EP3403061A1

EP3403061A1 - Spectrometer with a two-dimensional spectrum

Info

Publication number: EP3403061A1
Application number: EP16825730.1A
Authority: EP
Inventors: Stefan MÜNCH; Michael Okruss
Original assignee: Analytik Jena AG
Current assignee: Analytik Jena Gmbh+co Kg
Priority date: 2016-01-14
Filing date: 2016-12-20
Publication date: 2018-11-21
Also published as: DE102016124980A1; CN108738335A; WO2017121583A1; CN108738335B; US10488254B2; US20190025121A1

Abstract

A spectrometer assembly (10) with a two-dimensional spectrum comprising a first dispersing element (31) for the spectral decomposition of radiation in a main dispersion direction, an imaging optical system (17) for imaging in an image plane the radiation penetrating through an inlet gap (15) in the spectrometer arrangement (10) and enabling a two-dimensional spectrum to be produced, and a surface detector (39) with a two-dimensional arrangement of a plurality of detector elements in the image plane. Said spectrometer assembly is characterized in that a reflector, a refractor, a lens array or another optical element is arranged in the beam path at a point where the dispersed, monochromatic bundles are present in a separated manner, and the reflector, the refractor, the lens array or the other optical element have a surface in the form of a free-form surface wherein the surface occupied by the selected images of the inlet gap at different wavelengths in the image plane is optimised over a selected spectral range of the two-dimensional spectrum.

Description

Spectrometer with Two-dimensional Spectrum Technical Field

The invention relates to a spectrometer arrangement with two-dimensional spectrum containing

(a) a first dispersing element for spectral decomposition of radiation in a main dispersion direction,

(B) an imaging optics for imaging the radiation entering through an entrance slit in the spectrometer array in an image plane with which a two-dimensional spectrum can be generated, and

(c) an area detector with a two-dimensional arrangement of a plurality of detector elements in the image plane.

An example of such a spectrometer arrangement is an Echelle spectrometer with internal order separation. Another example is a long-slit spectrometer arrangement.

In an Echelle spectrometer, gratings with a staircase-like (echelle (French) = staircase) cross-section are used. By the step-like structure with a corresponding blaze angle, a diffraction pattern is generated which shows the diffracted intensity in high orders, e.g. concentrated in fiftieth to one hundredth order. As a result, high spectral resolutions can be achieved in a compact arrangement. The orders can overlap - depending on incident wavelengths. The orders are therefore dispersed again in the Echelle spectrometers with internal order separation across the dispersion direction of the Echelle grating to separate the various orders occurring. This gives a two-dimensional spectrum that can be detected with area detectors.

An Echelle spectrometer with internal order separation differs from Echelle spectrometers with external order separation in that in the latter only radiation from a small spectral range enters the spectrometer. In the case of spectrometers with internal order separation, the spectrum is generated in the form of a two-dimensional structure in the detector plane. This structure consists of spectral sections arranged essentially parallel to one another. The free spectral ranges of the respective diffraction orders combine to form a gap-free spectrum for a specific wavelength range. The use of a surface detector with a plurality of detector elements allows the simultaneous detection of a large wavelength range with high spectral resolution. The transverse dispersion is usually chosen to be so large that the orders are completely separated everywhere. To ensure this over the entire spectral range, there are spectral regions in which an unused gap arises between the individual orders. Thus, when using a prism for transverse dispersion in the short-wave spectral range due to the higher dispersion larger spaces than in the longer wavelength spectral range.

A disadvantage of the known arrangements is that the detectors generally have to be very large if larger spectral ranges with high resolution and sufficient light conductance are to be detected.

In atomic absorption spectroscopy and many other spectroscopic detection methods, the detection limit u.a. from the optical conductivity of the spectrometer used and the sensitivity of the arrangement. Higher spectral resolution results in higher sensitivity in cases where the resonance line used for analysis is not resolved. The spectral resolution of the arrangement depends i.a. from the slit width, the dimensions of the detector elements in the main dispersion direction of the Echelle grating, and the imaging quality. It is therefore desirable to obtain a high spectral resolution with simultaneously high light conductance.

The image of a spectral component of a point of the light source is always subject to certain aberrations. Generally, the aberrations are categorized according to the aberration theory of Seidel. In optical spectroscopy, in particular the aberrations astigmatism, coma and spherical aberrations are to be considered. Due to the spatial separation of the radiation beams for the different wavelengths and the resulting different beam paths, the bundles of different wavelengths are affected to a different extent by the imaging errors. A holistic treatment of the aberrations for all bundles is only conditionally possible. Optical spectrometers which have a large aperture ratio and / or a large entrance pupil and / or a large image field are particularly affected by the aforementioned aberrations.

In spectrometers with refractive imaging optics, in addition to the above-mentioned geometric aberrations, additional chromatic aberrations must be considered, especially longitudinal chromatic aberration.

It can be shown that aberrations, such as astigmatism and coma, cause the image of a point-like, monochromatic light source to spread over an area extends in the detector plane, which comprises a plurality of detector elements. If the image comprises several detector elements in the main dispersion direction, the spectral resolution is correspondingly reduced. The measurement of a signal with multiple detector elements leads to an increase in the readout noise, so that the signal-to-noise ratio and thus the detection limit of analytical measurements deteriorate.

