Spectrometer for spectrally measuring a specimen

Abstract

The present invention relates to a spectrometer for spectrally measuring a specimen. The spectrometer comprises a plurality of optical filter regions and at least one optical sensor. The filter regions each have a transmission function (01, 02, 03, 04). For each of the transmission functions (01, 02, 03, 04), an arithmetic mean of a first derivative of the relative transmission with respect to the wavelength is at most 1 1 / μm. Each measurement of a spectrum to be measured using the at least one sensor over the individual filter regions leads to a measured value. The spectrometer is configured to apply a reconstruction function which is designed to reconstruct the measured spectrum on the basis of the measured values. The spectrometer is also configured to determine the reconstruction function using at least one reference spectrum and the transmission functions (01, 02, 03, 04).

Description

[0001] Spectrometer for spectral measurement of a sample

[0002] The present invention relates to a spectrometer for the spectral measurement of a sample. The spectrometer comprises a plurality of optical filter areas and at least one optical sensor for measuring across a spectral measurement range of the spectrometer. Measurements of a spectrum to be measured with the at least one sensor across the individual filter areas each lead to a measured value. The spectrometer is configured to use a reconstruction function which is designed to reconstruct the measured spectrum based on the measured values.

[0003] DE 10 2021 105 869 A1 shows a spectral sensor system with an array of optical sensors arranged on an integrated circuit, and with an interface between the plurality of optical sensors and a first processing device. A plurality of sets of optical filters are configured as a layer arranged on the plurality of optical sensors. Each set of optical filters contains a plurality of optical filters. Each of the optical filters is configured to transmit light in a different wavelength range. The spectral sensor system comprises a processing device containing an artificial neural network configured to correct a spectral response generated by the plurality of optical sensors.

[0004] US 9,030,662 B2 shows a device for processing optical signals from a spectrometer. The device comprises an optical filter array, an optical sensor array, and a digital signal processing unit for digitally processing an output signal from the optical sensor array based on an L1-norm minimization algorithm. The optical filters and the resolutions achievable depending on the type of filters used are not described. Calibration of the optical filters is also not discussed. An embodiment with narrowband filter functions and a further embodiment with generic wavelength-selective filters are specified. An optimization of the filter design is not shown.

[0005] DE 11 2020 002 614 T5 shows a photodetector device with a plurality of light detector elements and with a plurality of filters. Each filter is arranged in front of a light-detecting surface of the corresponding light detector element. The filters are configured such that they each filter at least two different wavelength bands of the incident light. At least two wavelength bands are combined to span a predefined wavelength range. Each filter has a corresponding spectral sensitivity. A sum of the spectral sensitivity curves of the filters is constant over the predefined wavelength range.

[0006] DE 11 2019 003 825 T5 shows a system with two spectral modulators, with an optical light guide, with a photodetector and with an electronic control device. The first spectral modulator receives sample light and modulates the sample light according to a first spectral response pattern in order to generate a first modulated light. The second spectral modulator receives the first modulated light from the first spectral modulator via the light guide and modulates the first modulated light according to a second spectral response pattern in order to generate a second modulated light. The second spectral modulator transmits the second modulated light to the photodetector. The photodetector measures an intensity of the second modulated light and generates at least one signal which corresponds to the intensity of the second modulated light. The electronic control device determines a spectral distribution of the sample light based on the at least one signal.

[0007] EP 2 473 826 B1 shows a light sensor with a filter arrangement comprising a plurality of spectral filters for filtering incident light. Each spectral filter is configured to transmit a specific component of the incident light. An aperture arrangement with a plurality of apertures serves to transmit a portion of the incident light. A sensor arrangement is configured to capture the transmitted, filtered light. The sensor arrangement comprises an array of sensor elements for generating image-related signals. The sensor array is divided into a plurality of regions.Each region comprises a plurality of sensor elements and is associated with an aperture of the plurality of apertures and a corresponding spectral filter of the plurality of filters, such that an image-related signal generated by a sensor element of a particular region includes information concerning the direction of origin and the spectral composition of the light transmitted by the corresponding spectral filter.

