Optical adapter module and spectrum system

By designing an electro-optic adapter module, the problem of complex probe connection in existing spectral systems is solved, enabling flexible connection and signal processing of multiple probes, improving the system's adaptability and measurement efficiency, and supporting simultaneous analysis of multiple media.

CN121048747APending Publication Date: 2025-12-02ENDRESSHAUSER OPTICAL ANALYSIS INC
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Patent Information

Application Number
CN202510687188.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Priority Date
2024-05-29
Filing Date
2025-05-27
Publication Date
2025-12-02

AI Technical Summary

Technical Problem

Existing spectral systems require specific connector and fiber optic cable combinations when connecting probes and spectrometers, resulting in complex operation, poor flexibility, and difficulty in adapting to the simultaneous measurement needs of multiple probes.

Method used

An electro-optical adapter module was designed, comprising a housing, input and output interfaces, optical and electrical connections, capable of connecting multiple probes simultaneously, and realizing signal distribution and processing through optical selection circuits and optical devices, including optical demultiplexers, optical switches and collimators, to ensure signal transmission and adaptation.

Benefits of technology

It enables flexible connection and signal processing of multiple probes, simplifies the operation process, improves the system's adaptability and measurement efficiency, and supports the simultaneous analysis of various gas and solid mixtures.

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Abstract

The invention relates to an optical adapter module and a spectroscopy system. An electro-optical adapter module (1) is disclosed, comprising: a housing; at least one input interface (2) having a connector on the housing, the input interface (2) being designed to be connected to the probe (30) via a cable; an output interface (3) having a connector on the housing wherein the output interface (3) is designed to be connected to a spectral base module (20); having an in particular bidirectional electrical connection (4) from the input interface (2) to the output interface (3); a first optical connection for an optical input signal (19), in particular a measurement signal, from the input interface (2) to the output interface (3); and a second optical connection from the output interface (3) to the input interface (2) for an optical output signal (12), in particular an excitation signal. The invention also discloses a spectrum system.
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Description

Technical Field

[0001] This invention relates to an optical adapter module and a spectral system including the thereof. Background Technology

[0002] The general-purpose spectroscopic system is sold by the applicant, for example, under the name "Rxn5 Analyzer". This is a laser-based Raman analyzer designed for the petrochemical and other process markets.

[0003] Spectroscopic systems are used to determine the composition of gas mixtures, liquids, or solids without requiring valves, furnaces, columns, or carrier gases. The system consists of an actual spectrometer with a light source (typically a laser), diffractive or dispersive elements, and a detector. The spectrometer is connected to the process, i.e., the medium to be measured, via one or more probes connected to it via optical fibers. Instead of diffractive or dispersive elements, interferometers can be used. For example, up to four independent probes can be connected, operating simultaneously. Sequential or mixed use of two variants is also known.

[0004] It can measure gas mixtures with multiple components. Typical gases that can be analyzed are: H2, N2, O2, CO, CO2, H2S, CH4, C2H4, C2H6, Cl2, F2, HF, BF3, O2, and NH3. Mixtures of solids or liquids are also possible.

[0005] Different probes are used for each gas or medium. When operating a spectrometer using probes, the correct combination of connectors and optical fibers must be selected, as only probes with appropriate connector and fiber optic combinations can be connected. Summary of the Invention

[0006] This invention is based on the purpose of providing a universal spectral system.

[0007] The object of the present invention is achieved by an electro-optic adapter module comprising: a housing; at least one input interface having a connector on the housing, wherein the input interface is designed to be connected to a probe via a cable; an output interface having a connector on the housing, wherein the output interface is designed to be connected to a spectral base module; a particularly bidirectional electrical connection from the input interface to the output interface; a first optical connection from the input interface to the output interface for optical input signals, particularly measurement signals; and a second optical connection from the output interface to the input interface for optical output signals, particularly excitation signals.

[0008] One embodiment provides an electro-optical adapter module comprising: a first input interface having a connector on a housing, wherein the input interface is configured to be connected to a first probe via a first cable; at least one second input interface having a connector on a housing, wherein the input interface is configured to be connected to a second probe via a second cable; wherein a first optical connection transmits input signals from the first and second input interfaces to an output interface; and an optical selection circuit, particularly an optical demultiplexer or optical switch, which in the second optical connection distributes output signals from the output interface to the input interface.