State of the art

The echelle spectrometer arrangement known under the name "MOSES" is described in DE 10 2009 059 280 A1 and EP 2 516 975 B1. The arrangement has particularly few components and a high light conductance. The arrangement is equipped with a Echelle spectrometer with internal order separation in Littrow arrangement. The entire spectrum is mapped to a detector. Various dispersion arrangements, including a reflective prism, are disclosed for cross-dispersion.

An echelle spectrometer arrangement with astigmatism compensation is disclosed in DE 100 1 1 462 C2. The arrangement shows an Echelle spectrometer with internal order separation with two entrance slits of different orientation, which are arranged along the optical path in separate planes. This achieves astigmatism compensation for only one point in the image plane.

The term "Schmidt plate" or "Schmidt correction plate" rotationally symmetric dioptric optics are known, which are used to correct spherical aberration, coma and astigmatism, inter alia, in various types of telescopes, such as Schmidt telescopes or Schmidt-Cassegrain telescopes.

Li Xu, Kexin Chen, Qingsheng He and Guofan Jin published in "Design of freeform mirrors in Czerny-Turner spectrometers to suppress astigmatism" in Appl. Optics. Vol. 48, No. 15, p. 2871 of May 20, 2009 describes the correction of astigmatism in one-dimensional spectra in a Czerny-Turner spectrometer. The shape of the comparatively large camera mirror is changed to a free-form surface. In a second step, the collimator mirror is also designed as a freeform surface for additional coma compensation. The disadvantage of this arrangement is that the bundles for different wavelengths strongly overlap at these two points.

CN 103 175 61 1 B discloses a Czerny-Turner spectrometer in which a lens element with a free-form surface is arranged in front of the detector. The curvature of the surface in the direction of dispersion accounts for the correction of coma. The curvature of the surface perpendicular to the dispersion direction takes into account the correction of Astigmatism. The shape of the free-form surface is calculated by functionally determining the aberrations coma and astigmatism and from this a correction function is calculated. Other errors are ignored. WO 2013 106 307 A1 discloses the correction of astigmatism and coma with the aid of rotationally symmetrical aspherical corrector plates.

DE 695 182 44 T2 discloses a method for order harmonization using combinations of prisms.

US 8 681 329 B2 discloses a method for order harmonization using predispersion optics.

EP 0 744 599 B1 discloses an echelle spectrometer with an Echelle grating and a second grating for generating a transverse dispersion. The second grid consists of several sections for generating the dispersion in different spectral sections, for example UV and VIS. The document discloses that the grid may be formed rotationally symmetric asphere, i. that the grating surface can not be flat, but can be rotationally symmetrical curved to correct aberrations. The grid is arranged parallel beam path with overlapping bundles.

EP 0 445 934 B1 discloses a Littrow-type Echelle spectrometer with a prism for generating a transverse dispersion. The radiation is reflected by a hyperbolic secondary and an aspherical, rotationally symmetric primary mirror on the grid and then back in itself. The mirrors are arranged in the beam path at various locations with overlapping bundles.

EP 1 260 802 B1 discloses a prism spectrometer with a one-dimensional spectrum. The collimator assembly and / or the camera assembly of the spectrometer is provided with an aspherically curved correction mirror for correcting axial and off-axis spherical aberrations. Other aberrations are not considered. The document discloses various other spectrometer arrangements with different aspheric correction surfaces, all of which are located in the parallel beam path between the collimator and the camera. Disclosure of the invention

It is an object of the invention to provide an Echelle spectrometer arrangement of the type mentioned above with a two-dimensional spectrum, which is better detectable. According to the invention the object is achieved in that

(D) a reflector, a refractor, a lens array or other optical element is arranged in the beam path at a location where the dispersed monochromatic bundles are present separately, and

(e) the reflector, refractor, lens array or other optical element has a surface in the form of a free-form surface in which the occupied area of selected images of the entrance slit at different wavelengths in the image plane is optimized over a selected spectral range of the two-dimensional spectrum.

It is understood that the selected images have an intensity gradient, so that the surface has no sharp edge. As used herein, the term "area" refers to the area in which a high percentage, e.g., 90 to 99% of the intensity impinges on the detector.

With this arrangement, the relative bundle overlap is small. The relative bundle overlap is a percentage size and can be calculated explicitly for two wavelengths. The relative beam overlap at a particular location in the beam path is the reciprocal arithmetic ratio between the beam cross-sectional area of a selected monochromatic beam at that location and the subarea thereof, which is also spanned by a second monochromatic beam. The freeform surface is located at a location where the relative beam overlap is smaller than on the camera mirror. The relative beam overlap fulfills this condition only between camera mirror and detector and in the convergent and divergent beam path in the region of an intermediate image. However, it does not fulfill this condition in the parallel beam path, for example on the Echelle spectrometer.

Surfaces of mirrors, lenses and the like used in optics usually contain rotational symmetry or are sections of surfaces containing rotational symmetry, for example spheres, paraboloids or ellipsoids. This also includes surfaces in which the rotational symmetry axis does not penetrate the surface. This is the case, for example, with cylindrical surfaces or toroidal surfaces. Furthermore, anamorphic surfaces or surface sections of higher order belong to which have a mirror symmetry. Freeform surfaces are other surfaces, namely Surfaces which differ in shape from such rotationally symmetric or mirror-symmetric surfaces or surface cutouts.

