Open Access
Add to BibSonomyAbstract
We present a new design for the fabrication of concave gratings with large grating constants for flat-field miniature spectrometers with a wide spectral band. In this new design, one of the two optical paths for the holographic lithography of a curved grating structure with variable line spacing is modified by adding a concave lens in front of the point source. The addition of the concave lens allows the real point source, as well as the spatial filter for generating this point source, to be moved back. In this manner, the two spatial filters for generating two point sources are separated. Avoiding the physical conflict between these two spatial filters reduces the difficulty of fabricating large-constant concave gratings. Experimental results verify the feasibility of the proposed design in fabricating concave gratings with large grating constants. The resolution of a spectrometer using the fabricated concave grating is evaluated and found to be better than 1.1 nm across a spectral band ranging from 360 nm to 825 nm.
© 2016 Optical Society of America
1. Introduction
Portable miniature spectrometers are greatly desired in a variety of fields, such as environmental sensing, biological research, geological survey, and water safety [1–3 ]. Such high demand motivates researchers to develop low-cost and compact spectrometers with a wide spectral range and a high spectral resolution [4–7 ]. Among the different types of spectrometers, those with concave gratings have attracted increasing attention. In this type of spectrometer, a single concave grating serves the functions of light dispersion and light focusing, which are generally performed by a diffraction grating and mirrors in conventional spectrometers; this dual function thus ensures the compact configuration of this type of spectrometer [8–14 ].
For a concave grating spectrometer,the spectral range can be improved by increasing the detector length to achieve a wide spectral band. However, increasing the detector length inevitably increases the entire size of the spectrometer. Consequently, the portability of the spectrometer decreases. Angular dispersion can also be downsized by using a grating with a large constant to improve the spectral range of a spectrometer. In this method, increasing the detector length is unnecessary, and compactness can be maintained. Moreover, this method only requires concave gratings with large constants.
Mechanical ruling and holographic recording are two widely used methods to make a grating structure [15–17 ]. Ruling engines have been developed to fabricate gratings with constants or variable line spacing. Their advantages include high surface flatness and capability of developing complicated grating profiles, such as those with a sinusoidal shape. However, ruling a curved groove structure on a concave substrate presents a significant challenge because a complicated positioning system is required to fit not only the curved grating substrate but also the variable line spacing. Mechanical ruling can only be conducted by large firms. By contrast, the holographic recording method, in which two coherent laser beams are projected onto a substrate surface and made to interfere with each other, directly records grating patterns on a photoresist layer coated on a concave substrate. This method can efficiently produce curved concave gratings with variable line spacing at a relatively low cost and high throughput. These superiorities make the holographic recording method a good choice for laboratory research.
The holographic recording method requires a pair of high-quality coherent point sources, which must be close to each other when a large grating constant is desired. The generation of these two high-quality point sources requires two spatial filters, each of which consists of an objective and a pinhole. However, a physical conflict occurs between these two spatial filters when the two point sources are significantly close to each other. This physical conflict can be avoided by limiting the grating constant to a certain value. This limitation weakens the effectiveness of the holographic recording method.
In this paper, we present a new design to eliminate the physical conflict that exists in the conventional holographic recording method. In the new design, a major modification is made on one of the two optical paths. A concave lens is added and placed before either one of the two point sources to allow this point source to be moved back. The spatial filter for generating this point source is correspondingly moved back. In such a manner, the conflict between two spatial filters in a conventional setup is avoided. By locating the image of this moved point source at a specific position before being moved, the grating constant is maintained. Given that these two point sources have been separated, they can be made to be further close to each other. Hence, the grating constant can break the limitation and be enlarged. The principle, demonstration, and evaluation of this method are presented step by step in this research.