[0008] In the article by J. Oliver, Woong-Bi Lee and Heung-No Lee: "Filters with random transmittance for improving resolution in filter-array-based spectrometers" in Optics Express 21 ( 4 ), 2013 , pages 3969 to 3989 , a method for designing filters to improve the resolution of miniature spectrometers is proposed. The filters are each based on a multilayer stack of dielectric materials in which the layer thicknesses vary randomly by 1 pm and the refractive index contrast between the layers is maximized. The resulting white noise-like transfer functions are characterized by rapidly changing slopes and transmittance values ​​that fluctuate between 0 and 1.A matrix of N = 40 calculated transfer functions is used to reconstruct a synthetic sparse spectrum of a mercury arc emission, using Ll-norm minimization for spectral estimation. The spectral reconstructions and resolutions are validated based on the mean square deviation from the reference.

[0009] In the article by Cheolsun Kim, Pavel Ni, Kang Ryeol Lee and Heung-No Lee: “Mass production-enabled computational spectrometers based on multilayer thin films” in Scientific Reports 12, 1, 2022, pages 1-9, an experimental demonstration of a computational miniaturized spectrometer is described. For this purpose, a 6 x 6 square grid of multilayer filters fabricated by stencil lithography was applied to a CMOS image sensor. Thus, 36 intensities of the incident light are recorded in a single exposure. The spectrum of the incident light is reconstructed from the determined intensities using a numerical optimization technique based on Ll minimization. The spectra of individual LED sources and a halogen lamp in the range from 500 nm to 850 nm were reconstructed with a resolution of 1 nm.The reconstructed spectra were compared with reference spectra measured with a commercial grating-based spectrometer. The validation of the obtained spectra and the achieved spectral resolution of the computer-aided spectrometer are based exclusively on the reference spectra measured with a reference spectrometer.

[0010] The article by Cheolsun Kim, Dongj u Park, Jioh Lee and Heung-No Lee : "Deep learning-based single-shot computational spectrometer using multilayer thin films" in arXiv preprint , arXiv: 2204 . 02669 , 2022 , concerns another realization of a computational spectrometer , in which a deep learning algorithm is applied for spectral estimation .

[0011] In the article by Qiaoshuang Zhang et al.: "Fabrication of Bragg Mirrors by Multilayer Inkjet Printing" in Advanced Materials 34, 33, 2022, 2201348, a method for fabricating Bragg mirrors by inkjet printing is described. The Bragg mirrors are based on composite layers of a UV-curable polymer and TiCy nanoparticles. The photonic band gap and reflectivity can be adjusted by changing the number and thickness of the layers by varying the parameters of the inkjet printing process.

[0012] The solutions known from the prior art have the disadvantage that the transfer functions of the multilayer filters used are not optimized for high-resolution spectral reconstruction of broadband signals. Many different layers are required to achieve the spectral diversity between the filters. The optical transmission functions of the filters are characterized by strongly changing slopes, which leads to noisy reconstructions and spectral artifacts. A further disadvantage is the time-consuming and costly production of the filters in order to make them highly correlated and broadband. Each filter consists of several layers of different thicknesses. In the example mentioned above, a matrix of 36 different filters is formed by stacking 19 alternating layers of SiC and TiC using stencil lithography, which involves a vacuum deposition process.Another disadvantage of these multilayer filters is that they require intense light sources or highly sensitive optical sensors, since the moderate to low optical transmittance of these filters negatively influences the achievable signal-to-noise ratio and the achievable reconstruction quality. The multilayer filters have a narrow optical response, so the resulting system is particularly sensitive to the angle of incidence of the illumination source. A further disadvantage is the evaluation of the reconstructed spectra and achieved spectral resolutions based on the calculated mean squared error (MSE) between the reconstructed spectrum and a reference spectrum measured with a second standard spectrometer.This evaluation is not based on standard design parameters such as the number of filters, the sampling of the filter functions, the sensor used, or the robustness of the algorithm used. State-of-the-art solutions based on spectrally correlated broadband transmission filters in conjunction with subsequent reconstruction are characterized by the fact that the achievable spectral resolution is not only a direct function of the filter bandwidth and number of filters, but also depends on the spectral density of the illumination source and the spectral sampling of the filter responses. Thus, with a single set of optical filters and a single minimization algorithm, different spectral resolutions can be achieved depending on whether a sparse or a dense spectrum is considered.A sparse spectrum of this kind is characterized by the fact that, compared to its bandwidth, it contains only a few spectral bands or spectral lines that are greater than zero. A dense spectrum of this kind is characterized by the fact that, compared to its bandwidth, it contains only a few or no spectral bands or spectral lines that are equal to zero. Using the mean square deviation from the reference spectrum as the only figure of merit to estimate the spectral resolution means that this estimate has to be repeated for each differently measured spectrum, which requires the simultaneous use of a second spectrometer with a higher resolution. This negates the actual advantage of the described solution, namely the simplified design of the spectrometer.