[0009] When "the" input interface is referred to below, it always means an embodiment having more than one input interface—for example, as described in an embodiment having a first input interface and a second input interface. Embodiments with more input interfaces (e.g., four) are possible.

[0010] One embodiment provides that the first optical connection includes a mirror, an optical switch, an optical splitter, and / or a beam splitter.

[0011] One embodiment provides that the connectors for the input interface and the connectors for the output interface are designed differently.

[0012] One embodiment provides that the transmission optical fiber connects the input interface to the output interface and guides the optical input signal and the optical output signal.

[0013] One embodiment provides that the electro-optical adapter module includes an optical device for adapting the numerical aperture between the input interface and the output interface, particularly reducing the numerical aperture, having a collimator and at least one converging element, wherein, in particular, a filter is arranged between the collimator and the converging element.

[0014] One embodiment provides that the transmission optical fiber connects the input interface to the optical device.

[0015] One embodiment provides that the electro-optic adapter module includes a third optical connection for optical calibration signals from the input interface to the output interface.

[0016] One embodiment provides that the electro-optic adapter module includes a calibration unit for generating calibration signals.

[0017] One embodiment provides that the electro-optic adapter module includes a data processing unit for implementing signal processing, measurement acquisition, data processing, and / or probe control.

[0018] This objective is further achieved by a spectral system comprising: an electro-optic adapter module as described above; and a spectral base module comprising: a housing; an input interface having a connector on the housing, wherein the input interface is designed to connect to the output interface of the electro-optic adapter module; a spectrometer and a detector having at least one dispersive or diffractive element or interferometer, wherein the spectrometer is optically connected to the input interface and an optical input signal is directed to the spectrometer; a laser for emitting an optical output signal, wherein the laser is optically connected to the input interface; and a data processing unit for controlling the laser and the detector.

[0019] One embodiment provides that the spectrometer fiber connects the input interface to the spectrometer, wherein the spectrometer fiber is designed such that the intensity distribution of light guided through and emitted from the spectrometer fiber defines a gap.

[0020] One embodiment provides that the spectrometer fiber optic includes a plurality of fibers, wherein these fibers are arranged substantially in a circular manner on the side of the input interface, and wherein the fibers are arranged linearly on the side of the spectrometer.

[0021] One embodiment provides that the spectral system includes at least one probe having a cable, wherein the probe is connected via the cable to the input interface of an electro-optical adapter module.

[0022] One embodiment provides a spectral system including at least a first probe having a first cable, wherein the first probe is connected via the first cable to a first input interface of an electro-optical adapter module; and at least a second probe having a second cable, wherein the second probe is connected via the second cable to a second input interface of the electro-optical adapter module.

[0023] One embodiment provides that the base unit includes a calibration unit and is connected to a spectrometer. Attached Figure Description

[0024] Please refer to the following diagram for a more detailed explanation.

[0025] Figure 1a / b schematically illustrates the structure of a spectral system or probe.

[0026] Figure 2a / b shows the spectrometer fiber in various configurations.

[0027] Figure 3a -c shows a circuit diagram of a spectral system with one or four probes.

[0028] Figure 4 A spectral system with a probe is shown in an embodiment.

[0029] Figure 5 A spectral system with a probe is shown in an embodiment.

[0030] Figure 6 A spectral system with four probes is shown in an embodiment.

[0031] Figure 7 A spectral system with four probes is shown in an embodiment.

[0032] Figure 8 A base module with an optical adapter module is shown.

[0033] Figure 9a -c shows the optical adapter module in a different view.

[0034] Figure 10a / b shows an optical adapter module in one embodiment from a different view.

[0035] In the accompanying drawings, the same features are labeled with the same reference numerals. Detailed Implementation

[0036] The spectral system 100 includes an electro-optical adapter module 1 and a base module 20. It also includes one or more probes 30 and 31, 32, 33. The base module 20 specifically includes a laser 11 and a data processing unit 18.