2. Principle
Figure 1 schematically shows a flat-field concave grating spectrometer, for which the concave grating is designed. In the spectrometer, a light for spectrometric analysis raying from entrance slit A is projected onto the concave grating, where the light is dispersed, focused, and directed to a charge-coupled device detector. The X-axis is coincident with the grating normal. The XOY plane is a plane of symmetry called the dispersion plane. Origin O is at the grating center of a Cartesian coordinate system. A, B 1, and B 2 are all located in the meridional plane XOY. P is an arbitrary point in the grating. Points C and D represent two point sources for forming the required concave grating used for the dispersion and focusing of the light; these points are all located in the meridional plane XOY.
Figure 2 illustrates the principle of holographic recording for fabricating a concave grating. In a conventional setup, as shown in Fig. 2(a), the two point sources generated by two spatial filters are both directly projected onto a concave substrate, where the two beams interfere with each other. Bright and dark interference fringes with variable line spacing are generated and recorded onto the concave substrate. Grating constant d is determined by incident angles θ C and θ D and follows the relationship expressed in Eq. (1). When a large grating constant d is required, angles θ C and θ D should be close to each other. When the two point sources are considerably close, a conflict arises between the spatial filters. This conflict causes a grating constant limitation.
Fig. 2 Principle of holographical recording for fabricating concave grating. (a) A conventional setup, (b) A new method for fabricating concave grating.
To eliminate the physical conflict, we implement a major modification in the new recording setup, as shown in Fig. 2(b). One point source is directly projected onto the surface while the other one is made to reach the surface after passing through a concave lens. The concave lens here is a key component for the new design. By adding the concave lens, we can move point source D to a new place D 1 while retaining the image of point source D 1 at position D. The image at position D is used as an equivalent point source. In this way, the distance between the two recording points is increased, but the grating constant is unchanged. The difficulty in optical path configuration is reduced by using this method, and a grating constant that can break the limitation can be produced.
3. System design
A fabrication system is constructed to verify the feasibility of the new design. For a spectrometer using a concave grating, grating parameters with variable line spacing are comprehensively determined with the real optical path of the spectrometer. The coordinates of the two point sources are determined after determining the specifications of the spectrometer.
Similar to widely used commercial spectrometers, a spectral band of 360 nm to 825 nm and a spectral resolution better than 2 nm are considered. The overall size of our spectrometer should suit a volume no larger than 120 mm × 100 mm × 60 mm to achieve good portability. According to the specification of a commercial spectrometer (Torus Series, Ocean Optics) [18], the radius of the concave grating should around 85 mm for further experimental comparison. A radius of 83.68mm was chosen, which is a ready-made mold of concave substrate manufacture. A commercial concave lens with a focal length of minus 15.1 mm is selected. The width of the entrance slit is assumed to be zero during optimation for simplicity.
For the parameters of the optical path shown in Fig. 1, the geometrical theory of aberration is utilized to determine these parameters on the basis of the image quality on the detector array by appropriately setting the positions of the two recording sources and the spectrometer parameters, including the positions of the entrance slit and detector array shown in Fig. 1. The initial values of these spectrometer parameters are calculated with a computer procedure based on light path functions F, as shown in [19] and simply expressed in Eq. (2).
In Eq. (2), m is the order of the spectrum (m = 1 in this research); K is the number of grooves on the concave grating related to the wavelength and positions of the recording point sources C and D (Figs. 1 and 2 ). AP and PB are the optical paths from the entrance slit to the detector. P is an arbitrary point in the concave grating.
After initially determining these values, an optical design software, ZEMAX, is employed to optimize the initial values. Table 1 summarizes these parameters.
Table 1. Optimized parameters of the spectrometer
A fabrication setup is constructed on the basis of the values shown in Table 1 (Fig. 3 ). A HeCd laser source with a wavelength of 441.6 nm, a power of 150 mW, and a coherence length of 300 mm is employed as a laser source. The laser source is first passed through half-wave plate 1 to adjust the polarization direction and is then divided into two beams. One beam is directed into spatial filter 1 after being reflected by a mirror, and the other beam is directed into spatial filter 2 after the polarization direction is adjusted by half-wave plate 2. A concave lens is placed in the way of laser beam 1 to change the position of point source 1 so that the two spatial filters can be separated, as mentioned above. The grating aperture is 30 mm × 30 mm to match the divergence angle of the input fiber, which can obtain the maximum light energy efficiency.
