1. INTRODUCTION

Spectroscopy is currently experiencing a significant expansion of its application fields. While in the past the use of spectroscopic instruments was mainly focused on research or industrial testing laboratories, spectrometers have been introduced to industrial process control and to a variety of field applications today. In particular, a diversity of tasks is found in the food industry and in agriculture, including site-specific fertilization, soil analysis, or quality control of harvested crops [1–3]. The broadening of the application fields is associated with an increase of the spectroscopic systems’ requirements. Additionally, it is advantageous for economic aspects to address different applications with the same device. From this follows that future spectroscopic instruments have to fulfill demanding specifications, which sometimes even appear to be contradictory. In particular, an important aspect concerns the simultaneous recording of a broad wavelength range with a high spectral resolution, while additionally a short acquisition time and a compact instrumental concept have to be implemented. Already established spectroscopic systems only meet a limited number of these criteria but generally fail to fulfill the complete set of requirements. For example, widespread imaging spectrometers based on a concave grating mount offer a very compact setup, comprising only an entrance slit, an imaging reflection grating, and a detector line [4,5]. However, these imaging spectrometers generally suffer from an inevitable conflict between accessible wavelength range and spectral resolution. For example, the Zeiss MMS Series [6] has a size of approximately ${70}\;{{\rm mm}^{3\:}}\times \;{50}\;{{\rm mm}^{3\:}} \times \;{40}\;{{\rm mm}^3}$ and covers a large spectral range of 310–1100 nm with a low resolution of 10 nm (MMS 1) or acquires a smaller spectral range of 195–390 nm with a medium resolution of 3 nm (MMS UV). The latter one corresponds to a maximum resolving power ${\lambda / {\Delta \lambda }}$ of 130. On the other hand, high-performance spectroscopic systems, such as echelle spectrometers, are designed for ambitious optical requirements and, in particular, allow simultaneously combination of a large spectral range with a high spectral resolution [7]. Therefore, echelle spectrometers comprise two consecutively arranged dispersive elements. At first, the echelle grating is illuminated by the incoming light and generates a multitude of overlapping spectra of different high-diffraction orders. These superimposed spectra propagate to a second dispersive element, the cross-disperser, whose dispersion direction is oriented perpendicular to that of the echelle grating. The cross-disperser separates the overlying spectral bands of the different diffraction orders, which are finally imaged in stripes onto a two-dimensional (2D) array detector [8,9]. Recently, different strategies to improve echelle spectrometer concepts have been presented and discussed, in particular focusing on astigmatism compensation [10–12] or broadening the spectral distribution by introducing multifacet echelle gratings [13]. Due to their specific design concept, echelle spectrometers unfortunately often require precisely defined environmental conditions, show a complex setup, and cover a large volume. These types of instruments are commonly used for astronomical spectroscopy [14–16]. Compact echelle spectrometers for lab applications still need an extended volume. For example, the “Mechelle 5000” from Andor [17] requires a volume of approximately ${60}\;{{\rm mm}^{3\:}} \times \;{230}\;{{\rm mm}^{3\:}} \times \;{160}\;{{\rm mm}^3}$ and offers a maximum resolving power of ${\lambda / {\Delta \lambda }} = 6000$ for the spectral range 200–975 nm.

In order to achieve a beneficial convergence of both spectrometer concepts, especially to combine the compactness of classical imaging spectrometers and the optical performance of an echelle spectrometer, different new approaches were presented and discussed recently. In particular, the concept of a compact echelle-inspired cross-grating spectrometer was proposed, in which, however, the previous work was limited to theoretical discussions and to the presentation of an optical design [18].

In this contribution, we report on the complete realization of a cross-grating spectrometer based on a preceding optical design [18], show the results of practical performance tests, and demonstrate the system capabilities by the presentation of initial experimental measurements. In contrast to a “classical” echelle spectrometer with separated dispersing elements, the configuration presented here is decisively distinguished by the integration of a single dispersive element, in which both functionalities are combined. The implementation of the cross grating together with a folded, mirror-based optical path allows a compact footprint of the optical design measuring ${110}\;{{\rm mm}^{3\:}} \times \;{110}\;{{\rm mm}^{3\:}} \times \;{30}\;{{\rm mm}^3}$. The cross-grating spectrometer design utilizes the fourth to the 11th order for the echelle dispersion and allows coverage over a spectral range from 330 nm up to 1100 nm. For the spectral resolution, dependent on the specific diffraction order, a value of 0.6 nm at $\sim{589}\,\,{\rm nm}$ was experimentally demonstrated. A resolving power ${\lambda / {\Delta \lambda }}$ of 500 is obtained for the whole spectrum. For the central wavelength range, an even higher resolving power of more than 800 is achieved.

