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This is a proposal and description of a new spectrometer based on the Schwarzschild optical system. The proposed design contains two Schwarzschild optical systems. Light diverging from the spectrometer entrance slit is collimated by the first one; the collimated light beam hits a planar diffraction grating and the light dispersed from the grating i...
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Context 1
... proposal of this work is a reflective spectrometer in which both the collimating and the focusing optics are Schwarzschild optical systems optimized accord- ing to the procedure detailed in Section 2. At first sight, this means that the spectrometer comprises four mirrors. However, all the mirrors can be ar- ranged so that they have a common center. In this case, the collimator and focuser share the same con- vex mirror (R 3 ¼ R 2 ). Furthermore, a symmetrical configuration can be chosen in which the collimator and focuser are optimized for the same impact para- meter. In doing so, the two concave mirrors have the same radius (R 4 ¼ R 1 ) and can be built as a single mirror, as in the Ebert-Fastie design, provided there is sufficient spare space for the diffraction grating. A sketch of the proposed system is shown in Fig. 5. The slit center is located at O, and the axis Z contains the common center of curvature C and the grating center V g . The slit and grating grooves are perpendi- cular to the plane of the drawing, and it is assumed that the grating acts as the aperture stop. The ray following path OV 1 V 2 V g is the chief ray in the object space, and the ray that follows the path V g V 3 V 4 I s is the chief ray in the image space for an arbitrary ...
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... this section, we present a design procedure of a Schwarzschild type spectrometer based on the con- figuration depicted in Section 3 and the results of Section 2. This design procedure starts by choosing the parameters that are left free at the beginning of the computation. Even though there are several possible combinations of parameters, for simplicity of calculation, the following ones have been chosen: the convex mirror radius (R 2 ¼ R 4 ), the angle of in- cidence on the grating with respect to the Z axis (δ), the distance between the vertex of the convex mirror and the vertex of the grating (in Fig. 5 this is PV g ≡ d), the groove density (g), the grating order (typically, m ¼ AE1), and the design wavelength λ. There are some constraints that suggest or restrict the values of these parameters. First, they must be chosen to obtain a spectral image without vignet- ting in the desired spectral band of the instrument. Second, the convex mirror radius determines the size of the instrument. Third, once the radii of both mir- rors have been fixed, the grating density determines the system dispersion. Finally, since the spectral components diffracted further away from the center of curvature C present large optical aberration, the design wavelength chosen must be closer to the maximum if m ¼ −1, while it is chosen closer to the minimum wavelength if m ¼ ...
Context 3
... the grating is in place, the object position O and the radii ratio are chosen in such a way that a perfect collimated beam, as described in Section 2, is incident on the grating in a direction parallel to line OC. This direction makes an angle δ with the Z axis. In the image space, the wavelength diffracted at an angle δ 0 ¼ δ makes up an anastigmatic image at a point obtained from O by reflection across the Z axis. The diffraction grating can be rotated about the Y axis to change the wavelength that satisfies this condition. For this purpose, the relation between the incidence and diffraction angles ðθ g ; θ 0 g Þ and an- gles δ, δ 0 , α in Fig. 5 must be taken into ...
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... illustrate the performance of a Schwarzschild type spectrometer, an optimized system has been de- signed using the above formulas. The optical design program Oslo-Edu was used to carry out ray-tracing procedures. The spectrometer was designed to image a spectral band centered on 700 nm over the long side (8:8 mm) of a 2=3 in: CCD detector. With the para- meters of Table 1, this was achieved with a spectral coverage of 270 nm. Other parameters of the spectro- meter, such as the object position or the position of its anastigmatic image, can be easily calculated from the formulas in Section 4. A check was made first to ensure that astigmatism was minimized at the de- sign wavelength of 794 nm. Figure 7(a) shows the spot diagram for an on-axis point in an F=4 instru- ment. The symmetry of this spot along the horizontal dimension is evidence of the absence of Seidel's coma. Fig. ...
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Citations
... Recent advancements in the optical design of Schwarzschild imaging spectrometer have been driven by research exploring the use of spherical [27], aspherical [28], and freeform [29][30][31] mirrors. These studies aim to decrease system volume while enhancing performance. ...