Fig. 3 Experimental setup (a) The simulated setup of the recording system. (b) Experimental setup of the recording sources.
Figure 4 shows the concave grating with a curved groove shape and variable line spacing fabricated by using the setup shown in Fig. 3. The grating diffracts different colors under white light because of its variable grating constant and concave profile.
4. Experiments and results
After demonstrating the fabrication process, a prototype spectrometer is constructed to test the concave grating. A testing setup is built, as shown in Fig. 5 . All the components are fixed onto a plate for easy adjustment in the testing experiment, but they are not enclosed within a box with a minimum volume. A commercial slit with a size of 5 μm × 1 mm is selected according to the simulation of ZEMAX, which can achieve resolution better than 1.5 nm over the entir spectral range.A commercial detector (Sony ILX511B) with a pixel size of 14 μm, 2,048 total pixels, and a data processing unit are employed. The spectrometer size determined by the positions of entrance slit A, concave grating, and detector is shown as the dashed line area in Fig. 5; the length and width of this area are 120 and 100 mm, respectively. The size can meet the requirement of portability for miniature spectrometers.
The precise adjustment of these optical components is performed by using a super-continuum source (SuperK SELECT) that covers a wavelength ranging from 450 nm to 1,100 nm. When all the resolutions over the spectral bands measured by the super-continuum source are consistent with the simulated values, The positions of these components were fixed. The standard deviation of the relative errors of these two resolutions over the spectral range are lower than 10%.
Because the bandwidth of the supercontinuum is larger than 2nm in most spectral range, it is not suitable for testing the resolution, the simulated values of which is better than 1.1nm. Thus, after properly placing these optical components, four strictly evaluated laser sources with narrow spectral bandwidths are employed to test the spectral resolution. Figure 6 shows the spectrum testing results. The full width at half maximum method is employed to define the resolution values. Table 2 summarizes the experimental and simulated values, the maximum relative error between which is approximately 16%. The experimental results of the new spectrometer are comparable to the simulated results at the four wavelengths.
Table 2. Experimental and simulated resolution
The experimental resolutions are then compared with Torus, which has a similar spectral band of 360 nm to 825 nm. The resolution of the Torus spectrometer is better than 1.6 nm across the entire spectral band, and the length of its spectral field covered on the detector is 28.672 mm. The spectrometer resolution with the concave grating using the proposed method is better than 1.1 nm across the entire spectral band, and the length of its spectral field covered on the detector is only 22.4 mm, which is 78% of that of the commercial product. The remaining length of the detector can receive a spectral range of approximately 100 nm, which menas that the nominal spectral range can be expanded by about 21%.
5. Conclusion
In summary, a new method for fabricating concave gratings is theoretically and experimentally illustrated in this paper. In the new design, a concave lens is added to one of the two exposure optical paths to increase the distance between the two point sources. By using this method, we can reduce the difficulty in fabricating concave gratings with large constants. The experiments based on four laser sources reveal that the measured resolutions are comparable to the simulated ones and that the maximum relative error between them is less than 16%. The resolution of the spectrometer with the concave grating using the new method is 1.1 nm, which is better than that of a commercial flat-field concave grating spectrometer (i.e., 1.6 nm). The length of the spectral field covered on the detector is only 22.4 mm, which is 78% of that of the commercial product. The shortened detector length is beneficial for downsizing the spectrometer. The spectrometer using the concave grating with a large constant has a potential to expand the spectral band by approximately 100 nm.
Acknowledgments
This research was supported by a National Natural Science Foundation of China under Project No. 61205167 and a China Postdoctoral Science Foundation Funded Project under Project No. 2015M571033.