In particular, a two-dimensional spectrum may be generated with an arrangement having a second dispersing element for order separation by spectrally decomposing the radiation in a transverse dispersion direction which forms an angle with the main dispersion direction of the first dispersing element, so that a two-dimensional spectrum can be generated. However, there are also known long-slit spectrometers which have only one dispersive element. The second direction corresponds to the extended gap height.

The optimization of the free-form surface may be such that the totality of the deviations from stigmatic imaging of selected images of the entrance slit at different wavelengths in the image plane over a selected spectral range of the two-dimensional spectrum resulting from aberrations is minimized. As a result, small images of the entrance slit are generated, which are easy to detect. Alternatively or additionally, the optimization is carried out in such a way that the orders are arranged at desired distances from each other in the image plane. It is preferably provided that the element dispersing in the main dispersion direction is an Echelle grating. It can be provided in particular that the spectrometer is an echelle spectrometer with internal order separation.

In principle, the invention is also relevant to spectrometers with external order separation, e.g. Echelle spectrometer with external order separation and high gap, in which the aberrations over the entire gap height are limited by one or more free-form surfaces. It is also possible to provide a prism spectrograph in MOSES arrangement without Echelle gratings with a very high gap (long slit) and free-form mirrors.

The invention is relevant to spectrometers with 2D spectra. In the main dispersion direction, the radiation is spectrally decomposed by a first dispersion element. The direction is used either for a further spectral decomposition or for a distribution according to the location (field coordinate).

Unlike prior art arrangements, the present invention contemplates the area of a plurality of images of the entrance slit. Instead of an image of the entrance slit, using a beam computation program, the images of a single point, ie, an infinitesimally small entrance slit, for a plurality of wavelengths to be viewed as. It is not necessary to determine the causes of the surface shape and size of the images or to even describe them functionally. Rather, the result in the exit plane is optimized by adapting the freeform surface. With such an arrangement, on the one hand, a higher resolution can be achieved. On the other hand, the distribution of orders on the detector can be influenced. In particular, a uniform or more uniform distribution can be achieved. It is also possible to design the freeform surface in a manner in which only selected wavelength ranges, for example the wavelengths in the edge region of the detector are influenced.

By suitable shaping and positioning of one or more free-form surfaces in the spectrometer arrangement, a considerable reduction of the aberrations can be achieved.

In particular, a reflective, refractive or diffractive surface may be disposed at a location in the beam path where at least two monochromatic beams associated with the same echelle diffraction order are completely separated and / or where at least two monochromatic beams not belonging to the same echelle diffraction order are completed are separated and the reflective, refractive or diffractive surface is formed as a free-form surface, which minimizes the deviation from a stigmatic image on the detector for the individual monochromatic bundles independently of one another over a selected wavelength range of the two-dimensional echelle spectrum.

Different methods can be used to describe and produce the freeform surfaces. Either closed mathematical expressions are used. Examples are Chebyshev polynomials 1.Art or Zernike polynomials. Chebyshev polynomials are more suitable for rectangular areas. Zernike polynomials are more suitable for round surface. With the mathematical expressions also the deviations from a basic form, such as a plane, a paraboloid of revolution or another rotation-symmetrical surface can be described. Alternatively, the freeform surface can be described by using a mesh of vertices. The interpolation points enable the mathematical description of the area in sections. This can be done for example by various spline functions, bicubic interpolation and the like. For certain mathematical descriptions, the vertices themselves are not necessarily part of the surface (especially spline functions). For example, vertices are expressed as coordinates or wavelengths. The base network for the surface description should at least cover the area over which the bundles of all relevant wavelengths run.

The determination of the optimal shape, i. the parameter of said Frerformfläche, preferably carried out using a beam calculation program. Usually, first of all a suitable mathematical objective function, also called a merit function, is formulated. The merit function summarizes the various individual objectives to the optical model. A single target is expressed by a mathematical operand associated with a target value that the operand is to achieve.

A possible formulation of the merit function Φ is:

Here, φ designates the deviation of the i-th operand whose actual size j can be derived from the optical model from a desired target variable V * Pi = v. - ti

It is then determined which parameters of the optical system can be changed. The variable parameters include parameters of one or more free-form surfaces. Optimization algorithms seek values for the variable parameters that best meet the objectives of the optical model, i. the value of the objective function approaches the value 0 as far as possible. The value 0 of the merit function means full achievement of all defined objectives for the optical model. For example, the found parameters make it possible to minimize the totality of deviations from stigmatic mapping for selected images of entrance slits at different wavelengths in the image plane.

In a variant of the invention, it is provided that the free-form surface is optimized in such a way that the sum of the RMS function (root mean square function) of selected images of the entrance slit in the selected spectral range assumes a minimum. This feature describes the image quality over the entire image field. It can be provided in particular that individual RMS values are weighted. Alternatively, it is provided that the free-form surface is optimized such that the sum of the wavefront errors of selected images of the entrance slit in the selected spectral range assumes a minimum.

