Abstract
Spectrometer device (100) with entrance aperture (2), diffraction grating (3), two detectors (5a, 5b) to spectrally measuring the incoming light (L), the detectors being located on the same side of the dispersion plane. Two vertically focusing mirrors (4, 4a, 4b) focus the light onto detectors, the minors being arranged as front row mirrors (4b) and back row minors (4a) along two polygon graphs (6a, 6b) offset to each other and to the focal curve. The angles of deflection (cp, .sub.91) for the front row mirrors are <90°, allowing to minimize the offset (dl) of the front row minors (4b) to the focal curve. The distances (d) between the front row minors and corresponding detectors (5b) is minimized while still avoiding collisions between the detectors (5b) and their mounts with back row detectors (5a) and their mounts. The front row mirror elements are overlapping the adjacent back row mirror element.
Claims
1. An optical system comprising: at least one entrance aperture for entering light to be analyzed, at least one diffraction grating for spectral dispersion of the light, at least two detectors to measure the spectrum of the light. where the detectors are arranged on the same side of a plane of dispersion of the optical system, and at least two vertically focusing mirror elements for focusing the light onto said detectors assigned to said vertically focusing mirror elements, characterized in that the vertically focusing mirror elements are arranged as front row mirror elements and back row mirror elements along two polygon graphs offset to each other and to the focal curve, where each section of the polygon graph is parallel to its dedicated local tangent to the focal curve of the grating, such that the angles of deflection for the front row mirror elements are <90° allowing to minimize the offset of the front row mirror elements to the focal curve, the distances between said front row mirror elements and corresponding detectors assigned to said front row mirror elements is minimized while still avoiding collisions between the corresponding detectors and their mounts with back row detectors and their mounts, and at least one end of said front row mirror element is overlapping the adjacent back row mirror element or a receptive area of an adjacent direct light detector if regarded from the grating.
2. The optical system according to claim 1, wherein the shape of the reflecting surface of at least one of said vertically focusing mirror elements is a segment of a cone.
3. The optical system according to claim 1, wherein the shape of the reflecting surface of at least one of said vertically focusing minor elements is a cylinder.
4. The optical system according to claim 1, wherein at least one of the vertically focusing mirror elements is a flat mirror element deflecting the light onto one of said detectors which is assigned to said flat mirror element.
5. The optical system according to claim 1, wherein the absolute values of the angles of deflection of at least two vertically focusing mirror elements are different.
6. The optical system according to claim 1, wherein the—averaged or constant—radii of curvature of at least two vertically focusing mirror elements are different.
7. The optical system according to claim 1, wherein at least two vertically focusing mirror elements having different absolute values of the angles of deflection have the same—averaged or constant—radius of curvature.
8. The optical system according to claim 1, wherein at least one detector does not have a vertically focusing mirror element being assigned to it, the detector thus being positioned along a segment of the original focal curve of the grating so that a part of the spectrum is being imaged directly onto said detector.
9. The optical system according to claim 1, wherein at least one detector is equipped with a lens for vertical focusing.
10. The optical system according to claim 1, wherein the building principle of the optical system is a Paschen-Runge setup or a flat-field setup or a Czemy-Tumer setup or an Ebert-Fastie setup.
11. The optical system according to claim 1, wherein the detectors are line detectors, preferably CCD or CMOS detectors.
12. A spectrometer device comprising at least one optical system according to claim 1, further comprising an operating unit connected to at least the detectors to operate said detectors and to analyze the measured spectrum of the light.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0028] These and other aspects of the invention are shown in detail in the illustrations as follows.
[0029] FIG. 1: schematic view of a first embodiment of the optical system according to the present invention when measuring the diffracted light form an isometric view;
[0030] FIG. 2 schematic and detailed view of the vertically focusing elements and detectors in a first embodiment of the optical system in front view;
[0031] FIG. 3 schematic and detailed view of the vertically focusing elements in a second embodiment of the optical system in an isometric view;
[0032] FIG. 4 schematic and detailed view the vertically focusing elements and detectors in a third embodiment of the optical system in an isometric view;
[0033] FIG. 5 out of plane deflection and mirror-detector-setup in the different approaches for spatial arrangements of mirror-detector-setups (a) according to the state of the art, and (b) according to the present invention;
[0034] FIG. 6 minimum line width of a spectral line at a distance from the focal curve;
[0035] FIG. 7: section perpendicular to the plane of dispersion at the normal point to determine favorable geometry for achieving minimum safety distance s between two mirrors yielding the smallest width of the transition zone wT; and
[0036] FIG. 8 schematic view of light paths and angles for the optical system according to the present invention as a Rowland circle optic.
