Fast alignment of the Offner imaging spectrometer with spherical autostigmatic method

In this paper we have discussed the aberration properties and the design procedure of a spectrograph which uses a convex holographic grating as the dispersing element and a concave mirror as the focusing element. Both the concave mirror and the convex grating have common axis and they are concentric. The grating is constructed by recording the interference fringes on the convex surface which are formed by two convergent light beams incident from opposite sides of the axis. The illuminating source of the spectrograph is located on a plane perpendicular to the axis and passing through the common centre. It has been found that under certain conditions both positive and negative order spectra are perfectly focused on this plane. Aberration properties of the zero order image as well as the positive and the negative order spectral images have been studied by actual ray tracing. Using this system, design parameters of a medium-sized spectrograph having moderate dispersion and good resolution throughout theuv-visible region of the spectrum have been specified. The performance of the spectrograph has been evaluated by plotting spot diagram.

James Webb Space Telescope (JWST) has a segmented Primary Mirror (PM). PM is made of 18 beryllium hexagonal shaped segments. Flat-to-flat dimension of a segment is 1.315 meters. The PM is an ellipsoid of~ 6.5 meters in diameter with a conic constant of -0.99666 and a radius of curvature ~16 meters. After the PM, telescope are assembled and instruments are installed the observatory will go through environmental testing. The environmental test consist of acoustic and vibration test. The objective is to measure the change in the surface astigmatism of the Primary mirror segments at center of curvature before and after vibration and acoustic test. At the final stage of assembly the inner segments of the PM have no external fiducials. The challenge is to separate the alignment astigmatism from surface astigmatism without any external fiducials. This paper describes an alignment method that uses the print-through in the mirror segments as fiducials to separate the two astigmatisms.

In this paper we describe the basic principle and the resolution properties of a filter consisting of two similar concave gratings having circular grooves with variable spacing. These gratings can be fabricated by both mechanical ruling and holographic techniques. They are capable of producing an aberration-free image of a particular wavelength at the center of curvature when they are illuminated by a polychromatic beam parallel to the axis. Two such gratings having small central holes are mounted with a common axis. The centers of the two gratings are situated near the central holes. An exit pinhole is located at one of the centers of curvature. When the gratings are illuminated by a point source of white light located at the other center of curvature, an aberration-free image of a particular wavelength is formed at the exit pinhole. Although the exit pinhole has a finite diameter, light emerging from it is sufficiently monochromatic with a small bandwidth.

So far, we have considered refracting imaging systems: a spherical refracting surface in Chapter 1, a thin lens in Chapter 2, and a plane-parallel plate in Chapter 3. Now we consider the imaging properties of a spherical reflecting surface, i.e., a spherical mirror. These properties can be obtained in a manner similar to that for a spherical refracting surface. However, the geometry of the problem is different since now a ray incident on the surface is reflected back into the same medium containing the incident ray, instead of being refracted into another medium. Accordingly, it is instructive to draw object and image rays and not blindly use the imaging and aberration relations appropriate for a reflecting surface. In this chapter, we give the relations describing the primary aberrations of a spherical mirror for an arbitrary position of the aperture stop. These relations are applied to specific cases, one when the aperture stop is located at the mirror and the other when it is located at its center of curvature. It is shown that, in the first case, field curvature and distortion are zero. In the second case, coma, astigmatism, and distortion are zero. A numerical problem illustrates these results. <strong>4.2 PRIMARY ABERRATION FUNCTION</strong> Consider an imaging system consisting of a spherical mirror of radius of curvature <i>R</i> and focal length <i>f</i>&#x2032;. Let the aperture stop and the corresponding exit pupil of the system be located as indicated in Figure 4-1. The line joining the center of curvature <i>C</i> of the mirror and the center of the aperture stop (and, therefore, the center <i>O</i> of the exit pupil) defines the optical axis of the system. Consider an object lying at a distance <i>S</i> from the vertex <i>V</i>₀ of the mirror. Let the height of an object point <i>P</i> from the optical axis be <i>h</i>. The distance <i>S</i>&#x2032; and the height <i>h</i>&#x2032; of its Gaussian image <i>P</i>&#x2032; are given by (4-1) and (4-2a) (4-2b) respectively, where <i>M</i> is the magnification of the image.

Observations have been made of the SNR CTB 109 using the Westerbork Synthesis Radio Telescope at wavelengths of 49 cm and 21 cm, the Synthesis Telescope of the Dominion Radio Astrophysical Observatory at 21 cm, and the 46 m telescope of the Algonquin Radio Observatory at 4.6 cm. The spectral index of the integrated flux density of the SNR is given by alpha = 0.50 + or - 0.04; various maps are compared and show that, over the range of 4.6-49 cm, alpha does not vary across the SNR. Apart from the fact that the SNR shows an incomplete shell at both X-ray and radio wavelengths, there does not appear to be any correspondence of the finer details in the maps. There is no radio point source near to the position of the X-ray pulsar displaced by 3.6 arcmin from the center of curvature, but there is no indication, so far, that the pulsar is associated with the SNR.

