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A hyperspectral imaging system was demonstrated based on two acousto-optic tunable filters (AOTFs). Efficient regulation of the incoherent beam was executed by means of the wide-angular regime of Bragg diffraction in the birefringent materials. A double-filtering process was achieved when these two AOTFs operated with a central wavelength difference. In comparison with the single-filtering method, the spectral bandwidth was greatly compressed, giving an increment of 42.02% in spectral resolution at the wavelength of 651.62 nm. Experimental results and theoretical calculations are basically identical. Furthermore, the sidelobe was found to be suppressed by the double-filtering process with the first order maximum decreased from −9.25 dB to −22.35 dB. The results indicated high spectral resolution and high spectral purity were obtained simultaneously from this method. The basic spectral resolution performance was examined with a didymium glass by this configuration. We present our experimental methods and the detailed results obtained.
© 2016 Optical Society of America
1. Introduction
Noncollinear TeO2 Acousto-optic tunable filter (AOTF) because of its all solid state without moving parts, large angular aperture, rapid spectrum scanning and good optical quality can be widely applied in quantum electronics, spectrometry and fluorescence spectroscopy, telecommunication, medicine,atmospheric sciences, and spectral imaging [1–7]. It is a special spectral filter based on the acousto-optic interaction in an anisotropic transparent medium. The diffraction light wavelength can be tuned freely in a wide spectral range of tens microseconds. The time to change the filter equals the time it takes for the ultrasonic to traverse the crystal. A new filter is generated when a new ultrasonic frequency signal is applied in the crystal. When the unpolarized white light enters the acousto-optic crystal, it is diffracted by the traveling ultrasonic. Two orthogonal narrow-band diffracted beams are produced based on the phase-matching condition. The energy of the diffracted beam is mainly distributed at the plus first order and the minus first order. Due to its high spectral resolution capability, AOTF plays a more and more important role in the hyperspectral imaging application.
Spectral resolution is one of the important performance indexes for AOTF in practical imaging applications. When the incident wavelength is constant, the spectral resolution is inversely proportional to the spectral bandwidth. The excellent quality of the optical images can be obtained by narrowing spectral bandwidth. Generally spectral bandwidth can be narrowed by optimizing the crystal parameters, such as increasing the acousto-optic interaction length. However, it is too long to result in the inevitable decrease in the angular aperture, and thus leads to the decrease of the spatial resolution of AOTF [8–10]. Therefore the improvement of the spectral resolution is limited if we concentrate upon changing the fundamental parameters of the crystal. Incident light is filtered for successive two twice, namely the double-filtering, which is a method being able to further compress the spectral bandwidth. Double-filtering method based on a crystal has been reported. In 2005, Yaqoob and Riza reported a method that uses a bulk AOTF device in a unique double-pass for use with wavelength-multiplexed optical scanner (W-MOS) [11]. In 2008, Jang Woo- You et al reported a double-filter method based on a crystal with constant ultrasonic frequency. The method uses monochromatic light with wavelength of 632.8 nm to compress spectral bandwidth near the “intersection” where the two orthogonal polarized light responses at the same time. The results of experiment show that the spectral resolution increases by 20% to 30% and the first side lobe is compressed by 9.8% [12]. In 2009, Jean-Claude Kastelik et al presented an acousto-optic device based on two successive anisotropic interactions in paratellurite. And the AOTF has been tested by an argon laser [13]. Based on two crystals in imaging applications, in 2005, V. I. Pustovoit et al used two AOTFs to analyze the grass frog epidermic cell at three different wavelength [14]; in 2008, C. Zhang et al put forward the feasibility of double-filtering method based on two AOTFs from the theory [8]; in 2015, A. Machikhin et al reported an double-AOTF imaging system for biomedical applications [15]; in 2016, A. Machikhin et al showed an similar experimental setup for in situ measurement of the two-dimensional (2D) distribution of the surface temperature of microscopic specimens [16]. These studies have indicated that the spectral bandwidth of incident light can be compressed with the help of double-filtering method. However, the method of focusing on the further improvement of spectral resolution has not been reported.