2. CONCEPT, MECHANICAL LAYOUT, AND IMPLEMENTATION

The elaboration of the basic system concept has been driven by different aspects. The main issue was to demonstrate the “proof of concept” of a reflective cross-grating spectrometer, which offers, on the one hand, access to a broad spectral range with a high spectral resolution, and on the other hand it is characterized by a setup as compact as possible. To address a potentially broad diversity of spectroscopic applications with the instrument to be developed, an economic solution also has to be provided. Therefore, the entire spectral region is addressed, which is accessible with a simple and inexpensive two-dimensional silicon (Si) detector array. In particular, the use of expensive semiconductor-alloy-detector arrays, such as InGaAs detectors, is dispensable. Quantitatively, the complete wavelength range from the ultraviolet (330 nm) up to the near-infrared (1100 nm) is covered. To keep the optical setup dimensions small, a reflective, folded beam path based on a modified Czerny–Turner setup was applied, which was extended by an additional correction mirror for aberration compensation. Technological capabilities and limitations for the manufacturing of the cross grating substantially influence its specifications and its implementation into the optical design of the overall system. Against this background, we selected moderate multiple diffraction orders for the echelle dispersion (fourth to the 11th order), instead of high diffraction orders that are generally used in echelle spectrometers.

Figure 1 shows a horizontal cross section of the applied optical design. In the following, only a brief presentation of the basic characteristics is given; a comprehensive discussion of the optical design is found elsewhere [18]. The light to be analyzed enters the spectrometer by the entrance pinhole. The divergent light cone propagates to a concave mirror, generating a collimated ray bundle. In the optical path follows a correction mirror that is used for reducing aberrations. Subsequently, the parallelized ray bundle is directed towards the cross grating. There, the incident light is simultaneously diffracted in two orthogonal directions. The overlapping diffraction orders resulting from the echelle structure are decomposed by the orthogonally superimposed cross-dispersing grating. Finally, a focusing mirror directs and focuses the light separated by the echelle diffraction orders and by wavelength onto the 2D detector.

 

Fig. 1. Optical design layout of the all-reflective folded beam path cross-grating spectrometer. The ray bundle coming from the collimator is directed onto a toric-convex mirror, which serves for aberration correction. Subsequently, the ray bundle reaches the cross grating and is diffracted simultaneously in two orthogonal directions. Finally, the diffracted light is focused on a two-dimensional detector creating the spectral image.

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Fig. 2. Technical drawing as a 3D representation of the cross-grating spectrometer.

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Fig. 3. Mechanical drawing of the toric mirror for aberration compensation and mirror holder including the deformation mechanism. (a) 3D representation of the complete mirror holder comprising two main parts and a separating gap. (b) Side view of the mirror holder including the adjustment mechanics for mirror bending. (c) Reduced model of the mirror holder for a simplified representation of the leverage effect for mirror bending.

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Subsequently, the collimated ray bundle is directed to the toric correction mirror. This mirror has a projected cylindrical form with infinity radius of curvature in one direction and a small, convex curvature in the perpendicular direction. Quantitatively, the cylinder has a nominal focal length of $- 6135\,\,{\rm mm} $, which corresponds to a radius of curvature of more than 12 m. For a diameter $D$ of the toric mirror of ${D_1} = 20\,\,{\rm mm}$ and a radius of curvature of $r = 12\,\,{\rm m}$ follows corresponding to Eq. (1) a sag height of $s \approx 4\,\,{\rm \unicode{x00B5}{\rm m}}$:

 

Fig. 4. Interferometric measurement of the toric mirror after deformation (interferometer wavelength: 633 nm). (a) The interferogram shows a clear difference between the $x$ and $y$ direction. (b) The determined OPD map is sliced along the $x$ and $y$ axis. While the $y$ profile is quite smooth and shows a small PV value of 0.51 waves, the $x$ profile corresponds well to a spherical shape. The measured PV of 6.72 waves along $x$ corresponds to a profile height of 4.25 µm and fits well to the aimed sag height of approximately 4 µm.

