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One of the most challenging open questions of modern astrophysics and particle physics is the determination of the origins and the production mechanisms of the Ultra-High Energy Cosmic Rays (UHECR), i.e. particles with energy above the Greisen–Zatsepin–Kuzmin (GZK) limit, which is about 5×1019 eV. UHECRs can be studied in two ways: either via direct detection of the secondary particles, i.e. extensive air shower (EAS), produced by UEHRCs interaction with the atmosphere, or by observing during night the track of the UV fluorescence emitted by EAS. The origin direction of the cosmic rays can be therefore determined. While ground-based observatories are already operative, different optical configurations, based mainly on the Schmidt camera layout or double Fresnel lenses concept, can be envisaged for future space-based ones. Both solutions faced in the past technological issues: transmission and resolution at large field angles for Fresnel lenses and weight of the primary mirror for the Schmidt. However, recent advances in the technology of ultra-lightweight, large and deployable active mirrors made the Schmidt camera approach feasible, becoming the preferred option. This work describes a lightweight Schmidt space telescope design for UHECRs detection conceived for a mission intended to orbit at 600 km altitude. The instrument concept is a fast, high-pixelized, large aperture and large Field-of-View (FoV) digital camera, working in the near-UV wavelength range with single photon counting capability. The telescope will record the track of an EAS with a time resolution of 2.5 μs and a spatial resolution of about 0.6 km (corresponding to ~ 4’), thus allowing the determination of energy and direction of the primary particles. The proposed design has about 50° FoV and a 4.2 m entrance pupil diameter. The mirror is 7.5 m in diameter, it is deployable and segmented to fit the diameter of the considered launcher fairing (i.e. Ariane 6.2). The Schmidt corrector plate is a lightweight annular corona. This configuration provides a polychromatic angular resolution less than 4' RMS over the whole FoV with a very fast relative aperture, i.e. F/# 0.7. Thanks to its very large pupil and large FoV, the design could be fit for a space-based observatory, thus enhancing the science achievable with respect to the presently operating ground-based counterparts, such as Telescope Array and Auger. A key advantage of this catadioptric design over the classic all refractive adopted in the past is the higher attainable global throughput. This parameter guarantees to reach and fulfil the required instrument photon collection specifications.

The past three years have seen a global increase in explosive-based terror attacks. The widespread use of improvised explosives and anti-personnel landmines have caused thousands of civilian casualties across the world. Current scenario of globalized civilization threat from terror drives the need to improve the performance and capabilities of standoff explosive trace detection devices to be able to anticipate the threat from a safe distance to prevent explosions and save human lives. In recent years, laser-induced breakdown spectroscopy (LIBS) is an emerging approach for material or elemental investigations. All the principle elements on the surface are detectable in a single measurement using LIBS and hence, a standoff LIBS based method has been used to remotely detect explosive traces from several to tens of metres distance. The most important component of LIBS based standoff explosive trace detection system is the telescope which enables remote identification of chemical constituents of the explosives. However, in a compact LIBS system where Cassegrain telescope serves the purpose of laser beam delivery and light collection, need a design optimization of the telescope system. This paper reports design optimization of a Cassegrain telescope to detect explosives remotely for LIBS system. A design optimization of Schmidt corrector plate was carried out for Nd:YAG laser. Effect of different design parameters was investigated to eliminate spherical aberration in the system. Effect of different laser wavelengths on the Schmidt corrector design was also investigated for the standoff LIBS system.

The present study provides the theory base for designing flat-field Schmidt optical systems, based on the wavefront aberration of Petzval field curvature, a mathematic model of the Petzval radius is setting up. The radius of Petzval image surface is not equal to the focal length of the primary mirror or the focal length of the system. An aberration balancing method for flat-field Schmidt optical systems design is proposed: did not change parameters of the corrector, through adjusting the distance between the plate and the mirror to realize aberration equilibrium. The total physical track is more compact than equilibrium before.

Several designs are shown that are alternatives to Bernhard Schmidt’s largely unknown 1934 three lens corrector replacement for an aspheric plate in his famous telescope.