In this paper, the double-filtering method based on two acousto-optic crystals is addressed analytically and experimentally. Fix ultrasonic drive frequency bonded to the first crystal constant, and tuned ultrasonic drive frequency bonded the second one to compress spectral bandwidth. It can be tuned flexibly and rapidly in this method. We are concentrated on the system setup and its experimental results. To confirm the superiority of the double-filtering method, the reliability is also tested with the help of the auxiliary material.
2. Instrument specifications and experimental approach
For AOTFs in the experiment, tellurium dioxide (TeO2) single crystal was taken as the medium of acousto-optic interaction, and a y-163°-cut lithium niobate as piezoelectric transducer. In the design of AOTF1 and AOTF2, in order to improve the accuracy of measurement, optical rotation effect of the crystal was considered [17–19]. In the acoustic-optic interaction, there are two different polarization states for the incident light on the surfaces of the crystals, one for the extraordinarily polarized light and the other for the ordinarily polarized light. To simplify the design process, maintaining the two crystals has the same ultrasonic polar angle. Wave vector diagram illustrating the paratellurite is shown in Fig. 1(a). The incident, diffracted and acoustic wave vector are related by ki ± Kα = kd. is a physical constant related to the rotatory capacity of the TeO2 crystal . The angles of ultrasonic shearing wave with respect to the [110] axis in the () interaction plane of the crystal, θα1 = θα2 = 9°, and the length of the lithium niobate piezoelectric transducer is as follows L1 = 7 mm,L2 = 8 mm. In order to effectively eliminate the diffraction light drift, we set two wedge angles of 5.6° and 5° in the exit end face of AOTF1 and AOTF2, respectively. In the process of the design of the crystal, the diffract polar angle of AOTF1 is equal to the incident polar angle of AOTF2. Linear aperture angles are the same as 10 mm × 10 mm. When ultrasonic drive power Pa = 1.2 W and the incident wavelength is λ0 = 651.62 nm, spectral bandwidths of AOTF1 and AOTF2 are Δλ1 = 3.44 nm and Δλ2 = 2.83 nm, respectively, with the same diffraction efficiency of 88%.
Fig. 1 (a) Wave vector diagrams of the bifrequency interaction. (b) The calculated and measured tuning curves of ultrasonic frequency versus incident light wavelength for AOTF1 and AOTF2.
We performed the simulation and measurements for the AOTFs. The tuning relation of the AOTF1 for extraordinary input light and the AOTF2 for ordinary input light,which,under phase-matched conditions, are given by [20]:
where the subscripts of “e” and “o” indicate extraordinary and ordinary beam, respectively. faeo and faoe are the ultrasonic frequency for “e in o out” and “o in e out”, respectively. The velocity of ultrasonic wave Va can be calculated by Vα = (Vss2sin2θα + Vfs2 cos2θα)1/2, where Vss = 616 m/s and Vfs = 1024 m/s [17]. λ0 is the vacuum optic wavelength. The ni and nd are the indexes of refraction of the incident and diffracted light, respectively. θi and θd are the polar angles for incident light and diffracted light inside the crystal with respect to the optical axis, respectively. The diffraction efficiency of double-filtering can be expressed as [21]:where sinc (x) = sin (πx)/πx and the momentum vector mismatch Δk = ki-kd-Ka. η1 and η2 implies the diffraction efficiency of AOTF1 and AOTF2, the peak diffraction efficiency are indicated as η01, η02 respectively. Besides the diffraction efficiency, the spectral bandwidth of the AOTF is also a function of the acousto-optic interaction length and the incident angle, with the full-width half-maximum given by [22]:where the dispersion term b = 2π[Δn-λ0(∂(Δn)/∂λ0)], with the Δn = ne-no.The spectral response of the AOTF1 and AOTF2 in the range 410-850 nm was measured. According to the Eqs. (1) and (2), the tuning curves of the simulation and measuring results are shown in Fig. 1(b). The ultrasonic frequency tuning the beam with ordinary polarization is systematically higher than that tuning the beam with extraordinary polarization at the same incident light wavelength. It also can be seen clearly from the Fig. 1(b) that the measurement data agrees fairly well with the theoretical calculation.