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A mirror with such optical parameters is not a standard element and, to our knowledge, it is not commercially available. To provide the cylinder mirror with the correct curvature, we started with an original plane mirror and developed a deformation mechanism, which enables a weak and precisely adjustable bending of the mirror and additionally allows a permanent fixation of the final deformation state. The adjustment state of the bended mirror is measured using a Fizeau interferometer.

Figure 3(a) shows a 3D representation of the mechanical drawing of the toric mirror and mirror holder including the deformation mechanism. The parts are mounted on a simple post, which in turn is fixed to the base plate. The actual mirror holder and deformation mechanism consists of two parts, which both are fixed by gluing to the mirror. On the backside of the mirror, both mechanical parts are spatially separated by a small gap. One of both parts provides a stable mechanical connection to the carrying post; the second part is only connected to the mirror. In both parts, matching bore holes are drilled, through which a small screw (M2) with a thread pitch of 0.4 mm runs. The screw is freely moveable inside the bore holes and ends in a corresponding nut on the opposite side. The tightening of the screw creates a leverage effect and therefore induces a bending of the mirror in one direction. Figure 3(b) shows a side view of the mechanical drawing of the mirror holder. The leverage effect induced by the tightening of the screw is indicated schematically.

In a precise treatment, it would be necessary to consider the deformation of all contributing parts, including the mirror itself and also the mechanical parts of the holder. Such an accurate investigation is rather complex and requires sophisticated procedures, e.g., the use of finite-element methods. For our purpose of a proof of concept, the derivation of a precise and comprehensive deformation model is not necessary. In particular, the mirror bending is controlled by an interferogram, so it is sufficient to get a rough estimation of the relation between the adjustment accuracy of the screw and the bending effect of the mirror for a proper dimensioning of the mechanics. Therefore, the real shape of the mirror holder is reduced to a simplified model of a T-shaped structure [see Fig. 3(c)]. The schematic shows the mechanical lever (black) and the plane mirror, which becomes spherical due to the bending (red lines). The point of force positioned at the lower end of the lever indicates the tightening of the screw. In a further simplification it is assumed that the T-shaped structure will only be rotated around a pivot point fixed at the upper-right position of the mirror. The tightening of the screw moves the vertical lever to the right by the distance $b$ and lowers the left end of the horizontal mirror by the height $h$. This results in the bending of the mirror with the targeted sag height $s$ of about 4 µm. As can be seen in Fig. 3(c), $h$ is the height of a spherical cap with the base diameter ${D_2}$. Using Eq. (1) with $D = {D_2} = 40\,\,{\rm mm}$, a height $h$ of approximately 17 µm is expected. Related to our setting, assuming a mirror diameter ${D_1} = 20\,\,{\rm mm}$ and vertical lever with length $l = 30\,\,{\rm mm}$, the screw has to be moved over a distance $b \approx 25\,\,{\rm \unicode{x00B5}{\rm m}}$ ($b = {{lh} / D}$), which corresponds to a feasible adjustment accuracy of the screw (thread pitch 0.4 mm) in the range of $\sim{20}\,\,{\rm deg}$.

Actually, the parts of the mirror holder are also not completely rigid, so that distortion is introduced to the mirror holder by tightening the screw. Therefore, it can be presumed that a stronger turn of the screw has to be applied than the estimated $\sim{20}\,\,{\rm deg}$ to reach the target sag height, which further relaxes the adjustment accuracy. As mentioned before, the adjustment of the targeted cylindrical mirror curvature was controlled by interferometry in a separate tool. In its initial state the used plane mirror was characterized by a surface flatness of $\lambda /{10}$.

