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Abstract
We demonstrate a miniaturized broadband spectrometer employing a reconstruction algorithm for resolution enhancement. We use an opto-digital co-design approach, by firstly designing an optical system with certain residual aberrations and then correcting these aberrations with a digital algorithm. The proposed optical design provides an optical resolution less than 1.7 nm in the VIS-channel (400-790 nm) and less than 3.4 nm in the NIR-channel (760-1520 nm). Tolerance analysis results show that the components are within a commercial class, ensuring a cost-efficient design. We build the prototype with a size of 37x30x26 mm3 and demonstrate that by applying a restoration algorithm, the optical resolution can be further improved to less than 1.3 nm (VIS-channel) and less than 2.3 nm (NIR-channel).
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Spectrometry is a substance recognition technique that has been actively used in various fields from food sorting to Mars exploration [1–3]. Compared to other techniques, such as crystallography and chromatography, it allows performing non-destructive chemical and physical analysis of matter in different environments, thus more suitable for medicine and biology, pharmaceutical and chemical industries, forensic sciences, and homeland security [4–6]. In recent years, there is an increased demand for on-site measuring in field applications where immediate results are required [7,8], such as sugar and lactose quantification in food products or explosives detection [9,10]. Therefore, cost-effective, portable spectroscopic solutions which can be used by both experts and individual customers are compelling.
However, the miniaturization of such spectrometric devices is very complex for three main reasons. Firstly, most conventional spectrometers use a combination of multiple optical components to ensure high resolution and throughput, thus typically resulting in a bulky package and long optical path lengths [11–14]. Secondly, due to the limited diffraction efficiency of gratings, broadband spectrometers (e.g., covering the range from UV to NIR) typically utilize mechanical rotating turrets in their optical layouts [15,16], greatly increasing the complexity of a system. Therefore, available portable spectrometers usually work in a narrower spectral range (e.g., VIS or NIR) that reduces the versatility for potential applications. Finally, the traditional design architecture of a spectrometer is based on a linear sensor. Compared to a 2D sensor, it requires more complex optics to achieve a better light collection on a pixel. Without such optics, a high SNR and spectral resolution cannot be guaranteed.
In this work, we propose a cost-effective way to sense the desired analytes with high sensitivity, high reliability, and a sufficiently compact and portable device, providing a responsivity in a broad spectral range. To ensure the compactness together with high overall performance, we use an opto-digital co-design strategy, by firstly designing an optical system with certain residual aberrations and then correcting these remaining aberrations with digital algorithms. In Section 2, the optical design and tolerance analysis of the miniaturized spectrometric device are discussed. The proposed design covers a wide spectral range and is capable of providing a spectral resolution and signal to noise ratio (SNR) that are comparable with state-of-art spectrometers. In Section 3, we demonstrate a digital deconvolution algorithm for resolution enhancement as well as a multi-row readout strategy for SNR improvement. The assembled prototype is discussed in Section 4, together with the experimental results obtained with the proposed digital algorithms. Finally, conclusions are drawn and future work is discussed in Section 5.
2. Optical design and prototyping
2.1 State-of-the-art miniaturized spectrometers and main considerations for design
Based on the different principles for acquiring narrow bands, current state-of-art broadband spectrometric devices can be divided into four groups [8]: namely dispersive optics, Fourier transform-based, narrow filters, and computational methods.
The first and most commonly used method is dispersive optics-based. It has several examples of commercially implemented broadband miniaturized systems presented in Table 1. The spectral range of designs based on dispersive optics is limited by two major factors. Firstly, the free spectral range of such designs is restricted by high diffraction orders. Secondly, there are only a few commercial detectors capable of detecting light both in the VIS and NIR (wavelengths higher than 1000 nm) ranges. The latter leads to the use of two separate detectors that makes the optical layout more complex and increases the overall cost of a spectrometer. The design of a single-photon dispersive spectrometer has been reported recently [17], where a superconducting nanowire sensitive in the range from 600 to 2000 nm was used as a detector. Unfortunately, this detector needs to be cooled down to a temperature of 1.5K to provide superconductivity that makes such a system not portable.