[0037] Figure 1a A spectroscopic system 100 is illustrated by way of example. System 100 includes a light source 11 configured and arranged to illuminate a probe 30 with light 12. Thus, the laser 11 sends an “optical output signal” to the probe 30, which in the sense of this document is an “excitation signal” or “control light.” The probe 30 is in contact with a medium. In one embodiment, the probe 30 is not in contact with the medium, but instead sends or receives light from the medium. The light reaching the probe varies depending on the properties of the medium—for example, depending on the concentration of the substance in the medium. The modified light, referred to herein as the “optical input signal,” “measurement signal,” or “measurement light,” is collected by a collector 13 and fed to a waveguide, spectrometer fiber 17. In at least one embodiment, the collector may consist of one or more optical lenses.

[0038] Spectrometer fiber 17 images the collected measurement light onto a slit-shaped exit, which is collected and collimated by spectrometer 15 (see also...). Figures 4-7 ).like Figure 1aAs shown, the spectrometer 15 may include two lenses—a first lens for diverging the light emitted from the spectrometer fiber 17, and a second lens for collimating the diverging light and transmitting it to the dispersive or diffractive element 14. The dispersive or diffractive element 14 may be, for example, a grating, a prism, etc. The dispersive or diffractive element 14 separates the measurement light 19 from the probe 30 into its spectral components, allowing the light to be read out by the detector 16, which is typically designed as a two-dimensional array, such as a CCD array. A data processing unit 18 is connected to the laser 11 and the detector 16 (only the connection to the detector 16 is shown).

[0039] As an alternative to the embodiment with diffraction or dispersive elements 14, an interferometer with smaller structural variations can be used. The spectrometer includes an arrangement of parabolic and plane mirrors in the beam path, which first expands the radiation from the source (here, e.g., a blackbody), couples it between the two parallel mirrors, couples it out, and then focuses it again. The interferometer includes, for example, a beam splitter that forms two beams from the beam from the radiation source and recombines them, and a mirror drive that continuously changes the distance between the interferometer mirrors. If necessary, a HeNe laser is used as a reference radiation source to determine the position of the movable interferometer mirrors.

[0040] In at least one embodiment, the spectrometer 15 may be, for example, Raman type, and is configured to perform Raman spectroscopy analysis.

[0041] Figure 1b An embodiment of probe 30 is shown. The probe may include one or more lenses, mirrors, and possibly dichroic mirrors, filters, and optical fibers. Light is guided within the probe and directed onto the sample. An input signal, such as a Raman signal, is generated here. The input signal is captured and relayed via optics within the sample.

[0042] We will now discuss the spectrometer fiber 17. Figure 2a An embodiment of a spectrometer fiber 17 for transmitting light, having an input end 17.1 and an output end 17.2, is shown. The spectrometer fiber 17 can be designed as a single fiber or a bundle of fibers. As an example, the fiber includes seven optical guides, also referred to herein as filaments 17.3. The filaments 17.3 are arranged in a substantially circular manner at the input end 17.1. In this way, light from the input interface 21 (see below) of the base module 20 can be effectively captured without significant loss. The filaments 17.3 at the output end 17.2 are arranged such that the intensity distribution of the light transmitted and emitted by the fiber 17 defines a slit. Therefore, the output end 17.2 of the filaments 17.3 is generally arranged linearly. In this way, the filaments 17.3 image the intensity distribution of light at the input end 17.1, which is more or less cylindrically symmetrical with the substantially slit-shaped intensity distribution at the output end 17.2.

[0043] Each filament 17 includes a core made of, for example, polymer, glass, crystal, or air, and a reflective coating covering the side surfaces of the core. In this way, the filament 17.3 transmits light and retains it within the optical fiber 17. The number of filaments 17.3 is not limited to seven. The filaments 17.3 can be held together and / or positioned by one or more frames. In one embodiment, as... Figure 2b As shown, the filament 17.3 can be embedded in the forming element 17.4, wherein the forming element 17.4 supports and defines the path of the filament 17.3 and the cross-section of the optical fiber 17 from the input end 17.1 to the output end 17.2.

[0044] In one embodiment, a slotted structure is used after output 17.2.

[0045] As an alternative to the embodiment with linear filaments described above, a classic groove can be used.

[0046] Figure 3a -c shows a circuit diagram of a spectral system 100 with one or four probes. Figure 3a A setup with one probe is shown. Figure 3b , 3c A setup with several probes is shown.