References and links
1. S. Hu, Z. Y. Wen, Y. Q. Liang, X. Q. Du, and B. Zhang, “Microbiochemical analyzer based on continuous spectrum and its test for clinic use,” Guangpuxue Yu Guangpu Fenxi 26(9), 1769–1773 (2006). [PubMed]
2. D. S. Goldman, P. L. White, and N. C. Anheier, “Miniaturized spectrometer employing planar waveguides and grating couplers for chemical analysis,” Appl. Opt. 29(31), 4583–4589 (1990). [CrossRef] [PubMed]
3. G. M. Yee, N. I. Maluf, P. A. Hing, M. Albin, and G. T. A. Kovacs, “Miniature spectrometers for biological analysis,” Sens. Act. A 58, 61–66 (1997).
4. H. Kim, “Are subjects’ perceptual asymmetries on auditory and visual language tasks correlated?: a meta-analysis,” Brain Lang. 58(1), 61–69 (1997). [CrossRef] [PubMed]
5. M. Badieirostami, O. Momtahan, C. Hsieh, A. Adibi, and D. J. Brady, “Very-high-resolution tandem Fabry-Perot etalon cylindrical beam volume hologram spectrometer for diffuse source spectroscopy,” Opt. Lett. 33(1), 31–33 (2008). [CrossRef] [PubMed]
6. P. Kong, Y. Tang, X. Q. Bayanheshig, W. Li, and J. Cui, “Double-grating minitype flat-field holographic concave grating spectrograph,” Acta Opt. Sin. 33, 24–30 (2013).
7. M. Varasi, M. Signorazzi, A. Vannucci, and J. Dunphy, “A high-resolution integrated optical spectrometer with applications to fibre sensor signal processing,” Meas. Sci. Technol. 7(2), 173–178 (1996). [CrossRef]
8. J. Zeng, “Optimum design of miniature wide-waveband concave holographic grating monochromator,” Acta Opt. Sin. 32, 248–254 (2012).
9. C. H. Ko, W. C. Liu, N. P. Chen, J. L. Shen, and J. S. Lin, “Double reflection in the concave reflective blazed grating,” Opt. Express 15(17), 10498–10503 (2007). [CrossRef] [PubMed]
10. Q. Zhou, J. Pang, X. Li, R. Tian, and K. Ni, “Improving the spectral resolution of flat-field concavegrating miniature spectrometers by dividing a wide spectral band into two narrow ones,” Appl. Opt. (accepted).
11. Q. Zhou, L. J. Zeng, and L. F. Li, “Numerical simulation and experimental demonstration of error compensation between recording structure and use structure of flat-field holographic concave gratings,” Guangpuxue Yu Guangpu Fenxi 28(7), 1674–1678 (2008). [PubMed]
12. Q. Zhou, J. Pang, X. Li, R. Tian, and K. Ni, “A concave grting miniature spectrometer with an expanded spectral band by using two entrance,” Chin. Opt. Lett. (Article in press).
13. K. Chaganti, I. Salakhutdinov, I. Avrutsky, and G. W. Auner, “A simple miniature optical spectrometer with a planar waveguide grating coupler in combination with a plano-convex lens,” Opt. Express 14(9), 4064–4072 (2006). [CrossRef] [PubMed]
14. S. Grabarnik, R. Wolffenbuttel, A. Emadi, M. Loktev, E. Sokolova, and G. Vdovin, “Planar double-grating microspectrometer,” Opt. Express 15(6), 3581–3588 (2007). [CrossRef] [PubMed]
15. R. Brunner, M. Burkhardt, K. Rudolf, and N. Correns, “Microspectrometer based on holographically recorded diffractive elements using supplementary holograms,” Opt. Express 16(16), 12239–12250 (2008). [CrossRef] [PubMed]
16. E. Sokolova, “Simulation of mechanically ruled concave diffraction gratings by use of an original geometric theory,” Appl. Opt. 43(1), 20–28 (2004). [CrossRef] [PubMed]
17. I. Aubrecht, M. Miler, and I. Koudela, “Recording of holographic diffraction gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth,” J Mod. Opt. 45(7), 1465–1477 (1998). [CrossRef]
18. High throughput compact spectrometer, Torus Series, http://oceanoptics.com.
19. H. Noda, T. Namioka, and M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. 64(8), 1031–1036 (1974). [CrossRef]