To make it easier for designing Schmidt optical systems, based on wavefront aberration functions, a mathematical model of the corrector plate aspheric surfaces varies as a function of defocusing amount is established. It corrects not only the third-order spherical aberration, but also the 5th-order spherical aberration for the system. A series of Schmidt optical systems were designed as examples to evaluate the mathematical model of the aspherics. Results show that the mathematical model is precisely in fitting the needed shape of the corrector, and can be used for the systems for quick F ratio and large aperture. A mathematical model for reflective correctors shape is also established.

The methods of exact optics are here extended to cover the design of lens and mirror systems. Power series are given for the shapes of both Schmidt corrector plates and their complementary almost spherical mirrors. Their off-axis images are analysed. A meniscus glass corrector extends the prime focus field of an f/3.333 reflector with subarcsecond images by a factor greater than 10.

The Beijing-Arizona-Taiwan-Connecticut Color Survey of the Sky employs the 0.6/0.9 m Schmidt telescope of the National Astronomical Observatories, located at its Xinglong station (150 km northeast of Beijing), combined with a 20482 CCD data-taking system. Key to the success of this program is the development of a simple and efficient way to achieve supersky-quality, large-scale flat fields for our telescope-CCD combination. This is done by placing an isotropic diffuser right in front of the Schmidt corrector plate (the entrance pupil of the telescope) and illuminating the diffuser with scattered light off the dome screen. When we test this methodology by obtaining supersky flats at the zenith, we find that our "super" dome flats define the same large-scale inhomogeneities of the CCD that the supersky flat does, but with far greater signal-to-noise ratio. Hence, we show that defining our large-scale flat fields with our diffuser-dome technique is at least as good as using supersky flats for a ~1°-wide field of view. This methodology can be implemented with any Schmidt telescope with similar results. Various other data acquisition effects that can affect CCD results at the 1% level are also discussed.

Given a 3D reflecting surface G, which is not necessarily rotationally symmetric, away from a point source, and a direction e, we design a reflecting surface F so that the system (G,F) reflects all rays into the direction e. We also solve the near-field problem when the direction e is replaced by a given point R. The surface F satisfies a system of first-order partial differential equations that can be explicitly solved in terms of G and e. We also apply the same ideas to designing refracting plates, of which the Schmidt corrector plate is an example.

The National Ignition Facility (NIF) requires high resolution live images of regions inside the target chamber in order to align diagnostic instruments to fusion targets and to monitor target stability. To view the interior of the target chamber, we modified a commercial 11-inch Schmidt-Cassegrain telescope to develop the Opposed Port Alignment System (OPAS). There are two OPAS systems installed on the target chamber ports directly opposite the diagnostics. This paper describes the optical design, highlighting the two key modifications of the telescope. The first key modification was to reposition the Schmidt corrector plate and to uniquely mount the secondary mirror to a precision translation stage to adjust focus from 5.5 m to infinity. The stage is carefully aligned to ensure that the telescope’s optical axis lies on a straight line during focus adjustments. The second key modification was a custom three element lens that flattens the field, corrects residual aberrations of the Schmidt-Cassegrain and, with a commercial 1:1 relay lens, projects the final image plane onto a large format 50 mega-pixel camera. The OPAS modifications greatly extend the Schmidt-Cassegrain telescope’s field of view, producing nearly diffraction-limited images over a flat field covering ±0.4 degrees. Also discussed in the paper are the alignment procedure and the hardware layout of the telescope.

An analytical method for the design of achromatic corrector plates for either classical Schmidt cameras or related types of systems is presented. The method may be applied to the design of achromatic doublet correcting plates allowing for the attainment of any order of asphericity for the aspheric surfaces of the corrector plate.

To test the LASL lens design program's capabilities with aspherical surfaces, a conventional Schmidt telescope was analyzed and compared with a newly designed flat-field Schmidt design. The remarkable imaging qualities of the conventional design were demonstrated. Introducing a field-flattener lens near the focal surface of the curved field design resulted in increased chromatic defects and appreciable resolution loss. The LASL program makes a statistical analysis of the traced skew rays generating geometrical image spots.