In recent years, attention has been directed towards cost-effective and compact freeform Schwarzschild imaging spectrometers with plane gratings. The utilization of tolerance analysis serves as a potent approach to facilitate the development of prototypes. Conventional tolerance analysis methods often rely solely on the modulation transfer function (MTF) criterion. However, for a spectrometer system, factors such as the keystone/smile distortion and spectral resolution performance also require consideration. In this study, a tailored comprehensive performance domain tolerance analysis methodology for freeform imaging spectrometers was developed, considering vital aspects such as the MTF, keystone/smile distortion, and spectral resolution. Through this approach, meticulous tolerance analysis was conducted for a freeform Schwarzschild imaging spectrometer, providing valuable insights for the prototype machining and assembly processes. Emphasis was placed on the necessity of precise control over the tilt and decenter between the first and third mirrors, whereas the other fabrication and assembly tolerances adhered to the standard requirements. Finally, an alignment computer-generated hologram (CGH) was employed for the preassembly of the first and third mirrors, enabling successful prototype development. The congruence observed between the measured results and tolerance analysis outcomes demonstrates the effectiveness of the proposed method.
... Astigmatism in the classic Czerny-Turner imaging spectrometer is the dominant issue, and many efforts have been made to eliminate it by compensating the diffencence between the focal lengths in the tangential and sagittal planes for the two off-axis spherical mirrors [7]. This can be done by introducing divergent illumination on the plane grating through minimizing the distance between the entrance pinhole and the collimating mirror [8]; or using more spherical mirrors to build a concentric off-axis configuration [9,10]; or changing the spherical mirror type, e.g., using a toroidal focusing system through coordinate transformations, to increase the convenience of the freeform spectrometer construction. ...
... selected, the reflective focal length for each OAP segment, such as S-min f and S-max f can be derived from Eq. (9). Thus, together with the off-axis angles of βmin, βctrl and βmax, the specifications for each OAP segment are determined. ...
... Then, the parameters definitions for the OAP base and OAP segments are derived from the proposed procedure using Eqs. (3)(4)(5)(6)(7)(8)(9). ...
The classic Czerny-Turner spectrometer consists of a plane grating and two spherical mirrors. The optical path geometry adopted for incident and grating dispersed light is off-axis reflection, so the spherical collimating and focusing mirrors introduce coma and astigmatism. The conventional configuration is asymmetrical for coma automatic compensation, but suffers from astigmatism. We substitute the off-axis parabolic (OAP) surfaces for spherical surfaces of the collimating mirror and each sub-region of the focusing mirror, to achieve an aberration free configuration. The multiple OAP surfaces are then expanded and mixed, to construct a freeform surface integrating the collimating and focusing mirrors into a single element. Results show that a 0.1 nm spectral resolution is achieved over a bandwidth of 400 nm centered at 800 nm, in the designed spectrometer comprised of a plane grating and one freeform mirror. The construction method is advantageous to integrated optic design, and the resulting freeform mirror spectrometer is compact, and simplifies manufacture and alignment.
... Typical mirror systems like Czerny-Turner [10], Offner [11], Schwarzschild [12], and three mirror anastigmatic (TMA) [13], as well as the catadioptric Dyson system [14], are used widely for spectrometer designs [6,7,15,16] due to their simple configuration and superior performance. For the presented paper, the above system types are used to design a hyperspectral imaging spectrometer system for monitoring Earth's environment on a global scale [17]. ...
Hyperspectral-grating-based imaging spectrometer systems with F/3 and covering the visual–near-infrared (420–1000 nm) spectral range are investigated for monitoring Earth’s environmental changes. The systems have an entrance slit of 24 μm and a 6.5 nm spectral resolution. Both smile and keystone distortions are smaller than 20% of the pixel pitch. We benefit from the development in freeform technology and design 15 different systems with the help of off-axis aspheric and freeform surfaces. The potential of each system is explored with the help of nonspherical surfaces. Cross comparisons between different system types are summarized to give their advantages and disadvantages. In the end, detailed tolerancing of one selected system is presented to show the feasibility for fabrication.
