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Abstract
This contribution presents the design and implementation of a compact and robust Echelle-inspired cross-grating spectrometer which is arranged as a double pass setup. This allows use of the employed refractive elements for collimation of the incoming light and, after diffraction at the reflective crossed diffraction grating, for imaging the diffracted light onto the detector. The crossed diffraction grating combines the two dispersive functionalities of a classical Echelle spectrometer in a single element and is therefore formed by a superposition of two blazed linear gratings which are oriented perpendicularly. The refractive elements and the plane grating are arranged in a rigid objective group which is beneficial in terms of stability and robustness. The experimental tests prove that the designed resolving power of more than 300 is achieved for the addressed spectrum ranging from 400 nm to 1100 nm by using an entrance pinhole diameter of 105 µm. The utilization of a single mode fiber increases the resolving power to more than 1000, but leads to longer acquisition times.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Spectroscopy is a huge and growing market in the field of optics. Beside established application fields in research and industrial testing laboratories, new field applications arise like atmospheric monitoring [1], plastic waste sorting [2] or agriculture [3–5]. These evolving applications are associated with new or increasing requirements, which have to be satisfied by the spectroscopic device. In particular, compact and robust spectrometers are demanded which are able to acquire a broad spectrum with high resolution. Unfortunately, typically employed compact imaging spectrometers, which are based on a concave grating mount, suffer from the inevitable trade-off between large spectral range and high spectral resolution [6–8]. Hence, they have to be optimized regarding specific demands and are therefore inadequate for highly demanding applications. In contrast, classical Echelle spectrometers are able to simultaneously acquire the demanded wide spectrum with high resolution [9–10]. Here, the light sequentially passes two dispersive elements. The first element, the Echelle-grating, is a diffraction grating which is used in high diffraction orders creating highly resolved, but overlapping partial spectra. The diffracted light propagates to a second element, the so-called cross disperser, which is perpendicularly oriented to the Echelle grating and separates the overlapping spectra. Finally, the light is imaged onto a two-dimensional array detector. Echelle spectrometers exhibit very high performances and are therefore used in numerous demanding applications like chemistry [11–15], astronomical spectroscopy [16–19] or laser-induced breakdown spectroscopy [20–23]. Unfortunately, Echelle spectrometers are vulnerable to harsh environmental conditions and require large dimensions [22,24]. Therefore, they are inadequate for most field applications.
In order to overcome current limitations, different improvements of existing spectrometer concepts were proposed. One line of development focuses on the optimization of imaging quality, for example by employing divergent grating illumination [25] or additional cylindrical elements [26–27] to correct astigmatism. Unfortunately, most of these attempts require additional components which increases system size. In contrast, Fu et al. [28] replaced the focusing mirror of an Echelle spectrometer by a concave cross dispersion grating and thus, achieved a more compact system with good imaging quality. However, the size reduction of their proposed spectrometer is limited as it still requires a collimation mirror and two gratings. A different course of development concentrates on Echelle-inspired compact cross-grating spectrometers [29–31], which are intended to bridge the gap between classical Echelle spectrometers and established compact spectrometers. The basic idea is to combine the two dispersive functionalities of a classical Echelle spectrometer in a single element – the cross-grating. Hence, this approach aims at reducing the size of an Echelle spectrometer while keeping the optical performance high. Recent work reported on a folded Czerny-Turner configuration which detects the spectral range from 330 nm up to 1100 nm with a resolving power $R = {\lambda / {\Delta \lambda }}$ better than 500 [31]. The optical design has a compact size of 110 mm x 110 mm x 30 mm, but suffers from a lack of robustness and is therefore not applicable in harsh situations.
