1. Introduction

As one of accurate and nondestructive methods for material identification and component analysis [1,2], Raman spectroscopy has been applied widely in fields including medicine [3,4], geology [5,6], physics [7,8], biology [9,10], and chemistry [11,12]. In recent years, the spatial heterodyne spectrometer (SHS) has emerged as a novel type of Fourier interferometer. The SHS offers advantages that include a one-time measurement capability, high stability, large throughput, and broadband or high spectral resolution, which makes the spatial heterodyne Raman spectrometer (SHRS) highly suitable for accuracy Raman spectrum measurement applications.

However, because of the restrictions of the Nyquist sampling theorem, it is difficult for the SHRS to meet requirements for high spectral resolution and a broadband spectral range simultaneously [13]. Some new structures have been proposed to solve this restriction in conventional SHS equipment, with particular focus on replacement of the normal grating with a multi-grating structure consisting of many sub-gratings with different groove densities [14–16]. However, direct replacement of the normal grating with a multi-grating will reduce the signal light throughput. Additionally, the intensity of the spectrum within each wave band will decrease as the number of sub-gratings increases. Researchers have also focused on the replacement of normal gratings with echelle gratings with multiple orders. With its mixture of different diffraction orders, the double-echelle SHS (DESHS) can realize high-resolution and broadband measurement capabilities [17]. However, to eliminate the effects of ghosts and shadows, the DESHS structure requires a mask to be inserted at the focal plane of the imaging optics to select the spectral information for one specific order of the two echelle gratings [18–20], which then prevents the overall spectrum from being obtained in a single measurement process. However, ghosts and shadows can still be detected in the spectral information when using this structure. Replacing one echelle grating with a mirror (mirror-echelle SHS, or MESHS) can solve these problems in the DESHS [21]. However, the introduction of the mirror reduces the spectral resolution by half, thus losing the advantage of the system. In addition, the field-widening theories for the echelle grating and the mirror are not suitable, and this indicates that the field-of-view (FOV) of the MESHS cannot be improved as compared with the conventional SHS.

In response to the issues noted above, we proposed the concept of the grating-echelle SHS (GESHS) structure, which replaces one normal grating in the conventional SHS with an echelle grating. The proposed GESHS structure can not only use the characteristics of multiple diffraction orders to achieve high resolution and broadband measurements in a single measurement process without using a mask or sacrificing the spectral resolution, but also can increase the FOV by introducing field-widening prisms that correspond to the normal grating and the echelle grating based on field-widening theory. As a result of the different diffraction characteristics of the normal grating and the echelle grating, the mathematical expressions for the Littrow wavenumber and the other spectral parameters in the GESHS are different to the corresponding expressions for the conventional SHS.

In this article, the mathematical derivation process for the principles and the expressions of the GESHS is presented. The calibration theory is also discussed in detail. On this basis, using the field-widening theory, we have designed and manufactured suitable field-widening prisms for both the normal grating and the echelle grating and applied them in the Raman experiment to broaden the FOV of the spectrometer; this is why we ultimately called the proposed structure the field-widened grating-echelle spatial heterodyne Raman spectrometer (FWGE-SHRS). In experiments, the detailed Raman spectra of chemicals acquired at different integration times, laser powers, and concentrations are studied in detail. The Raman spectra of mixtures of inorganic powders in plastic bags of various thicknesses and the Raman spectra of a mixture of organic solutions in a glass bottle are also presented.

