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Abstract
To quickly evaluate holographic photopolymers with different formulations, the most effective method is to record a volume holographic grating in the samples and detect the grating’s diffraction in real time. Since the volume grating is highly sensitive to incident angle, existing schemes need to precisely control many space-related parameters. This study proposes an improved scheme, in which two different sized spots are used to reduce the requirements for the overlap of the two spots and the installation precision of the samples. Transmittances, diffractive efficiencies and diffractive asymmetries are obtained at a high sampling rate, through a specifically designed algorithm with the data from uncalibrated high-speed photodiodes. The experimental results show that the proposed scheme performance well in evaluating holographic photopolymer.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Compared with DVD storage, volume holography storage is regarded as the read-only storage of next generation, due to its high-density optical storage property. It has been promoted for more than 20 years since F. H. Mok firstly stored 500 high-resolution holograms in a 1 cm3 LiNbO3 cube [1]. In recent years, photopolymers have become the most popular materials for volume holography, due to their wide-range property modifiability and various formulations [2–6]. Therefore, photopolymers are widely studied and optimized for various applications [6–10]. To evaluate the holographic recording performance of photopolymers, real-time detecting the diffraction efficiency from a forming volume holographic grating is an efficient method [5,11–13]. Generally, double-color and time division multiplexing (TDM) are two main schemes.
In double-color scheme, two sets of lasers with different wavelengths are required to build the test platform. One laser whose wavelength can match the absorption spectra of the tested samples well is used to record volume gratings in the samples, while the other laser whose wavelength out of the samples’ absorption bands is used to detect the diffraction of the gratings in real time [2,14–16]. Double-color scheme is uneconomical to develop new formulations, because the detection beams with different wavelengths are needed to keep the wavelengths away from various absorption bands, for which additional lasers or other kind of monochromatic light sources are required [17,18]. Moreover, both of sample consistency and installation precision are highly demanded because of the angular sensitivity of the volume gratings. Hence, TDM based scheme is developed.
In TDM scheme, only one laser with wavelength matching the samples’ absorption spectra well is needed for evaluating the polymerization of holographic photopolymers [12]. In more details, the laser is divided into two beams to interfere with each other and form a volume grating inside the photopolymers. During the process, one beam is periodically blocked, while the other beam is used as a detection beam to get the diffraction of the grating in the meantime. TDM scheme is relatively simple, in which the Bragg condition is easily to meet in detections. However, it still has many drawbacks. When only one detector is applied, it is hard to obtain transmittance simultaneously and eliminate errors from continuous changing absorptivity [19]. When two detectors are used, the information during recording moment is given up [4,12,20], so that more information will be missed. In addition, the duty ratio of detection time (DRDT) in a period blocking mode should be as short as possible to reduce influences from dark reactions [4,20]. Moreover, the two beams need to overlap each other precisely in the samples.
To reveal more information and decrease errors from DRDT and imperfect overlapping of two beams, in this study we propose an improved TDM scheme and data extracting algorithm for polymerization evaluation. The experimental setup is shown in Fig. 1. Firstly, one aperture is inserted into one beam to control its size much smaller than that of the other beam, so that it is easy for one spot to be completely covered by the other spot, which greatly reduces the requirements for sample installation consistency. Secondly, two photodiodes are applied for high-speed detecting, which can achieve higher sampling rate and lower cost than most commercial power meters. In addition, both of them are permitted to receive light during recording, so that the phenomenon of asymmetric diffraction can be revealed. Thirdly, a data extracting algorithm is established and tested to diminish errors from disagreement of gains, background noises and beam diameters. The principle and performance details of the scheme and the algorithm are discussed in the next section.
2. Method
2.1 Experimental setup
As shown in Fig. 1, a single longitudinal mode 532 nm laser is expanded by a beam expander with spatial filter. The expanded beam is split into two beams using a polarized beam splitter (PBS). The two beams interfere at the location of the photopolymer. One half wave plate (HWP1) is tuned to ensure the two beams have equal power density. The second half wave plate (HWP2) is used to make the two beams have same polarization. The diameter of one beam is limited by an aperture (Aperture2), which make it easy to put the small beam inside the big beam within the interference zone. The transmitted lights of the two beams are collected by two photo diodes, respectively. Noticing that, two beams are symmetric with respect to the normal line of the photopolymer surface to form an unslanted grating.