INVOLVED BY REFERENCE (RULE 20.6) In a preferred embodiment of the invention, it is provided that the freeform surface is optimized in such a way that the sum of the areas of selected images of the entrance slit, ie the totality of the deviations from a stigmatic image, assumes a minimum for selected images in the selected spectral range. The freeform surface can be optimized by optimizing various parameters. Depending on the position in the image field, the deviations from the stigmatic image for the individual images can be weighted differently. In particular, the scattering widths in the main dispersion direction and in the transverse dispersion direction can be weighted differently for the individual images.

In a particular embodiment of the invention, it is provided that the free-form surface is optimized in such a way that the totality of the deviations from a stigmatic image assumes a minimum for selected images from different spectrometer configurations. This particularly applies to spectrometers that sequentially capture different wavelength ranges. Again, the objective of the minimum deviation from the stigmatic mapping for the individual images can be weighted differently.

The deviation from the stigmatic mapping for an image of the entrance slit can be determined by evaluating the scattering of the intersection points of discrete virtual beams of a monochromatic beam with the detector plane. The usual measure of the spread is the root mean square (RMS) function.

Alternatively, it is provided that the free-form surface is optimized in such a way that the entirety of the weighted wavefront errors of selected images of the entrance slit in the selected spectral range assumes a minimum.

The objective function can also take into account the order distances, so that the differences of the order distances over the entire image field are minimized by optimizing the free-form surface.

In a particularly preferred embodiment of the invention, the optical element with the free-form surface is a folding mirror in front of the detector. "Before" here means that the folding mirror is the last optical element in the beam path in front of the detector, where the beam bundles of different wavelengths are already largely separated The relative bundle overlap is smaller than on the camera mirror This allows a wavelength-dependent adaptation As the path from the imaging optics to the detector narrows, the diameter of the beam bundles narrows, allowing the use of smaller mirrors with free - form surfaces Beams of different wavelengths are also reduced. Accordingly, the local adaptation of the applicate, ie the local z-coordinate of the surface and the curvature, can be used to optimize the imaging quality of the monochromatic bundles. A mirror further corrects the imaging quality for the respective beams regardless of their wavelengths. This is particularly important for dynamic spectrometer systems in which different spectral sections can be registered, of great importance.

It is preferably provided that the imaging optics is arranged in a Littrow arrangement. Then only slight aberrations need to be corrected.

In a further embodiment of the invention it is provided that the collimator and / or camera optics is realized by lenses or lens systems. The optical element with the free-form surface is used here in addition to the correction of the geometric aberrations and to minimize the chromatic aberrations generated by the imaging lenses.

In a further embodiment of the invention, it is provided that the second dispersing element is a prism with a surface which is likewise designed as a free-form surface, and the free-form surfaces have a shape in which the deviations due to aberrations from a stigmatic image of selected images of the Entrance slits at different wavelengths in the image plane over a selected spectral range of the two-dimensional echelle spectrum are optimized. But it is also conceivable that one or more additional free-form surfaces in the beam path by means of separate optical elements, such as additional mirrors or lenses, be realized. It has been found that the image quality over the image field can be further improved if several free-form surfaces influence the bundles independently. Due to the overall larger number of area parameters, more freedom is available when using several free-form surfaces in the optimization, in order to effectively limit higher-order aberrations in particular.

In a particularly preferred embodiment of the invention it is provided that at least one free-form surface is formed such that the orders occupy a selected position in the image plane and preferably have uniform distances in the image plane. For example, when a quartz prism is used to separate the orders in the transverse dispersion direction in a conventional arrangement, the orders are closer together in the long-wavelength spectral range than in the short-wavelength spectral range. For clean detection of the spectra must be between adjacent Regulations exist a certain distance. In the case of order separation with a quartz prism, however, said distance becomes larger and larger towards the short-wave spectral range. As a result, a substantial part of the detector surface remains unused. The relative shift of the images of the orders can avoid this effect: if the order distances are reduced by suitable design of the freeform surface in the short-wave spectral range, a smaller detector can be used. An increase in the order spacing in the long-wave spectral range allows a larger gap height of the entrance slit in the transverse dispersion direction and thus a larger light conductance.

Freeform mirrors can be designed as rigid bodies. For this purpose, a reflective coating on a carrier substrate or a polished metal mirror are suitable. However, it is also possible to realize reflective surfaces through dynamic systems and adaptive optics to account for dynamically varying imaging conditions. In one embodiment of the invention, it is therefore provided that the free-form surface is formed by a plurality of micromirrors whose position can be adjusted by means of associated actuators.

A particularly advantageous embodiment of the invention results when existing spectrometers are retrofitted with a freeform surface. In this way, the resolution and performance of existing spectrometer can be further improved without much effort. The invention therefore also includes, in particular, an optical component having a surface in the form of a free-form surface for retrofitting a spectrometer arrangement in which it is provided that the surface of selected images of the entrance slit at different wavelengths in the image plane over a selected spectral range of the input slit in the free-form surface due to aberrations two-dimensional echelle spectrum is optimized.