2. Principle

2.1 Basic theory

Figure 1 illustrates the experiment optical path of the FWGE-SHRS. During the Raman signal excitation process, the light beam output by the laser is finally focused via collimation lens L₁ onto the sample surface after being filtered using a linear variable filter and a clean-up filter and then having its direction changed by the mirror and the dichroic beam splitter. The Raman signal light that is excited by the sample is then collected by collimation lens L₁ and filtered using the long-pass and short-pass filters. The filtered signal light is finally collected by collimation lens L₂ and launched into optical fibers for the spectral analysis. The core component of the experiment’s optical path is the principal prototype of the FWGE-SHRS. The signal light from the fiber output port is first collimated to a specific size by collimation lens L₃ and is then divided into two beams by the beam splitter. One of the beams is diffracted by the first order of the normal grating G, and the other beam is diffracted by several orders of the echelle grating E; both the normal grating and the echelle grating are set in the Littrow condition [22], which can be expressed for the respective gratings as:

 

Fig. 1. Optical layout of the experimental light path for the spatial heterodyne Raman spectrometer based on the field-widened grating-echelle structure.

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For the on-axis incident light signal, the diffraction equation for the two gratings with the off-Littrow wavenumbers can be expressed as follows:

The two coherent light beams from the normal grating and the echelle grating exit the beam splitter and are then collected using the imaging optics. For the two coherent plane wavefronts are produced at the output whose wavevectors are inclined to the optical axis by small diffraction angle β_G and β_E, the spatial frequency f_x of the interference fringes generated on the charge-coupled device (CCD) detector can be expressed as [22]

In the conventional SHS consisting of two normal gratings, the spatial frequency can be rewritten as f_x = 4(σ−σ_LG)tanα_LG, and when the wavenumber σ is equal to the Littrow wavenumber σ_LG, the spatial frequency f_x is equal to zero. However, Eq. (7) clearly shows that for the grating-echelle SHRS (GESHRS) consisting of one normal grating and one echelle grating, if σ_LG ≠ σ_LEm and if the wavenumber σ is equal to σ_LG or σ_LEm, the spatial frequency is not equal to zero; this means that both σ_LG and σ_LEm cannot be the Littrow wavenumber of the GESHS. By setting f_x in Eq. (7) to be equal to zero, the Littrow wavenumber of the GESHS can be calculated using

To aid in the analysis of the spectral performance of the GESHS and to have the same calibration standard for both the normal grating and the echelle grating during construction of the instrument, it is helpful to set the Littrow wavenumber of the normal grating to be equal to the Littrow wavenumber of the p-th diffraction order of the echelle grating, and this Littrow wavenumber can be written as σ_LGEp = σ_LG = σ_LEp. Under this condition, the difference between the Littrow wavenumber of the GESHRS σ_LGEm and the Littrow wavenumber of the echelle grating σ_LEm can be expressed as:

Equation (11) clearly shows that Δ_GEm increases proportionally as the diffraction order m decreases. By combining Eq. (2) with Eq. (11), the Littrow wavenumber σ_LGEm can be expressed as

When σ_LG = σ_LEp, the Littrow wavenumber σ_LGEm can finally be expressed more concisely as

To avoid ambiguity in the spectral information being caused by the one-dimensional interference fringes, the normal grating in GESHS is tilted at a small angle ε to introduce an extra spatial frequency f_y and thus generate two-dimensional interference fringes. The introduced spatial frequency f_y of the interference fringes can be expressed as

For the two-dimensional interference fringes generated on the CCD detector, the intensity distribution can finally be expressed as [23]

By assuming that the width of the signal light received by the CCD detector is W_L, then the effective areas illuminated by the light of the normal grating and the echelle grating can be expressed respectively as

By combining the grating-echelle structure with the definition of the resolution limit [24] in the two-dimensional SHS, the spectral resolution δ_σ of the GESHRS can be calculated to be

The corresponding resolution power R can then be given by

In each row of the detector, when it is assumed that the number of the pixels is N_p, the spectral range Δ_σ of the GESHRS can be calculated as follows:

The detectable maximum and minimum wavenumbers for each diffraction order of the FWGE-SHRS can be calculated as σ_LGEmmax= σ_LGEm + Δ_σ/2 and σ_LGEmmin= σ_LGEm - Δ_σ/2, respectively. To ensure the integrity of the spectrum obtained, it is important to set the detectable wavenumber ranges of pairs of adjacent diffraction orders to be partially overlapping during the design process of the FWGE-SHRS; this can be expressed as σ_LGEmmin < σ_LGEm−1max.

