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Abstract
The contradiction between spectral resolution and throughput for the optical spectrometers is still a problem that needs to be solved. We introduce a simple and feasible method of the digital projection slit (DPS), which can improve both the spectral resolution and throughput of the optical spectrometer. The DPS spectrum is accurate and reliable without using the optical transfer function (OTF) of the optical spectrometer. The method has been successfully applied in the fiber spectrometer and the Raman spectrometer. The resolution of the recovered spectra can be increased by ~3 times and the throughput can be increased by ~5 times.
© 2017 Optical Society of America
1. Introduction
The optical spectrometer is widely used in many fields as a very commonly analytical tool. The narrow slit is a key part in the optical spectrometer to improve the spectral resolution at the price of reducing the throughput. The contradiction between spectral resolution and throughput for the spectrometer is still a problem. The problem limits the detection of weak signals for the conventional spectrometer, such as astronomy [1, 2], biomedical spectroscopy [3, 4], and Raman spectroscopy [5–7]. The previous methods to overcome the contradiction can be split into two categories: the physical method and the numerical method.
The physical methods use a special physical aperture to increase light throughput without loss of spectral resolution, including the coded aperture and the analog optical slicers. The coded aperture spectrometer, such as Hadamard-transform spectrometer, replaces the slit with a two-dimensional coded matrix [8–10]. Ideally, smaller coded mask features yield better resolution both spectrally and spatially, but diffraction and optical blur negate the advantages for smaller features [11]. The analog optical slicers method transforms a large light beam into a narrow spot without a change of divergence. Such optical slicers can be large in size and limited in getting high spectral information from all the different beam portions [12–16].
The numerical method improves spectral resolution and signal-noise-ratio (SNR) based on de-convolution, which is performed after the spectral information is captured by the detector [17, 18]. For example, the High-throughput Computational Slit (HTCS) method can increase the resolution of the test spectrum by 7 times, 50% higher resolution than their control spectrum [19]. The previous numerical method need collecting optical transfer function (OTF) of the spectrometer in advance. The deviations and errors in the modeled OTF relative to the true OTF will result in inaccuracies in the resulting spectrum produced.
In this paper, we introduce a feasible method of the digital projection slit (DPS), which can improve both the spectral resolution and throughput of the optical spectrometer without modifying the physical slit or requiring the instrument’s optical parameters. Firstly, the principle of the DPS method based on the spectra superposition is presented. Secondly, the DPS recovered spectrum is validated by our home-made spectrometer, which is accurate and reliable to coincide well with the standard spectrum. Lastly, the DPS method has been applied in the fiber spectrometer and the Raman spectrometer successfully.
2. Theory and Methods
An overview of the DPS is shown in Fig. 1. A high-resolution spectrum P0 can be obtained with an ideal narrow slit as shown in Fig. 1(a), while a high-throughput spectrum Pr with a wide slit is shown in Fig. 1(b). This is the contradiction between spectral resolution and throughput of the optical spectrometer. In the DPS method, we split the wide slit to several continuous virtual narrow slits. Pr should be superposed by several high-resolution spectra Pi from the virtual slit as shown in Fig. 1(b). Each spectrum of Pi has the identical peak profile with a wavelength shift. Pr can be expressed as the following formula:
where m is the number of Pi, λ is the central wavelength for P0, Δλ is the shift of central wavelength for each spectrum of Pi, n is the noise. The array L is the intensity distribution of the light beam at the slit.
Fig. 1 Overview of a DPS. (a) The spectral peak acquired with a narrow slit. (b) The spectral peak acquired with a wide slit. (c) The schematic lay-out of the optical spectrometer. (d) The high-resolution spectrum with a narrow slit. (e) The high-throughput spectrum with a wide slit. (f) The high-resolution and high-throughput recovered spectrum by the DPS process.
In order to simply the calculation, Pr can be given by:
where matrix H is a projection operator, which is given by a function of L and Δλ. To obtain P0 from Eq. (2), the core problem is an ill-posed inverse problem. Here, we apply the Landweber algorithm to seek the maximum likelihood parameters until convergence [20, 21], according to the following formula:where k is the number of iterations, the relaxation factor α is an adjustable parameter, ranging from 1 to 0.01.We use a homemade optical spectrometer to validate the DPS method. The schematic lay-out is shown in Fig. 1(c). The grating of the spectrometer is 600 l/mm. The spectrum is captured by the CCD (Newton CCD DU920P from Andor, England) with 26 μm pixel width. The zero-order diffraction pattern is recorded by the CMOS (UCMOS0300 from Cossim, China). The light source is the Renishaw Raman Calibration Source (Gloucestershire, U.K.), which is mainly mixing the Ne and Ar gas light source. The individual fiber diameter of “spot-to-line” converter is 300 μm in the fiber spectrometer. A 785 nm laser is used as the excitation light source in the Raman spectrometer.
The construction of the projection operator H is necessary for the DPS method. As mentioned above, H is given by a function of L and Δλ. L is the intensity distribution of the light beam at the slit. To retrieve the intensity distribution L, we record the zero-order diffraction pattern by a CMOS when every spectrum measurement. L is simple calculated from the reverse process of Fraunhofer diffraction. Δλ is the shift of central wavelength for each spectrum of the virtual slits. In order to simply the calculation, the width of the virtual slit is specified to be the same as the single pixel of CCD, while Δλ is the shift of wavelength for a pixel. In this paper, we use the 26 μm slit in our reference spectrum. Generally, a narrower slit than detector pixel width is little help to improve spectral resolution. It should be noted that the DPS method does not use the optical transfer function, but introduce intensity distribution L at the slit by monitoring the zero-order Fraunhofer diffraction pattern.