This contribution presents a completely new system approach of a cross-grating spectrometer, which pays special attention on robustness and additionally, deals with further challenges of the cross-grating approach. Therefore, a double-pass configuration is implemented by employing two groups of refractive elements which form a rigid objective group. Light coming from the entrance fiber is first collimated, then diffracted at the reflective cross-grating mounted at the backside of the objective and finally focused onto a 2D detector. This approach is not only beneficial in terms of robustness and stability but also allows to correct aberrations like astigmatism in a sufficient manner. This is, in general, of particular importance for cross-grating systems as the grating diffracts the light with moderate to large diffraction angles in two directions. The cross-grating itself is a superposition of two blazed gratings with very different profile heights. Hence, the fabrication of the cross-grating is very challenging. The fabrication process, which is used for this contribution, comprises three steps. First, direct writing photolithography is used to create the grating structure in photoresist. In a second step, the grating structure is copied into OrmoComp by UV imprinting. Finally, an aluminum coating is applied to provide a broadband reflectivity for the whole addressed spectral range. The spectrometer is designed to work with the 4th to 12th main diffraction orders to simultaneously acquire the complete spectral range from 400 to 1100 nm. Sufficient light is fed into the spectrometer by a 105 µm fiber which allows a resolving power of more than 300 for the whole spectrum. A smaller fiber core diameter of approx. 5 µm allows for an even higher resolving power of more than 1000 for the whole spectrum at the expense of detectable light.
2. Concept and optical design
The proposed spectrometer is designed as a double-pass setup made of two lens combinations and a plane reflective cross-grating, which covers a spectral range from 400 nm to 1100 nm. Hereby, the upper limit correlates to the spectral sensitivity of the silicon detector array while the lower limit is caused by the choice of glasses for the refractive elements. In particular, most high index glasses, which are beneficial for aberration correction, show a low transmittance below 400 nm. The specified resolving power of the spectrometer is better than 300 for the full spectrum. Figure 1 shows the optical design of the system (Figs. 1(a) and (b): cross section in two perpendicular directions, Fig. 1(c): 3D-model). Furthermore, Fig. 1(a) contains surface numbers corresponding to the lens data in Table 1. The key parameters of the system are listed in Table 2. The commercial optical design software Zemax OpticStudio [32] was used to model and optimize the system. The implementation of the cross-grating was realized using a user-defined surface which calculates the two-dimensional grating equation corresponding to [33].
Fig. 1. Optical design shown as (a) y-z cross section, (b) x-z cross section, and (c) shaded model (3D-model). The optical surfaces, which are numbered corresponding to the lens data (cf. Table 1), are depicted in (a). The inset in (a) schematically shows the position and the orientation of the grating.
Table 1. Lens parameters of the double-pass spectrometer
Table 2. System key parameters of the double-pass spectrometer
The light enters the spectrometer by a fiber (surface 0) with a core diameter of 105 µm which is used as the entrance pinhole. The diverging beam bundle with a numerical aperture (NA) of 0.1 is collimated by two lens groups and hits the reflective cross-grating (surface 8). Main and cross dispersion grating are both designed with a period of 8 µm. They are used in the 4th to 12th diffraction order (main grating) and in the 1st order (cross dispersion grating). The cross-grating is fixed on a wedge (surface 6) at the backside of the second lens group to introduce a tilt about both, the local x-axis (-12°) and y-axis (-3°), respectively. The diffracted light again passes the two lens groups and is focused onto a 2D detector (surface 9). We employed a monochrome CCD camera (Allied Vision GE2040 [34]) as the detector array. The different main diffraction orders form separated lines on the detector. Each line corresponds to a specific part of the full spectrum, called a partial spectrum, which can be analyzed.
In a first step, basic relations of the system are described. The linear dispersion of the cross-grating depends on the dispersion in both diffraction directions, but it is mainly determined by the main grating which is working in high diffraction orders. By assuming the main grating in classical mount at an angle of incidence of zero, the linear dispersion can be approximated using Eq. (1) [9] with the focal length f, diffraction order m, grating period p and diffraction angle β.