The aspheric plate at the center of curvature of a spherical primary is replaced by a small aspheric corrector at a minified pupil located inside a reimaging camera. The correctors are identical for each reimaging camera because the spherical aberration of the primary sphere is identical and symmetrical for all field positions. The magnitude of the field aberrations is evaluated over a range of primary focal ratios and minified pupil diameters. The major term is the increased field angle through the minified aspheric corrector. The field and chromatic aberrations in such a camera are compared with the equivalent full-aperture Schmidt corrector. Field-of-view partitioning enables each subfield to be designed for specific observational requirements, such as multiple-fiber spectrography or CCD imaging. Field partitioning is shown to be a powerful means for the replacement of the large aspheric corrector of a Schmidt telescope by a multiplicity of small reimaging subsystems. The cost to fill the typical wide field of a Schmidt telescope with reimaging modules is approximately 1% the cost of a Schmidt aspheric plate.

The image plane of Newton-Schmidt system is between Schmidt corrector and spheric mirror, which is difficult to be received. Cassegrain-Schmidt system is put forward to shift the image plane behind the primary mirror 1 . Based on the third order aberration theory and Gaussian formula, and choices of defocus u and neutral zoneh n , new parameters obscuration ratio of two Cassegrain mirrorsD and magnification of the secondary mirror E and concentric condition of two Cassegrain mirrors, the equation of corrector including the 2 nd and 4 th order terms of the even aspheric plate is established. Then the 4 th , 6 th and 8 order terms of Schmidt corrector plate are solved by inverse-ray tracing to correct high order spherical aberration. To reduce chromatic aberration of Cassegrain-Schmidt system, new types of achromatic Cassegrain-Schmidt systems are put forward and discussed. Keywords: Cassegrain-Schmidt system, Schmidt corrector pl ate, Aberration theory, Defocus, Achromatic.

Schmidt system is a famous optical system. The corrector equation based on the third-order aberration theory has been acknowledged all along. When the previous equation is confirmed in characteristic of the aspheric surface equation and optical design program ZEMAX, it is found that the equation of the corrector has some errors. Analyses of this problem are given. A new corrector equation is established. The new equation is confirmed seriously by the optical design program ZEMAX again, it can be deduced that the coefficient α=1/2r 02 , and the spherical aberration coefficient ΣS 1 =0. This improvement is very useful for the optical design of Schmidt system, which quickens the optimization and easily reaches the optimal design data.

Original Schmidt-like spherical aberration corrector is designed. Corrector consists of spherical surfaces, and it can be used for telescopes and cameras instead of aspherical Schmidt corrector for the ground and Space optics. Corrector can be easily made of any transparent material ? Fused Quartz, UBK7 glass, etc., for very large spectral region ? from IR to UV. These optical systems are especially recommended for Space telescopes intended for observation of the large fields in a large spectral region.

An optical system consisting of a reflecting mirror with a Schmidt corrector plate is presented as a possible design of a space-based observatory for high energy (up to 10 20 eV) cosmic rays, by monitoring the fluorescence showers induced after interaction by cosmic rays with the Earth atmosphere. An instrument of that kind is currently into the evaluation phase as an external payload for the International Space Station. The basic requirements demand a system with large field of view, up to ±30°, and large collecting aperture, ≥2 m diameter, to achieve a sufficient sensitivity and event statistics. Among several possible optical systems for this purpose, the Schmidt camera is the simplest, matching most of the optical technical requirements, with some problem for the obscuration due to the focal plane at such extreme field of view. This paper presents ray-tracing simulations for different designs of large aperture (> 2m) Schmidt cameras with FOV from 40° to 50°, with F/# ≈ 0.7 and ground resolution from 1 to 2 km from a LEO. Better performances are achieved with an aspheric mirror, but performances using of a spherical mirror are acceptable with some compromise in resolution. The overall geometrical transmission ranges from 40% to 78%, according to the selected geometry and FOV. Possible technologies for the construction of the main mirror and all other components, including supporting mechanics will be also discussed.