[0047] As described above, the spectral system 100 includes an electro-optical adapter module 1 and a spectral base module 20. The base module 20 includes a housing with an input interface 21 having a connector, wherein the input interface 21 is designed to connect to the output interface 3 of the optical adapter module 1. The input interface 21 and the output interface 3, or the corresponding connector, are designed to be complementary to each other. The base module 20 includes a spectrometer 15 and a detector 16 having at least one dispersive or diffractive element 14 (or interferometer; see above), wherein the spectrometer 15 is optically connected to the input interface 21, and an optical input signal 19 (i.e., a measurement signal from the probe 30) is directed to the spectrometer 15 and converted into an electrical signal in the detector 16, which is further processed by the data processing unit 18. The base module 20 also includes a laser 11 for emitting an optical output signal 12 (i.e., control light), wherein the laser 11 is optically connected to the input interface 21, for example, via an optical fiber.

[0048] The electro-optical adapter module 1 includes a housing with at least one input interface 2, the input interface 2 having a connector on the housing, wherein the input interface 2 is designed to be connected to probe 30 via a cable. Module 1 may, for example, include four input interfaces 2 for connecting up to four probes 30, 31, 32, 33. Adapter module 1 includes an output interface 3 with a connector, wherein the output interface 3 is designed to be connected to the spectral base module 20 (see above). Adapter module 1 includes a unidirectional electrical connection from probe 30 to base module 20, but preferably includes a bidirectional electrical connection 4 from input interface 2 to output interface 3. Thus, electrical signals are forwarded from the data processing unit 18 in base module 20 to probes 30, 31, 32, 33. Module 1 transmits optical input signals 19 from input interface 2 to output interface 3 via a first optical connection, i.e., in particular, measurement signals from probes 30, 31, 32, 33 to base unit 20, and finally to detector 16. In the case of multiple probes, at least two possibilities exist. Any optical fiber is combined into an optical fiber bundle (see...). Figure 6 Alternatively, the input signals can be expanded and collimated; then they can be "superimposed" and then refocused. Multiplexer 27 or demultiplexer 5 can also be used for this purpose; see below.

[0049] The adapter module 1 transmits the optical output signal 12, in particular the excitation signal (control light), from the laser 11 to the probes 30, 31, 32, and 33 via a second optical connection from the output interface 3 to the input interface 2.

[0050] Compared to a system with only one probe 30 ( Figure 3a In contrast, the system with four probes 30, 31, 32, and 33 has an additional demultiplexer 5 or switch for the control light from laser 11, i.e., the control light is sequentially distributed from one source to the four probes; see also Figure 3b Therefore, the demultiplexer 5 is a 1 to n distributor, where n is the number of probes. In one embodiment, the receiver is not multiplexed, meaning that any ambient light or sunlight is also measured. In one embodiment, each probe is provided with a laser. Figure 3c Multiplexer 27 is shown, which is an n-to-1 converter for the input signals of probes 30, 31, 32, and 33. Demultiplexer 5 and multiplexer 27 can also be used.

[0051] In one embodiment, system 100 includes both a demultiplexer 5 and a multiplexer 27. Each embodiment has its advantages and disadvantages. Figure 3b In the illustrated embodiment, light from all four probes arrives at the detector simultaneously, even if no laser light is present at three of the probes (ambient light can still be measured). Figure 3b In the illustrated embodiment, this does not occur, but the laser must still be distributed. Figure 3c The embodiments in the text are more complex and require more space.

[0052] exist Figure 3a In this configuration, base module 20 includes a calibration unit 22 that sends a calibration signal to spectrometer 15. This module can also be located externally, in which case the calibration signal 23 is routed via adapter module 1; see below. Adapter module 1 can also include a calibration unit. The calibration unit ensures that errors, for example, caused by temperature differences in the optical system, are detected and corrected. The calibration unit is, for example, a broadband white light source (e.g., for intensity or y-axis calibration), which may have an inert gas lamp (neon, argon, etc.) with defined peak values ​​for x-axis calibration, a laser irradiating a diamond, one or more NIST standards, etc.

[0053] The connectors for the input interface 2 and output interface 3 of the adapter module 1 can be designed differently; examples are FC / PC connectors, LC connectors, or MTP connectors.