We aimed on a focal length of approx. 76 mm and a resolving power of 300 which corresponds to Δλ=1.33 nm at a wavelength of 400 nm. As the light is diffracted by the main grating in the 12th diffraction order, one can observe a separation of approx. 190 µm on the detector. This shows that the linear dispersion of the grating is large enough to separate the fiber core images which are created with an image scale of -1. The cross dispersion is primarily used to separate the overlapping high diffraction orders. Hence, in cross-dispersion direction it is mainly important that the imaged diffraction orders fit properly on the detector. Therefore, the linear dispersion (Eq. (1)) can be used to approximate the extent of the full spectrum on the detector which gives ∼7 mm for the chosen parameters. The grating itself acts as the aperture stop of the system. Therefore, the grating size is important to determine the NA of the system. The diameter d of the full beam on the grating is $d \approx 2 \cdot NA \cdot f^{\prime}$. For the chosen parameters the beam diameter is 15.2 mm. This is smaller than the chosen grating size of 20 mm x 20 mm which is suitable for fabrication and mounting. The last important basic system parameter is the wedge angle. The wedge tilts the beam path in order to create a symmetry regarding the optical axis between incident ray and diffracted ray. Equation (2) describes the necessary relation between the incidence angle α and the wedge angle γ:After deriving basic system parameters, the following paragraphs discuss the real optical design in detail. The combination of two lens groups with different functionalities is introduced to achieve an appropriate imaging performance on the detector. The first lens group (lens group 1) is inspired by the ‘landscape lens’ known from photography and corrects the system for astigmatism and field curvature. Additionally, the group itself is corrected for axial chromatic aberration, but suffers from spherical aberration. This remaining spherical aberration is corrected by the second lens group (lens group 2). This group is designed as an apochromatic group comprising the high index crown glass N-LAK14 (Schott) and the low index material CaF2, which has an anomalous partial dispersion behavior. This combination corrects axial chromatic aberration for the group itself and spherical aberration for the whole system, which results in reduced coma. As the spectral resolution of the cross-grating spectrometer is limited by chromatic aberration, the proper material choice is decisive for this approach. The plane backside of lens group 2 provides the option of attaching a wedge which carries the cross-grating and introduces the tilt. The tilt of the cross-grating and the off-axis-positions of both the entrance pinhole and the detector are necessary to create a symmetry in the system regarding to light traveling forward and light traveling backward, while at the same time orienting the cross-grating in a way that a high diffraction efficiency can be achieved. This symmetry facilitates to correct lateral chromatic aberration and coma for the whole system and results in reduced aberrations for the central wavelength in the central diffraction order. Light of other wavelengths passes the system on asymmetric beam paths, which results in slightly increased aberrations. The lens data including radii, thicknesses and glasses of the proposed system are listed in Table 1. The diameters of lens group 1 and 2 measure 50 mm and 40 mm, respectively. The full length of the system is 150 mm.
Figure 2 shows the simulated spot diagram on the detector for different wavelengths in different main diffraction orders of the 1st cross dispersion order. Each main diffraction order is represented by 5 spots corresponding to 5 wavelengths, which are equidistantly distributed over the wavelength range of each partial spectrum. As the spot sizes are small compared to the detector size each spot is represented by a single symbol. A dotted line connecting the spots of one specific main diffraction order visualizes the position of the whole main diffraction order on the detector. The lowest main diffraction order (4th) comprises the longest wavelengths. With increasing diffraction order, the spectral bandwidths of the corresponding partial spectra are decreasing and are shifted to smaller wavelengths.
Fig. 2. Simulated spots for different wavelengths and main diffraction orders on the detector, where the spots are colored corresponding to the diffraction order. The position of each diffraction order is depicted by a dotted line. Each order corresponds to a specific design wavelength range which is denoted on the right.
To determine the imaging quality of the spectrometer the RMS (root mean square) spot radii for specific wavelengths in the different diffraction orders were analyzed. RMS spot radii in the range between 11 µm and 22 µm were obtained for the optimized system. The larger RMS values are observed at the edges of the detector as a consequence of increasing aberrations. The RMS spot radii for the center wavelengths of all diffraction orders are below 16.6 µm. The achieved spot sizes are adequate, because the fiber core diameter of 105 µm, which is imaged with an image scale of about -1, is approx. 2-5 times larger than the RMS spot diameter of the system. Hence, the fiber core, which acts as the entrance pinhole for the system, limits the spectral resolution of the system. For this reason, it is not necessary to further optimize the system to reach the diffraction limited spot radii which are in the range of 2.4 µm (400 nm) to 6.7 µm (1100 nm).