[0013] The object of the present invention is to overcome the above-described disadvantages of the solutions known from the prior art.

[0014] The above object is achieved by a spectrometer according to the appended claim 1.

[0015] The spectrometer according to the invention is used for the spectral measurement of a sample. The spectrometer can be an NIR spectrometer, a VIS / NIR spectrometer, a VIS spectrometer, or an MIR spectrometer. The spectrometer can also be a full-range spectrometer, which allows measurements in the infrared, visible, and optionally also the ultraviolet spectral range. The spectrometer is preferably designed as a compact miniature spectrometer.

[0016] The spectrometer allows a measurement across a spectral measurement range of the spectrometer. The measurement range is characterized by a smallest measurable wavelength and a largest measurable wavelength, between which the measurement range extends. In order to enable the measurement across the spectral measurement range of the spectrometer, the spectrometer has a plurality of optical filter regions that are formed on one or more optical filters. In a preferred embodiment, one of the filter regions is formed on one of the filters, so that the number of filter regions is equal to the number of filters. In further preferred embodiments, several or all of the filter regions are formed on one of the filters or on the one filter. For example, the filter properties of the filter can change gradually in its main extension plane, resulting in the plurality of filter regions.In order to enable measurement across the spectral measurement range of the spectrometer, the spectrometer also has at least one optical sensor. The term “optical” here refers to the visual range and / or also to the infrared and ultraviolet ranges of the electromagnetic spectrum, whereby the measurement range of the spectrometer can extend over part or all of the aforementioned ranges. Accordingly, the filter areas and the at least one sensor are designed for part or all of the aforementioned ranges of the electromagnetic spectrum. The spectrum to be measured, i.e. the radiation whose spectrum is to be determined, passes through the individual filter areas to the at least one sensor. The at least one sensor measures the intensity of the radiation incident on it by integrating it over the spectral measurement range of the spectrometer; preferably independently of the wavelength.

[0017] The filter areas each have a transmission function, which can also be referred to as a transfer function. The transmission function describes the dependence of a relative optical transmission of the respective filter area on the wavelength across the spectral measuring range of the spectrometer. The relative optical transmission is between zero and one, with one representing complete transparency and zero representing complete opacity in relation to the respective wavelength. Since the spectrum to be measured passes through the individual filter areas to the at least one sensor, measurements of the spectrum to be measured with the at least one sensor across the individual filter areas each lead to a measured value. One of the measured values ​​is obtained for each of the filter areas, so that the number of measured values ​​equals the number of filter areas.

[0018] The transmission functions have special properties. According to a first property, an arithmetic mean of a first derivative of the relative transmission with respect to the wavelength over the spectral measurement range is at most 1 1 / pm for each of the transmission functions. Thus, the curves of the transmission functions do not have any large inclines or declines on average and can therefore be characterized as smooth. The transmission functions are smooth compared to the transmission functions of the filters of the prior art solutions described above, which are highly variable. The arithmetic mean of the first derivative of the relative transmission with respect to the wavelength over the spectral measurement range is preferably at most 0.5 1 / pm and more preferably at most 0.1 1 / pm for each of the transmission functions.Preferably, the arithmetic mean of the absolute value of the first derivative of the relative transmission with respect to the wavelength over the spectral measurement range for each of the transmission functions is at most 1 l / pm, more preferably at most 0.5 l / pm and even more preferably at most 0.1 l / pm. According to a preferred second property, an average relative transmission over the spectral measurement range for the transmission functions is at least 0.5 on average. The filter regions are therefore significantly more transparent than the filters of the prior art solutions described above. The average relative transmission over the spectral measurement range for the transmission functions is preferably at least 0.7 on average and more preferably at least 0.8 on average.

[0019] The spectrometer is configured to apply a mathematical reconstruction function which is designed to reconstruct the measured spectrum based on the measured values. This results in a reconstructed spectrum which comes as close as possible to the measured spectrum, i.e. the actual spectrum of the sample in its relevant properties and in its complete course across the spectral measurement range. In preferred embodiments, the spectrometer comprises a signal processing unit for processing the measured values. The signal processing unit is configured accordingly to apply the mathematical reconstruction function in accordance with the above explanations. In alternative preferred embodiments, the spectrometer is designed to use a cloud to apply the mathematical reconstruction function in accordance with the above explanations.