[0054] Figure 4 An embodiment with probe 30 is shown. Adapter module 1 has a transmission fiber 9 that connects the input interface 2 of adapter 1 to its output interface 3 and leads out via optical input signal 19 and optical output signal 12. Base module 20 is connected to adapter 1 via the input interface 21 of the base module. Spectrometer fiber 17 is then arranged on the input interface 21. To filter control light 12 that does not directly reach the detector, base module 20 includes a filter 25.

[0055] exist Figure 5 In this embodiment, the electro-optical adapter 1 includes an optical device 6. The optical device 6 is used to reduce the numerical aperture of a device having one or more collimators 24 and at least one converging element 26, wherein a filter system 25 having one or more filters is arranged between the collimators 24 and the converging element 26. Therefore, the filter system 25 is repositioned to the adapter 1, thereby allowing a smaller filter to be used for the same purpose. Figure 3a Optical device 6 is not shown in -c, but it may be used there. In one embodiment, filter system 25 is included in probe 30 but not in base module 20 or adapter module 1.

[0056] As described above, a necessary aspect of the electro-optic adapter 1 is the connection between various probes and various photoconductors and connectors. Therefore, adapter 1 adapts the probes to the spectrometer 15. The components of adapter 1 are designed accordingly; specifically, the collimator 24, filter system 25, and focusing element 26 are designed accordingly. Figure 4 For example, no numerical adjustment is provided.

[0057] Figure 6Showing from Figure 4 The device includes four probes 30, 31, 32, and 33 and an optical device 6, as well as a transmission optical fiber 9 for forwarding input and output signals 12 and 19. Additionally, the optical device 6 can be used, as shown in the figure.

[0058] Figure 7 A system 100 with four probes 30, 31, 32, and 33 is shown. Signals 12 and 19 are forwarded via a mirror 7 and a beam splitter 8. Other embodiments include optical switches and / or optical splitters.

[0059] Electrical signal line 4 is not in Figures 4 to 7 As shown, but as described above, it is necessary and pervasive. In one embodiment, adapter module 1 includes additional electronics, such as a data processing unit, which implements other functions for signal processing, measurement acquisition, or probe control in adapter module 1.

[0060] Figure 8 A base module 20 with an electro-optic adapter module 1 is shown. A laser 11 is not shown. The adapter module 1 is connected to the input interface 21 of the base module 20 via its output interface 3. Also visible is the input interface 2 of the adapter module 1 (here, designed as a possible connection probe).

[0061] Figure 9a An electro-optical adapter module 1 with an input interface 2 is shown, which has a connector on the housing, through which the electro-optical adapter module 1 can be connected to a probe 30. Figure 9b Shown in a rotated view. Output interface 3 is visible and designed for various connections. The first visible element is electrical connection 4. The illustrated embodiment has two electrical connections 4. The connection between excitation signal 12 and measurement signal 19 is visible. In this embodiment, adapter module 1 also includes a line 23 for calibration signals. Figure 9c A cross-section is shown.

[0062] Figure 10a An electro-optical adapter module 1 with four input interfaces 2 is shown, each with a connector on the housing. This means that up to four probes can be operated. Figure 10b It is shown from the other side.

[0063] List of reference numerals in the attached figures

[0064] 1. Electro-optical adapter module 17.1 Input Terminal 17.2 Output Terminal 2.1 output interface 17.3 filaments 3.1 output interface 17.4 Molded Components 4 Electrical Connections 18 Data Processing Units 5. Demultiplexer 19 Measurement Signal / Measurement Light 6. Optical devices 20 base modules 7. Reflector 21 20 input interface 8 beam splitters 22 Calibration Units 9. Transmission fiber optic cable 23 Calibration Signal 11 Lasers 24 Collimator 12 Excitation signal / control light 25 Filter System 26 Converging Components 13 Collectors 27 Multiplexer 14 Dispersion or diffraction elements 30 probes 31 probes 15. Spectrometer 32 probes 16 detectors 33 probes 17. Spectrometer Fiber Optic 100 Spectral System

Claims

1. An electro-optical adapter module (1), comprising: - Casing; - At least one input interface (2) having a connector on the housing, wherein the input interface (2) is designed to be connected to the probe (30) via a cable. - An output interface (3) with a connector on the housing, wherein the output interface (3) is designed to connect to the spectral base module (20). - It has an electrical connection (4) from the input interface (2) to the output interface (3), particularly a bidirectional electrical connection; - A first optical connection from the input interface (2) to the output interface (3) for optical input signals (19), particularly measurement signals; and - A second optical connection from the output interface (3) to the input interface (2) for optical output signals (12), particularly excitation signals.