In order to increase the spectral resolution, it is possible to reduce the size of the fiber core diameter, but this results in less detectable light. We aimed at a resolving power R higher than 300 for the whole spectral range. This demand is fulfilled with the 105 µm fiber in the designed spectrometer. For a more detailed characterization of the system and to demonstrate the spectral resolution limit of the design, the initial fiber was replaced by a single mode fiber with a core diameter of approximately 5 µm. In particular, the optical aberrations are larger than the fiber size of 5 µm and can be investigated in the experimental demonstration.
Figure 3 shows a simulated detector image of the system which was created using the geometric image analysis tool from OpticStudio. Figure 3(a) exhibits the full detector size of 15 mm x 15 mm. The system is illuminated by a circular fiber with a diameter of 105 µm. For each diffraction order the spot images of three wavelength pairs are simulated. The spot pairs correspond to the central wavelength of each diffraction order and to the edges of the respective partial spectra. The spectral separation between the two points of each spot pair is chosen to match a resolution better than 300 in each case. Figure 3(a) shows that the spots of each pair can be separated proving that the demanded resolving power of 300 is achieved. Additionally, spot pairs corresponding to the wavelengths 589.0 nm and 589.6 nm (sodium D-line) are simulated. This wavelength pair is imaged onto the detector in the 8th and 9th diffraction order. The spot pair of the 8th order is marked by the upper red rectangle in Fig. 3(a). Figures 3(b),(c) show a detailed view on this spot pair for different fiber core diameters. For a large fiber diameter (105 µm) the resulting spot distributions are broad, overlap significantly and are not adequately resolved (Fig. 3(b)). In contrast, for a small fiber diameter of 5 µm (Fig. 3(c)), well separated spots can be clearly distinguished, indicating a resolution smaller than 0.6 nm.
Fig. 3. Simulated detector image with pairs of spots for different wavelengths and diffraction orders. (a) Full detector image with a size of 15 mm x 15 mm. The wavelength separation between two spots of a spot pair corresponds to a resolving power of 300 or higher. The fiber diameter is 105 µm. It can be seen that all spots in all diffraction orders are well resolved except of the red marked spot pairs. These red marked spots correspond to the wavelengths 589 nm and 589.6 nm. (b), (c) Detailed view on the spot pair 589 nm/589.6 nm in the 8th diffraction order for different fiber core diameters. The spots cannot be resolved for the large fiber diameter of 105 µm (b), but are resolvable for a 5 µm (c) fiber.
Finally, a tolerance analysis was conducted to allow a proper fabrication of the spectrometer. Therefore, a user-defined merit function was created which measures the distance between adjacent spot pairs. Thereby, the changing spot positions and RMS spot radii due to fabrication tolerances are considered for the full spectral range at a resolving power of 300. The chosen tolerance values (listed in Table 3, thickness tolerance in Table 1) are typical standard values which can be realized without additional effort. A Monte-Carlo analysis using 1000 systems showed a variation of the spot distance below 5 µm which is significantly smaller than the fiber core diameter of 105 µm. The sensitivity analysis revealed as the worst offenders the grating tilt tolerance, the tolerance of the refractive index of the CaF2 and N-PK51 elements and the surface form tolerance of the grating surface. To conclude the tolerance analysis, the fabrication of the spectrometer is possible with standard tolerances.
Table 3. Tolerances for material properties and surfaces according to ISO 10110
3. Manufacturing of the crossed diffraction grating
The crossed diffraction grating is the key element of the spectrometer system and is formed by two perpendicularly oriented blazed gratings. While the cross dispersion grating is specified for the 1st diffraction order, we use the main grating in the 4th to 12th order. Both gratings are designed with a grating period of 8 µm. This results in very different profile heights for both grating structures. Additionally, it has to be considered, that the reflective grating structure is the last surface in the double-pass setup (cf. inset of Fig. 1(a)). That means that the light passes the grating substrate and the material of the structured layer in both directions (incoming and outgoing). In particular, for the design of the cross-grating height, the refractive index of the structured layer material has to be taken into account. Here, OrmoComp is used which has a refractive index of nD=1.520 [35]. To blaze the gratings for 700 nm, which is the central wavelength of the 7th main dispersion and 1st cross dispersion order, blaze angles of 11.03° (main dispersion) and 1.95° (cross dispersion) are necessary. These used blaze angles are the half angles between the real ray angles of incidence and exitance at the grating surface which are determined using Zemax Optic Studio.