[0020] The spectrometer is also configured to determine the reconstruction function using at least one reference spectrum and the transmission functions. The reference spectrum extends over the spectral measurement range of the spectrometer and its course over the entire spectral measurement range is completely determined and known. The reference spectrum can be a sparse spectrum or a dense spectrum. The spectrometer preferably comprises at least one light source for emitting radiation, this radiation having the reference spectrum. The spectrometer preferably comprises a plurality of these light sources, each for emitting a radiation, each radiation having one of the plurality of different reference spectra. The radiation having the reference spectrum passes through the individual filter areas, such that a calibration measurement value is obtained at the at least one sensor.The reconstruction function can now be optimized so that applying the reconstruction function to the calibration measurement values ​​leads to the respective reference spectrum as accurately as possible. The resulting reconstruction function is to be stored, in particular, in the form of software in the spectrometer or in a cloud assigned to the spectrometer, so that the reconstruction function can be applied by the spectrometer for later measurements. Since the reconstruction function is determined by the spectrometer itself, this can also be referred to as autocalibration. This autocalibration does not require any external devices, such as a reference spectrometer. This autocalibration can also be repeated during later operation of the spectrometer. In preferred embodiments, the signal processing unit for determining the reconstruction function is configured as explained above.In alternative preferred embodiments, the spectrometer is designed to use a cloud to determine the reconstruction function according to the above explanations.

[0021] A particular advantage of the spectrometer according to the invention is that it can be designed with little effort and is compact. Compared to the prior art solutions described above, higher spectral resolution and fewer spectral artifacts are possible due to the smooth transfer functions. The filter areas can be manufactured cost-effectively. Adaptation to various measuring tasks is easily possible. A high signal-to-noise ratio can be achieved with the spectrometer because the filter areas have a high optical transmittance, which enables the use of cost-effective sensors with low efficiency. The spectrometer is therefore suitable for spectrophotometric measurements of highly absorbent samples. Collimation lenses are also unnecessary.In contrast to the Bragg filters used in the state of the art, the filter areas used enable a high degree of robustness of the spectrometer with respect to the angle of incidence of the radiation to be measured that strikes the filter areas. A further advantage is that, compared to the state of the art, no second high-resolution spectrometer is required to validate the reconstructed spectra.

[0022] A particular advantage of the spectrometer is that the filter regions with the defined properties of their transmission functions can be produced cost-effectively; for example, using a wet-chemical manufacturing process, so that complex vacuum manufacturing processes are not necessary. Therefore, in preferred embodiments, the optical filter regions each have at least one wet-chemically applied transmission layer. The transmission layers are preferably applied using an inkjet printing process. A first of the transmission layers of the respective filter region is preferably applied to a transparent substrate. The filter regions preferably consist of a polymer or an inorganic material. The filter regions can also be formed by using a single material in different thicknesses, so that the filter regions only differ in their thickness.Alternatively, the filter regions can preferably be physically produced with the defined properties of their transmission functions. For this purpose, nanopores are preferably introduced into a substrate, with a gradient of the nanopores across a main extension plane of the filter regions leading to different average refractive indices and thus to different transmission functions.

[0023] The transmission layers each have a thickness that is preferably between 100 nm and 10 pm. The thickness is determined indirectly from the specified transmission function.

[0024] In principle, at least several of the optical filter regions can each have only one transmission layer. In preferred embodiments, at least several of the optical filter regions each have two to ten transmission layers arranged one above the other. In preferred embodiments, a majority of the optical filter regions each have two to ten transmission layers arranged one above the other. In further preferred embodiments, a majority of the optical filter regions each have two to six transmission layers arranged one above the other.

[0025] In the spectrometer according to the invention, a comparatively small number of filter areas allows a very precise reconstruction of the measured spectrum. Therefore, in preferred embodiments, the number of filter areas is between 5 and 30. Due to the comparatively small number of filter areas, the spectrometer can be designed compactly. In preferred embodiments, the filter areas are arranged in a matrix and therefore form a filter matrix. Preferably, one of the optical sensors is arranged behind each of the optical filter areas, for which the sensors are also arranged in a matrix and form a sensor matrix. The spectrometer therefore has an equal number of filter areas and sensors. In alternative preferred embodiments, the spectrometer has only one sensor, which measures sequentially one after the other across the individual filter areas.This is preferably done by moving the sensor and the filter areas relative to each other.