To validate the DPS method, we use the Renishaw Raman Calibration Source as the calibration standard spectra. The spectra at 0.2 second exposure time are shown in Fig. 1. For evaluating the quality of the spectra, the spectral resolution is defined by the full width half maximum (FWHM) of the spectrum, the SNR is the ratio of the peak value of the signal to the root mean square of the noise. The reference spectrum with a 26 μm slit is shown in Fig. 1(d). Figure 1(e) shows the test spectrum obtained with a 130 μm slit. The throughput of the test spectrum is increased by 4.75 times to the reference spectrum. The recovered spectrum from the test spectrum by DPS process is shown Fig. 1(f). It is noted that at the wavelength of 750.5 nm, the spectral resolution of the DPS spectrum is 0.33 nm, while the reference and the test are 0.34 nm and 0.80 nm respectively. The resolution of the DPS spectrum is 2.42 times higher than the test spectrum. In the DPS method, the spectral resolution of the DPS spectrum is close to the reference spectrum, because the width of the virtual slit is 26 μm as same as the reference. The spectral resolution of the DPS spectrum just depends on the width of virtual slit. The SNR of the DPS spectrum is 225.84, while the reference spectrum is 77.32. The SNR of the DPS spectrum is 2.92 times higher than the reference spectrum. The improvement of SNR is benefit from the increasing throughput in the DPS processing. Moreover, the DPS method does not bring any side peak, which are in perfect agreement with the standard atomic spectrum.
3. Results and Discussion
The DPS method has promising application potentiality in a variety of spectroscopy, especially in two areas. One is the resolution improvement of the optical spectrometers with wide aperture, such as the fiber spectrometer. The wide aperture always makes the spectral resolution poor. Here, we apply the DPS method in the fiber spectrometer to improve the spectral resolution without changing the aperture size. The other is the throughput improvement in the weak signal measurement. The Raman spectroscopy is a typical signal measurement, which often requires high-resolution to discern Raman emission lines. We also apply the DPS method in the Raman spectrometer to improve the throughput without sacrificing resolution.
In the application of the fiber spectrometer, we still measure the spectra of the Renishaw Raman Calibration Source at 0.1 second exposure time as shown in Fig. 2. The green spectrum is the reference with the 26 μm slit. The blue one is the test with the 300 μm slit. The orange one is the recovered spectrum by the DPS process. At the wavelength of 763 nm, the resolution of the DPS spectrum is 0.37 nm, while the test spectrum is 1.13 nm and the reference spectrum is 0.39 nm. The resolution of the DPS spectrum is 3.05 times higher than the test spectrum. The SNR of the DPS spectrum is 32.56, while the reference spectrum is 6.21. The SNR of the DPS spectrum is 5.24 times higher than the reference spectrum. Comparing the DPS spectrum with the Ne atomic spectrum and the Ar atomic spectrum, the reliability and the accuracy of the spectrum can be guarantee. We can observe that the two peaks are recovered well in the DPS spectrum, which are assigned to the 747.2 nm and 754.4 nm lines from the Ne atomic emission. The two peaks are buried by noise in the reference spectrum, while they cannot be recognized in the test spectrum because of the low resolution.
The Raman spectra of norfloxacin at 0.5 second exposure time are shown in Fig. 3. The sample of norfloxacin (AR) was purchased from Aladdin (Shanghai, China). The green spectrum is the reference with the 26 μm slit. The blue one is the test with the 130 μm slit. The throughput of the test spectrum is increased by 4.85 times to the reference spectrum. The orange one is the recovered spectrum by the DPS process. The SNR of the DPS spectrum is 72.25, while the reference spectrum is 18.07. At the wavenumber of 500 cm−1, the resolution of the DPS spectrum and the reference spectrum is 6.5 cm−1 and 6.3 cm−1. The SNR of the DPS spectrum is 4 times higher than the reference spectrum, while the spectral resolution remains about the same. Using the DPS method, the two triplets centered on wavenumber 400 cm−1 and 458 cm−1 are clearly resolved from the test. The peaks at the wavenumber of 555.5 cm−1 and 573.1 cm−1 are recovered without side peak, while the peaks are buried in the noise of the reference spectrum because of the low-throughput.
Conclusions
The DPS method has been validated to improve the spectral resolution and the throughput of the optical spectrometer, which also has been applied successfully in the fiber spectrometer and the Raman spectrometer. We have demonstrated that the DPS recovered spectra are very accurate and reliable when comparing them to the reference spectra. By monitoring the zero-order Fraunhofer diffraction intensity pattern, the DPS method may spawn in a new generation of commercial slit-based spectrometer.
Funding
National Natural Science Foundation of China (NSFC) (21273159, 21305101, 61378048 and 81671727); National Key Research and Development Program of China (2017YFC0803600); Natural Science Foundation in Tianjin (13JCQNJC05100); Tianjin Research Program of Application Foundation and Advanced Technology (14JCZDJC34700); Open Funding Project of State Key Laboratory of Precision Measuring Technology and Instruments (PIL1605); Program for New Century Excellent Talents in University (NCET-11-0368).
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