To fabricate the grating, we used a three-step process. First, a grating master is created in photoresist AZ4562 (Merck KGaA) by a highly flexible direct writing photolithography setup [36,37]. Subsequently, the photoresist structure is copied into OrmoComp by UV imprinting using a PDMS stamp on top of a 1.1 mm thick B33 glass substrate. Finally, the grating substrate is covered by a reflective aluminum layer and diced into a squared sample with a size of 20 mm x 20 mm. To prepare a grating of this size, partial fields are stitched together achieving an overlay accuracy below 100 nm [36]. As the stitching orientation is parallel to both linear gratings, unwanted periodicity errors occur which result in disturbing stray light and grating ‘ghosts’ (see section 4 and Fig. 7). The untreated side of the grating substrate is glued onto the wedge so that the reflective surface exhibiting the grating structure is the last surface in the double pass setup (cf. Figure 1).
Figure 4 exhibits the topography of the fabricated cross-grating measured by a white light interferometer. In particular, Fig. 4(a) shows an overview of the grating structure, while Figs. 4(b) and 4(c) display the cross section of the gratings in main and in cross dispersion direction, respectively. For the blaze angles we measured 10.6° (main dispersion) and 1.8° (cross dispersion). From this follows that the fabricated grating slightly deviates from the design requirements. The blaze angle is slightly too low for both dispersion directions which results in a shift of the most efficient wavelengths to shorter wavelengths. The deviation is small and in an acceptable range for the experimental tests.
Fig. 4. Measurement of the fabricated cross-grating with a white light interferometer. (a) Overview. (b) Cross section along main grating. (c) Cross section along the cross dispersion grating. The grating period is 8 µm in both directions. The measured blaze angles are 10.4° and 1.8° for the main dispersion and cross dispersion grating, respectively.
4. Implementation and performance tests
4.1 Mechanical design and implementation
Figure 5 shows a side view of the mechanical design of the lab demonstrator. The spectrometer consists of three modules which are mounted on a standard baseplate. The modules in Fig. 5 are colored to facilitate a better understanding of the setup. The first module is the tiltable and displaceable fiber mount (yellow) which allows for a suitable adjustability and a reproducible replacement of the input fiber. For our experiments we used FC/PC fibers with core diameters of 5 µm or 105 µm respectively and a nominal numerical aperture of 0.1.
Fig. 5. Side-view on the mechanical design of the demonstrator exhibiting the fiber mount (yellow), the objective group (green) and the gimbal mount of the camera (blue). The light coming from the fiber output (bottom right) is imaged by the objective onto the camera (red housing).
The second module is the objective mount comprising the two lens groups and the cross-grating (green). The two lens groups are fixed in the mechanical mount after alignment and do not require any further adjustment. The glass wedge tilts the cross-grating with respect to the optical axis of the lens groups. The front side of the wedge has a plane surface and a cylindrical shape with a diameter of 40 mm and can be easily attached and aligned to the seconds lens group. The cross-grating is mounted on the opposite side of the wedge, where the form changes to a squared shape with a size of 20 mm x 20 mm. The cross-grating is glued to the tilted surface in such a way that the squared edges coincide. To reach the desired angular position of the glass wedge and the cross-grating to the lens groups we attached the wedge to the second lens group with an index matched immersion fluid. Then we turned the wedge to the proper position corresponding to the transmitted diffraction orders and fixed it mechanically to the rest of the objective. The position of the whole objective module is fixed with respect to the fiber input and the CCD camera (red housing), which is mounted in the third module (blue).