... Para ello, en este trabajo se han analizado sistemas que utilizan únicamente elementos esféricos con redes de difracción clásicas (no corregidas en aberraciones) y con un número de elementos lo más reducido posible. En concreto la investigación se ha centrado en el sistema Offner aunque también se ha extendido a otras configuraciones concéntricas como el sistema Dyson [18,25] o el sistema Schwarzschild [26]. ...
... Al mismo tiempo han permitido analizar y explorar nuevas configuraciones en las que la rendija de entrada del espectrómetro se encuentra fuera del plano de dispersión [27,28]. Finalmente cabe destacar la utilidad de estas técnicas de diseño que, además del sistema Offner, han sido aplicadas con éxito en otros sistemas concéntricos formadores de imagen [31] y de espectrometría de imagen [18,25,26]. ...
A hyperspectral sensor or imaging spectrometer is a device that collects spatial and spectral information in hundreds of contiguous and closely spectral bands. Hyperspectral imagers have many applications in several areas such as agriculture, geology, oceanography, forestry, medicine, colorimetry, security, military and others. Most of the existing hyperspectral systems were developed considering satellite or high altitude flying aircrafts applications. However, the specific development of these technologies allows their use in many other less expensive applications. In this context, the work presented in this thesis allows building high quality and low cost Offner imaging spectrometers. Rapid and efficient methods were used for the design, assembly and characterization of this type of spectrometers. Two laboratory setups developed from analytical model-based designs have been assembled showing high spectral and spatial resolutions and low distortions without specific aberrations corrected gratings nor non-spherical elements.
... Astigmatism in the classic Czerny-Turner imaging spectrometer can be reduced or removed by compensating the focal lengths of the mirrors in the tangential and sagittal planes. This can be done by adding elements such as a cylindrical lens [6], a cylindrical mirror [7], a tilted parallel plate [8], a small piece of glass using as a 1D waveguide [9], a toroidal lens [10], or a customized lens [11], or one more mirror to change to the Schwarzschild spectrometer [12]; changing one element, e.g., using a convex grating [13], and using a toroidal focusing mirror [14,15]; or introducing divergent illumination by minimizing the distance between the input entrance slit and the collimating mirror [16]. With the development of new design methods of freeform optics [17,18], spectrometer designs that leverages freeform surfaces have been reported [19]. ...
We present the optical design of a Czerny-Turner imaging spectrometer for which astigmatism is corrected using off-the-shelf optics resulting in spectral resolution of 0.1 nm. The classic Czerny-Turner imaging spectrometer, consisting of a plane grating, two spherical mirrors, and a sensor with 10-μm pixels, was used as the benchmark. We comparatively assessed three configurations of the spectrometer that corrected astigmatism with divergent illumination of the grating, by adding a cylindrical lens, or by adding a cylindrical mirror. When configured with the added cylindrical lens, the imaging spectrometer with a point field of view (FOV) and a linear sensor achieved diffraction-limited performance over a broadband width of 400 nm centered at 800 nm, while the maximum allowable bandwidth was only 200 nm for the other two configurations. When configured with the added cylindrical mirror, the imaging spectrometer with a one-dimensional field of view (1D FOV) and an area sensor showed its superiority on imaging quality, spectral nonlinearity, as well as keystone over 100 nm bandwidth and 10 mm spatial extent along the entrance slit.
... Some methods have been investigated to reduce or remove astigmatism [8], for example, using freeform mirrors [9], taking toroidal focusing mirror [10], compensating optics before the entrance slit [11], and introducing divergent illumination [12,13]. However, these methods are limited because they all need to satisfy a(some) condition(s) of the parameters of the Czerny-Turner spectrometer as compensating the astigmatism. ...
... The modified Czerny-Turner type with a plane grating is easy to fabricate and has low cost. However, this type of imaging spectrometer has an f-number larger than f/4 as Mouriz et al. presented, and the entrance slit length is only 4 mm [14]. To obtain a faster speed and a longer entrance slit, methods including the adoption of aspheric mirrors [15] and freeform mirrors [16] are utilized. ...