The Large sky Area Multi-Object fiber Spectroscopic Telescope is a very special reflecting Schmidt telescope with a 40 m long optical axis between the reflecting Schmidt correcting plate and the spherical main mirror. In the middle is located the spherical focal plane of 1.75 m in diameter. The reflecting Schmidt correcting plate serves not only to correct wavefront by active optics but also to point and track celestial objects by normal tracking with collaboration of the focal plane to form a special mounting and tracking system. In this paper, the operational principle and technical specification of the tracking system is briefed. Design and test measurement as well as driving mode of both the Schmidt plate and the focal plane are investigated with structural calculations and analyses. The paper is closed with the conclusion that the mounting and tracking system is to meet global technical specifications of the LAMOST excellently.

The Hobby-Eberly Telescope uses a 11-meter diameter F/1.45 segmented spherical primary mirror. A spherical mirror of this size generates large amounts of spherical aberration. To be used successfully in a tilted optical Arecibo type telescope, the spherical aberration needs to be corrected. This means that tracking of astronomical targets is achieved through moving a tracker optical package which imposes somewhat severe packaging constraints. Given these packaging constraints, novel methods must be employed to correct the aberrations with the Spherical Aberration COrrector contained in the moving tracker optical package. The paper reviews the pertinent requirements, constraints and the resultant design of the Hobby-Eberly Telescope Four Mirror Spherical Aberration Corrector.

To correct spherical aberration of a spherical mirror the apochromatic meniscus lens may be used. The linear observation of light beams is taken as a set parameter. The location of meniscus lens, concerning spherical mirror and its radiuses correction are taken as corrective parameters. In this case the dependence of parameters, determining the sphere of meniscus system existence, was received. The meniscus lens was received on the condition of aplanatic correction of aberrations. The transformation of this corrector in a two component system leads to the original construction of the optical scheme. The versions of a practical application of the received lens design were considered.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The paper relates to different inventions, comprising three diffraction-limited catadioptric designs. All the systems use only spherical shaped surfaces and are designed from one kind of optical material only. In the examples the glass BK7 from the Schott-catalogue was used. The first example gives a three element design reaching equal performance as a Schmidt camera but with only 25 percent of its length. Additionally the field is flat and conveniently located behind the system. The second example is designed to reduce the central obstruction. It's somewhat based on the principle of the Houghton-camera. For a f-number 4 system with 1000 millimeters focal length it gives outstanding image quality at a 5 degree's field--even capable for diffraction-limited visual use. For reduced f-number 5,6 the image is diffraction-limited at the whole field. In terms of color correction it outperforms every Schmidt-Cassegrain or apochromatic triplet of even arbitrarily more reduced light gathering power. The third example is the equivalent for the so-called Wynne corrector triplet that corrects the aberrations of a parabolical mirror. But the invented corrector corrects additionally the spherical aberration of a spherical mirror. The corrector is able to correct all third order aberrations without introducing longitudinal and lateral color.

The fabrication and testing of a corrector mirror for a reflective Schmidt camera is to be presented. With a reflective corrector, the incident beam has to be off-axis. The corrector is tilted at an angle of 30 degrees with the optical axis to implement this requirement. The figure of the corrector, which composes of the toric term, rotational symmetrical and rotational nonsymmetrical aspherical terms, poses a certain degree of challenge for fabrication. The total correction is 46 waves peak to valley at 632.8 nm wavelength.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We use the two-dimensional Chebyshev polynomials as the basis for decomposition of test data over rectangular apertures, particularly for anamorphic optics. This includes simple optics such as cylindrical lenses and mirrors as well as complex optics, such as aspheric cylindrical optics. The new basis set is strictly orthogonal over rectangles of arbitrary aspect ratio and they correspond well with the aberrations of systems containing such type of optics. An example is given that applies the new basis set to study the surface figure error of a cylindrical Schmidt corrector plate. It is not only an excellent fitting basis but also can be used to flag misalignment errors that are critical to fabrication.