[0026] As already explained above, one advantage of the invention is the robustness of the spectrometer with respect to the angle of incidence of the radiation to be measured. In principle, there is a deviation in the transfer functions of the individual filter areas due to non-perpendicular irradiation of the radiation to be measured, although this deviation is very small thanks to the invention. If one considers an average deviation in the transfer functions of the individual filter areas in a range between perpendicular irradiation and irradiation deviating by 10° from the perpendicular irradiation, this average deviation for each of the filter areas is preferably at most 2%; and more preferably at most 1%.

[0027] In preferred embodiments, the reconstruction function is determined by solving a minimization problem; in particular by convex optimization. This is preferably carried out by applying the method of least squares, in particular including L1 regularization, L2 regularization or a regularized regression method such as LASSO or a basis pursuit optimization method. In contrast to the prior art, the reconstruction function is preferably not determined on the basis of the mean square deviation. The reconstruction function is preferably determined in a frequency domain in which the transmission functions and the reference spectrum are transformed. The Fourier transform is preferably used for this transformation. The reconstruction function is preferably determined by machine learning.Many methods are known from the state of the art that can be used for this task. In preferred embodiments, the reconstruction function is determined using artificial intelligence.

[0028] Preferably, only a few regulation parameters are used for the regularization, which are determined from a preliminary spectral reconstruction of the reference spectrum and an evaluation, for example, using the MSE. For the preferred LI or L2 regularization, an objective function is used, which is obtained, for example, from the following: with |s| > 0 or : with |s| > 0

[0029] Input variables:

[0030] A measured calibration matrix of the N

[0031] Transmission functions with a sample M (NxM)t> Transformation matrix (MxM)

[0032] D measured intensity behind the individual filter areas

[0033] (Nxl ) y regulation parameters

[0034] Output quantities : s spectral components (Mxl ) of the reconstructed spectrum

[0035] In preferred embodiments, at least one wavelength-dependent restriction is defined for determining the reconstruction function, whereby the course of the reconstruction function is already restricted in advance. This leads to the resulting reconstruction function enabling a more precise reconstruction and reducing the effort required to determine the reconstruction function. This restriction is preferably defined by a sparse spectrum of the light source.

[0036] The light source is preferably designed to emit homogeneous illumination, which in particular also achieves uniform reflection to the individual filter areas. In further embodiments, the spectrometer comprises several light sources; for example, if, as described above, the filter areas differ only in their optical thickness.

[0037] In preferred embodiments, the spectral measurement range of the spectrometer extends over at least 300 nm, more preferably over at least 400 nm, and even more preferably over at least 500 nm. An advantage of the spectrometer is that it allows reconstruction over a wide bandwidth.

[0038] The first derivatives of the relative transmission with respect to wavelength of the individual transmission functions are characterized by their small size. Preferably, a standard deviation o of the first derivative of the relative transmission with respect to wavelength across the spectral measurement range is also small for each of the transmission functions, preferably at most 5.0 1 / pm and more preferably at most 3.0 1 / pm. Accordingly, the transmission functions are very smooth.

[0039] Further details and developments of the invention will become apparent from the following description of preferred

[0040] Embodiments of the invention, with reference to the drawings. Shown are:

[0041] Fig. 1: a diagram illustrating transmission functions of filter areas of a preferred embodiment of a spectrometer according to the invention;

[0042] Fig. 2: a diagram illustrating an angular dependence of a transmission function of a filter area of ​​a preferred embodiment of the spectrometer according to the invention;

[0043] Fig. 3: a diagram illustrating an angle dependence of a transmission function of a filter according to the prior art;

[0044] Fig. 4: a diagram illustrating properties of the transmission functions shown in Fig. 2 and Fig. 3;

[0045] Fig. 5: a diagram of a preferred

[0046] Embodiment of the spectrometer according to the invention reconstructed spectrum;

[0047] Fig. 6: a diagram of a spectrum reconstructed with a spectrometer according to the prior art; Fig. 7: a diagram of another with a preferred

[0048] Embodiment of the spectrometer according to the invention reconstructed spectrum;

[0049] Fig . 8 : a diagram of another with a preferred

[0050] Embodiment of the spectrometer according to the invention reconstructed spectrum in comparison with the measured spectrum;

[0051] Fig . 9 : a diagram of further with a preferred

[0052] Embodiment of the spectrometer according to the invention reconstructed spectra in comparison with the measured spectrum;

[0053] Fig . 10 : a diagram of a preferred

[0054] Embodiment of the spectrometer according to the invention reconstructed spectrum compared to the measured spectrum; and

[0055] Fig. 11: a flow chart illustrating the operation of a preferred embodiment of the spectrometer according to the invention.