Table 1. State-of-art miniaturized broadband spectrometers and our target performance
The second method is based on applying a Fourier transform, which measures the temporal light coherence while shifting the mirror in one of the interferometer arms. In this way, the intensity as a function of the light path difference is captured and used for the reconstruction of an original spectrum. The spectral resolution that can be reached by such a system is limited by the maximum optical path difference and is not higher than 7.5 nm in current broadband state-of-art devices [18]. Thirdly, a common implementation of a spectrometric device based on narrow filters contains a Fabry-Perot interferometric layout, where the trade-off between the resolution and spectral range is invariably present. Thus, the resolution of a broadband system based on Fabry-Perot filters is usually limited by 8-12 nm [19,21]. At last, computational based spectrometers create wavelength-dependent patterns at an image plane which are used afterwards for the reconstruction of the incident spectrum by solving linear equations. It has been shown that a resolution of 2.1 nm can be obtained in the spectral range from 400 to 900 nm while preserving the size relatively compact [20]. However, this approach requires a complex calibration procedure and is highly sensitive to temperature fluctuations and vibrations.
As seen from Table 1, our target is to develop a miniaturized spectrometer sensitive in a broad spectral range from 400 to 1520 nm, while keeping the spectral resolution lower than 4 nm. To our knowledge, there is no such design combining a high spectral resolution, a broad spectral range and a miniaturized housing in one single device. A multi-channel spectrometer design has been reported [22], where the broad spectral range is divided into several channels. Each channel contains its blazed diffraction grating to maximize the overall diffraction efficiency in a broad spectral range. Employing the same strategy, we propose a different optical layout, allowing us to simplify and further miniaturize the spectrometer.
Instead of using a line sensor, as in most spectrometers, in our design, we use a 2D SONY IMX990 sensor sensitive in a broad spectral range from 400 to 1700 nm. A 2D sensor allows using one detector for several spectral channels, by dividing the sensor’s area into several parts. Furthermore, a 2D sensor helps to soften the tolerances to fabrication and assembly of a miniaturized spectrometer, since light is not required anymore to be collected on one pixel, as in the case of a line sensor. To complement the spectrometer design, we also demonstrate the use of an algorithm for computational reconstruction of the non-aberrated spectrum. It results in a more flexible optical design, allowing the presence of residual optical aberrations in a system.
2.2 Optical design and modeling
The overview of the proposed optical design is given in Fig. 1. The light comes from the entrance slit (size of 15x500 um2) through the mechanical aperture, which is used to define the NA (0.12) and to reduce the amount of stray light in the rest of the system. Afterwards, the light is collimated by an achromatic doublet lens, providing excellent collimation across the whole spectral range. To have a spectrometer system with one entrance port, the wavelength division block, comprising the dichroic beamsplitter and flat mirror, is placed after the lens. After the beamsplitter, the spectrum is broken down into two light paths: VIS (400-790 nm) and NIR (760-1520 nm). The VIS-channel reflects towards the first diffraction grating, whereas the NIR-channel transmits through the beamsplitter and reflects from the flat mirror towards the second diffraction grating.
Fig. 1. Optical configuration overview. The blue, green, and red rays correspond to 400, 600, and 790 nm in the VIS-channel and to 775, 1200, 1550 nm in the NIR-channel, respectively.
The lines density of the gratings is chosen to provide an identical diffraction angle for the central wavelength in both channels (1200 lines/mm for VIS and 600 lines/mm for NIR). Thanks to that, the dispersed light follows the same optical path after diffraction from the gratings in the two channels. As a result, we could use one cylindrical mirror and one sensor for both channels to perform the imaging of the entrance slit. It considerably simplifies the system since these two components are used by both channels at the same time. In turn, the implementation of a cylindrical mirror in the layout helps to avoid spectral distortion (known as "smile") due to imaging only across the meridional plane.
Figure 2 illustrates the image obtained in Zemax OpticStudio after ray tracing through the suggested configuration shown in Fig. 1. Each channel occupies half of the sensor and does not overlap with the neighboring range. The spectral data can be read out by defining a specific row number for each channel, as indicated by red lines in Fig. 2.