The camera was fixed to a gimbal mount which allows tilting about the x- and y-axis. Furthermore, the mount allows the camera to be rotated and displaced with respect to the z-axis. This is necessary to align the camera properly and to create a sharp image of all diffraction orders on the detector. Needless to say, that the distance between fiber mount and CCD camera is large enough to allow all necessary adjustments. As an optimization criterion for the alignment, the spot size on the detector of several spectral lines was used. In particular, a mercury cadmium (HgCd) lamp and laser lines at 405 nm, 532 nm, 635 nm and 1060 nm were used for the alignment.
4.2 Throughput measurement
A key parameter for the functionality of the system is the throughput, which is the ratio of the detected light to the incoming light. This parameter is a good measure for the diffraction efficiency of the mounted cross-grating which dominates the overall efficiency of the system. Furthermore, it includes the transmittance of all optical elements (e.g. lens groups, wedge). In order to measure the throughput, the laser power of the different alignment lasers was measured twice, once at the fiber output and once in the image plane. To suppress the contribution of unwanted diffraction orders, a pinhole was placed in the image plane in front of the power meter. The results of the throughput measurements are shown in Fig. 6. In more detail, each of the diagrams of Fig. 6 shows the measured throughput for a selected cross-dispersion order (2nd, 1st, 0th and –1st) as a function of the main diffraction order.
Fig. 6. Measured throughput of the realized setup for different laser sources and main grating diffraction orders in the 2nd (a), 1st (b), 0th (c) and -1st (d) diffraction order of the crossdispersion grating. A pinhole in front of the power meter is used to suppress unwanted diffraction orders during the measurement.
Since the cross dispersion grating is blazed for the 1st diffraction order and a wavelength of 700 nm (see section 3), we also expect the highest efficiency in this range which is confirmed by the measurements. In particular, the highest throughput was found at 635 nm in the 1st cross dispersion diffraction order (Fig. 6(b)), for all other undesired orders a much lower throughput was measured (Figs. 6(a), (c), (d)). A further insight is obtained by regarding the distribution of light of one wavelength among different main diffraction orders. In particular, for the 1st cross dispersion order which can be used for the spectroscopic measurement, ∼29.5% of the red light is collected in different main grating orders (5th: 3.5%, 6th: 4.2%, 7th: 20.3%, 8th: 1.5%). For wavelengths which differ stronger from the blaze wavelength, a reduced throughput is measured in the 1st cross dispersion order. While for the green light (532 nm) still a high throughput of ∼25% (5th: 1.4%, 6th: 1.4%, 7th: 1.0%, 8th: 15.6%, 9th: 5.9%)) was found, a considerable smaller throughput of ∼8% is measured for blue and infrared light. As expected, the light deviating from the blaze-wavelength is redistributed to other cross diffraction orders. In particular, the blue and green light is measured mainly in the 2nd cross dispersion order (Fig. 6(a)), the infrared light and parts of the blue light are detected in the 0th cross dispersion order. While the 0th cross dispersion order is not applicable, technically the use of the 2nd order for spectroscopic measurements is possible. In this case it must be ensured that the light is properly imaged onto the detector.
4.3 Performance tests
After implementation and alignment of the full spectrometer, different measurements were conducted. In a first step, the continuous spectrum of a halogen lamp is fed to the spectrometer. The source emits light in the range of approx. 370 nm up to 1100 nm. The peak intensity is reached for ∼700 nm and decreases to the edges of the spectrum. The acquired camera image for an acquisition time of 1.5 ms is shown in Fig. 7 and exhibits a complex structure. The acquired image is overexposured to improve the visibility of the diffraction orders, grating ghosts and other stray light. The most important contributions refer to both different cross dispersion orders and different main dispersion orders. In particular, light of the 0th, 1st and 2nd cross dispersion order is captured by the detector. The bright lines in the 1st cross dispersion direction, which corresponds to different main diffraction orders, are labeled with the corresponding order number. In agreement with the throughput measurements it can be observed that the 1st order, which is intended for spectral measurements, is much brighter than the 0th and the 2nd order. The overexposure of the image reveals grating ghosts which appear as darker lines between the bright lines of the 1st cross dispersion grating. These grating ghosts originate from stitching errors during the fabrication process of the cross-grating (see section 3). Fortunately, these ghosts are weak compared to the desired signal and mainly appear on detector pixels between the main orders, which are not used for the calculation of the spectrum. The varying intensity distribution of the different partial spectra originates from the wavelength-dependent throughput of the system, the quantum efficiency of the detector and the characteristic spectrum of the source.
