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Abstract
We introduce an absorption spectrum measurement method in the visible regime based on dual interferometer configuration. The proposed method can realize the measurement of the absorption spectrum by addition and calculation of the alternating current (AC) components of interferograms from dual symmetrical interferometers in one measurement, with no need to subtract twice-measured spectrum data with or without samples in the traditional single interferometer method, thus expanding the dynamic range of measurement, especially suitable for weak absorption. The absorption spectra of FB570-10 bandpass filter and NF533-17 notch filter measured by this method conform to the official data.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fourier transform spectroscopy (FTS) has been used successfully in spectroscopy for decades. The principle is to use the Fourier transform of interferogram collected by two beam interference to obtain the spectral information of the incident light [1,2]. The core of FTS is the Michelson interferometer. The incident light beam is divided into two beam replicas of the same amplitude, which are reflected by the fixed mirror and moving mirror [3]. In the visible range, FTS retains advantages such as high absolute frequency accuracy, high throughput, high-frequency resolution, and broad wavelength coverage [3]. Compared to dispersive optics or filter-based spectroscopy, the advantages of FTS also include a larger signal-to-noise ratio, compact size, and high sensitivity [4]. FTS requires control of the optical path differences (OPDs) with high precision, it is easily achieved in the relatively long mid-infrared wavelengths from the interference fringes of the He-Ne laser [3]. However, in the visible range, the shorter wavelengths lead to the tracking resolution of the conventional He-Ne laser does not meet the Nyquist sampling theorem, therefore, the complicated optical setups are needed. The spectral folding technique and preselection optical filters provide high resolution in a restricted regime, but it is hard to use in a single measurement [5]. Many kinds of position sensors, such as the linear variable differential transformer (LVDT) and the interferential scanning grating (ISG), have been used in the UV-visible FTS, however, these instruments require stringent operational conditions [6]. The heterodyne interferometer uses a phase-locked loop to lock the phase difference between a reference beat frequency signal and a measurement beat frequency signal to feedback control the velocity of the moving mirror [7]. Alternatively, the beam-folding technique provided a method to satisfy the tracking resolution by subdividing the interference fringes of the He-Ne laser [8,9]. High-precision absorption spectra are required in many cases such as using the shift in the absorption spectrum to judge whether the CH3OOH remains in a liquid layer between the ice grains [10], detecting the Zwikker- and Parri color by means of visible absorption spectra [11]. Generally, the absorption spectrum is measured by using single interferometer method [12–14]. The absorption spectrum is obtained by subtracting the spectrum with samples from the one without, for the reason that the subtraction of interferograms in twice measurements is hard to achieve due to the position-tracking misalignment of the interferograms. However, the subtraction of spectra is hard to identify the very weak absorption due to a limited resolution of Analog to Digital (A/D) conversion. In addition, the instability of the light source, the noises and the position-tracking interferogram misalignment in the twice measurements lead to measurement accuracy decreased. A higher dynamic measurement range, i.e., a higher-resolution Analog-Digital Converter (ADC) and a lower noise level is necessary for narrowband absorption spectra.
In this paper, a visible absorption spectrum measurement method based on dual interferometer configuration is presented. The four-path beam-folding configuration is adopted to improve tracking resolution. The difference between the dual interferometer configuration and the previous one used in the radiation spectrum measurement is in deploying the two symmetrically arranged interferometers to render both interferograms to be detected simultaneously, one with absorbent material and the other without, the dual interferometer configuration can realize the position-tracking alignment and synchronization of the interferograms, with and without samples, of both symmetrical interferometers, thus the addition of AC components of the interferograms can be achieved in synchronous optical path difference[OPD]. The interferogram addition method based on dual interferometer configuration reduces the measurement errors caused by the position-tracking misalignment and unstable light source and noises in twice measurements. In contrast of the spectral subtraction, the sum of AC components of interferogram signals can be amplified by programmable gain amplifier before A/D conversion, so its A/D conversion resolution can be enhanced without changing the ADC, for this reason, the weak absorption spectrum can be easily measured. The method enhances the dynamic range of the measurement signal and ensures the synchronization in OPD thus improves the accuracy of measurement data. A FB570-10 BP filter and a NF533-17 notch filter are used as absorbent materials to verify the feasibility of the measurement method based on dual interferometer configuration. The testing results by the measurement are similar to official data of samples.