The described spectrometer arrangement can have a radiation source with a continuous spectrum between 190 nm and 860 nm, in particular a Xe high-pressure short-arc lamp. It is particularly suitable for atomic absorption spectroscopy (AAS).

The spectrometer arrangement described can have an inductively coupled plasma (ICP). It is also suitable for optical emission spectroscopy (ICP-OES).

Embodiments of the invention are the subject of the dependent claims. An embodiment is explained below with reference to the accompanying drawings. Brief description of the drawings

Fig. 1 is a schematic representation of an Echelle spectrometer array with internal order separation in Littrow arrangement.

FIG. 2 schematically illustrates the position of the orders of an echo spectrum on the detector.

3 shows the images of the entrance slit in the exit plane for various

Wavelengths evenly over the relevant for the spectra recording

Image field are distributed, in an arrangement of the prior art.

FIG. 2 shows the images of the entrance slit analogous to FIG. 3 with an arrangement according to the invention with optimized free-form surfaces.

5 shows the image of the entrance slit in the exit plane for a wavelength in a prior art arrangement in an enlarged view.

6 shows the image of the entrance slit analogous to FIG. 5 in an arrangement according to the invention with optimized free-form surfaces in an enlarged view

Presentation.

Fig. 7 is a schematic illustration of a Littrow-type internal order separation Echelle spectrometer array with lens optics.

8 shows the dependence of the longitudinal chromatic aberration 5f as a function of

Wavelength λ for a simple lens and an achromatic lens doublet.

FIG. 9 shows the images of a point light source for different wavelengths generated by the spectrometer setup in FIG. 7 in the image plane.

Fig. 10 shows the achievable improvement of the image quality over the whole

Image field. Description of the embodiments

FIG. 1 is a schematic representation of a particularly simple spectrometer arrangement, indicated generally at 10. The spectrometer arrangement 10 includes an entrance slit 15, an off-axis paraboloid as a collimator mirror 17, a backside mirrored prism 21, and an Echelle grating 31. At the exit plane of the spectrometer array 10, a detector 39 is provided for receiving the generated spectra. In front of the detector 39, a deflecting mirror 35 is arranged, with which the dispersed radiation is deflected in the direction of the detector 39. The roof edge 22 of the prism 21 is substantially perpendicular in the plane of representation. The grating lines of the echelle grating 31 are indicated by dashes 30.

The spectrometer assembly 10 comprises in addition to the above-mentioned optical components further components such as a housing, a base plate, fastening and adjustment means, mechanical drives and electrical components for controlling the optical components and for receiving and evaluating the signals at the detector 39, the simplicity here are not shown half. Radiation from a radiation source 1 1, which enters the spectrometer arrangement 10 through the entrance slit 15, is represented by a beam 24. Such a radiation source 11 is, for example, a xenon short-arc high-pressure lamp or a deuterium emitter, as used in atomic absorption spectroscopy. Alternatively, the radiation of an emission source, for example an inductively coupled plasma source (ICP), can be imaged onto the entrance slit. Depending on the application and laser, hollow cathode lamps, mercury vapor lamps and the like can be used as a radiation source 1 1. Finally, the arrangement is also suitable for spectral analysis of radiation sources themselves. The radiation 24 is collimated at the collimator mirror 17 to form a parallel bundle 19. The parallel bundle 19 strikes the prism 21 at an angle of incidence α and is dispersed in a transverse dispersion direction as shown. The transverse dispersion direction is defined by the position of the prism 21. The bundle 19 runs in the prism 21 to the mirrored rear side 23. There, it is reflected and travels back again through the prism 21. In the present embodiment, the operation of the spectrometer is illustrated by means of 3 different wavelengths. These are thus predispersed in three different directions, represented by the bundles 25, 27 and 29, on the prism. The angle of incidence at the prism 21 is selected so that the incident beam 19 is well separated from the reflected beams 25, 27 and 29. The reflected, still parallel bundles 25, 27 and 29 fall on the Echelle grating 31. There they are dispersed in a main dispersion direction. The main dispersion direction is transverse to the transverse dispersion direction. The echelle grating 31 is positioned such that the radiation continues to travel back to the prism 21, still in parallel bundles, at a very small angle. There it is redispersed in the transverse dispersion direction, reflected and dispersed once more. The further parallel bundles 32, 34 and 36 are then focused on the off-axis mirror 17, this time the camera, in the image plane with the detector 39.

In front of the detector 39, the deflection mirror 35 is arranged, with which the focused bundles 38, 40 and 42 are deflected. The bundles 38, 40 and 42 belonging to different wavelengths are already separated just before the detector 39. This is illustrated by the landing surface 44 for each bundle 38, 40 and 42 on the mirror 35. The deflected bundles then strike the detector 39 in the exit plane. The detector has a plurality of detector elements 54 with columns 50 and rows 52.