Figure 4 shows the interferometric measurement of the toric mirror after deformation (interferometer wavelength: 633 nm). The interferogram is shown in Fig. 4(a), demonstrating that the mirror is mainly deformed along the $x$ axis. This leads to the wanted toric shape. Figure 4(b) shows cross sections of the calculated optical path difference (OPD). The $y$ profile is very smooth with a peak-to-valley (PV) value of 0.51 waves. In contrast, the $x$ profile shows a distinct spherical shape with a PV of 6.72 waves, which corresponds to a profile height of 4.25 µm. This is very close to the aimed sag height of approximately 4 µm. This measurement proves that the adjustment mechanism is properly dimensioned. The final adjustment state was found experimentally by a fine adjustment of the toric mirror, while we optimized the spot size on the camera. This method allows us to take manufacturing tolerances of the other elements into account and compensate for them with the exact toric mirror bending.

After the reflection at the toric mirror, the ray bundle is incident on the cross grating. The cross grating combines two perpendicularly oriented blazed line gratings with periodicities of 10 µm (echelle grating) and 5.2 µm (cross-dispersion) and profile depths of 1.5 µm and 150 nm, respectively. The cross-grating profile was manufactured in photoresist by direct laser-beam writing, on which an aluminum coating was subsequently deposited. Therefore, a ${{\rm SiO}_2}$ wafer was used as a substrate, which was covered with a photoresist layer by spin-coating. For the lithography process, a commercial laser system was applied (Heidelberg Instr. Mikrotechnik GmbH, DWL 2000), using a working wavelength of 413 nm and a nominal minimum structure size of 0.7 µm. The entire cross grating was written consecutively in bands of 160 µm width, oriented parallel to the echelle structure. The overlay accuracy between adjacent bands measures approximately 200 nm, which may cause the occurrence of “ghost images” and a decay of spectral purity. A more detailed description of the manufacturing process is found elsewhere [19]. Figure 5(a) shows the color-coded topography of the cross grating measured by white-light interferometry.

 

Fig. 5. (a) Surface structure of a cross grating manufactured by laser-direct writing measured with white-light interference microscopy. The blaze-shaped echelle structure has a periodicity of 10 µm and a depth of 1.57 µm. The cross-dispersing grating also exhibits a blazed form with 5.2 µm periodicity and 150 nm depth. (b) Measured diffraction efficiency for different main dispersion orders at specific wavelengths in the first cross-dispersion direction.

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The light incident on the two-dimensional cross grating is diffracted simultaneously in two orthogonal directions. The echelle grating operating in higher diffraction orders is vertically oriented, and the cross-dispersion grating is aligned horizontally. In order to implement a planar configuration, the cross grating is tilted by 22.5 deg and 4.2 deg about the local horizontal and vertical axes, respectively. In particular, this setting allows the chief ray to remain in the plane of incidence for the central wavelength of 765 nm in the fifth order (Littrow configuration for cross-dispersion grating). A key parameter of the cross grating is its diffraction efficiency. To measure the diffraction efficiency, the cross grating was illuminated successively with different collimated laser beams of wavelengths 405, 532, and 635 nm. Hereby, it was ensured that the cross grating was mounted and illuminated similarly as in the final spectrometer. Figure 5(b) shows the measured diffraction efficiencies of the most important main dispersion orders in the first cross-dispersion direction. The measurement proves that the performance of the cross grating is reasonable for the targeted proof of concept. To reach the theoretical predictions described in [18], improved manufacturing techniques must be developed.

To simplify the assembly and adjustment process, the manufactured cross grating is mounted on a double-wedge-shaped compensation plate, which in turn is mounted on a standard element holder. This allows an adjustment process oriented along the main axis of the system. Furthermore, disturbing light originating from unused diffraction orders is deflected out of the optical plane and hits either the black-coated housing or the black-coated aperture of the subsequently following focusing mirror. This mirror directs and focuses the light onto the 2D detector array. As a detector array we apply the CCD sensor of a monochrome camera (AlliedVision, Prosilica GE2040 [20]) with an active sensor area of ${15.10}\,\,{\rm mm} \times {15.16}\,\,{\rm mm}$ (pixel size ${7.4}\,\,\unicode{x00B5}{\rm m} \times {7.4}\,\,\unicode{x00B5}{\rm m}$; ${2040}\,\,{\rm pixels}\times {2048}\,\,{\rm pixels}$). To avoid disturbing reflection effects, the camera is used without a coverslip in front of the sensor. Therefore, the whole system including the camera was assembled and aligned under cleanroom conditions. Finally, the spectrometer was encapsulated by an adapted housing, protecting against disturbing light and contamination. The inner walls of the housing are black coated to absorb stray light.