2. The electro-optical adapter module (1) according to claim 1, comprising: - A first input interface (2) having a connector on the housing, wherein the input interface (2) is designed to be connected to a first probe (30) via a first cable. - At least one second input interface (2) having a connector on the housing, wherein the input interface (2) is designed to be connected to a second probe (31, 32, 33) via a second cable. - Wherein, the first optical connection transmits the input signal (19) from the first input interface (2) and the second input interface (2) to the output interface (3). - Optical selection circuit (5), particularly optical demultiplexer or optical switch, which distributes the output signal (12) from the output interface (3) to the input interface (2) in the second optical connection.

3. The electro-optical adapter module (1) according to claim 2. in, The first optical connection includes a mirror (7), an optical switch, an optical splitter and / or a beam splitter (8).

4. The electro-optical adapter module (1) according to any one of the preceding claims. in, The connectors of the input interface (2) and the output interface (3) are designed differently.

5. The electro-optical adapter module (1) according to any one of the preceding claims. in, The transmission fiber (9) connects the input interface (2) to the output interface (3) and transmits the optical input signal (19) and the optical output signal (12).

6. The electro-optical adapter module (1) according to any one of the preceding claims, comprising, between the input interface (2) and the output interface (3): - Optical device (6), which is used to adapt the numerical aperture to the collimator (24) and at least one converging element (26), particularly to reduce the numerical aperture, wherein, in particular, a filter (25) is arranged between the collimator (24) and the converging element (26).

7. The electro-optical adapter module (1) according to the preceding claim. in, The transmission fiber (9) connects the input interface (2) to the optical device (6).

8. The electro-optical adapter module (1) according to any one of the preceding claims, comprising: - A third optical connection from the input interface (2) to the output interface (3) for the optical calibration signal (23).

9. The electro-optical adapter module (1) according to the preceding claim, comprising: - Calibration unit (23) used to generate the calibration signal.

10. The electro-optical adapter module (1) according to any one of the preceding claims, comprising: - A data processing unit for implementing signal processing, measurement acquisition, data processing and / or control of probe (30).

11. A spectroscopic system (100), comprising - The electro-optical adapter module (1) according to any one of the preceding claims; and - Spectral base module (20), the spectral base module (20) includes ▪ Shell; ▪ An input interface (21) having a connector on the housing, wherein, The input interface (21) is designed to be connected to the output interface (3) of the electro-optical adapter module (1). ▪ A spectrometer (15) having at least one dispersive or diffractive element (14) or interferometer and a detector (16), wherein the spectrometer (15) is optically connected to the input interface (21) and the optical input signal (19) is transmitted to the spectrometer (15). ▪ A laser (11) for emitting the optical output signal (12), wherein the laser (11) is optically connected to the input interface (21); and ▪ Data processing unit (18) for controlling the laser (11) and the detector (16).

12. The spectral system (100) according to the preceding claim. in, The spectrometer fiber (17) connects the input interface (21) to the spectrometer (15), wherein the spectrometer fiber (17) is designed such that the intensity distribution of light guided through and emitted from the spectrometer fiber (17) defines a gap.

13. The spectral system (100) according to the preceding claim. in, The spectrometer fiber (17) includes a plurality of fibers, wherein the fibers are arranged substantially in a circular manner on the side of the input interface (21), and wherein the fibers are arranged linearly on the side of the spectrometer (15).

14. The spectroscopic system (100) according to any one of claims 11-13, comprising - At least one probe (30) having a cable, wherein, The probe (30) is connected to the input interface (2) of the electro-optic adapter module (1) via the cable.

15. The spectroscopic system (100) according to any one of claims 11-13, comprising - At least one first probe (30) having a first cable, wherein, The first probe (30) is connected to the first input interface (2) of the electro-optic adapter module (1) via the first cable. as well as - At least one second probe (31, 32, 33) having a second cable, wherein the second probe (31, 32, 33) is connected to the second input interface (2) of the electro-optic adapter module (1) via the second cable.

16. The spectral system (100) according to any one of claims 11-15. in, The base module (20) includes a calibration unit (22) and is connected to the spectrometer (15).