In the exit plane, the orders 56 generated by the echelle grating 30 are perpendicular. A typical structure of an echelle spectrum is illustrated with reference to FIG. The echelle grid generates a plurality of orders n, labeled 56. Due to the transverse dispersion of the prism 21, the orders are separated transversely to the main dispersion direction. Between the orders there is an order distance 58. In FIG. 2, the wavelength λ increases within an order from top to bottom and it falls with the ordinal number n from left to right. This is illustrated by arrows 66 and 68. Accordingly, there are larger wavelengths, eg the IR range, left in the spectrum and smaller wavelengths, eg the UV range, right in the spectrum. The prism dispersion is wavelength dependent with the commonly used materials. Accordingly, the orders in the long-wave range 70 are closer together. The order distances 58 increase in the direction of the short-wave region 72. At the same time, a free spectral range, ie the length of an order, of the Echelle grating in the long-wave range is greater. It can be seen in FIG. 2 that not only detector regions between the orders but also in the edge region are unused. The described arrangement is essentially known from DE 10 2009 059 280 A1. It requires very few optical components. This allows the cost-effective generation of a spectrum with low reflection and transmission losses at high light conductance and small device dimensions. Images generated in the image plane of a point light source having a plurality of discrete wavelengths are shown in FIG. Image 102 is an example of an image of a point light source at a particular wavelength. The images of the point light source are enlarged by a factor of 20 compared to the detector surface. Here, a flat deflection mirror was used. One recognizes that from the bundle of a wavelength occupied area in different areas is different sizes. In particular, the dimensions in the main and transverse dispersion directions are not the same. The Spot 100 has small dimensions in both directions. By contrast, a spot 102 of the same order at the edge of the image field occupies a rather large area. Although it is possible in this design to receive the signal with a plurality of detector elements and sum up. However, the signal then also has a larger offset due to the dark current on each of the detector elements 54. Due to the read-only noise for each detector element, the signal-to-noise ratio of the overall signal also deteriorates. Spots 104 and 106 in higher orders have very large expansions in the direction of transverse dispersion. Figure 5 shows a typical spot 108 from the peripheral area in detail, having dimensions in the range of 80 microns.

Free-form surfaces are now defined for the spectrometer described, which minimizes the entirety of the aberrations over the entire relevant image field. A first free-form surface is formed on the deflection mirror 35. A second free-form surface is formed on the prism 23.

In order to produce a suitable freeform surface, it is first necessary to define its shape. This requires the implementation of an optimization algorithm. In the present exemplary embodiment, an optical model for the above spectrometer is selected whose properties without free-form surface are already optimized with regard to the imaging quality by selecting a parabolic collimator mirror and Littrow arrangement as described above. The objective is to further improve the imaging quality of selected parts of the image field by replacing existing mirror surfaces. The mirror surfaces are freely mathematically describable. In the present embodiment, two existing planar mirror surfaces are replaced by reflective freeform surfaces. It is understood that additional free-form surfaces may be used that are added to the optics.

Freeform surfaces with a basic shape without edges and jumps are used, which have a steady course corresponding to the imaging errors.

In the present embodiment, the optimization is carried out by means of a beam calculation program. So no light source is required, but the light source can be selected so that it has all the properties required for the bill. Within the image field, a group of point images representative of the entire spectrum is defined. Dot images are different spectral images of a single field point in the entrance column plane. In the same way but can also pictures of multiple points can be used. Especially with small columns, one field point is sufficient. In the present embodiment, a dense dot image network was used. Although this requires a higher computing power in the area optimization, but provides a better quality of the calculated solution.

In the present embodiment, the surfaces of the deflection mirror 35 and the prism rear side 23 are described by means of Chebyshev polynomials (1st type), which are defined by their parameters. The mathematical expression for a surface description using Chebyshev polynomials of the 1st kind is:

z is the dependent area coordinate (applicate), x and y are the independent local location coordinates. X and Y are (as opposed to x and y) normalized coordinates (corresponding to the size of the area). To optimize the surface shape, the polynomial degrees N and M are defined in both dimensions and various parameters are released, in particular some or all of the polynomial coefficients C, but also, for example, the curvature c of the spherical basic shape.

The one-dimensional Chebyshev polynomials have the form:

T _n (k) = cos (n cos ^- 1 (), n = 0 · oo, fe e [-1,1] k is the independent locus coordinate, n is the polynomial degree.

In the case of the embodiment, a polynomial degree of 4x4 was chosen for both surfaces. As free parameters for the optimization of the free-form surface, all coefficients cy and the curvature c of the surfaces were selected. In addition, other parameters of the optical model were released, such as the detector tilt or the distance between the detector and the free-form mirror. For optimization, enough pixels are used to match the polynomial degree used.

It defines the parameters that may be varied during optimization. This includes the definition of boundary conditions. Thus, the mirror size must not exceed a selected value to prevent vignetting. Another important constraint is the preservation of the spectral geometry on the detector from the spectral image of a structure without free-form surfaces. Consequently, in the merit Function predetermined a target position on the detector for the individual images of the entrance slit. However, the weighting of compliance with these positions is set very low to allow for some distortion of the spectrum. Unlike in photography (keyword distortion), these are unproblematic when taking a spectral image. Admitting a certain distortion of the two-dimensional spectrum structure in the optimization has a tremendously positive effect on the quality of the solution in terms of image sharpness.

Furthermore, certain free-form parameters can be fixed, for example in order to fulfill a symmetry requirement on the surface.