3. PERFORMANCE TEST AND INITIAL SPECTROSCOPIC EXPERIMENTS

Following the completion of the spectroscopic instrument, different performance tests and application measurements were performed. The overall accessible bandwidth of the spectrometer design ranges from a minimum of 330 nm to a maximum of 1100 nm. The entire wavelength range is separated in partial spectra, each associated to a specific diffraction order, displayed as a linear spectral band on the detector and characterized by its specific position and orientation. In total eight partial spectra are recordable (from the 11th order ranging from 330 nm to 370 nm down to the fourth order comprising 820 nm up to 1100 nm). Corresponding to the optical design [18] the spectral resolution increases with increasing diffraction order and ranges between 0.4 and 1.1 nm for a pinhole size of 40 µm.

As a first experimental test the spectrum of a halogen lamp (low-voltage halogen lamp, OSRAM 64623 HLX, using Xenon as the filler gas [21]) is captured (see Fig. 6). The evaluable spectral intervals of the individual diffraction orders are indicated (marked with “X”). The contribution of the halogen lamp displays as distinctly pronounced continuous spectral bands separated in the different diffraction orders. Across the different partial spectra, the entire spectrum of the halogen lamp extends from 370 nm (10th order) up to approximately 1000 nm (fourth order). In the 11th order only a very weak signal was detected. The measured intensity distribution for the different partial spectra results from the wavelength-dependent efficiency of the cross grating for the different diffraction orders, the quantum efficiency of the camera, and the characteristic emission curve of the spectral lamp. In particular, the overall spectral extent of the halogen lamp is smaller than the accessible bandwidth of the spectrometer.

 

Fig. 6. Measured continuous spectra of a halogen lamp. The contributions of the fourth up to the 10th order are clearly observable. In the 11th order only a very weak signal was detected.

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Additionally, the line spectra of four different discharge lamps were recorded comprising a mercury (Hg), a sodium (Na), a cadmium (Cd), and a caesium (Cs) lamp. Figure 7(a) shows the superposed spectra of the discharge lamps exhibiting specific discrete intensity peaks as a negative image for improved visibility. For the image composition the chosen spectral lines on the measured images were cropped and manually recomposed using different acquisition times ranging from 10 ms to 10 s for each shown spectral line. This approach allows us to display many spectral lines originating from different sources in a single image with roughly comparable signal heights. The specific spectral lines are labeled with table values. The shortest displayed discrete wavelength in the ultraviolet (Cd line at 361 nm) is found in both the 10th and in the 11th order. Respectively, long wavelengths (Cs lines at 801.6 nm, 852.1 nm) appear in the fourth and fifth order. Further peaks detected in the long wavelength range are the Cs lines at 917.2, 920.8, 1002.4, and 1012.3 nm. The Cs lines at 1002.4/1012.3 nm can also be detected in the third order, which is only partially imaged onto the detector. Corresponding to these lines, a spectral range of approximately 976–1142 nm is covered by the third order on the detector. Due to the low diffraction order and the increasing aberrations at the edge of the detector, the resolution in this order is lower. We measured a FWHM of 12 pixels and a distance of 49 pixels for the closely adjacent Cs lines. This corresponds to a FWHM resolution of approximately 2.4 nm. Nevertheless, this order can also be used for measurements. The allocation of the characteristic lines on the 2D detector allows a precise wavelength calibration for the partial spectra related to the different diffraction orders. The analysis of Figs. 6 and 7(a) reveals that the spectral bands can be well described by linear functions with different orientations. The precise orientation can be found using the different spectral lines. A detailed view on closely adjacent spectral lines allows an estimation of the spectral resolution of the cross-grating spectrometer. In particular, the constituents of the wavelength pair 588.995 nm and 589.592 nm (Na D lines) are recognized as clearly separated. Figure 7(b) shows a magnified section of this specific area of the recorded spectra. This detailed view displays slightly aberrated (mainly astigmatism) but clearly separated spots of the neighboring spectral lines from which a resolution of 0.6 nm can be derived. Figure 7(c) shows a cross section through both spots along the evaluated diffraction order exhibiting a distinguished minimum between the two maxima. To analyze the spectral performance in all diffraction orders, we measured the full width half-maximum (FWHM) of specific spectral lines in all orders. By calculating the ratio of pixel distance to wavelength distance of these lines, the resolution in all orders can be derived. Furthermore, one can approximate the theoretically covered spectrum on the detector. The influence of position errors of the spectral lines is low on the calculated spectral range and resolution. The error of the FWHM is assumed to be in the range of one pixel. For comparison, theoretical resolution values based on the RMS criterion obtained from the optical design are given. These data are summarized in the following Table 1. Based on the given data, the resolving power ${\lambda / {\Delta \lambda }}$ in the fourth to 11th order is higher than 500. Considering only the central wavelength range, which is imaged with less aberrations on the detector, a resolving power of more than 800 is obtained.