As an important performance index of the SHS, the FOV can be improved greatly by introducing field-widening prisms into the light path, as shown in Fig. 1, based on field-widening theory [22]. To field-widen the GESHS, the respective rotation angles of the field-widening prisms P_G and P_E can be calculated using

2.2 Calibration theory

During the calibration process for the conventional SHRS, it is only necessary to determine one Littrow wavenumber with two known emission lines from the standard light source; then, we can solve for the corresponding parameters of the spectrometer. However, Eq. (9) shows that there are four unknown parameters of the spectrometer that must be solved, which means we must determine at least four Littrow wavenumbers with eight known emission lines in four different diffraction orders. This not only makes the experimental process very cumbersome, but also makes solution of the equation groups a very complex task.

As mentioned earlier, it is helpful to set the Littrow wavenumbers σ_LGEp = σ_LG = σ_LEp; this means that the parameters for the normal grating and the echelle grating can both be calculated when σ_LGEp is determined. Therefore, the focus of the calibration process is to determine the Littrow wavenumber of the p-th diffraction order in GESHS, denoted by σ_LGEp.

During the calibration process, if the two known emission lines lie within the m-th diffraction order of the GESHS, then the Littrow wavenumber σ_LGEm can be calculated using

Because the echelle grating has multiple diffraction orders, the calibration process of σ_LGEp is divided into two cases. In the first case, the two known emission lines lie within the p-th diffraction order of the GESHS, the Littrow wavenumber σ_LGEp can be calculated using Eq. (25), and the Littrow wavenumbers of the normal grating and the echelle grating of the p-th diffraction order can then be calculated to be σ_LG = σ_LEp= σ_LGEp.

In the second case, the two known emission lines lie within the n-th (n = p−1, …, p−q + 1) diffraction order of the GESHS, the Littrow wavenumber σ_LGEn can be calculated using Eq. (25), and the corresponding spectral resolution can be calculated using Eq. (26). In this case, we require another known emission line that lies within the p-th diffraction order of the GESHS to determine σ_LGEp, and this can be expressed as:

In the two cases described above, after the Littrow wavenumber σ_LGEp has been determined, based on Eq. (1) and Eq. (2), and when groove densities of 1/d_G and 1/d_E are known parameter, the respective Littrow angles of the normal grating and the echelle grating can be calculated using

Based on the analysis above and Eq. (13), after the Littrow angles have been determined, the value of Δ_GESHS can then be determined, and the Littrow wavenumber can be obtained for each diffraction order σ_LGEm using Eq. (13). According to Eq. (18), after the spectral resolution and the Littrow angles have been determined, the width of the signal light received by the CCD detector can then be calculated using

The effective areas of the normal grating and the echelle grating can then be calculated using Eq. (16) and Eq. (17), respectively.

3. Experimental

3.1 Breadboard

The optical light path of the experimental breadboard is shown in Fig. 2 and the optical parameters of the components used to construct the breadboard system are listed in Table 1. In the excitation and collection part of the experimental optical path, the linear variable filter can adjust the laser power output from the solid-state 532 nm laser in a linear manner from 0 to 400 mW; the 15-mm-focal-length collimation lens L₁ collimates the laser beam on the sample and collects the Raman signal light beams; the 700 nm short-pass filter (84-714, Edmund Optics) and the 532 nm long-pass filter (532-LAB-80AC-2.5, CNI) were used to filter out any useless fluorescent light and reject the laser light; the 75-mm-focal-length collimation lens L₂ then converged the filtered signal light beam into the input port of a 1.5-mm-diameter silica fiber set at the focal plane of the filter.

 

Fig. 2. Optical light path of the experimental breadboard for the spatial heterodyne Raman spectrometer based on the field-widened grating-echelle structure.