In addition to the mathematical description of the free-form surface, the images in the image plane must also be described mathematically. These descriptions are included in the calculation of the value of the merit function. The merit function includes the mathematically expressed goals for the optimization and their relative weighting. The smaller the value of the merit function, the better the optical arrangement fulfills the objectives. In the present exemplary embodiment, the totality of the deviations from stigmatic mappings for the considered wavelengths is calculated and minimized. In the case shown, the goal of minimizing the deviation from the stigmatic mapping is weighted equally for the individual wavelengths under consideration. However, for each individual image, the goal of minimizing the deviation from the stigmatic image in the main dispersion direction is weighted 10x higher than in the transverse dispersion direction. In addition, the weighting for preserving the geometry of the spectrum starting from the spectral image in the arrangement without free-form surfaces is less weighted than the minimization of the aberrations 10.OOOx.

The result is shown in FIG. 4 and in detail in FIG. It can be seen that the spot 110 is considerably smaller than in FIG. 3 or FIG. 5. As in FIG. 3, the images of the point light source in FIG. 4 are enlarged by a factor of 20 relative to the detector surface. The light is concentrated on a significantly smaller number of detector elements, so that the dark current and the readout noise are lower. The orders can be more closely collapsed in a second step so that smaller detectors can be used. The images of the entrance slit for different wavelengths are narrower and overlap less Thus, the spectral resolution is greater. Overall, the spectrum is better detectable.

FIG. 7 schematically shows another particularly suitable spectrometer arrangement, which is designated generally by 200. The arrangement comprises a radiation source 211, an entrance slit 215, an achromatic lens doublet 202, a purely transmissive prism 204, whose roof edge 222 is substantially perpendicular to the plane of view, and an echelle grating 231. In the exit plane of the spectrometer arrangement 200, a detector 239 is provided for recording the generated spectra. In front of the detector 239, a deflection mirror 235 is arranged, with which the dispersed radiation is deflected to the detector 239.

The radiation emitted by the source 211 is introduced through the entrance slit 215 into the actual spectrometer. The radiation travels from the gap to the achromatic lens doublet 202, from which the radiation is collimated. Radiation passes from the lens combination as a parallel bundle 219 to the transmissive prism 204, which disperses the radiation in the transverse dispersion direction as shown. The dispersed radiation, represented by the parallel bundles 225, 227 and 229 of three different wavelengths, passes to Echelle grating 231, where they are also dispersed in the main dispersion direction.

The radiation is offset by a very small angle back to the prism 202. There it is again dispersed in the transverse dispersion direction. The further parallel bundles 232, 234 and 236 are then focused by the lens doublet 202, which this time acts as a camera, in the image plane with the detector 239.

In front of the detector 239, the deflecting mirror 235 is arranged, with which the focused bundles 238, 240 and 242 are deflected. The bundles 238, 240 and 242 belonging to different wavelengths are already largely separated just before the detector 239 - the relative bundle overlap is small. This is illustrated by the landing area 244 for each bundle 238, 240 and 242 on the mirror 235. The deflected bundles then strike the detector 239 in the exit plane.

The typical spectral shape generated on the detector 239 of Echelle grating 231 and prism 204 corresponds again to the diffraction order structure shown in FIG.

The illustrated spectrometer arrangement 200 corresponds to a Littrow arrangement. Littrow arrangements have a small number of optical components and thus low radiation losses and can be built very compact. Littrow spectrometers with lens optics as collimator or camera optics are typically used only for spectrometers with very narrow wavelength ranges. The reason for this is the wavelength-dependent errors (chromatic aberration), which are inevitably induced by a lens optic. Particularly problematic in the present case is the longitudinal chromatic aberration, ie the dependence of the focal length of a lens or a lens system on the wavelength. Achromatic lens combinations can be used to reduce the longitudinal chromatic aberration. Achromatic lens doublets typically consist of a concave high refractive lens, such as flint glass, and a lower dispersion convex lens, such as crown glass. Such a combination allows elimination of focus error and spherical aberration for two design wavelengths. FIG. 8 shows the dependence of the longitudinal chromatic aberration Sf as a function of the wavelength λ for a simple lens 302 and an achromatic lens double! 304. For a single lens, the focus error 5f may be eliminated for only one wavelength 306, in the case of one achromatic doublet for two wavelengths 308 and 310,

FIG. 9 shows the images of a point light source for different wavelengths generated by the above-described spectrometer setup in the image plane. The spectrometer generates a spectrum in the range between 600 nm and 1000 nm wavelength. The collimator and camera use an achromatic lens doublet with design wavelengths at 700 nm and 900 nm '. As deflecting mirror 35 in front of the detector, a plane mirror is used. The detector is positioned so that midway between the two design wavelengths the aberrations (geometric plus chromatic aberrations) become minimal - here represented by the pixel 312. At the edges of the spectrum, the aberrations increase sharply - the areas of the point source images taken become greater. The images are magnified both in the main dispersion direction and in the transverse dispersion direction. Predominant is the remaining longitudinal chromatic aberration that an achromatic lens doublet still has - it manifests itself as local defocusing. Representative of this are the two pixels 314 and 316 at the bottom and top of the range.

For further correction of the aberrations occurring over the entire image field, in particular for minimizing the chromatic errors, the deflection mirror 35 can be converted before the detector 39 to a free-form surface. The mathematical surface description, the determination of the freely variable parameters in the optical model and the surface optimization process are identical to the procedure described in the first embodiment.