Fig. 7. Acquired detector image of a halogen lamp with an acquisition time of 1.5 ms. The 0th (red), 1st (green) and 2nd (yellow) diffraction orders of the cross dispersion direction can be observed. The main orders in the 1st cross dispersion direction are also labeled.
In a second step, different line spectra of discharge lamps were recorded and analyzed. In particular, the spectral lines are used for the wavelength calibration and an easy estimation of the spectral resolution of the spectrometer. Figure 8 shows a superposition of acquired images of different emission lines of mercury-cadmium (HgCd), sodium (Na) and caesium (Cs) lamps, which were used for these measurements. The 105 µm fiber was applied. In order to obtain a high visibility, different images with exposure times between 200 µs and 2 s are cropped and arranged together in a single negative image. This allows for a superposition of many spectral lines in one image with similar signal heights. The image shows spectral lines in the 5th main diffraction order up to the 12th order. The spectral line with the shortest detectable wavelength is the mercury h-line with a wavelength of 405 nm, which appears in the 11th and 12th order. The Cs lines at 1002/1012 nm are detected in the 5th and 6th order and exhibit the spectral lines with the longest detectable wavelength. Hence, suitable spectral lines are available for the wavelength calibration and for the estimation of the spectral resolution of the spectrometer. For example, the 577/579 nm double line originating from the HgCd source (yellow circle) is clearly resolved which corresponds well to the designed resolving power of 300. In contrast, the well-known sodium D line at 589.0/589.6 nm is not resolvable with the 105 µm fiber as it is predicted by the optical design.
Fig. 8. Superposed image of different emission lines from HgCd, Na and Cs lamps for different acquisition times. The 105 µm fiber was used for these measurements. The green numbers denote the main diffraction order in the 1st cross dispersion direction.
The spectrometer is designed with a rather large fiber core diameter to reach short acquisition times at the expense of a moderate spectral resolution. In order to increase the spectral resolution, the spectral calibration was also conducted with a single mode fiber with an approx. fiber core diameter of 5 µm. This results in longer acquisition times but allows a better characterization of the optical performance of the system. Figure 9 shows the simulated and measured spot images of the system for 5 different spectral lines for both fibers. In particular, the spectral lines at the wavelengths 405 nm, 589/589.6 nm, 672 nm, 852 nm and 1012 nm were chosen since they offer a good sampling over the whole spectral range. It becomes obvious that simulation and measurement are in good agreement. This means that our design approach is appropriate to simulate the system. Furthermore, it shows that the implementation of the system was successfully realized. As expected, the spot shape of the small fiber varies for different wavelengths due to the optical aberrations. In contrast all the 105 µm spots show a clear circular shape because the fiber core diameter dominates over the optical aberrations. Furthermore, the measurement proofs that the 589/589.6 nm spot pair, which corresponds to the sodium D line, can be resolved by the spectrometer with 5 µm fiber.
Fig. 9. Measured and simulated spot images for 5 different spectral lines and fiber diameters of 5 µm and 105 µm. Measurement and simulation are in good agreement.