[0056] Fig. 1 shows a diagram for the exemplary representation of transmission functions O1, O2, O3, O4 of four filter regions of a preferred embodiment of a spectrometer according to the invention (not shown). A sensor (not shown) of the spectrometer receives radiation to be measured via the filter regions (not shown). The filter regions each consist, for example, of four transmission layers (not shown) which are arranged one above the other and have different thicknesses. The wavelength X in pm is plotted on the abscissa axis of the diagram. The relative transmission T is plotted on the ordinate axis. The four transmission functions O1, O2, O3, O4 extend over the ultraviolet range, the visible range and the infrared range of the electromagnetic spectrum from 0.3 pm to 1.2 pm, which also represents a spectral measurement range of the spectrometer (not shown).The four transmission functions 01, 02, 03, and 04 show an average transmission of the individual filter ranges (not shown) that is greater than 0.8. The four transmission functions 01, 02, 03, and 04 exhibit the property that the arithmetic mean and the variance of the first derivative of the relative transmission with respect to wavelength are each very small across the spectral measurement range. Therefore, these transmission functions 01, 02, 03, and 04 exhibit a smooth curve.

[0057] Fig. 2 shows a diagram illustrating the dependence of a transmission function of a filter region (not shown) of a preferred embodiment of the spectrometer according to the invention (not shown) on an angle of incidence of a radiation to be measured. This transmission function has the properties explained with reference to Fig. 1. The wavelength X in pm is plotted on the abscissa axis of the diagram. The relative transmission T is plotted on the ordinate axis. A transmission function 06 recorded for perpendicularly incident radiation and a transmission function 07 recorded for radiation inclined 10° to the normal hardly differ. This demonstrates that the spectrometer according to the invention (not shown) is robust against inclinations of the incident radiation to be measured.

[0058] Fig. 3 shows a diagram illustrating the dependence of a transmission function of a filter (not shown) of a spectrometer (not shown) according to the prior art on the angle of incidence of the incident radiation to be measured. This filter is a Bragg filter. Its transmission function varies significantly more than the transmission functions θ1, θ2, θ3, θ4, θ6, θ7 (shown in Fig. 1 and Fig. 2) of the filter areas of the spectrometer according to the invention and also has a significantly lower average transmission. The wavelength X in pm is plotted on the abscissa axis of the diagram. The relative transmission T is plotted on the ordinate axis. A transmission function θ1 recorded for perpendicularly incident radiation and a transmission function θ2 recorded for radiation inclined 10° to the normal sometimes differ more significantly than the one shown in Fig.2 shows the transmission function of the filter area of ​​the spectrometer according to the invention.

[0059] Fig. 4 shows a diagram illustrating properties of the transmission functions shown in Fig. 2 and Fig. 3. The wavelength X in pm is plotted on the abscissa axis of the diagram. The difference ΔT between the transmission for perpendicularly incident radiation and the transmission for radiation inclined 10° to the normal is plotted on the ordinate axis. A graph 13 drawn with a solid line represents this difference ΔT for the transmission function of the filter area of ​​the spectrometer according to the invention shown in Fig. 2. A graph 14 drawn with a dashed line represents this difference ΔT for the transmission function of the filter of the spectrometer according to the prior art shown in Fig. 3.It is clear that the difference AT for the transmission function of the filter range of the spectrometer according to the invention is approximately zero over the entire measurement range, but the difference AT for the transmission function of the filter of the spectrometer according to the prior art often assumes absolute values ​​greater than 0.1. Thus, the spectrometer according to the prior art is not robust against inclined incident radiation, so that measurement errors are to be expected.