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Table 1. Essential parameters for the optical elements used in the experimental breadboard

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In the principal FWGE-SHRS prototype, the 150-mm-focal-length lens L₃ collimated the signal light emitted from the fiber output port. The core section of the FWGE-SHRS was composed of a 50.8 × 50.8 × 50.8 mm³ cubic beam splitter, an echelle grating and a normal grating (Changchun Institute of Optics, Fine Mechanics and Physics) set in the Littrow condition, and two field-widening prisms (Changchun UP Optotech (Holding) Co., Ltd) that correspond to the echelle grating and the normal grating. The imaging optics comprised a camera lens (AF-S Micro Nikkor 105 mm 1:2.8G ED, Nikon) that was used for imaging of the two-dimensional interference fringes generated by the echelle grating and the normal grating. The image was received by a CCD detector (iKon-L 936, Andor) that was cooled to −80°C to reduce thermal noise and enhance the detector’s weak signal detection capability.

During the spectral analysis process, the two-dimensional interference fringes received by the detector were transformed into a corresponding two-dimensional spatial frequency using the two-dimensional fast Fourier transform (2DFFT) function. In the restoration of the spectroscopy results, the phase correction method [26] and the background removal function [27] were used to convert the spatial frequency accurately into the Raman spectrum and separate the signal from the background noise effectively.

3.2 Calibration

The interferogram for the mercury lamp produced by the FWGE-SHRS and the corresponding calibration results are shown in Fig. 3. Figure 3(b) clearly shows that the three spatial frequencies obtained from the mercury lamp’s interferogram, as shown in Fig. 3(a), are distributed over the m = 14, 15 diffraction orders of the FWGE-SHRS. In Fig. 3(c) and Fig. 3(d), in the m = 14 diffraction order, the spatial frequencies f₁ = −424 and f₂ = −308 correspond to the wavelengths of 579.067 nm and 576.961 nm, respectively; in the m = 15 diffraction order, the spatial frequency f₃ = 53 corresponds to the wavelength of 546.075 nm. The distribution of the two-dimensional spatial frequencies clearly corresponds to the second case mentioned in the discussion of the calibration theory.

 

Fig. 3. (a) Interferogram of the mercury lamp produced by the FWGE-SHRS. (b) Two-dimensional spatial frequency obtained from the 2D FFT of the interferogram. (c) Spatial frequency f_x of the m = 14, 15 diffraction orders. (d) Corresponding detailed Raman spectrum of the mercury lamp after calibration.

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Using Eqs. (25)–(27), we are able to calculate the Littrow wavelengths of the m = 14, 15 diffraction orders to be λ_LGE15= λ_LG= λ_LE15= 546.935 nm and λ_LGE14= 571.443 nm, along with the spectral resolution of δ_σ= 0.5434 cm⁻¹. According to Eqs. (28) and (29), by combining the Littrow wavelength λ_LG = λ_LE15 with the groove densities of 1/d_G and 1/d_E, the Littrow angles for the normal grating and the echelle grating can be calculated to be α_LG = 4.706° and α_LE= 8.492°, respectively. The width of the signal light received by the CCD detector can be calculated using Eq. (30) to be W_L = 39.724 mm, and the definite value Δ_GESHS can also be determined using Eq. (13) to be Δ_GESHS= 784.139 cm⁻¹. By combining the Δ_GESHS value with Eq. (13), the Littrow wavelengths can be calculated for all the diffraction orders, and the other spectral parameters are listed in Table 2.

Table 2. Spectral parameters of the different diffraction orders

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The results in Table 2 show that the Littrow wavenumbers satisfy the relationship σ_LGEmmin < σ_LGEm−1max, which means that the spectral ranges for each diffraction order are partially overlapped, and the overall detectable spectral range is thus continuous. By setting the wavenumber of 532 nm to be the zero wavenumber, the overall spectral range is from −43.158 cm⁻¹ to 3422.156 cm⁻¹ with four diffraction orders. For each pair of adjacent diffraction orders, the overlapping spectral range is 328.758 cm⁻¹.