Testing the optical figure and focal length of laser mirrors with radii of curvature in the 10 to 100 m range is difficult. If the mirror is concave, a source can be placed at the center of curvature. Air turbulence over these long path lengths makes interferometry difficult, however, and greatly reduces measurement accuracy. Convex mirrors are even more difficult to measure. A solution is to produce a slightly converging or diverging beam from a virtual source. The actual optical path in which turbulence may develop can then be made very short. A three-element test system consisting of a parabola, a transmission sphere, and a folding flat is described. It is capable of measuring both optical flats and convex or concave mirrors up to 40 cm in diameter with radii of curvature from 10 m to infinity. System accuracy is 1/20th wave rms in optical figure and 0.2% in radius of curvature. A discussion is given of the systematic errors introduced when the parabola is used in other than parallel light.

A new infrared meridian instrument is being developed at Pulkovo Observatory. The main purpose of the instrument is to extend the fundamental coordinate system to the K-infrared waveband and to faint stars at visual and I-wavebands. The instrument has a 30-cm primary mirror made from astrositall. An intermediate focal plane is used to introduce luminous reference marks. One can obtain autocollimated images of the marks at the intermediate focal plane with the use of a polished chamber located around the central hole of the primary mirror. The secondary mirror of the telescope forms images of the marks and of their autocollimated counterparts and passes them to the plane of a photodetector (Fig. 1.). The luminous marks give a reference frame for the measurements. These measurements are not affected by displacements of any optical unit placed after the intermediate focal plane or by displacements of the detector. The measurements are done relative to the coordinates of the average between positions of the luminous mark and its autocollimated image. Any small constant difference between the center of curvature and the optical axis position can be determined in the laboratory.

Sparse aperture telescopes represent a promising technology for increasing the effective diameter of an optical system while reducing the weight and the size. Multiple-mirror telescope (MMT) and multiple-telescope telescope (MTT) are two types of sparse aperture systems. The primary mirror of MMT consists of a number of segments that are all parts of a single primary-mirror conic. The configuration of the sparse aperture is related to the performance of the MMT. Golay configuration is nonredundant sparse aperture. Entrance pupil characteristics of Golay 6 MMT are studied to research the relationships between the sub-mirrors on the primary mirror and the shapes of sub-apertures on the entrance pupil of Golay 6. Overlay factor and efficiency factor are proposed to achieve the optimal fill factor on the entrance pupil. Given the relative aperture of Golay 6 MMT, there is some concern that the fill factor on the entrance pupil is larger than the overlay fill factor on the spherical sparse aperture primary mirror. The maximum fill factor and the maximal overlay factor are discussed, and the tangency condition when sub-mirrors of Golay 6 MMT are tangency is derived. Two Cassegrain telescopes having a spherical primary mirror with Golay6 configuration and with an aspherical secondary mirror are designed. The fill factor on the entrance pupil can be larger than the overlay factor on the primary mirror at the certain occasion. Based on the relationships between the fill factor and the overlay factor, the rational parameters of sub-mirrors on the primary mirror can be selected.

The California Extremely Large Telescope (CELT) is a joint project of the University of California and the California Institute of Technology to build and operate a 30-meter diameter telescope for research in astronomy at visible and infrared wavelengths. The current optical design calls for a primary, secondary, and tertiary mirror with Ritchey-Chretien foci at two Nasmyth platforms. The primary mirror is a mosaic of 1080 actively stabilized hexagonal segments. This paper summarizes the recent progress on the conceptual design of this telescope.

In order to obtain the intensity distribution of a 351 nm focal spot and smoothing by spectral dispersion (SSD) focal plane profile of a SGII-upgraded facility, a type of off-axis imaging system with three spherical mirrors, suitable for a finite distance source point to be imaged near the diffraction limit has been designed. The quality factor of the image system is 1.6 times of the diffraction limit tested by a 1053 nm point source. Because of the absence of a 351 nm point source, we can use a Collins diffraction imaging integral with respect to λ=351 nm, corresponding to a quality factor that is 3.8 times the diffraction limit at 351 nm. The calibration results show that at least the range of ±10 mrad of view field angle and ±50 mm along the axial direction around the optimum object distance can be satisfied with near diffraction limited image that is consistent with the design value. Using this image system, the No. 2 beam of the SGII-upgraded facility has been tested. The test result of the focal spot of final optics assembly (FOA) at 351 nm indicates that about 80% of energy is encompassed in 14.1 times the diffraction limit, while the output energy of the No. 2 beam is 908 J at 1053 nm. According to convolution theorem, the true value of a 351 nm focal spot of FOA is about 12 times the diffraction limit because of the influence of the quality factor. Further experimental studies indicate that the RMS value along the smoothing direction is less than 15.98% in the SSD spot test experiment. Computer simulations show that the quality factor of the image system used in the experiment has almost no effect on the SSD focal spot test. The image system can remarkably distort the SSD focal spot distribution under the circumstance of the quality factor 15 times worse than the diffraction limit. The distorted image shows a steep slope in the contour of the SSD focal spot along the smoothing direction that otherwise has a relatively flat top region around the focal spot center.