The thus achievable improvement of the image quality over the entire image field is shown in FIG. It can be seen that, especially at the edge of the wavelength range (pixels 324 and 326), the images of the point light source are many times smaller than the corresponding pixels of the same wavelength in a structure without free-form correction mirror I (FIG. 9: 314, 316). As in FIG. 9, the images of the point light source in FIG. 10 are enlarged by a factor of 20 relative to the detector surface. The light is concentrated on a significantly smaller number of detector elements, so that the Dark current and the Ausleserauschen are lower. The orders can be more closely collapsed in a second step so that smaller detectors can be used. The images of the entrance slit for different wavelengths are narrower and overlap less Thus, the spectral resolution is greater. Overall, the spectrum is better detectable.

Claims

claims

Spectrometer arrangement (10) with two-dimensional spectrum containing

(a) a first dispersing element (31) for spectrally decomposing radiation in a main dispersion direction,

(B) an imaging optics (17) for imaging the radiation entering through an entrance slit (15) in the spectrometer assembly (10) in an image plane with which a two-dimensional spectrum can be generated, and

(c) a surface detector (39) having a two-dimensional arrangement of a plurality of detector elements in the image plane,

characterized in that

Arrangement according to claim 1, characterized by a second dispersing element (21) for order separation by means of spectral decomposition of the radiation in a transverse dispersion direction which forms an angle with the main dispersion direction of the first dispersing element (31), so that a two-dimensional spectrum can be generated.

Arrangement according to claim 1 or 2, characterized in that the free-form surface is formed such that the total resulting due to aberrations aberrations of a stigmatic imaging of selected images of the entrance slit at different wavelengths in the image plane over a selected spectral range of the two-dimensional spectrum is minimized.

Arrangement according to one of the preceding claims 2 or 3, characterized in that the dispersing in the main dispersion direction element is an Echelle grating.

5. Arrangement according to claim 4, characterized in that the spectrometer is an echelle spectrometer with internal order separation.

6. Arrangement according to one of claims 4 to 5, characterized in that a reflective, refractive or diffractive surface is arranged at a location in the beam path, where at least two of a same echelle diffraction order associated monochromatic bundles are completely separated and / or where at least two monochromatic bundles which do not belong to the same echelle diffraction order are completely separated and the reflecting, refractive or diffractive surface is designed as a free-form surface, which determines the deviation from a stigmatic image on the detector for the individual monochromatic bundles over a selected wavelength range of the two-dimensional echelle. Minimized spectrum independently.

7. Arrangement according to one of the preceding claims, characterized in that all components are formed such that monochromatic bundles of at least two wavelengths from the same main dispersion order within the free spectral range at the location of the free-form surface are completely separated and / or monochromatic bundles of two points in Entry gap with different positions of the gap height at the location of the surface are completely separated.

8. Arrangement according to one of the preceding claims, characterized in that the free-form surface is optimized such that the sum of the RMS function of selected images of the entrance slit in the selected spectral range assumes a minimum.

9. Arrangement according to one of the preceding claims 1 to 7, characterized in that the free-form surface is optimized such that the sum of the wavefront error of selected images of the entrance slit in the selected spectral range assumes a minimum.

10. Arrangement according to one of the preceding claims 1 to 7, characterized in that the free-form surface is optimized such that the sum of the areas of selected images of the entrance slit in the selected spectral range assumes a minimum.

1 1. Arrangement (10) according to one of the preceding claims, characterized in that the optical element with the free-form surface is a folding mirror in front of the image plane.

12. Arrangement (10) according to one of the preceding claims, characterized in that the imaging optics is arranged in Littrow arrangement.

13. Arrangement (10) according to one of the preceding claims 2 to 12, characterized in that the second dispersing element is a prism with a

Surface is also formed as a free-form surface, and the free-form surfaces have a shape in which optimized due to aberrations aberrations of a stigmatic imaging of selected images of the entrance slit at different wavelengths in the image plane over a selected spectral range of the two-dimensional echelle spectrum optimized are.

14. Arrangement according to one of the preceding claims, characterized in that at least one free-form surface is formed such that the orders occupy a selected position in the image plane and preferably uniform

Have gaps in the image plane.

15. Arrangement according to one of the preceding claims, characterized in that a free-form surface is formed by a plurality of micromirrors or by another adaptive optical element whose shape and / or position is adjustable by means of associated actuators.

16. Arrangement according to one of the preceding claims, characterized in that the imaging optics is formed with spherical mirrors and at least one surface of an optical element in the collimated beam path is formed as a free-form surface, which is optimized so that the totality of the deviation from a stigmatic imaging is minimal for selected images of the entrance slit in the relevant wavelength range.

17. Arrangement according to one of the preceding claims, characterized in that the imaging optics comprises a lens or a lens system.

18. Optical component having a surface in the form of a free-form surface for retrofitting a spectrometer arrangement according to claim 1, characterized in that in the free-form surface the area of selected images of the entrance slit occupied by aberrations at different wavelengths in the image plane over a selected spectral range of the two-dimensional Echelle spectrum is optimized.