Fig. 2. (a) Image simulation with a set of six predefined wavelengths. The red lines demonstrate the chosen rows for data readout. (b) Cross-section with FWHM values shown next to corresponding peaks.
The overview of the aberrations of the optical system is represented by the Zernike polynomial coefficients, as shown in Table 2. The high astigmatism comes from the cylindrical mirror serving as an imaging element. It does not alter the image along the dispersion plane and can be ignored. The spherical aberration is low and does not have a significant impact on the image quality. The coma aberration stems from the off-axis incidence of the light on the cylindrical mirror, which contributes mostly to the asymmetrical shape on the spectral peaks, as shown in Fig. 2(b). It results in worse imaging in a region of the short wavelengths both in the VIS and NIR channels (blue rays in Fig. 1). In the end, the optical resolution shows a wavelength dependence and is lower in both channels in the region of short wavelengths. The resolution of the VIS and NIR channels are summarized in Table 4 (Section 4.2), ranging between 1.75 and 1.48 nm in the VIS channel and between 3.51 and 2.75 nm in the NIR channel. Typically, coma aberration can be corrected by using more optical components or more complicated optical surfaces. Instead, we propose a digital deconvolution algorithm to correct the coma during the signal processing which also ensures a high spectral resolution and a cost-effective design.
Table 2. Representative Zernike polynomial coefficients for the VIS channel (similar in the NIR channel). The coefficients are given in waves.
2.3 Tolerance analysis
To realize the micro-spectrometer system, the influence from misalignments of the optical components and the inaccuracies of the optical surfaces should be considered in advance. These errors are usually caused by limited manufacturing tolerances of the mechanical housing and holders. Furthermore, no optical component can be made perfectly; thus, potential inaccuracies in their fabrication also should be taken into account. Therefore, an evaluation of the sensitivity to such misalignments and fabrication errors was performed.
As a function of merit, the mean resolution for three wavelengths in both channels (specified as in Fig. 2) was used. To keep the spectral resolution lower than values specified in Table 1, we defined a 10% degradation of the mean resolution in both channels as acceptable. We also controlled the position of the spectra on the sensor, ensuring that they do not fall outside the active sensor area and do not overlap with each other. Table 3 lists the tolerances obtained after performing a tolerance analysis. As seen, none of the tolerances requires a precision or high precision tolerance class.
Using the defined values as maximum possible misalignments, we performed 500 Monte Carlo simulations to analyze the influences of the alignment errors on the spectral resolution. The results both for the VIS and NIR channels are provided in Fig. 3. According to these simulations, there is 80% probability that the mean resolution value is better than 1.8 nm for the VIS-channel and better than 3.5 nm for the NIR-channel.
Fig. 3. Results of the performed Monte Carlo analysis for the VIS (left) and NIR (right) channels. The vertical dashed lines correspond to the nominal mean spectral resolution.
3. Digital algorithms
3.1 Deconvolution reconstruction algorithm
The classical optical design strategy aims at minimizing optical aberrations, as this ensures high performance. However, it often requires more complicated optics and puts additional restrictions on a system (e.g., most optimal relative positioning of optical elements). Due to the rapid development of image processing techniques, many co-design methods have been proposed to design optical systems with fewer components but with residual aberrations which are digitally corrected to further improve the performance [25–27]. Here, we apply this computational imaging strategy to our spectrometer results.
An optical spectrometer is an imaging system that transfers an image of the entrance slit to a sensor. Imaging in every optical system can be described as a convolution of an image entering an optical system and a transfer function of the system. Such transfer function is called point spread function (PSF) and describes the response of an imaging system to a point source or point object. By knowing the PSF of the system, one can estimate how an initial object would look in a system without optical aberrations (ideal imaging system). In general, such restoration techniques can be classified into two groups [28]: blind and non-blind deconvolution methods.
The first type ’guesses’ the transfer function from a measured spectrum, without any prior information. For example, it can be realized through the kernel estimation by the Gaussian fitting of the measured spectral peaks [29]. Other authors utilized Tikhonov regularization to restore degraded Raman spectra [30–32]. However, those blind deconvolution methods are typically complex and sensitive to noise. Besides, they work with symmetrical transfer function estimates, whereas the transfer function in our optical system is asymmetrical.