4. Results and Discussion

4.1 Raman spectrum detection and analysis of a mixture of organic solutions with different diffraction orders

Figure 4(a) shows the two-dimensional spatial frequency obtained from the interferogram of a mixture of organic solutions. The detailed spatial frequencies in the different diffraction orders are shown in Fig. 4(b), the parameters that describe the relationship between the diffraction order m and the spatial frequency f_y are listed in Table 3, and the interval between pairs of adjacent diffraction orders is 58 times the spatial frequency f_y. Each peak in the two-dimensional spatial frequency range extends in both the f_x direction and the f_y direction, which means the signal peak has a certain width in both directions. When compared with the MESHRS, where the interval between each pair of adjacent diffraction orders is only 3 times the spatial frequency f_y [21], and the DESHRS, where the interval between each pair of adjacent diffraction orders is 15 times the spatial frequency f_y [17], the larger interval for the diffraction orders in the GESHRS effectively prevents interference of the spatial frequencies f_x in the different diffraction orders, and also resolves the ambiguities of the Raman peaks.

 

Fig. 4. (a) Two-dimensional spatial frequency obtained from the 2D FFT of the interferogram of the mixture of organic solutions. (b) Detailed spatial frequencies and transferred Raman peaks corresponding to each diffraction order m. (c) Measured Raman spectra of carbon tetrachloride, acetone, cyclohexane, and the mixture of these compounds acquired with a laser power of 180 mW and an integration time of 16 s.

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Table 3. Relationship between the diffraction order m and the spatial frequency f_y

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From the conversion of the spatial frequency and the corresponding Raman spectra shown in Fig. 4(b), we clearly see that the spatial frequencies of the different diffraction orders correspond to the Raman peaks in different wavenumber ranges. Figure 4(c) shows the measured Raman spectra of carbon tetrachloride (CCl₄), acetone, cyclohexane, and a mixture of these compounds as acquired using a laser power of 180 mW and an integration time of 16 s. For CCl₄, the Raman peaks are mainly distributed within the detectable spectral range of the m = 15 diffraction order; the Raman peak at 218 cm⁻¹ is assigned to mode E; the Raman peak at 315 cm⁻¹ is assigned to mode T₂; the Raman peak at 458 cm⁻¹ is assigned to mode A₁; the Raman peak at 762 cm⁻¹ is assigned to the combination mode T₂ + A₁; and the Raman peak at 789 cm⁻¹ is assigned to mode T₁ [28]. For acetone and cyclohexane, the Raman peaks are mainly distributed within the detectable spectral ranges of the m = 14 and m = 12 diffraction orders. The Raman peaks at 532 cm⁻¹, 788 cm⁻¹, 1068 cm⁻¹, 1222 cm⁻¹, 1432 cm⁻¹, 1706 cm⁻¹, 2848 cm⁻¹, 2923 cm⁻¹, 2964 cm⁻¹, and 3008 cm⁻¹ correspond to the spectrum of acetone [29]. For cyclohexane, the Raman peaks at 803 cm⁻¹, 2853 cm⁻¹, and 2939 cm⁻¹ are assigned to mode A_1g; and the Raman peaks at 1030 cm⁻¹, 1276 cm⁻¹, 1446 cm⁻¹, and 2924 cm⁻¹ are assigned to mode E_g [30,31]. The high intensity Raman peaks of CCl₄ were detected by the m = 15 diffraction order, and the high intensity Raman peaks of acetone and cyclohexane were mainly detected by the m = 12 diffraction order. The Raman peaks of CCl₄ at 762 cm⁻¹ and 789 cm⁻¹ and the Raman peaks of cyclohexane at 788 cm⁻¹ and 803 cm⁻¹ are detected simultaneously by the m = 15 and m = 14 diffraction orders, and the Raman peak of acetone at 1706 cm⁻¹ is detected simultaneously by the m = 14 and m = 13 diffraction orders.