2. Optical setup of the system
The setup of the absorption spectra measurement system is shown in Fig. 1(a). The system is divided into two parts, the position-tracking interferometer on the left side and the measurement interferometers on the right side, that share the common optical translation stage. The position-tracking interferometer uses a four-path beam-folding configuration to generate the position-tracking signal of OPD, it provides sampling interval signals for the measurement interferograms [8]. The measurement interferometers use two large-diameter hollow retroreflectors and a larger-sized beam splitter to obtain double interferogram signals. The installation diagram is shown in Fig. 1(b), the position-tracking interferometer, shown on the right-hand, is used for position tracking. In contrast, the measurement interferometers, shown on the left-hand, to generate the measurement interferograms. The position-tracking interferometer and the measurement interferometers are arranged symmetrically. The four-path beam-folding configuration consists of a movable part (two corner retroreflectors) and a fixed part (a corner retroreflector, a reflector and double prism). The movable part and moving mirror are placed back-to-back on the same optical stage. The direction of the beam for the measurement interferometers is shown in this figure.
When the optical stage traverses a distance $x$ from the zero-path difference (ZPD) position, the resultant OPD is $8x$ in the position-tracking interferometer [8]. The translational imperfections of FTS will cause misalignment errors, including horizontal axis, vertical axis, and rotation errors, which will cause the non-synchronization of sampling interval signals. The deployment of retroreflectors and the symmetrical arrangement between the position-tracking interferometer and the measurement interferometer had been adopted to counteract these errors [8]. This method is used to remain synchronous and eliminate the measurement errors caused by the translational imperfections of FTS in the dual interferometer system.
For a conventional Michelson interferometer, the interferogram ${I_p}(x)$, detected by the photodetector is
The four-path beam-folding configuration increase the change rate of fringe intensity by a factor of 4 for position-tracking interferometer [8]. Therefore, the position-tracking interferometer gives rise to an interferogram:
Here, ${I_p}_0$ is the maximum intensity of the fringes, and ${\sigma _0}$ is the wavenumber of the He-Ne laser. ${I_p}(x)$ is used to generate the position-tracking signal of OPD by restraining DC component and doing zero-crossing comparison.
The absorption of the beam splitter is neglected and assumed the transmission and reflectance of the splitting film are 50% respectively. The beam through the beam splitting film will cause multiple beam interference, that contributes to the fact that there is a phase difference of π/2 between the reflected and transmitted waves [15]. For the photodetector1, both of interference beams are reflected and transmitted once by the splitting film that leads to the phase difference counteracted. For the photodetector 2, one interference beam is reflected twice, and the other beam is transmitted twice, thus the additional phase difference is π. In the experiment, this conclusion has been validated by using the He-Ne laser as the measured light.
Supposed the intensity detected by photodetector1 is
The intensity detected by photodetector2 is
where the B(σ) is the spectrum of the incident beam measured, and ${I_0}$ is the total intensity of input light beam.
When an absorbent sample is put in the measurement optical path, the AC component of the interferogram, can be written as
We obtain after simple addition operation:
Two IPL10530DAL photodiodes are used as the photodetector1 and photodetector2 to keep the same spectra responsivity. The result of Eq. (7) is the sum of AC components [SAC] of interferograms measured at photodetector1 and photodetector2 circuits. An amplifier is used to adjust magnification of the photodetector1 circuit that makes the SAC signal nearly zero when no absorbing sample is put in. For a narrowband absorption sample, the SAC of interferograms is very small, so a programmable gain amplifier is used to calculate and amplify it in order to achieve a high digitized resolution.
The B(σ) of Eq. (5) and B(σ)α(σ) of Eq. (7) can be obtained by FFT, and thus, the absorption curve α(σ) of absorbent material can be deduced.
3. Results and discussion
A He-Ne (632.8 nm) laser is used as the reference light, while the super bright white light LED is used as the measurement light source, and the number of acquired data is 4096(scan length of ∼162µm). The amplifier gain of photodetector1 circuit is fine adjusted so that the AC components of double interferogram signals measured at photodetector1 and photodetector2 nearly cancel out each other when no absorbent material is put in front of photodetector2. The performance of the dual interferometer configuration system is evaluated by measuring the spectral characteristics of a FB570-10 bandpass filter and a NF533-17 notch filter. The spectra measured for the two filter are illustrated in Figs. 3 and 5.
Fig. 3. (a) Spectrum of the white light LED measured by the photodetector1. (b) Corresponding spectrum of the SAC signal. (c) Absorption curve of the FB570-10 BP filter measured by system.
