed with aligned fiber images and Raman spectra from copper phthalocyanine.     

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.     

Analysis of reentrant two-mirror nonplanar ring laser cavity

A rigorous analysis is performed on the reentrant nonplanar ring laser cavity constructed by a Herriott-type multipass cell. Since the cavity is highly nonplanar, the angle between the incident planes at each reflection becomes different from that of the image rotation angles. The beam rotation, astigmatism, and spherical aberration are considered to obtain a self-consistent solution of the Gaussian beam. It turns out that spherical aberration is an important issue for this nonplanar resonator. Without taking into account the spherical aberration, a stable resonator would be difficult to realize. Using a self-consistent Gaussian beam propagation method, the laser beam characteristics are solved analytically. The results are compared with that of the 2 x 2 ABCD method.     

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.     

空间相干光通信外差效率及天线像差的影响

空间相干光通信中接收天线像差会使光外差效率下降.对本振光为高斯分布,信号光为爱里斑分布的光外差效率进行了研究,给出了无像差时外差效率的解析表达式.当焦平面上爱里斑半径与本振高斯光束光腰半径之比为1.71时,有最大外差效率81.45%.然后以本振光为理想的高斯光束,信号光受像差的影响,研究了倾斜、离焦、球差、彗差、像散等像差引起的光外差效率损失,给出了存在像差时外差效率的一维积分表达式.研究表明即使在采用离焦校正后,一个波长的球差引起的附加外差效率损失仍可达0.9 dB.因此对于爱里斑位于光轴上的接收天线,在设计时需仔细处理球差的影响.     

Well-corrected Two-element Telescope with a Flat Image

The three element Schmidt-Cassegrain telescope is a well-known catadioptric system that can be corrected for spherical aberration, coma, astigmatism and Petzval curvature. This paper describes a version with the same aberration correction, but with only two elements. There are just three optical surfaces that need to be made, two of which are aspheric. Because of the simplicity of this two-element design, alignment and environmental stability should be better than that of more conventional systems. It is also a very compact system, with a length that is only 45 per cent of the system focal length. Performance numbers for a typical design are given, as well as an explanation of the theory behind this new system.     

Adaptive optics for in-orbit aberration correction: spherical aberration feasibility study

We investigate the feasibility of using an adaptive mirror for in-orbit aberration corrections. The advantage of an in situ aberration correction of optical components in the space environment is that the mirror shape can be adjusted in an iterative fashion until the best image is obtained. Using the actuator spacing, corresponding to one half of the Nyquist frequency, the Strehl ratio of the corrected wave front improves to 0.95 when the mirror is fabricated with 6.5 waves of spherical aberration. The Strehl ratio decreases to 0.86 when the number of actuators is reduced by a factor of 4, in a two-dimensional adaptive optics model.     

Comparative analysis of doublets versus single-layer diffractive optical elements in eyepiece or magnifier design

We quantify the impact of eye clearance requirement on the performance of eyepieces utilizing doublets versus diffractive optical elements on aspheric substrates. In this study, the doublets were designed to be cemented on-axis elements. Specifically, four different values of eye clearance were implemented: 17, 20, 23, and 26 mm. For each value, axial and lateral color, spherical aberration, coma, astigmatism, field curvature, and distortion were compared. Each system under comparison was optimized for the same focal length, a 9 mm exit pupil, photopic wavelengths (513-608 nm), and a 40 degrees full field of view. We demonstrate that the single-layer diffractive optical element supports an eye clearance value of approximately 80% of the effective focal length, while the doublet drops below desired specifications at approximately 65% of the effective focal length.     

Aberration measurement of photolithographic lenses by use of hybrid diffractive photomasks

In optical lithography the degradation of image quality due to aberrations present in the exposure tool is a serious problem. Therefore it is desirable to establish a reliable aberration measurement procedure based on the analysis of printed images in the photoresist. We present what is to our knowledge a new method for characterizing the aberrations of an exposure tool using a hybrid diffractive photomask. By utilizing each different impact on the aberrated image from each diffracted illumination, we were able to extract the aberration present in the stepper system. We experimentally verified this method with a G-line stepper and verified its spherical aberration astigmatism.     

Axial irradiance of a focused beam

The principal maximum of axial irradiance of a focused beam with a low Fresnel number does not lie at its focal point; instead it lies at a point that is closer to the focusing pupil. It has been shown by the numerical example of a weakly truncated Gaussian beam that its value increases and its location moves closer to the pupil when spherical aberration is introduced into the beam. Such an increase has been referred to as "beyond the conventional diffraction limit." Similarly, an increase in the value and a shift in the location of the principal maximum of axial irradiance of a uniform beam toward the pupil by the introduction of some spherical aberration has been characterized as an unexpected result. We explain why and how such a result comes about and that it neither invalidates any diffraction limit nor is it unexpected. We illustrate this for uniform as well as Gaussian beams of various truncation ratios. Both focused and collimated beams aberrated by spherical aberration or astigmatism are considered.     

Analysis of Seidel aberration by use of the discrete wavelet transform

Seidel aberration coefficients can be expressed by Zernike coefficients. The least-squares matrix-inversion method of determining Zernike coefficients from a sampled wave front with measurement noise has been found to be numerically unstable. We present a method of estimating the Seidel aberration coefficients by using a two-dimensional discrete wavelet transform. This method is applied to analyze the wave front of an optical system, and we obtain not only more-accurate Seidel aberration coefficients, but we also speed the computation. Three simulated wave fronts are fitted, and simulation results are shown for spherical aberration, coma, astigmatism, and defocus.     

Space-resolving flat-field extreme ultraviolet spectrograph system and its aberration analysis with wave-front aberration

The Nam aberration of a flat-field extreme ultraviolet spectrograph system, composed of a varied line-spacing concave grating and a toroidal mirror, was analyzed by calculating the wave-front aberration with respect to an astigmatic reference surface. The toroidal mirror was used to compensate for the astigmatism that was due to the grazing incidence of light at the concave grating. The spectrograph system could form a space-resolved spectrum along the sagittal direction. The spectral and spatial resolutions of the spectrograph system were estimated from the root-mean-square spot size. The actual spectral resolution of the spectrograph system was measured from extreme ultraviolet spectra obtained from plasmas produced by an iodine laser having an energy of 0.5 J in a 4-ns duration, and it was compared with the calculated value.     

Spherical aberration gauge for human vision

Spherical aberration affects vision in varying degrees depending on pupil size, accommodation, individual eye characteristics, and interpretations by the brain. We developed a spherical aberration gauge to help evaluate the correction potential of spherical aberration in human vision. Variable aberration levels are achieved with laterally shifted polynomial plates from which a user selects a setting that provides the best vision. The aberration is mapped into the pupil of the eye using a simple telescope. Calibration data are given.     

Aplanatic corrector designs for the extremely large telescope

The next century is knocking on our door, bringing with it the possibility of telescopes even bigger than the 8-10-m-class instruments that have proliferated over the past decade. The fixed spherical reflector is the most economical and pragmatic way to construct an extremely large primary mirror (30-50 m in diameter). Although spherical mirrors have virtues such as manufacturability and identically figured segments, they also create great amounts of spherical aberration and coma. Here we show that there are several catoptric (all-reflecting) corrector designs that enable a fast telescope based on a spherical primary mirror.