DETAILED DESCRIPTION OF EMBODIMENTS
[0037] FIG. 1 shows a general arrangement of the optical system 1 in a Paschen-Runge-setup comprising the entrance aperture 2, through which the light L to be analyzed is entering in the optical system 1, the grating 3 for spectral dispersion of the light L, the vertically focusing mirror elements 4 for focusing the light L and the detectors 5 to measure the spectrum of the light L. In order to focus the dispersed light, the vertically focusing mirror elements 4 are arranged along two polygon graphs 6a, 6b offset to each other and to the focal curve. Each section of a polygon graph is parallel to its dedicated local tangent to the focal curve of the grating 3, which then is measurable by the detectors 5 to which each vertically focusing element 4 is assigned. Since the vertically focusing mirror elements are arranged along the polygon graphs 6a, 6b, the detectors 5 or their medians and the focal curve can superimpose each other. It is particularly important in this optical system that the adjacent ends 7a, 7b of the vertically focusing elements 4 are overlapping and that the maximum distance d calculated according to equation (1) between vertically focusing mirror element and detector is minimized. By choosing an angle of deflection of |φ|<90°, in this example 60°, for the front row mirror elements an almost gap-free measurement of the covered wavelength range can be assured.
[0038] FIG. 2 shows the detail of the arrangement of vertically focusing mirror elements 4 and detectors 5 as used in the embodiment shown in FIG. 1. The vertically focusing mirror elements 4 of the embodiments of FIG. 1 and FIG. 4 are arranged along two polygon graphs 6a, 6b offset to each other and to the focal curve. In the perspective of FIG. 2, the two polygon graphs 6a, 6b fall on each other, which is why only one polygon graph is visible. Each section of a polygon graph is parallel to its dedicated local tangent to the focal curve of the grating 3. In this embodiment, the vertically focusing mirror element 4a is assigned to the detector 5a, and the vertically focusing mirror element 4b is assigned to the detector 5b. For an easier handling of these elements, each detector 5a and vertically focusing mirror element 4a are mounted on a base plate 9. This also applies to the detector 5b with its respective vertically focusing mirror element 4b. The vertically focusing mirror elements 4a, 4b are arranged within distances d(4a) and d(4b) calculated according to equation (1) to the focal curve and the medians of the detectors 5a and 5b are superimposing the focal curve.
[0039] In general, the angle of deflection φ can be less than or equal to 90°. Here the angles of deflection φ of the adjacent vertically focusing elements are unequal and have values of 90° for the mirror element 4a and 60° for the mirror element 4b. A further influence on vertical focusing is done by the curved surface 8 of the mirror elements 4a, 4b. The curved surface 8 has one radius of curvature ρ(4a)=27.5 mm for mirror element 4a which is a cylindrical surface and another radius of curvature ρ(4b)=35 mm for mirror element 4b which is also a cylindrical surface. This embodiment allows for overlapping adjacent ends of vertically focusing mirror elements while minimizing d(4b). This embodiment also allows an easy exchange of vertically focusing elements 4, such that the mirror elements can easily be exchanged by flat mirror elements to dampen focusing thus decreasing intensity levels when needed. Further, it would also be feasible to replace a focusing mirror element with a combination of a flat deflection mirror element and a focusing lens.