Fig. 4. (a) Spectrum of the NF533-17 notch filter measured by the traditional method. (b) The subtraction result of double spectra (with sample and without sample). (c) Absorption curve of the NF533-17 notch filter measured by the traditional method.
Fig. 5. (a) The SAC signal of interferograms (without amplification). (b) The SAC signal of interferograms (with 40 times amplification). (c) Absorption curve of the NF533-17 notch filter measured by the system (with 40 times amplification).
3.1 Test analysis of the FB570-10 bandpass filter
The data of the FB570-10 bandpass filter given by the official website are as follows. The central wavelength (CWL) is 570 ± 2 nm, and the full width at half maximum (FWHM) is 10 ± 2 nm, and the minimum of the transmission at peak (T) is 50%. The transmission is only guaranteed for the specified CWL, the performance may vary from lot to lot.
Figure 2(a) and (b) show the interferogram measured at photodetector1, the SAC of interferograms in turn.
The spectra measured by the system are illustrated in Figs. 3(a) and (b). Figure 3(a) shows the spectrum, deduced from the interferogram recorded by the photodetector1, of the white light LED, i.e., the B(σ). The spectrum shown in Fig. 3(b) is the FFT result of SAC of interferogram, i.e., the B(σ)α(σ). In the absorption curve of the FB570-10 BP filter measured by the system [Fig. 3(c)], the CWL is 569.4nm (17561cm-1), and the FWHM is 8.7 nm, and the T is nearly 0.5. The measured spectra data is basically consistent with the official. It is verified that the dual interferometer configuration method is feasible in the measurement of the absorption spectrum.
3.2 Test analysis of the NF533-17 notch filter
The NF533-17 notch filter is used to verify the measurement accuracy of narrowband absorption. The data of the NF533-17 notch filter given by the official website are as follows. The CWL is 533 ± 2 nm and the FWHM is 17 ± 2 nm, moreover, the passbands are 400∼517 nm and 548∼710 nm. The spectra measured by the traditional FTS absorption measurement method and measured by the dual interferometer configuration method are shown in Figs. 4 and Figures 5 respectively.
Figure 4(a) shows the spectrum when put the NF533-17 notch filter into the photodetector 2. The spectrum shown in Fig. 4(b) is the subtraction result between the spectrum when no sample put into the photodetector 2 and the spectrum of the Fig. 4(a). In the absorption curve of the NF533-17 notch filter measured by the traditional method [Fig. 4(c)], the CWL is 530.5 nm (18850.3cm-1), and the FWHM is 15.7 nm, especially, the absorption rate is only nearly 80%.
Due to a limited ADC resolution, the very low SAC level of interferogram showed in Fig5. (a) leads to the loss of many SAC details after A/D conversion, that have a bad effect on the accuracy of measured spectra. In order to reduce the influence caused by the quantization errors, the SAC signal is amplified by the programmable gain amplifier. Figure 5(b) shows the SAC signal of interferogram by 40 times amplification, after A/D conversion more details of the interferogram can be obtained under the same ADC resolution, in other words, the digitized interferogram with a high resolution is obtained, at the same time, the noise is also reduced due to the limitation of the amplifier bandwidth. In the absorption data of the NF533-17 notch filter measured by the system [Fig. 5(c)], the CWL is 531.03nm(18831.36cm-1), the FWHM is 16.38nm, and the absorption rate is nearly 100%.
Comparing Fig. 5(c) with Fig. 4(c), the measured data by the dual interferometer configuration system is more consistent with the official data, moreover, the noise is obviously less than Fig. 4(c). The results illustrate the system is very suitable for the narrowband absorption spectrum measurement.
4. Conclusion
In conclusion, the visible Fourier transform absorption spectrum measurement method based on the dual symmetrical interferometer configuration can avoid the position-tracking misalignment errors in twice measurements of single interferometer system, and reduce the errors resulting from the instability of the light source and the noise in interferograms during the twice measurements. The absorption spectrum is deduced by the addition and calculation of AC components of interferograms from dual symmetrical interferometers in once measurement with no need for the subtraction of spectra data. The four-path beam-folding configuration is used to generate the position-tracking signal of OPD to provide sampling interval signals. The dual symmetrical interferometers can work together simultaneously, which retains the synchronization of the measurement interferometers so that the SAC of both interferograms can be obtained, and then the absorption curve is deduced. The system is applicable to the spectrum measurement of weak absorption such as the narrowband absorption, because the SAC signal of interferogram can be amplified by programmable gain amplifier, in other words, the quantization errors is reduced, thus the accuracy of the system is improved. Moreover, the dual symmetrical interferometer method also simplifies the calculation to measure the absorption spectrum.