The optical design and fabrication of a fast f/1.4 prototype camera for the JNLT are briefly described. The f/1 semisolid Schmidt-Cassegrain camera configuration (a corrector lens plus two aspheric mirrors) developed by Nariai and Yamashita (1987) on the basis of third-order aberration theory is adopted, but the design is modified to reduce the number of aspheric surfaces from four to two. Computer-controlled polishing achieved accuracy of 150 and 200 nm for the corrector plate and secondary mirror, respectively. The use of a constant-radial-shearing interferometer to test the Schmidt corrector plate is explained, and it is reported that the assembled camera had MTF of 55 percent for 100 lp/mm when imaging a 5-micron slit placed in the focal plane.

The classic Schmidt design has its aspheric corrector plate designed for and located at the center of curvature of its companion spherically concave primary mirror. So configured, it is well corrected for objects at infinity imaged at focus. Any closer object, however, is imaged with increasing spherical aberration as its distance from the corrector plate is diminished. Shifting the unchanged corrector plate toward its primary mirror increases the range of object distances for which the system retains excellent stigmatic correction. At the corrector plate's near-optimum location, this range may extend from a few of the primary mirror's radii in front of the corrector plate to infinity. Coma increases, but likely will remain tolerably small except for very fast systems.

Two types of achromatic Schmidt corrector plate are described; both give an on-axis Strehl number S ⪆ 0.8 over an extended wavelength region. It is found that this specification can only be achieved by combining a positive and a negative plate and by restricting the speed ratio D/N3 of the system. The theory is illustrated by numerical examples.

Summary In this paper the profile of an improved aspheric plate is obtained which minimizes the off- axis errors of Schmidt cameras over a given field. In the case of monochromatic systems these errors are reduced to two-fifths those of the classical Schmidt if axial stigmatism is retained or to one-third if some spherical aberration is introduced into the system. In the case of chromatic systems a method is given of calculating the equation of the profile which minimizes the overall errors for different spectral ranges over given fields.

The full aperture meniscus corrector catadioptric lens is a compact, fast flat-field configuration which should find application in wide field, long focal length systems which place a premium on high acutance image quality; i.e., aerial photography. Additionally, since the lens power is mainly in the primary mirror, the meniscus corrector catadioptric lens is capable of covering a much wider spectral bandwidth than can be achieved with a refractor of comparable aperture and focal length. The basic configuration consists of a primary mirror, a weak meniscus corrector lens and a single positive lens close to the image plane, to flatten the field. The under-corrected spherical aberration of the primary mirror is essentially balanced out by the over-corrected spherical aberration contributed by the weak meniscus lens. When design requirements dictate a smaller f-number, the single corrector lens generally evolves into a multiple lens configuration used in either the single pass or double pass mode. Axial color correction is achieved by either the achromatic single glass meniscus lens, or the two glass meniscus doublet. Characteristically, the higher order spherical aberration is corrected by the meniscus lens thickness as the f-number is decreased. However, for large scale systems the corrector thickness may become prohibitive. For the large scale designs the utilization of an aspheric figure on one of the corrector surfaces will produce a significantly thinner lens element. Similarly, the benefits of aspheric surfaces can be realized in the field flattening lenses. For a wide field of view, covering a square/circular field format, the obstruction is quite large; in fact, complete occultation is common in these instances. Consequently, the wide field versions will have to be used in the slit field mode with the resultant bar obstruction. However, this poses no serious problems in aerial photographic applications since the utilization of these designs would be either in the "push broom" or the scanning mode which would require auxiliary mirrors.

The fabrication of aspheric elements by means of replication has become a very important method of supplying otherwise difficult to produce components. The Schmidt Corrector Plate is a typical example, the major benefit being projection TV for the consumer market. However, prior to this it is necessary to develop an objective test method. This paper describes a laser ray trace method of measuring the aspheric profile to ±5 il and subsequently using the derived coefficients to calculate the system M.T.F.' Using this as the quality criteria an objective test method has evolved. The systems shortcomings are discussed, and it is concluded that a useful production test method has been developed.