[0060] Fig. 5 shows a diagram of a spectrum 16 reconstructed using a preferred embodiment of the spectrometer according to the invention (not shown). This spectrum was reconstructed from 10 measured values ​​using a reconstruction function. These 10 measured values ​​were obtained by taking individual measurements over 10 filter areas (not shown), the filter areas having transmission functions as explained in relation to Fig. 1. The filter areas each comprised four transmission layers (not shown). A spectrum 17 to be measured had only a first spectral line at 0.9 pm with a half-width of 0.9 nm and a second spectral line at 1.1 pm with a half-width of 5 nm. The wavelength X in pm is plotted on the abscissa axis of the diagram. The relative intensity I is plotted on the ordinate axis.The reconstructed spectrum 16 shown is largely similar to the measured spectrum 17 , so that the graphs are aligned. The reconstructed spectrum 16 shown shows no detectable artifacts.

[0061] Fig. 6 shows a diagram of a spectrum 18 reconstructed using a spectrometer according to the prior art. This spectrum was reconstructed from 10 measured values ​​using a reconstruction function. These 10 measured values ​​were obtained by taking individual measurements over 10 filters (not shown), wherein the filters have transmission functions defined according to the prior art, as explained above with reference to Fig. 3. The filters each comprised 32 transmission layers (not shown). The spectrum 17 to be measured was again the spectrum explained with reference to Fig. 5, so that the reconstructed spectra 16, 18 shown in Fig. 5 and Fig. 6 enable a comparison between the invention and the prior art. The wavelength X in pm is plotted on the abscissa axis of the diagram. The relative intensity I is plotted on the ordinate axis.The spectrum 18 reconstructed with the prior-art spectrometer is shown with a thicker line and shows noticeable differences from the measured spectrum 17. Artifacts are visible at several wavelengths. To obtain a similarly accurately reconstructed spectrum as in Fig. 5, a prior-art spectrometer with at least 40 filters (not shown) would be required.

[0062] Fig. 7 shows a diagram of a further spectrum 19 reconstructed using a preferred embodiment of the spectrometer according to the invention (not shown). The reconstruction was carried out in the same way as was explained above with reference to Fig. 5. The spectrum 17 to be measured again had a first spectral line at 0.9 pm with a half-width of 0.9 nm and a second spectral line at 1.1 pm with a half-width of 5 nm. The wavelength X in pm is plotted on the abscissa axis of the diagram. The relative intensity I is plotted on the ordinate axis. The reconstructed spectrum 19 shown is very similar to the measured spectrum 17, so that the graphs essentially run on a line. The reconstructed spectrum 19 shown has no discernible artifacts.

[0063] Fig. 8 shows a diagram of a spectrum 21 reconstructed using a preferred embodiment of the spectrometer according to the invention (not shown) in comparison to a measured spectrum 22, such as that exhibited, for example, by radiation reflected from a polymer (not shown). The wavelength X in gm is plotted on the abscissa axis of the diagram. The relative intensity I is plotted on the ordinate axis. The reconstructed spectrum 21 shown is largely similar to the measured spectrum 22. It has no discernible artifacts.

[0064] Fig. 9 shows a diagram of further spectra 23 reconstructed using a preferred embodiment of the spectrometer according to the invention (not shown) in comparison to a measured spectrum 24, such as that exhibited, for example, by radiation reflected from a polymer (not shown). The wavelength X in gm is plotted on the abscissa axis of the diagram. The relative intensity I is plotted on the ordinate axis. The reconstructed spectra 23 shown are largely similar to the measured spectrum 24.

[0065] Fig. 10 shows a diagram of a spectrum 25 reconstructed using a preferred embodiment of the spectrometer according to the invention in comparison to a measured spectrum 26, such as that which comprises radiation absorbed by a solution (not shown) of a dye and a polymer. The wavelength X in gm is plotted on the abscissa axis of the diagram. The relative intensity I is plotted on the ordinate axis. The reconstructed spectrum 25 shown is largely similar to the measured spectrum 26. It has no discernible artifacts.

[0066] Fig. 11 shows a flow chart illustrating the operation of a preferred embodiment of the spectrometer according to the invention. A start is formed by an unknown spectrum which is measured with the spectrometer. As explained with reference to Fig. 1, a number N of measurements are carried out over N filter areas (not shown) of the spectrometer (not shown), each of the filter areas having a transmission function Ai (X), so that N transmission functions Ax (X) to A N (X). Thus, N output signals Ti to I N which each represent a measured value. The N output signals Ti to I are then processed. N to obtain a reconstructed spectrum s(A) as the target by applying a reconstruction function. The reconstruction function was previously determined by solving a minimization problem.