[0040] In a second embodiment, shown in FIG. 3, the vertically focusing mirror elements are conical mirrors. The longitudinal axis A of each of the vertically focusing mirror elements 4 is intersecting the polygon graph 6 each section of which is parallel to their dedicated local tangent to the focal curve. The distance between the polygon graph sections and the local tangents is given by equation (1) where ρ.sub.cyl must be substituted with ρ.sub.Avg, the average radius of curvature of the focusing conical mirror element featured in this embodiment. Adjacent vertically focusing conical mirror elements 4 have equal angles of deflection, in this case 90°. Since the radii of curvature of the conical mirror elements are different at each point along its longitudinal axis, equation (1) will provide different distances d for each point along the mirror element's longitudinal axis from the focal curve. Therefore, the longitudinal axis of the mirror element is intersecting the polygon graph and the axis cannot be on the graph itself. Since the radius of curvature on one end of the conical mirror element is smaller than on the opposing end, the corresponding distances are different and therefore adjacent and identical conical mirror elements can overlap like shingles of a roof providing quasi-continuous coverage of the wavelength range with minimized widths of the transition zones between adjacent conical mirror elements. The tangential focus of the wavelength of the spectral line falling on a particular spot of the conical mirror element is of course again unaffected by the deflection out of the plane of dispersion or the vertical focusing in the direction perpendicular to the plane of dispersion. Therefore, the detector cannot be parallel to the plane of dispersion like in other embodiments but must be tilted around the point where the beam from ρ.sub.Avg hits it, staying in plane with the longitudinal axis of the conical mirror element at the same time. Through appropriate tilting, a correct tangential focus for every wavelength hitting each spot along the conical mirror's longitudinal axis is achieved. It is also possible to use adjacent conical mirror elements having different ρ.sub.Avg and/or different angles of deflection φ.
[0041] The third embodiment in FIG. 4 has a larger number of detectors 5 than vertically focusing mirror elements 4. It is necessary that each vertically focusing mirror element 4 is assigned to a detector 5, but in order to detect the light it is not necessary that each detector 5 has an assigned vertically focusing mirror element 4. These direct imaging detectors 5c that do not have an assigned vertically focusing mirror element 4 are arranged directly along a segment of the focal curve of the grating 3. Anyhow, these direct imaging detectors 5c must be considered as an adjacent vertically focusing element 4 alike, such that the adjacent ends 7a, 7b of the direct imaging detector 5c is overlapped by the adjacent ends of the adjacent vertically focusing mirror elements 4. Using a direct imaging detector 5c without a vertically focusing mirror element 4 enables that a part of the spectrum is imaged directly onto the detector 5. The embodiment 3 of FIG. 4 also uses vertically focusing mirror elements 4 with different radii of curvature ρ for the curved surfaces 8. The-vertically focusing element 4b has an infinite radius of curvature ρ, such that the curved surface 8 appears planar. Whereas the vertically focusing element 4a has a smaller radius of curvature ρ than the vertically focusing element 4b, such that the curved surface 8 appears cylindrical. The difference of the radii of curvature ρ of the light focusing elements 4a, 4b means that vertical focusing is achieved effectively with focusing mirror element 4a whereas mirror element 4b doesn't do any focusing at all. In order to use the same base plates for both detector units the angles of deflection are chosen to be the same, namely φ=90° in this example.
[0042] FIG. 5 shows an out of plane deflection and mirror-detector-setup in the different approaches for spatial arrangements of mirror-detector-setups (a) according to the state of the art, and (b) according to the present invention. FIG. 5a shows an optical system is according to the state of the art as disclosed in FR2953017B1, where a deflection angle of φ=+90° is used for both rows of mirror-detector-setups (front and back row mirrors) arranged along two polygon graphs widely offset against each other. Here, the mirror elements 10s have a larger distance to each other in order to deflect the incident light L from the dispersion plane DP towards the detectors 11s as deflected light LD. With a smaller distance the detectors 11s for back row and front row mirrors 10s or their mounts would collide. In order to match the long distance between front row mirror 10s and detector 11s, the vertical curvature of the mirror element 10s is adapted. Nevertheless, the position of the front row mirror elements 10s far away from the focal curve leads to a larger area of the spectral line at the off-focus position of the front row mirror 10s resulting in overlapping effects between neighboured mirrors of the front row and the back row resulting in part of light close to the edge of the mirror 10s will not be reflected by the dedicated front row mirror, but unintentionally penetrates to the back row mirror 10s. FIG. 5b shows the optical system 1 according to the present invention featuring minimized transition zones at the edge of the front row mirror elements 4, 4b. Deflection mirrors used at the light pickup are cylindrical in both approaches in order to provide vertically focusing mirror elements 4, 4a, 4b. The distance d.sub.1,2 of the mirror axis to the focal curve FC is calculated according to formula (1) when inserting deflection angles φ.sub.1,2 (see FIG. 7 for more details). When using an angle of deflection φ.sub.1 less than 90°, the distance Δ=d.sub.1-d.sub.2 between both mirrors is much less compared to FIG. 5a resulting in a shorter distance d.sub.1 between front row mirror element 4, 4b to the corresponding detector 5, 5b providing on one hand a smaller height of the optical system 1 (the detector position according to the state of the art as shown in FIG. 5a is added to FIG. 5b as dashed lines for a better comparison). On the other hand, the closer distance d.sub.1 to the focal curve FC leads to minimized transition zones at the edge of the front row mirror elements 4, 4b. The angle of deflection φ.sub.2 for the back row mirror element 4, 4a of 90° is just an example and can be different for other embodiments.