We have developed and experimentally validated an absorption spectrum measurement method in the visible regime based on dual interferometer configuration. The obtained absorption curves of the FB570-10 bandpass filter and the NF533-17 notch filter are measured in our experimental system, are consistent with the official data. Therefore, the method can be used to measure the absorption spectrum.
Funding
Science and Technology Development Plan of Shandong Province (No. 2013GGX10119).
Acknowledgments
We gratefully acknowledge the support from the Science and Technology Development Plan of Shandong Province [China] (Grant No. 2013GGX10119)
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. V. Jovanov, E. Bunte, H. Stiebig, and D. Knipp, “Transparent Fourier transform spectrometer,” Opt. Lett. 36(2), 274–276 (2011). [CrossRef]
2. M. Schardt, P. Murr, M. Rauscher, A. Tremmel, B. Wiesent, and A. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24(7), 7767–7776 (2016). [CrossRef]
3. A. Oriana, J. Réhault, F. Preda, D. Polli, and G. Cerullo, “Scanning Fourier transform spectrometer in the visible range based on birefringent wedges,” J. Opt. Soc. Am. A 33(7), 1415–1420 (2016). [CrossRef]
4. E. Heidari, X. Xu, C.-J. Chung, and R. T. Chen, “On-chip Fourier transform spectrometer on silicon-on-sapphire,” Opt. Lett. 44(11), 2883–2886 (2019). [CrossRef]
5. F. Grandmont, L. Drissen, and G. Joncas, “Development of an Imaging Fourier Transform Spectrometer for Astronomy,” Proc.SPIE 4842, 392 (2003). [CrossRef]
6. G. Michel, K. Dohlen, J. Martiganc, J. C. Lecullier, P. Levacher, and C. Colin, “Interferential scanning grating position sensor operating in space at 4 K,” Appl. Opt. 42(31), 6305–6313 (2003). [CrossRef]
7. R. P. Cageao, J.-F. Blavier, J. P. McGuire, Y. Jiang, V. Nemtchinov, F. P. Mills, and S. P. Sander, “High-resolution Fourier-transform ultraviolet–visible spectrometer for the measurement of atmospheric trace species: application to OH,” Appl. Opt. 40(12), 2024–2030 (2001). [CrossRef]
8. X. Z. Wang, K. Y. Chan, and S. K. Cheng, “Near UV-near IR Fourier transform spectrometer using the beam-folding position-tracking method based on retroreflectors,” Rev. Sci. Instrum. 79(12), 123108 (2008). [CrossRef] .
9. R. K. Chan, P. K. Lim, X. Wang, and M. H. Chan, “Fourier transform ultraviolet-visible spectrometer based on a beam-folding technique,” Opt. Lett. 31(7), 903–905 (2006). [CrossRef]
10. S. A. Epstein, D. Shemesh, V. T. Tran, S. A. Nizkorodov, and R. B. Gerber, “Absorption Spectra and Photolysis of Methyl Peroxide in Liquid and Frozen Water,” J. Phys. Chem. A 116(24), 6068–6077 (2012). [CrossRef]
11. M. Meusel, M. Frizler, P. Ottersbach, L. Peters, and M. Gütschow, “The use of visible absorption spectra to evaluate different color reactions for the detection of cyclic ureides,” Pharmazie 62, 416–418 (2007). [CrossRef]
12. M. R. Glick, B. T. Jones, B. W. Smith, and J. D. Winefordner, “Fourier transform atomic absorption flame spectrometry with continuum source excitation,” Anal. Chem. 61(15), 1694–1697 (1989). [CrossRef]
13. J. Eberhard, P. S. Yeh, and Y. P. Lee, “Laser-photolysis/time-resolved Fourier-transform absorption spectroscopy: Formation and quenching of HCl(v) in the chain reaction Cl/Cl2/H2,” J. Chem. Phys. 107(16), 6499–6502 (1997). [CrossRef]
14. J. Dong and K. Matsumoto, “Method and apparatus for measuring light absorption spectra,” US patent US6434496B1 (2002).
15. E. Hecht, Optics, 4th ed. (Addison-Wesley, 1998).