An optical system is described which is corrected for spherical aberration, coma, astiq- matism, Petzval curvature, longitudinal and lateral color, secondary color, spherochromatism and chromatic variation of all the field aberrations. It has very good performance on a flat image over an extremely broad spectral range, from the ultraviolet to the infrared. It has also been designed to cover a very broad temperature range. All spherical surfaces are used, and only one glass type. With BK-7 glass, the Catadioptric design has a spot size of four arc-seconds over a 3 degree diameter field of view flat image at f/2.5, over the whole^ ^^ ^f is essentially ^changed over ?Introduction^i-' ^oughton1 found a waY to replace the Schmidt corrector plate of the Schmidt telescope with a triplet lens located at the center of curvature of the spherical primary mirror Figure 1 shows how this looks. It has two big advantages over the conventional o°h 4- telesc°Pe:4_ .^he absence of aspheric surfaces and the possibility of correcting spher­ ochromatism. It still has a curved image and is equally as long as the Schmidt. By sep­ arating the components of the triplet so that there are appreciable airspaces between the elements, Houghton was also able to control oblique spherical aberration ^tween theStopSpherical Mirror

Sands showed the equivalence of the third-order aspheric surface contribution of the aberration polynomial to the third-order inhomogenous surface contribution. This fact is exemplified by the substitution of an axial gradient for the aspheric surface of the Schmidt corrector plate. It is shown that a gradient-index corrector plate system is limited in its off-axis performance by fifth-order oblique spherical aberration just as the conventional Schmidt system is.

The recent need in space astronomy for wide-field telescopes having the best transmission and exempt from the chromatic aberration in uv, the severe conditions of the aspheric surface quality for the shortest wavelength, leads to new developments both in the theory and design of those surfaces. A two-surface all-reflective Schmidt telescope is analyzed (1) with Fermat’s principle and (2) with Abbe sine condition. A dioptric elasticity method is presented to aspherize the primary mirror which is a nonaxisymmetric surface. Experimental results are given for an f/1.5, 180 mm focal length all-reflective Schmidt.

The great flexibility of the 200-inch mirror required the development of new and elaborate support systems to maintain the figure in all orientations. New methods had, therefore, to be devised for testing the mirror in the telescope while on these supports. The final figuring was done on the mountain on the basis of these tests.To increase the effectiveness of the instrument, corrector lenses were designed by Ross greatly to enlarge the field of the main mirror. Likewise the method of evaporating a reflecting coat of aluminum was developed by Strong to replace the old silvering procedures. Several new optical designs were introduced in the spectrographs to make optimum use of the light collected. These included the use of (1) a composite of four “blazed” gratings to permit a collimator aperture of 12 inches; (2) Schmidt cameras with half-strength corrector plate placed practically in contact with the grating, the light passing through the plate twice (this eliminates many vignetting problems and permits higher speeds and larger fields); and (3) a combination of a quartz aplanatic sphere with a Schmidt camera for the shortest focal-length camera to obtain a much higher speed (F/D = 0.7) than would otherwise have been possible.

The paper discusses the problem of designing the aspheric surface of a Schmidt camera so as to obtain optimum performance, in an agreed sense, over the field taken as a whole. A solution is obtained in a form which allows the optimum plate-profile to be quickly determined for a Schmidt camera of given aperture-ratio and field-size, working over a given spectral range. It is shown that at apertures near f/3 the optimum plate can be obtained by slightly decreasing the strength of an ordinary “color-minimised” Schmidt plate, while in wide-field systems working at apertures near f/1, it is better to use a plate with neutral zone at the edge of the aperture.

A method of balancing the optical aberrations over a wide angular field of a Schmidt optical system is described. This design method is demonstrated for a Schmidt optical system of focal ratio F:0.7 and covering an angular field of 40°. The reduction in off-axis secondary aberrations is obtained by computing a “wide angle” aspheric corrector plate through the use of “Lucy’s Approximate Method” instead of using the conventional “exact equations.”

The theory of the Schmidt telescope has been based on consideration of the properties of a spherical mirror.1 It develops that a spherical mirror, in conjunction with a correcting lens of little or no magnification mounted at the center of curvature of the mirror, provides a system with properties unique among reflectors, a system altogether free from the monochromatic aberrations of the third order with the exception of curvature of field. If the theory is developed along more general lines with no apriori assumptions as to the shape of the mirror, or the distance between mirror and correcting lens, a whole family of telescopes may be obtained, all members of which are free from spherical aberration and also obey the sine condition for freedom from coma.