[0043] FIG. 6 shows the minimum line width t of a spectral line at a distance d from the focal curve. Here, a Rowland-grating has a radius of curvature (ROC) R.sub.G and an illuminated area on the grating 3 having the width W employs a light pickup around the normal point N, which is also the focal point lying on the focal curve FC of the normal wavelength λ at β=0°. The angle ξ corresponds to the half illumination angle of the grating. The width t of the spectral line at β=0° at a distance d from the focal point N is determined by the formulae:
t=2d tan ξ (2)
[0044] where
sin ξ=W/2R.sub.G (3)
[0045] FIG. 7 shows a section perpendicular to the plane of dispersion at the normal point to determine favorable geometry for achieving minimum safety distance S between two vertically focusing mirror element mirrors 4, 4a, 4b, one of the front row and the other of the back row, yielding the smallest width of the transition zone of a spectral line illuminating both vertically focusing mirror elements 4a, 4b. The following formulae can be derived from FIG. 7:
h.sub.1,2=ρ.sub.cyl-1,2(1-cos (arcsin (b/2ρ.sub.cyl-1,2))) (4)
A′.sub.1,2=b/2 cos (φ.sub.1,2/2) (5)
B′.sub.1,2=b/2 sin (φ.sub.1,2/2) (6)
Δ=d.sub.1-d.sub.2 (7)
A.sub.1,2=A′.sub.1,2−h.sub.1,2 sin (φ.sub.1,2/2) (8)
B.sub.1,2=B′.sub.1,2+h.sub.1,2 cos (φ.sub.1,2/2) (9)
B′.sub.1(A.sub.2)=(A.sub.2/cos (φ.sub.1/2)) sin (φ.sub.1/2)=A.sub.2 tan (φ.sub.1/2) (10)
S=Δ+B′.sub.1(A.sub.2)−dm/cos (φ.sub.1/2)−B.sub.2 (11)
[0046] where dm denotes the center thickness of the mirror element and b the height of the mirror element. To execute further deliberations, one can estimate reasonable maximum mirror heights b. In spark OES, the distance between electrode tip and sample (=counter electrode) is generally between 2 mm and 5 mm. A coupling lens or an imaging coupling mirror or mirror setup will image the light from the generated plasma onto the entrance aperture, illuminating its full height of up to 5 mm. In a spectrometer optics, imaging errors of the diffraction grating 3 will cause the lines to (among other things) become longer than the height of the entrance slit. As a rule of thumb for Rowland circle gratings, a length of 7mm on average can be assumed. To focus light from the entire length of the spectral line onto the sensor of the detector 5 using a cylindrical mirror at a φ=90° angle of deflection as realised in the back row mirror elements 4, 4a in the present invention, the cylindrical mirror height needs to be b=10 mm high (=))7 mm/cos(45°)).
[0047] Only spectral lines falling entirely onto a vertically focusing mirror element 4, 4a, 4b are considered useable which makes the width of the transition zone WT between adjacent mirrors:
WT=2 t(β) (12)
[0048] Since the widths of the transition zones WT in both approaches (state of the art and present invention according to FIG. 5a and 5b) are determined solely by d.sub.1, the distance of the front row mirrors (lying closest to the diffraction grating) to the focal curve FC. Assuming the same radius of curvature ρ.sub.cyl-2 for the back row mirror elements 4, 4a, 10s in approaches according to FIG. 5a and 5b, the task is the minimisation of Δ, the distance between the two polygon graphs 6a, 6b for both approaches. Here, we will set the safety distance s at the closest proximity between front and back row mirror elements 4, 4a, 4b to S=1 mm to find appropriate values for ρ.sub.cyl-1, φ.sub.1 and φ.sub.2. Assuming dm=2.2 mm and b=10 mm and taking the values of dm and b for both front and back row mirror elements 4, 4a, 4b and further assuming R.sub.G=400 mm and W=40 mm making sin ξ=0.05 (formulae 2+3), one will obtain for the setups as shown in FIG. 5a (state of the art optical system 1s) and 5b (present invention optical system 1):
TABLE-US-00001 Optical ρ.sub.cyl-1 = 75 mm, ρ.sub.cyl-2 = 27.5 mm φ.sub.1 = φ.sub.2 = 90° system 1s: Optical ρ.sub.cyl-1 = 35 mm, ρ.sub.cyl-2 = 27.5 mm φ.sub.1 = 60°, φ.sub.2 = 90° system 1:
[0049] Using those values yields the following results for the widths of the transition zones WT for the approaches in FIG. 5a (state of the art optical system 1s) and FIG. 5b (present invention optical system 1) at the normal point N:
TABLE-US-00002 Optical d.sub.1 = 26.517 mm and d.sub.2 = 9.723 mm WT = 2.6517 mm system 1s: Optical d.sub.1 = 15.155 mm and d.sub.2 = 9.723 mm WT = 1.5155 mm system 1:
[0050] The smaller transition zone WT for the optical system 1 compared to the larger transition zone WT for the optical system ls shows the improved performance of the optical system 1 according to the present invention.