The experimental arrangement is shown in Fig. 2, which is composed of a broadband light source, a large-caliber beam collimation system, three polarizers, two AOTFs and a photoelectric detector (energy with photomultiplier, spectral bandwidth with high-resolution spectrograph). The optical radiation from the Halogen lamp passed a collimating system and propagated in form of a collimated optical beam. In order to avoid the overlapping of the zero and first order beam in space, an iris diaphragm was used in the system to limit the angle of the convergence of the incident light. We used a linear polarizer 1 before the AOTF1 to obtain an extraordinary polarized incident light beam. The beam is normally incident upon the surface of AOTF1. As a consequence of the anisotropic acousto-optic interaction in AOTF1, the polarization of the diffracted beam in the plus first order was ordinary. The plus first order diffracted beam and zero-order transmitted beam were separated in air by a 6.3° angle. The zero-order beam was blocked off. In order to obtain the highest diffraction efficiency, it must also meet the momentum matching condition within the AOTF2, so the diffracted beam from the AOTF1 passed through the polarizer 2 and then perpendicularly incident upon the surface of AOTF2. The diffracted beam in the plus first order at the AOTF2 output has extraordinary polarization. The polarizer 3 transmitted only the plus first order diffracted beam. Finally, the filtered light was collected by a spectrograph or a photomultiplier. The spectral aberrations and spatial distortions can be caused by the phenomenon of light beam diffraction in TeO2 crystal [23]. So the optical image deformations must be considered in hyperspectral imaging application. This configuration, as two AOTFs are placed fore and aft, is helpful to eliminate the aberration and distortion [24]. It should be pointed that the compensation of the image shift caused by the AOTF1 is equal to opposite shift produced by the AOTF2.
3. Experimental results
The experiments are carried out in the study of compression of double-filtering on the spectral bandwidth. The plus order diffraction light is formed after acousto-optic interaction in AOTF1 with the optical wavelength λ01 and the spectral bandwidth Δλ1. Diffraction light with wavelength λ02 and spectral bandwidth Δλ12 are formed after being filtered in AOTF2. The ultrasonic driving frequencies bonded on AOTF1 and AOTF2 are f01 and f02 respectively. It is found by adjusting f02 that spectral bandwidth decreases with the increase of center wavelength interval, and the diffraction efficiency decreases gradually. Figure 3(a) shows the basic principle of double-filtering method. First adjusting the ultrasonic frequency f01 and f02 to achieve that diffraction light wavelength λ01 = λ02, at this point, the overlapping area of spectral bandpass of AOTF1 and AOTF2 is maximum, and the spectral bandwidth Δλ12 also is maximum. Then keep the ultrasonic frequency f01 constant and adjust the f02 to increase the ultrasonic frequency difference Δf (|f01- f02|) gradually, lead to a gradual increase of center wavelength interval Δλ of diffraction beam out from the two crystals, a gradual decrease of overlapping area of spectrum bandpass, which means that spectral bandwidth Δλ12 becomes smaller and smaller. Each diffracted beam has a certain spectral bandwidth, so the theoretical range of the spectral bandwidth is 0 to Δλ2.
Fig. 3 The theoretical calculation and experimental results of double-filtering for the peak diffraction efficiency η01 = η02 = 88% at the central wavelength of λ0 = 651.62 nm. (a) The theoretical calculation of double-filtering that the central wavelength intervals are 0.4 nm, 0.8 nm, 1.2 nm and 1.6 nm. (b) The measuring results for the central wavelength λ01> λ02. (c) The measuring results for the central wavelength λ01< λ02.