As a contrary, the second group relies on known transfer functions from measurements. It provides a more accurate description of the transfer function and, hence, typically more accurate deconvolution results. The non-blind deconvolution method was reported to restore the spatial resolution of astronomical images [33,34]. In this work, we apply such a non-blind approach in a spectrometric application to greatly improve the spectral performance. We use two different ways to specify the transfer function of our spectrometer: by ray tracing in Zemax OpticStudio and by determining it from the freestanding peaks of a measured spectrum, as described in Section 4.2.
In the suggested design, a restoration method can help to reduce the influence of coma aberration on the optical resolution of the system. In the case of one-row readout, a 2D PSF is not needed and can be simplified to a 1D line spread function (LSF). Here, we estimated the LSF by ray tracing an infinitely narrow slit image through the optical system in Zemax OpticStudio. The deconvolution method was implemented in MATLAB, as depicted in Fig. 4. Firstly, the Fast Fourier Transform (FFT) of both the original spectrum s and the line spread function l is calculated. Then the ratio between these functions in the frequency domain S and L is taken. Finally, the Inverse Fast Fourier transform (IFFT) is applied to transfer the deconvoluted spectrum from a frequency domain DS to a spectral domain ds.
To illustrate the algorithm’s output, we ray traced two spectral peaks at 401.5 and 403.0 nm through the system. As was pointed out already in Fig. 2(b), the spectral resolution in this wavelength region is equal to 1.75 nm. Therefore, two peaks with a spectral separation of 1.5 nm are barely resolvable, as seen in Fig. 5(a). Furthermore, the coma tail is present and spreads out down to 392.0 nm. The spectrum after the deconvolution algorithm was applied is shown in Fig. 5(b). Two peaks are clearly resolvable with a FWHM less than 1 nm for both peaks.
As explained in Section 2.2, the coma aberration in the proposed design is wavelength-dependent. Therefore, to apply the deconvolution method to a broad spectrum, the whole range has to be divided into N segments and the LSF to be individually estimated for each of them. An example of the segmented deconvolution is presented in Section 4.2, where the algorithm is applied to real measurement data.
3.2 Multi-row readout for SNR improvement
The SNR is an essential property of the spectrometer to determine its performance. To detect substantially different values, close to each other with maximum sensitivity, one needs a high SNR value. Typically, a SNR higher than 100 is required to get distinct spectral information.
Conventional spectrometers collect all light on one line detector and do not require additional signal processing. Whereas in the proposed design, as Fig. 2 illustrates, the power at a specific wavelength is distributed among the number of pixels (wavelength footprint). Therefore, with one-row readout (red lines in Fig. 2) an extensive amount of energy entering the system is not used, in turn deteriorating the SNR of the spectrometer. However, by averaging the signal across all pixels inside the wavelength footprint, the SNR can be improved. In the proposed design, a footprint has a shape of a straight line that allows to average the signal along one column:
where I is the irradiance at the pixel, x and y the pixel row and column number, λ the wavelength, and N the number of rows to be used for averaging. Theoretical simulations have shown that by changing the number of readout rows from 1 to 100, the SNR value can be improved by a factor of 10 (square root of readout rows). Such an algorithm can be compared with the time averaging of a signal when the same spectrum is taken multiple times to reduce the noise magnitude. However, time-averaging increases the time required to perform one measurement, whereas the multi-row readout works with one frame. Time averaging and multi-row readout can be potentially combined to further improve the SNR of the measurements.4. Experimental results
4.1 Prototyping
To provide a proof-of-concept demonstration, we designed the mechanical housing for assembling the optical spectrometer. The picture of the assembled spectrometer is provided in Fig. 6. Stereolithography was chosen as technology for 3D printing the mechanical holders since it yields the highest resolution among currently available commercial techniques suitable for fast prototyping. The minimal feature size in the XY plane is 130 $\mathrm {\mu }$m with an accuracy of 50 $\mathrm {\mu }$m. The housing consists of three parts, printed separately and later assembled through gluing and threaded joints. The mechanical aperture, lens, two gratings and cylindrical mirror are mounted within the designed holders printed as one part with the spectrometer housing parts. The entrance slit was produced using photolithography and afterwards glued on the SMA fiber connector (red in Fig. 6).