[0051] FIG. 8 shows a schematic view of light paths and angles for the optical system according to the present invention as a Rowland circle optic, where β denotes the occurring angles of diffraction, α the angle of incidence, ω the angle of incidence of the middle beam onto the focusing mirror element relative to the perpendicular, O the offset increasing with β, t the linewidth at distance d increasing with β, N the normal point, W the illuminated grating width, RG the radius of curvature of the grating and the determination of ξ. From FIG. 8 we see that although distance d and angle ξ stay constant along the course of the focal curve (in this case the Rowland circle) for angles of diffraction β>0°, the length of the light path from the axis of the cylindrical mirror element 4, 4a, 4b to the pixel band l.sub.p of the detector 5, 5a, 5b increases with increasing β according to the formula:
l.sub.p=d/cos ω (13)
[0052] and center points of the axis of the cylindrical mirror and the pixel band are offset against each other by offset O:
O=d tan ω (14)
[0053] To calculate the width t(β) of a spectral line for β other than 0 on the mirror surface, d must be replaced by (l.sub.p/cos ω) in formula (2) yielding:
t(β)=2d tan ξ/cos.sup.2 ω (15)
[0054] where ω is specific to and dependent on the course of the focal curve FC. For a Rowland circle optics ω=β applies.
[0055] For determining angles of diffraction and focal points on the focal curve the grating equation:
n G=sin α+sin β (16)
[0056] and the back-focus equation:
[00002]
[0057] with: n order of diffraction [0058] G grating constant (number of grooves per mm @ grating centre) [0059] λ diffracted wavelength [0060] α angle of incidence [0061] β angle of diffraction [0062] L.sub.A distance between the entrance aperture and grating centre [0063] L.sub.B distance between the focal point of the diffracted λ and the grating centre [0064] R radius of curvature of the grating substrate [0065] λ.sub.0 exposure wavelength used during grating manufacturing [0066] C.sub.f flat field constant;
[0067] are used; if C.sub.f=0, all elements comprising an optical system are located on a circle called the Rowland circle.
[0068] The vertically focusing mirror elements of the embodiments shown in the FIG. 1 to FIG. 8 are mostly described as cylindrical mirrors, but it is also possible to have mirror elements with a curved surface 8 that have an infinite radius of curvature ρ and thus are planar or a curved surface 8 that comprises several radii of curvature ρ forming a conical surface. Therefore, flat, cylindrical or conical mirrors can be used. It is especially beneficial if a combination thereof is used in the optical system 1. Focusing lenses, like rod lenses or cylindrical lenses, can be used in all embodiments described above e.g. in combination with flat deflection mirrors instead of vertically focusing mirror elements as vertically focusing elements 4.
[0069] The setup of the optical system 1 in a Paschen-Runge-Setup as described above is not intended to be restrictive, rather the embodiments of the FIG. 1 to FIG. 8 of the optical system 1 are also suitable for a Flat-Field-Setup or a Czerny-Turner-Setup or an Ebert-Fastie-Setup.
[0070] Furthermore, the detectors 5, as well as the direct imaging detectors 5c, in all embodiments described above are line detectors, such as CCD or CMOS detectors.
[0071] At least one of the optical systems 1 described above and an operating unit can be used in a spectrometer device, which is not described further. Thereby the operating unit is connected to at least the detector arrangement of at least two detectors 5 in order to operate these at least two detectors 5 and to analyze the measured spectrum of the light L.