 

Fig. 7. (a) Negative image of the superposed line spectra of four different discharge lamps [mercury (Hg), sodium (Na), cadmium (Cd), and caesium (Cs) lamps]. The shortest displayed discrete wavelength (361 nm) in the ultraviolet is found in both the 10th and the 11th order. The spectral lines for the largest wavelength are recorded at 1002 nm and 1012 nm in the fourth order. (b) Separated spectral lines at 589.0 nm and 589.6 nm indicate a spectral resolution of 0.6 nm. (c) Profile across the spectral lines at 589.0 and 589.6 nm showing a distinguished minimum between the two maxima.

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Table 1. Spectral Range and Resolution for Different Diffraction Orders

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As an additional experimental test, the spectrum of the sun was recorded. Therefore, sunlight was fed by a simple fiber collimator into a glass fiber, which ends at the input of the cross-grating spectrometer. On the input side, the fiber collimator offers a limited beam diameter of approximately 3.3 mm and a focal length of 18 mm at 543 nm. The core of the optical fiber measured 25 µm with a numerical aperture of 0.1. Obviously, since sufficient sunlight is available, this simple light collection optics was not optimized with respect to efficiency but serves as an easy-to-realize test setup. Figure 8(a) shows the measured spectral intensity as a function of the wavelength for the different diffraction orders. Again, the directly measured intensity results from the intensity distribution of the source, the quantum efficiency of the camera, and on the wavelength-dependent efficiency of the optical components for the different diffraction orders. In general, the solar spectrum is characterized by a continuous curve, which additionally exhibits discrete Fraunhofer absorption lines resulting from the atomic contribution of the solar photosphere. The continuous spectrum resembles a blackbody radiation with a temperature of approximately 5800 K, attenuated by the absorption of the Earth’s atmosphere. When regarding the curves of the partial spectra for the different diffraction orders in Fig. 8(a), it can be concluded that the combined overall spectrum shows a continuous spectral profile with an intensity maximum at approximately 550 nm. In addition to the basic continuous curve, also discrete line spectra are observable, comprising particularly the hydrogen lines (${{\rm H}_\alpha }$ at 656 nm, ${{\rm H}_\beta }$ at 486 nm, and ${{\rm H}_\gamma }$ at 434 nm) and typical element peaks, e.g., for Mg, Fe, and Ca. Furthermore, in the long-wavelength range, the concise absorption spectra for molecules (${{\rm H}_2}{\rm O}$ and ${{\rm O}_2}$) resulting from the Earth’s atmosphere are also observable. A closer look to the partial spectrum of the 10th diffraction order [see Fig. 8(b)] shows that the nearby Ca lines in the UV range at 393.3 nm and 396.8 nm can be detected as well resolved.

 

Fig. 8. Solar spectrum as a composition of several partial spectra acquired with the cross-grating spectrometer. In addition to the discrete Fraunhofer absorption lines (e.g., hydrogen lines ${{\rm H}_\alpha }$, ${{\rm H}_\beta }$ and ${{\rm H}_\gamma }$, and metal lines Ca, Mg, and Fe), the molecular absorption spectra from the Earth’s atmosphere (${{\rm H}_2}{\rm O}$ and ${{\rm O}_2}$) are also observable.