In this experiment, the incident wavelength was set as λ0 = 651.62 nm. Incident light passed through AOTF1 and AOTF2 successively, center wavelength interval Δλ = 0, in which the spectral bandwidth was compressed from Δλ1 = 3.44 nm to Δλ2 = 2.25 nm. The double-filtering results were obtained by changing the driven frequency of f02 as shown in Figs. 3(b) and 3(c). Increase or decrease of λ02 caused by adjusting f02 will lead to increase of the center light wavelength interval of the two filters. Decrease of λ02 increased the center wavelength interval from 0 to 1.6 nm, in which spectral bandwidth of incident beam in the process of the double filtering decreased from 3.44 nm to 1.93 nm. That was, the spectral bandwidth was compressed by 42.9%, and the peak diffraction efficiency dropped to 43.9%; On the other hand, increase of λ02 increased the center wavelength interval from 0 to 1.63 nm, spectral bandwidth dropped from 3.44 nm to 1.96 nm. In other words, the spectral bandwidth was compressed by 42.02%. At the same time, the peak diffraction efficiency dropped to 41.93%.
Theoretical calculations as well as experimental measurement were performed for the experimental system. Theoretical calculation based on the Eqs. (3) and (4) are used to calculate the bandwidths and peak diffraction efficiency. When the incident light passes through AOTF1 the spectral bandwidth is Δλ1 = 3.02 nm. When the incident light passes through AOTF2 the spectral bandwidth is compressed to Δλ12 = 1.77 nm, and the peak diffraction efficiency drops to η12 = 77.43%. Then adjust f2 to increase the center light wavelength interval from 0 to 1.63 nm, the corresponding spectral bandwidth is compressed to Δλ12 = 1.62 nm, and the peak diffraction efficiency is drops to η12 = 44.4%. Spectral bandwidth of the incident light is compressed by 46.36% in the process of the double filtering, that is to say, the spectral resolution is improved by 86.42%. Figures 4(a) and 4(b) show the relationship between the center wavelength interval and the spectrum bandwidth and peak diffraction efficiency. It can be seen from Fig. 4(a) that the larger the center wavelength interval, the greater the spectral bandwidth compression and the higher spectral resolution. In Fig. 4(b), the peak diffraction efficiency gradually decreases with the increase of central wavelength interval according the theory and the measurement results. In order to improve measurement precision, all the data in the experiment were obtained by averaging the testing values of repeated measurements. There is a slight deviation between the measurement results and theoretical calculation, because that the error was induced in the production process of AOTFs, such as, crystal cutting, coating, welding, etc. In this double-filtering method, although there is some energy losses, the spectral resolution get improved greatly. It should find a balance point of the spectral bandwidth and the diffraction efficiency in practical applications. That is to say, we should not only have a narrow spectral resolution, but also to maintain relatively high diffraction efficiency.
Fig. 4 Calculation and measurement results of the center wavelength interval versus spectral resolution and diffraction efficiency at λ0 = 651.62 nm.
The experimental system is used to carry out detailed study on sidelobe suppression effect. It was found that after the incident light was filtered for twice continuously, the peak sidelobe ratio increased greatly. The peak sidelobe ratio, namely the signal to noise ratio, which is the ratio of signal to noise in an electronic device or electronic system, and can also be used to evaluate the purity of the spectrum in the spectral measurement. When ultrasonic power Pα = 1.2 W, the incident wavelength λ0 = 651.62 nm, the center wavelength interval of AOTF1 and AOTF2 Δλ = 0, the measurement results of the incident light passing through the single filtering and the double filtering are shown in Fig. 5. It can be seen from the figure that sidelobes at all levels have obvious inhibitory effect. The measurement results show that the maximum of the first order sidelobe drops from −9.25 dB to −22.35 dB, namely the maximum of the first order sidelobe is suppressed by 13.1dB, which means that the double-filtering method can effectively enhance the spectral purity of the diffraction beam.