As detailed in the analysis above, for the three types of measured organic solution, the intervals of some of the Raman peaks are close together and overlap with each other. For example, in the measured Raman spectrum of the mixture of organic solutions, the Raman peak of CCl₄ at 789 cm⁻¹, the Raman peak of acetone at 788 cm⁻¹, and the Raman peak of cyclohexane at 803 cm⁻¹ clearly overlap with each other, and the relative intensity of the mixed Raman peak is higher than the individual peaks for each organic solution. However, the overlap of some of the Raman peaks does not affect identification of the characteristics of the organic solution, and each type of organic solution can still be identified clearly. As shown in the analysis of the interferogram of the mixture and the single types of organic solutions, the FWGE-SHRS demonstrates its ability to detect and analyze the components of the mixed organic solutions over a broad spectral range and with a high spectral resolution. When compared with the small interval between the adjacent diffraction orders in the two-dimensional spatial frequency results generated by the conventional DESHRS, the large interval between adjacent diffraction orders in the two-dimensional spatial frequency results generated by the FWGE-SHRS are better for prevention of spectral interference between the different spatial frequencies; this is highly meaningful when used in measurements with multiple diffraction orders.

4.2 Raman spectral and SNR analyses of sulfur with various integration times

Figure 5(a) shows the Raman spectra of solid sulfur when measured using different integration times at the same laser power of 20 mW. Because of the flammability of solid sulfur, we used a laser power of 20 mW to study the vibrational Raman spectrum of sulfur at various integration times, which also represents a test of the measurement capability of the designed FWGE-SHRS under relatively low Raman excitation conditions at the same time. The results of the experiment show that all three characteristic Raman peaks at 153 cm⁻¹, 218 cm⁻¹, and 472 cm⁻¹ were detected clearly. The Raman peaks at 153 cm⁻¹ and 218 cm¹ were assigned to the antisymmetric bond-bending mode and the symmetric bond-bending mode of the S₈ molecule, respectively. The Raman peak at 472 cm⁻¹ is caused by the symmetric bond-stretching mode of the S₈ molecule [32].

 

Fig. 5. (a) Raman spectra of solid sulfur as measured using the FWGE-SHRS under conditions of different integration times and the same laser power of 20 mW. (b) SNR plot of the measured Raman spectra of solid sulfur under conditions of different integration times and the same laser power of 20 mW.

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The performance of the measured Raman spectrum is usually quantified using the signal-to-noise ratio (SNR), which can be written as

Furthermore, as shown in Fig. 6, we compared the Raman spectrum of sulfur as measured using a commercial instrument, the B&W Tek i-Raman Pro [33], with that measured using the designed FWGE-SHRS. Under the measurement conditions of a 0.5 s integration time and 8 mW of laser power, the spectrum measured by the i-Raman Pro has high background noise and the characteristic peaks are at least two orders of magnitude lower than those measured by the designed FWGE-SHRS under the same conditions. According to the analysis above, the FWGE-SHRS has great potential for use in Raman spectrum measurement.

 

Fig. 6. Comparison of the measured sulfur Raman spectrum from an i-Raman Pro instrument from B&W Tek with that from the designed FWGE-SHRS under the same conditions of an integration time of 0.5 s and 8 mW laser power.