[0067] List of reference symbols

[0068] 01 Transmission function

[0069] 02 Transmission function

[0070] 03 Transmission function

[0071] 04 Transmission function

[0072] 05

[0073] 06 Transmission function

[0074] 07 Transmission function

[0075] 08

[0076] 09

[0077] 10

[0078] 11 Transmission function according to the state of the art

[0079] 12 Transmission function according to the state of the art

[0080] 13 Di f ference AT

[0081] 14 Di f ference AT according to the state of the art

[0082] 15

[0083] 16 reconstructed spectrum

[0084] 17 measured spectrum

[0085] 18 spectrum reconstructed according to the state of the art

[0086] 19 reconstructed spectrum

[0087] 20

[0088] 21 reconstructed spectrum

[0089] 22 measured spectrum

[0090] 23 reconstructed spectrum

[0091] 24 measured spectrum

[0092] 25 reconstructed spectrum

[0093] 26 measured spectrum

Claims

Patent claims 1. A spectrometer for the spectral measurement of a sample; comprising a plurality of filter regions formed on one or more optical filters and at least one optical sensor for measuring across a spectral measurement range of the spectrometer; wherein the filter regions each have a transmission function (O1, O2, O3, O4, O6, O7) which describes a dependence of a relative transmission of the respective filter region on the wavelength across the spectral measurement range of the spectrometer; wherein an arithmetic mean of a first derivative of the relative transmission with respect to the wavelength across the spectral measurement range for each of the transmission functions (O1, O2, O3, O4, O6, O7) is at most 1 1 / pm; wherein measurements of a spectrum to be measured (17, 22, 24, 26) with the at least one sensor across the individual filter regions each lead to a measured value;wherein the spectrometer is configured to apply a reconstruction function designed to reconstruct the measured spectrum (17, 22, 24, 26) based on the measured values; and wherein the spectrometer is further configured to determine the reconstruction function using at least one reference spectrum and the transmission functions (01, 02, 03, 04, 06, 07).

2. Spectrometer according to claim 1, characterized in that an average relative transmission over the spectral measurement range for the transmission functions (01, 02, 03, 04, 06, 07) is on average at least 0.

5.

3. Spectrometer according to claim 1 or 2, characterized in that a standard deviation of the first derivative of the relative transmission with respect to the wavelength over the spectral measurement range for each of the transmission functions (01, 02, 03, 04, 06, 07) is at most 5.0 1 / pm.

4. Spectrometer according to one of claims 1 to 3, characterized in that it comprises at least one light source for emitting radiation having the reference spectrum.

5. Spectrometer according to one of claims 1 to 4, characterized in that the optical filter areas each have at least one wet-chemically applied transmission layer.

6. Spectrometer according to claim 5, characterized in that the at least one transmission layer is applied by an inkjet printing process.

7. Spectrometer according to claim 5 or 6, characterized in that at least several of the optical filter regions each have two to ten of the transmission layers arranged one above the other.

8. Spectrometer according to claim 7, characterized in that the transmission layers each have a thickness which is between 100 nm and 10 pm.

9. Spectrometer according to one of claims 1 to 8, characterized in that the number of filter areas is between 5 and 30.

10. Spectrometer according to one of claims 1 to 9, characterized in that the filter areas are arranged in a matrix and form a filter matrix, wherein one of the optical sensors is arranged behind one of the optical filter areas, for which the sensors are arranged in a matrix and form a sensor matrix.

11. Spectrometer according to one of claims 1 to 9, characterized in that it has only one sensor which is designed to measure sequentially one after the other across the individual filter areas.

12. Spectrometer according to one of claims 1 to 11, characterized in that an average deviation of the transfer functions of the filter areas due to a non-perpendicular irradiation in a range between a perpendicular irradiation and an irradiation deviating by 10° from the perpendicular irradiation is in each case at most 2%.

13. Spectrometer according to one of claims 1 to 12, characterized in that the determination of the reconstruction function is carried out by a convex optimization or by the application of artificial intelligence.

14. Spectrometer according to one of claims 1 to 13, characterized in that the determination of the reconstruction function takes place in a frequency space in which the transmission functions (01, 02, 03, 04, 06, 07) and the reference spectrum are transformed.

15. Spectrometer according to one of claims 1 to 14, characterized in that the spectral measurement range of the spectrometer extends over at least 400 nm.

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