In order to characterize the performance of the spectrometer in detail, a further analysis based on the captured spectral lines was conducted. The positions of the partial spectra on the detector can be well described by linear functions. Specific spectral lines in each partial spectrum can be used as supporting points to find the correct orientation of each linear function. Thus, it is possible to conduct the wavelength calibration of the spectrometer and to approximate the start and stop wavelength of each partial spectrum on the detector. These calculated start/stop wavelengths correspond to the detector position and do not consider throughput or detector efficiency. There will be, for example, no meaningful measurable signal at the stop wavelength of the 5th diffraction order since the silicon detector is not sensitive at 1255 nm. By analyzing the full width half maximum (FWHM) of chosen spectral lines in each diffraction order, one can further obtain the resolving power ${\lambda / {\Delta \lambda }}$ of the system. Therefore, we used the start wavelength of each partial spectra and divided it by the measured FWHM, which is the median FWHM of important spectral lines with evaluable signal intensity. The measured spectral range, FWHM and the resulting resolving power for all diffraction orders are listed in Table 4 and Table 5 for 105 µm and 5 µm fiber core diameter, respectively. The measurement proves that the desired resolving power of 300 is achieved for all diffraction orders for the 105 µm fiber core diameter. As expected the resolving power improves slightly for larger diffraction orders. An even higher resolving power of more than 1000 for the outer diffraction orders and well above 2000 for the 8th and 9th diffraction order are achieved with the smaller fiber. These central diffraction orders propagate through the system on a nearly symmetric beam path and are therefore imaged with best performance. In contrast, the smaller and larger diffraction orders suffer from increasing optical aberrations which occur for non-symmetric beam paths in the double-pass setup (cf. section 2). Hence, they have a lower resolving power.
Table 4. Measured spectral range, FWHM and resulting resolving power for 105 µm fiber core diameter
Table 5. Measured spectral range, FWHM and resulting resolving power for 5 µm fiber core diameter
4.4 Exemplary measurements
Finally, exemplary measurements are conducted to prove the working principle and to test the evaluation software. Figure 10 depicts measured source spectra of a halogen lamp (Fig. 10(a)) and a HgCd discharge lamp (Fig. 10(b)) which were acquired using the 105 µm fiber. Thereby the complete spectrum (black) is reconstructed by summation of the signals of the partial spectra (colored). The acquisition times are 400 µs and 1200 µs for the halogen lamp and the HgCd lamp, respectively. The halogen spectrum is continuous with a peak intensity at a wavelength of approx. 700 nm and drops towards shorter and longer wavelengths. In contrast the light of the HgCd lamp comprises characteristic spectral lines in the wavelength range from 400 nm to 700 nm. Like it was observed before, both spectra exhibit a wavelength-dependent intensity distribution of the different partial spectra, which is caused by the wavelength-dependent throughput of the system, the quantum efficiency of the detector and the characteristic source spectrum.
Fig. 10. Spectral measurement conducted with 105 µm fiber of (a) halogen lamp with 400 µs acquisition time and (b) HgCd discharge lamp with 1200 µs acquisition time. The complete spectrum (black) is reconstructed by summation of the partial spectra signals (colored).
5. Conclusion
In conclusion, we presented the design and implementation of a new type of an Echelle-inspired double-pass cross-grating spectrometer. The spectrometer consists of several refractive elements, which are used twice to collimate the incoming light first and afterwards, to image the diffracted light onto the detector. The diffracting element is a plane cross-grating consisting of two perpendicularly oriented linear blazed gratings. It diffracts the light in two directions and combines the functionality of the two dispersion directions of a classical Echelle spectrometer in a single element. The proposed spectrometer combining the cross-grating and the double-pass concept is compact, robust and easy to adjust. The experimental tests proved that the optical design model is well suited to simulate the performance of the system. As predicted, the resolving power R of more than 300 for the whole spectral range from 400 nm to 1100 nm is achieved using an entrance fiber core diameter of 105 µm. A reduction of the fiber core diameter down to approx. 5 µm increases the resolving power to more than 1000, but leads to longer acquisition times. The presented double-pass cross-grating spectrometer is able to bridge the gap between classical Echelle spectrometers and established compact spectrometers. Based on the presented results it is possible to tune wavelength range and resolution to specific applications.
Funding
Carl Zeiss Spectroscopy GmbH; European Social Fund (2016 FGR 0031); Bundesministerium für Bildung und Forschung (13FH027IX5); Deutsche Forschungsgemeinschaft (497866273).
Acknowledgments
The authors gratefully thank Marko Stumpf for his valuable help and advice during the fabrication process of the cross-grating.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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