[0072] The embodiments shown here are only examples of the present invention and must therefore not be understood as restrictive. Alternative embodiments considered by the skilled person are equally covered by the scope of protection of the present invention.
LIST OF REFERENCE NUMERALS
[0073] 1 optical system according to the present invention [0074] 1s optical system according to the state of the art [0075] 2 entrance aperture [0076] 3 grating [0077] 4, 4a, 4b vertically focusing mirror elements (present invention) [0078] 5, 5a, 5b detectors (present invention) [0079] 5c direct imaging detectors [0080] 6, 6a, 6b polygon graphs, segments are parallel to local tangents to the focal curve behind the mirror elements [0081] 7a, 7b adjacent ends of the vertically focusing elements [0082] 8 curved surface [0083] 9 base plate [0084] 10s vertically focusing mirror elements (present invention) [0085] 11s detectors according to the state of the art [0086] 100 spectrometer device [0087] α angle of incidence [0088] β angle of diffraction [0089] φ angle of deflection [0090] φ.sub.1 angle of deflection of from row vertically focusing mirror element 4b [0091] φ.sub.2 angle of deflection of back row vertically focusing mirror element 4a [0092] ξ angle given by: sin ξ=W/2 R.sub.G [0093] ω angle of incidence of middle beam onto vertically focusing mirror element relative to the perpendicular [0094] A longitudinal axis [0095] A′.sub.1,2 distance given by: A′.sub.1,2=b/2 cos (φ.sub.1,2/2) [0096] A.sub.1,2 distance given by: A.sub.1,2=A′.sub.1,2−h.sub.1,2 sin (φ.sub.1,2/2) [0097] B′.sub.1,2 distance given by: B′.sub.1,2=b/2 sin (φ.sub.1,2/2) [0098] B.sub.1,2 distance given by: B.sub.1,2=B′.sub.1,2+h.sub.1,2 cos (φ.sub.1,2/2) [0099] B′.sub.1(A.sub.2) distance given by: B′.sub.1(A.sub.2)=(A.sub.2/cos (φ.sub.1/2)) sin (φ.sub.1/2)=A.sub.2 tan (φ.sub.1/2) [0100] b length (height) of the vertically focusing mirror element 4 perpendicular to axis A as shown in FIG. 3. [0101] d distance from the focal curve according to formula (1) [0102] d.sub.1 distance between the focal curve and the axis of the deflecting surface of the vertically focusing front row mirror [0103] d.sub.2 distance between the focal curve and the axis of the deflecting surface of the vertically focusing back row mirror [0104] Δ is the difference between d.sub.1 and d.sub.2, where said difference corresponds to the distance between the two polygon graphs 6a, 6b [0105] Δs distance between back row vertical focusing elements and front row vertical focusing elements in the deflection plane for the optical system according to state of the art [0106] D.sub.A distance between the entrance aperture and the grating center [0107] D.sub.B distance between the focal point of the diffracted wavelength λ(β) and the grating center [0108] DP dispersion plane [0109] dm center thickness of the vertically focusing mirror element [0110] FC focal curve [0111] h.sub.1,2 height of the curvature of the vertically focusing mirror elements given by: h.sub.1,2=ρ.sub.cyl-1,2 (1-cos (arcsin (b/2ρ.sub.cyl-1,2))) [0112] Ip pixel band of the detector [0113] L light from the sample [0114] LD deflected light [0115] N normal point, focal point of normal wavelength for β=0 [0116] O offset between the center points of the axis of the cylindrical mirror and the pixel band of the detector [0117] ρ.sub.Cyl radius of curvature of the curved surface 8 [0118] ρ.sub.Cyl-1 radius of curvature of the curved surface 8 of front row vertically focusing mirror element 4b [0119] ρ.sub.Cyl-2 radius of curvature of the curved surface 8 of back row vertically focusing mirror element 4a [0120] R.sub.G radius of curvature of the grating 3 [0121] S safety distance given by: s=A+B′.sub.1(A.sub.2)−dm/cos (φ.sub.1/2)−B.sub.2 [0122] t line width at a distance d from the focal curve [0123] W illuminated width of the granting 3 [0124] X horizontal axis [0125] Y axis perpendicular to X-axis and Z-axis [0126] Z vertical axis