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4.3 Raman spectral and SNR analyses of organic solutions with various laser powers and various concentrations

Figure 7(a) shows the Raman spectra of acetone as measured under the conditions of the same integration time of 25 s and different laser powers, and the vibrational Raman peaks are all identified well when the laser power decreases from 200 mW to 20 mW. The Raman peak at 532 cm⁻¹ corresponds to the in-plane deformation mode of C-(=O)-C. The Raman peak at 788 cm⁻¹ corresponds to the symmetric stretching mode of C-C(=O)-C. The Raman peak at 1068 cm⁻¹ is caused by the rocking vibration of CH₃-C(=O-). The Raman peak at 1222 cm⁻¹ is caused by C-C stretching in the methyl group. The Raman peak at 1358 cm⁻¹ is assigned to the CH₃ umbrella mode. The Raman peak at 1432 cm⁻¹ is assigned to the CH₃ deformation vibration. The Raman peak observed at 1706 cm⁻¹ is caused by C = O stretching. The Raman peaks at 2848 cm⁻¹ and 2923 cm⁻¹ are both caused by CH₃ symmetric stretching, and the Raman peaks at 2964 cm⁻¹ and 3008 cm⁻¹ are both caused by CH₃ asymmetric stretching [29].

 

Fig. 7. (a) Raman spectra of acetone as measured by FWGE-SHRS under conditions of the same integration time of 25 s and different laser powers. (b) Raman spectra of methanol versus different concentrations as measured by FWGE-SHRS under the conditions of the same integration time of 20 s and a laser power of 180 mW.

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Figure 7(b) shows the Raman spectra of methanol versus different concentrations as measured under conditions of the same integration time of 20 s and the same laser power of 180 mW. The Raman peak at 1038 cm⁻¹ is assigned to the stretching vibration mode of -CO and the Raman peak at 1454 cm⁻¹ is assigned to the deformation vibration mode of -CH₃. The two main Raman peaks at 2835 cm⁻¹ and 2945 cm⁻¹ are assigned to the symmetric and antisymmetric stretching vibration modes of the -CH₃ group, respectively [34]. As Fig. 7(b) shows, the vibrational Raman peaks are all identified clearly when the concentration is reduced from 99% to 30%. The detection capabilities of the FWGE-SHRS shown in this experiment are highly promising for application to the measurement of chemicals using different laser powers and chemical concentrations.

4.4 Raman spectrum detection and analysis of a mixture of inorganic powders in different containers

Figure 8 shows the measured Raman spectra of sodium sulfate (Na₂SO₄), calcium carbonate (CaCO₃), and sodium nitrite (NaNO₂), along with the measured Raman spectra of a mixture of these inorganic powders in different containers. All spectra were measured under conditions of laser power of 120 mW and an integration time of 20 s. From Fig. 8, we see that the Raman peaks for these inorganic powders are distributed within the detectable spectral ranges of the m = 15 and m = 14 diffraction orders in the designed FWGE-SHRS. In this part of experiment, the thickness of the plastic bag was 0.04 mm, and the thickness of both the glass bottle and the plastic bottle was 1 mm. All three containers were transparent.

 

Fig. 8. Measured Raman spectra of Na₂SO₄, CaCO₃, NaNO₂, and of a mixture of these compounds in different containers under conditions of a laser power of 120 mW and an integration time of 20 s.

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As shown in Fig. 8, for the Raman spectra of Na₂SO₄, the Raman peaks at 449 cm⁻¹ and 467 cm⁻¹ are assigned to the bending vibration mode v₂(E); the Raman peaks at 620 cm⁻¹, 632 cm⁻¹, and 647 cm⁻¹ are all assigned to the bending vibration mode v₄(F₂); the highest Raman peak at 993 cm⁻¹ is assigned to the symmetric stretching mode v₁(A₁); the Raman peaks at 1101 cm⁻¹, 1131 cm⁻¹, and 1152 cm⁻¹ are all assigned to the antisymmetric stretching mode v₃(F₂) [35]. For the Raman spectra of CaCO₃, the Raman peaks at 154 cm⁻¹ and 281 cm⁻¹ are assigned to the lattice mode; the Raman peak at 711 cm⁻¹ is assigned to the in-plane bending mode v₄(E); and the Raman peak at 1085 cm⁻¹ is assigned to the symmetric stretching mode v₁(A₁) [36,37]. For the Raman spectra of NaNO₂, the Raman peaks at 120 cm⁻¹ and 154 cm⁻¹ are assigned to the lattice mode; the Raman peak at 828 cm⁻¹ is assigned to the bending vibration mode v₄(A₁); and the Raman peak at 1328 cm⁻¹ is assigned to the symmetric stretching mode v₁(A₁) [38].