We also conducted a spectral scanning experiment with a didymium glass to examine the resolution performance of this system. The experimental results of scanning spectrum of didymium glass were obtained by the single-filtering (AOTF1) and double-filtering in the 500-770 nm region as shown in the Figs. 6(a)-6(c). AOTF1 and AOTF2 can increase the sampling interval and reduce the scanning repetitions to improve scanning speed during the scanning process. AOTFs wavelength conversion speed can reach dozens of even a few microseconds, so 100 nm bands fully completed within one second. In order to get a lot of data, however, we have enough data transmission and acquisition time after the each measurement point. With the help of AOTF1, we noticed that the resolving power is relatively poor and even can’t distinguish at 526.44 nm, 581.11 nm and 742.82 nm as shown in the Fig. 6(b). It is seen in Fig. 6(a) that the transmittance of didymium glass in the range 500-620 nm and 720-770 nm are lower than in 720-770 nm. In order to make the resolving power of the double-filtering system more obvious, we divide the whole spectrum into three bands, and use three kinds of different light intensity to measure. The measuring results are shown in Fig. 6(c). It can be seen that the wave shape and position of the Figs. 6(a) and (c) are basically similar. As a result of this comparison we can see that the spectral resolution of double filtering is much better than that of the single filtering on account of it gives narrower spectral bandwidth. According to actual needs, the spectral resolution of this system will be further improved by increasing center wavelength interval. Spectral resolution and diffraction efficiency are two important performance parameters of the acoustic optic tunable filter. In practical imaging applications, in order to obtain better spectral resolution, we hope that the spectral bandwidth is narrow. It is requested to select larger ultrasonic frequency difference; however, in order to obtain the strong light signal, we hope with high diffraction efficiency, which requires the selection of smaller frequency difference. We can only balance the relationships between them, so that the ultrasonic frequency interval is neither too large nor too small. The ultrasonic frequency difference should be properly selected to ensure that the spectral width and the diffraction efficiency are in a reasonable range. The purpose of this paper is, even if the incident light has been filtered for successive twice to verify that the spectral bandwidth can be further improved. It is clear that the diffraction efficiency is too low to have adverse effects on the system. We can only contact the actual application environment inducing a reasonable balance value, which is also our main research content in the future.
Fig. 6 The transmitted spectrum for didymium glass was measured in the range 500-770 nm. (a) The incident beam passed the didymium glass was obtained by spectrograph (spectral resolution is 0.02nm). (b) The incident beam passed the didymium glass and AOTF1 was obtained by spectrograph. (c) The incident beam passed the didymium glass, AOTF1 and AOTF2 was obtained by spectrograph. The sampling step and center wavelength interval are 0.26 nm and 0.5 nm, respectively.
4. Conclusion
In conclusion, the hyperspectral imaging system was built based on two AOTFs. The driving frequency of AOTF1 was kept constant, tuned the driving frequency of AOTF2 to achieve the goal of spectral bandwidth compression. When the incident light wavelength was 651.62 nm, and the center wavelength interval was increased from 0 to 1.6 nm, the spectral bandwidth decreased from 3.38 nm to 1.93 nm. Compared to a single filter, this means that the spectral bandwidth was compressed by 42%. It is noticed that the diffraction efficiency decreased with the increase of center wavelength interval. Therefore, we should balance the relationship between the bandwidth and the efficiency in practical application. In addition, the double-filtering method can also suppress the sidelobes intensity on both sides of the center wavelength. The maximum of the first order sidelobe was suppressed by 13.1 dB, which indicates that this method can effectively enhance the spectral peak to sidelobe ratio. The spectral resolution of the system was tested with a didymium glass. The feasibility of the double-filtering method was confirmed and good results obtained. Preliminary results shown that the hyperspectral imaging system based on the two acousto-optic tunable filters is completely doable.
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