We contrast two approaches to the optics of reflection in concave spherical mirrors. In the Optics (ca. 165), Ptolemy employed the cathetus principle as a regulative rule to account qualitatively for visual appearance in concave spherical mirrors. In his Magia naturalis (1589) and De refractione (1593), Della Porta's analyses rested on the assumption of a reciprocal relation between reflection in concave mirrors and refraction in glass spheres. These two historical cases highlight two fundamentally different conceptions of optics: Ptolemy explained optical phenomena based on vision, whereas Della Porta explained the same phenomena by appealing to the geometrical action of light. The shift from perception to the geometry of light rays marks an important development in the history of optics. The elimination of vision from the equation, as it were, ushered in modern optics.

An off-axis three-mirror detection system with a large field of view is designed in order to improve the space target detection capability. The optical system is a Cook-TMA with the focal length of 127mm, the F number of 2, the field angle of 25° × 25° and the spectral range of 400-700nm. The primary mirror and the tertiary mirror of the off-axis three mirror system are all designed by free form surfaces: the primary mirror is characterized by Zernike polynomial and the tertiary mirror is described by XY polynomial. At the same time, we analyze the related characteristics of Zernike polynomial and XY polynomial. The results show that the free form surfaces have great advantages in improving the field of view and the imaging quality of the off-axis optical system. The system has high energy concentration and good imaging quality, which can capture and track the target in a wide range is suitable for wide area target monitoring.

A collimator was required to qualify the Advanced Land Imager (ALI) instrument of the EO-1 new millennium satellite for focus, MTF measurements, and distortion. It was used during assembly of the instrument and during thermal cycling while the instrument was in a vacuum tank. It had to be diffraction-limited over a 3 X 3 degree field of view and over a waveband of 400 to 2500 nm, have no obstruction, and have a virtual exit pupil that could be imaged onto the entrance pupil of the telescope. To satisfy these requirements the collimator, external to the vacuum tank, was built comprising a spherical mirror with exit pupil at its center of curvature, a full-aperture beamsplitter in collimated space, and a single lens to flatten the field. The optical layout and method of verifying collimation will be presented as well as optical performance, of interest since no corrector plate could be used as in the usual Schmidt camera configuration.

Silicon carbide (SiC) is well known as an excellent material for high performance optical applications because it offers many advantages over other commonly used glasses and metals. The excellent attributes of SiC include high strength, high hardness, low density, high thermal resistance, and low coefficient of thermal expansion. The effect of CO2 laser and its tool path on SiCwere investigated. The process started by creating laser pre-cracks on the desired pattern. Subsequently, laser assisted polishing was conducted on the same tool path. The surface showed a sharp increase in material removal in the areas with laser pre-cracks. This high difference in material removal was used not only to fabricate a ⌀ 1100 mm concave mirror with 127 μm in depth but also to generate macro and micro patterns. Grooves from 2 mm to 200 μm in width and 5 μm to 20 μm depth were successfully generated.

We propose and experimentally demonstrate the Transformable Reflective Telescope (TRT) kit for educational purposes and for performing various optical tests with a single kit. The TRT kit is a portable optical bench setup suitable for interferometry, spectroscopy, measuring stray light, and developing adaptive optics, among other uses. Supplementary modules may be integrated easily due to the modular design of the TRT kit. The kit consists of five units: a primary mirror module, secondary mirror module, mounting base module, baffle module, and alignment module. Precise alignment and focusing are achieved using a precision optical rail on the alignment module. The TRT kit transforms into three telescope configurations: Newtonian, Cassegrain, and Gregorian. Students change telescope configurations by exchanging the secondary mirror. The portable design and the aluminum primary mirror of the TRT kit enable students to perform experiments in various environments. The minimized baffle design utilizes commercial telescope tubes, allowing users to look directly into the optical system while suppressing stray light down to ∼ 10 − 8 point source transmittance. The TRT kit was tested using a point source and field images. Point source measurement of the Newtonian telescope configuration resulted in an 80% encircled energy diameter of 23.8 µm.