In the Raman spectra of the mixture when measured in the three different containers, the vibration bands of Na₂SO₄ all remain clearly visible. Although the Raman peaks of CaCO₃ and NaNO₂ are relatively weaker than those of Na₂SO₄, they can still be identified clearly in the Raman spectra of the mixed inorganic powders. Both CaCO₃ and NaNO₂ have a Raman peak at 154 cm⁻¹ caused by the lattice mode, and the overall Raman peak at 154 cm⁻¹ in the Raman spectra of the mixture is clearly the result of superposition of the intensities of both Raman peaks of these two inorganic powders. However, we can still identify the compositions of the inorganic powders easily from their characteristic Raman peaks, e.g., the highest Raman peak for each type of inorganic powder caused by the symmetric stretching mode v₁(A₁). Comparison with the Raman spectra of the mixture of the organic solutions shows that all Raman peaks for these three inorganic powder types are separated well within the Raman spectrum of the mixture of inorganic powders.

To quantify the measurement performance for the Raman spectrum of the mixture when it is placed in the different containers, we take the Raman peak at 933 cm⁻¹ as I_p and substitute it into Eq. (31) along with the measured SNRs of the mixtures in the plastic bag, the glass bottle, and the plastic bottle of 462, 415, and 291, respectively. There are no differences among the spectral resolutions and the spectral ranges obtained for the mixtures in the three types of transparent container under the same integration time and laser power conditions. However, the intensity and the SNR of the Raman spectra in the plastic bottle are clearly lower than the corresponding characteristics in the plastic bag and the glass bottle, which may be caused by the higher reflection characteristic of the thick plastic. The analysis above demonstrates the ability of the FWGE-SHRS to identify the components of mixed inorganic powders and to measure the samples when sealed in transparent containers.

5. Summary and conclusions

In this paper, we proposed the concept of a grating-echelle spatial heterodyne spectrometer structure. By combining the GESHS with field-widening prisms, a high-resolution, broadband spatial heterodyne Raman spectrometer based on a field-widened grating-echelle structure was designed and experiments were performed to demonstrate its capabilities. The mathematical expressions and the corresponding derivation process for the Littrow wavenumber and the other spectral parameters in FWGE-SHRS are presented here. The combination of the normal grating with the echelle grating provides a broadband spectral range and a high spectral resolution with measurement of multiple diffraction orders. Additionally, the GESHS not only eliminated ghost images without using the mask required in the conventional DESHS structure, but also can be field-widened to enlarge its FOV.

With the measured Raman spectra and the corresponding analyses performed for mixtures of organic solutions with four diffraction orders and inorganic powders, the designed FWGE-SHRS demonstrated its high-resolution, broadband measurement capabilities in Raman detection, which can aid in the analysis of the components of mixed target materials by measuring the Raman spectrum of the mixture. The interferogram generated by FWGE-SHRS can also avoid interference among the spatial frequencies in the different diffraction orders, and also resolved the ambiguous nature of the Raman peaks. The measured Raman spectrum of the mixed inorganic powders also demonstrates an ability to detect samples sealed in transparent containers. From the experimental results and analysis performed for solid sulfur, acetone, and methanol, we can see that the designed FWGE-SHRS can measure chemicals under conditions involving different integration times, laser powers, and concentrations. Comparison between the FWGE-SHRS and a commercial spectrometer under the same conditions also demonstrates that the FWGE-SHRS has a considerable advantage in the Raman measurement field. All the analyses presented above show that the designed FWGE-SHRS is suitable for use in high-resolution, broadband Raman spectrum measurements with a wide range of potential applications.