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Finally, the cross-grating spectrometer was applied to analyze the different components of a bundle of plant leaves. Figure 9(a) shows a color photo of the whole bundle, in which four selected details of the scene are indicated. The details comprise a red, a yellow, a green natural, and a green artificial leaf. For the photo and the spectroscopic measurements, the plant bundle was illuminated by direct sunlight. For each selected position of the plant bundle, the corresponding set of partial spectra is displayed in Fig. 9(b). Each diagram displays the spectral curves for five diffraction orders, in particular comprising the ninth down to the fifth order, representing an overall wavelength range from 350 to 900 nm. The spectra recorded for the red leaf are restricted to wavelengths larger than approximately 550 nm, and therefore only the fifth and sixth diffraction orders show significant contributions. In comparison, for the partial spectra for the yellow leaf, further contributions of the seventh and eighth diffraction orders are added, shifting the lower end of the wavelength spectrum to approximately 420 nm. The comparison of the partial spectra related to both green leaves, the natural green and the artificial green leaf [third and fourth partial spectra of Fig. 9(b)], is of particular interest. Both diagrams are dominated by the contribution of the seventh order with a reflection maximum at about 550 nm. A considerable difference between both partial spectra becomes obvious when comparing the relation of the reflectance maximum in the visible spectral range in the seventh diffraction order [R(550 nm; seventh] and the respective maximum in the near-infrared of the fifth diffraction order [R(750 nm; fifth)]. For the natural green leaf this relation R(750 nm; fifth)/R(550 nm; seventh) = 0.8, where instead for the artificial green leaf a substantial lower relation of R(750 nm; fifth)/R(550 nm; seventh) = 0.4 was found. This behavior of increased reflectance in the NIR spectral range for the natural green leaf is also known as the red-edge effect and can be attributed to the characteristics of the chlorophyll, which is missing in the artificial plant. Additionally, the finding is supported by a closer look to the partial spectrum of the fifth order for the natural green leaf, which shows a strong increase in the reflectance in the region between 680 and 710 nm. In contrast, the comparable spectrum for the artificial leaf shows a much smoother increase in the same spectral domain. Finally, it should be noted that the specific illumination characteristics induced by sunlight appear in the partial spectral domain, especially in the fifth order where the ${{\rm O}_2}$ absorption lines at 759 nm are strongly pronounced.

 

Fig. 9. Bundle of plant leaves analyzed with the cross-grating spectrometer. (a) Photo of the whole scene indicating the selected positions for a 1) red, 2) yellow, 3) natural green, and 4) artificial green leaf. (b) Recorded partial spectra corresponding to the selected scene positions. In particular, the comparison of the natural and the artificial green leaves emphasizes the red-edge effect, which can be attributed to the characteristics of the chlorophyll in the natural plant.

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4. CONCLUSION

Starting from an optical design model we presented the implementation of a new type of an all-reflective cross-grating spectrometer, combining a folded mirror design based on a Czerny–Turner configuration, a cylindrical correction mirror, and a two-dimensional echelle-type cross grating. The cross-grating concept combines the functionality of a main grating acting in several higher diffraction orders and a perpendicularly oriented cross-disperser for separating the overlapping higher diffraction orders in a single element. This spectrometer concept allows us to at least partially overcome the classical conflict in spectrometer design to simultaneously fulfill a high spectral resolution while offering a large accessible wavelength range in a compact setup without moving opto-mechanical parts. A detail in the implementation of the setup concerns a toric-convex mirror with a large radius of curvature for aberration compensation. We realized this toric mirror with a sag height of 4.25 µm by a specific deformation of a plane mirror. In particular, we demonstrated the access to a broad spectral range from the UV at approximately 330 nm up to the NIR range at 1100 nm with a resolving power higher than 500. For the sixth order, a spectral resolution smaller than 0.6 nm was obtained. Further, we demonstrated the applicability of the cross-grating spectrometer by presenting some test measurements.

Future work aims to optimize the technology to manufacture the cross grating, in particular to achieve a high diffraction efficiency and to improve the lateral accuracy of grating periodicity to further suppress ghost imaging. Additionally, a software-based calibration process of the individual partial spectra has to be implemented, to be able to create a single continuous spectrum from the UV up to the IR range, which allows a more simplified analysis and comparison of different spectra.