We present the design and practical implementation of a visible/near-infrared imaging spectrometer. The design of the spectrometer is based on an Offner relay. The approach presented allows an effective design for the Offner type imaging spectrometer to achieve a large flat field and to have minimum astigmatism, which is the dominant residual aberration over the full interested wavelength range. The system works at the wavelength range from 400 to 1000 nm with a high spectral resolution of 0.6 nm/pixel, a relatively low f-number of f/2.3, and a large flat field of 12 mm. The performance measurement of the achieved prototype shows that only a low smile distortion ( < 0.1 pixel) and a small spectral keystone distortion ( < 0.07 pixel) are present. The instrument has the advantages of a compact configuration and a light weight. We present some actual images at different working wavelengths.
... Although the Czerny-Turner spectrometer is an appropriate instrument for those experiments which need high spectral resolution, its astigmatic structure cannot provide a good spatial resolution, so it is rarely used as the imaging spectrometer for remote sensing (especially the far-ultraviolet imaging spectrometer). A special spectrometer based on a concentric off-axis dual reflector system was introduced and analyzed in [19]. A condition for elimination of astigmatism was presented in that paper, but the authors did not talk about the coma aberration. ...
... which is the stigmatic condition given in [19]. Combining Eqs. ...
... Indeed, the coma-free condition did not verify whether it is correct until a spectrometer utilizing the aberration theory, which has a smaller peak-tovalley value than a spectrometer not using it, like R 2 R 3 , is built. This means that the concentric and symmetrical spectrometer designed in [19] does not correct coma. Furthermore, Eq. (41) shows the necessity of the calculation of the spectrometer parameters. ...
A specific imaging spectrometer based on a concentric off-axis dual reflector system is proposed, free of astigmatism and coma. The described imaging spectrometer consists of four spherical mirrors and a plane grating. The analytic theory of aberrations and the optical path-length concept are used to derive the astigmatism elimination and coma removal. It is shown that the astigmatism in these imaging spectrometers is eliminated by characterizing three angles, and the coma is corrected when unequal mirror radii are configured in collimating and condensing optics. The developed aberration principle is verified by comparing the performance of the astigmatism-eliminated spectrometer with the spectrometer which has neither astigmatism nor coma.
... However, the fabrication of the convex grating is more difficult than that of the plane grating, the price of the convex grating is higher than that of the plane grating, and the diffraction efficiency of the convex grating is less than that of the plane grating. A Schwarzschild spectrometer utilizing double Schwarzschild optical systems and a plane grating was suggested and demonstrated in [7]. Here, each Schwarzschild optical system was composed of two concentric spherical mirrors. ...
A modified Schwarzschild imaging spectrometer utilizing three nonconcentric aspheric mirrors and a plane grating is designed that can handle low F -number, long slit, and broad spectral range. Based on the geometrical aberration theory and Rowland circle condition, the astigmatism-correcting method of the Schwarzschild imaging spectrometer is analyzed. The design procedure of initial parameters is programmed using Matlab software. As an example, a modified Schwarzschild imaging spectrometer operating in 400–1000 nm waveband with F -number of 2.5 and slit length of 13 mm is designed, and good imaging quality is obtained.
... Our approach leads to improved designs in a more exact, simpler and more general way than in previous approaches. In Ref. 8 we have designed a Schwarzschild objective with an infinite conjugate as a part of a spectrometer; a generalization for arbitrary object an image conjugates is presented in this work. In section 2, a simple condition to remove the DRT astigmatism is found. ...
Differential Ray Tracing (DRT) is applied to optimize the design of a Schwarzschild objective with large aperture and for arbitrary object position. This optical system lacks of cylindrical symmetry about the non-paraxial base ray, causing astigmatism of a pencil of rays around this ray. The analysis determines the mirror radii ratio that makes the pencil anastigmatic, leading to an excellent image performance. In particular, the classical aplanatic Schwarzschild design is obtained in the limiting case where the base ray becomes paraxial. One example of a design, similar to a typical commercial objective for microscopy, is presented and the image quality is analyzed with an optical design program.