The design was based on the sensor SONY IMX 990, however, at the time of writing, it was not yet released for purchase as an off-the-shelf device. Therefore, we replaced it with a camera from XIMEA with AMS CMOSIS CMV2000 sensor. This sensor has the same pixel pitch (5.5 µm) and diagonal such that for imaging in both channels no modifications in the previously proposed optical design are needed. However, it provides a spectral sensitivity only in a limited wavelength range from 300 to 1000 nm. Since both channels follow a similar optical path, we assume that the imaging quality in the left-out range (from 1000 to 1520 nm) in the NIR-channel can be estimated from the performance of the system in the VIS channel.
4.2 Experimental results: with and without restoration algorithm
To examine the spectral resolution of the assembled demonstrator, we used the calibration Ar-Hg source that provides a spectrum with distinctive spectral lines in the range from 300 to 1000 nm. Preliminarily, a calibration was performed to relate the pixel number to wavelength. Since a diffraction angle has a non-linear dependence on wavelength, a polynomial fit is needed for precise calibration.
The spectrum measured after calibration is shown in Fig. 7(a), whereas the comparison between simulated and measured numerical FWHM values of the spectral peaks is given in Table 4. The mean spectral resolution in the VIS-channel is 1.79 nm that falls into the range predicted by the Monte-Carlo analysis in which possible misalignments were considered. For the NIR-channel, we use the representative wavelength of 912 nm. The measurements show a spectral resolution of 3.35 nm, satisfying the simulation result of 3.40 nm. Due to the wavelength limitation of the sensor, we are not able to estimate the resolution for the other NIR wavelengths. Based on the behavior at 912 nm, we expect that the resolution for the other NIR wavelengths shows comparable results to the obtained simulation values (as shown in Fig. 7).
Fig. 7. The measured spectrum of the Ar-Hg source without (a) and with the restoration algorithm applied (b). The inlets illustrate two spectral peaks at 577 and 579 nm.
Table 4. The comparison of the resolution (FWHMs of spectral peaks) achieved through simulations, measurements, and with the reconstruction algorithm applied. Theoretical minimum values correspond to the same geometrical layout without aberrations present.
As was presented in Section 3.1, the effect of aberrations present in a system can be digitally corrected by employing a deconvolution restoration algorithm. In the case of a broad spectrum, it has to be divided into several segments to estimate the LSF for each of them individually. Here, the LSFs were estimated by deconvolution of a slit function and one of the freestanding peaks from the measured spectrum. The slit function is a 1-D rectangular function with a width equal to the entrance slit width. In comparison with the LSF obtained by ray tracing in Zemax OpticStudio (Section 3.1), this method provides a more precise estimation of the LSF since it uses an actual image of the entrance slit. The design model does not describe misalignments that occurred during the assembly of the spectrometer, whereas a real image results from propagation through an assembled system.
Thus, the VIS channel was divided into three segments: 400-520, 520-640, and 640-780 nm. The peaks at 435, 546 and 764 nm, respectively, were used to estimate the LSF for each of the segments. In the case of the NIR channel, we used one peak at 912 nm for the whole spectral range from 760 to 1000 nm. A low-pass frequency filter was additionally applied to the restored spectrum to reduce the noise in the original spectrum that was amplified after deconvolution.
The spectrum after restoration using the proposed algorithm and filtering is shown in Fig. 7(b). The comparison between FWHM values of the spectral peaks in the measured and restored spectra is provided in Table 4. As seen from Fig. 7(b), the spectral peaks after restoration are more symmetrical and have no coma tail as in the measured spectrum. To evaluate the restoration algorithm, Table 4 lists the values of the theoretical minima for each of the examined spectral peaks. These values are calculated for the proposed optical design, having perfect imaging properties (no aberrations). For this estimation, only the layout’s geometry, grating dispersion and slit width are considered. As seen, the FWHM values of the reconstructed spectrum are close to the theoretically achievable minimum, proving the efficiency of the proposed algorithm.
Such an algorithm can soften the requirements one applies to an optical configuration of a spectrometer, as was shown in the example of the presented design. Aberrations and non-perfect imaging properties are compensated by reconstruction algorithms. A calibration light source can be replaced by a tunable light source or a set of laser sources to estimate the LSFs more evenly for a higher number of segments. Furthermore, such a LSFs estimation can be performed on a per-device basis. Then the algorithm may compensate not only the residual aberrations in the optical design but also additional aberrations caused by misalignments during the assembly of a specific device.
4.3 Data processing with multi-row readout strategy
The SNR is estimated by taking 100 measurements with an integration time sufficient to have the sensor almost fully saturated (>90% of the maximum level). The standard deviation of the signal over these 100 measurements is a good indication of the noise level. Then, the SNR is calculated as follows:
where µ is the average and σ is the standard deviation over 100 measurements. As light source, we used a halogen-deuterium light source AvaLight-D-S that has a broad spectrum in the entire range of interest from 400 to 1000 nm.Figure 8 demonstrates one of the raw frames used for SNR calculation. The red line indicates the one-row readout, and it was used as a central row in the multi-row readout. The calculated SNR with single-row readout is presented in Fig. 9 (blue curve). The integration time is 3 ms. The SNR value can be estimated based on the maximum values that correspond to almost fully saturated pixels. Thus, for the case of one-row readout, the SNR was higher than 100. As we explained in Section 3.2, this value can be improved by implementing a multi-row readout. The proposed algorithm was applied to read out the data from the same 100 measurements. The results for 10, 50, and 100 rows readout are given in Fig. 9. As can be seen, even the readout using 10 rows improves the SNR value by a factor of 4, whereas 100 rows bring an improvement of 10 times, giving a value of SNR higher than 1000.
Fig. 8. Cropped raw frame (VIS-channel) with the spectrum of a halogen-deuterium light source imaged on a sensor. The red line depicts the row used as a central in the multi-row readout.
Thus, the multi-row readout complements the design, employing a 2D sensor, and helps to deal efficiently with all light present on the sensor area. Depending on the required specifications, multi-row readout can be combined with the reconstruction algorithm to have both the advantages of high optical resolution and high SNR.
5. Conclusion
We have designed and demonstrated a miniaturized broadband spectrometer employing a deconvolution reconstruction algorithm for resolution enhancement. The developed demonstrator operates in the range from 400 to 1000 nm, which can be expanded to 1520 nm with the use of a sensor as described in Section 2.2. The size of the device is 37x30x26 mm3, including housing and electronics. The spectrometer has a resolution less than 1.9 nm in the VIS and less than 3.5 nm in the NIR range. We have shown that the resolution can be further improved by applying a restoration algorithm. In this way, we obtained a spectral resolution less than 1.3 nm in the VIS and less than 2.3 in the NIR range. We also presented an effective method to read out data from a 2D sensor without deteriorating the SNR performance of the spectrometer. A SNR value higher than 1000 was achieved with an integration time of 3.2 ms.
The proposed optical design is pioneering for 2D sensor-based spectrometers. It allows using one sensor for optical detection in a broad wavelength range and helps to soften the tolerances for fabrication and assembly of a miniaturized spectrometer. The suggested restoration algorithm is aimed to mitigate the requirements on the optical configuration of spectrometers by shifting the complexity from the optical part to digital post-processing. The algorithm can be further improved by employing advanced iterative techniques with a more precise description of noises present in the unrestored signal. In turn, the spectrometer can be further miniaturized by employing imaging diffraction gratings. Therefore, in our future work, we will explore new possibilities of merging optical design with digital restoration algorithms.
Funding
European Union’s Horizon 2020 Research and Innovation program under the Marie Sklodowska-Curie Action (765635, xCLASS); Fonds Wetenschappelijk Onderzoek (FWOTM1039); Vrije Universiteit Brussel (Hercules, Methusalem, OZR).
Acknowledgment
We thank Vrije Universiteit Brussel and Anteryon B.V. for providing the necessary equipment and software licenses.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data generated in this work is available from the corresponding author upon reasonable request.
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