2.2 Algorithm and measuring step
Due to the maturity of semiconductor industry, photodiodes can maintain excellent linearity in a very large range, therefore, the output of photodiode can be expressed as follows
where m is amplification of photo diode, b is total background of environment and photo diode, p(t) denotes power-density of beam light and s represents area of light beam.Step1: Record background signal
Removing the photopolymer and turning off shutter1 make p(t) = 0, thus the output is regarded as amplified background signal, for PD1 and PD2 they are
Step2: Obtain signal intensity ratioKeep the photopolymer removed, when shutter1 and shutter2 are both open, power density of photo diodes are equal, that is p1(t)=p2(t)=p0 . Then, outputs are
From Eqs. (2)–(5), the signal intensity ratio is gotPlace the photopolymer on the sample holder, keep shutter1 open but shutter2 work in a period blocking mode. The beam corresponds to PD1 has smaller diameter. When shutter2 is closed, the transmitted and diffractive beams have a same beam size, thus, the output of PD1 and PD2 are
The diffractive efficiency excluding absorption effect isNoticed that, p1(t) and p2(t) cannot be directly acquired in the mentioned steps. But the Eq. (9) can be transformed into expression with only measured values
The p1(t) and p2(t) are affected by transmittance T(t) and diffractive efficiency η. Therefore, the output of PD1 and PD2 can be expressed as follows
Eliminate η with Eqs. (11) and (12), get the transmittance2.3 Data process method
To get diffractive efficiencies and transmittances, Step1 and Step2 of section 2.2 are easy to realize. More importantly, for the step3, the measured data of PD1 and PD2 with closed shutter2 should be extracted from uninterruptedly collecting data of PD1 and PD2. The sum of PD1 and PD2 is firstly got. Then, with the processes of denoising and low pass to the sum, the time points (tc) with closed shutters are found by extracting the time from the peaks of the sum. At last, P1(t) and P2(t) are got by extracting the values of PD1 and PD2 at tc. With all the data that got from Step1∼3, the η(t) and the T(t) can be got from Eqs. (10) and (13). Figure 2 shows the process.
3. Results and discussion
3.1 Performances of multiple testing
Because of inevitable air flow, oscillation or stress release, the evaluation of photopolymer generally needs certain times of repeated testing to find the best curve to approach the real polymerization property. Figure 3 shows test results from 6 different areas of a same sample. The shutter2 was periodically closed for 0.02 seconds every 2 seconds. The bandwidth of PD1 and PD2 was ∼10 MHz, and the sampling rate of acquisition card was set to 1 kHz. The signal received by PD1 and PD2 is shown in Figs. 3(a) and 3(b). Figure 3(c) presents the relationship between diffractive efficiencies and exposure. Figure 3(d) presents the relationship between transmittances and exposure.
Fig. 3. Performance of six tests of same kind of samples. Voltages directly received from (a) PD1 and (b) PD2 are inputted into Eqs. (10) and (13) to get (c) diffractive efficiencies and (d) transmittance.
For gains of PD1 and PD2 are different, and the beam diameters of two beams are different, the maximum voltages got from PD1 and PD2 are also different in Figs. 3(a) and 3(b). In Fig. 3(a), the beginning values of these tests mean the beginning intensity of transmitted beam without exposure, the difference of beginning values means the absorption of each sample is slightly different. In Fig. 3(c), diffractive efficiencies are different from test to test, but transmittances show better consistence in Fig. 3(d). The difference in consistency between Figs. 3(c) and 3(d) is consistent with general understanding, that is, the variation in transmittance is not sensitive to air flow, oscillation or stress release.
3.2 Working with different amplitude-ratios of PDs
A set of samples with a same formulation was tested for three different amplitude-ratios between PD1 and PD2. The amplitude-ratio was defined as ${{\overline{\overline {{P_1}}} } \mathord{\left/ {\vphantom {{\overline{\overline {{P_1}}} } {\overline{\overline {{P_2}}} }}} \right. } {\overline{\overline {{P_2}}} }}$, which was adjusted by selecting different gain values of photodiodes. Other setting was same as section 3.1. Test results of three kinds of amplitude-ratios using the method mentioned in section 2.2 are shown in Fig. 4. Each curve in Fig. 4 corresponds to the most sensitive performance of multiple tests.
Fig. 4. (a) Diffractive efficiencies and (b) transmittances of three kinds of amplitude-ratios between PD1 and PD2: 0.2564; 2.5829 and 0.9648.
Obviously, the method mentioned in section 2 is well adapted with different amplitude-ratios. The diffractive efficiencies and transmittances show excellent consistency, even though the voltage signal amplitude-ratio between PD1 and PD2 are different.
3.3 Working with different DRDTs
It is easy to inference that a bigger DRDT will cause diffractive efficiency growing slower compare to a smaller DRDT, because discontinuous exposure decreases amount of effective exposure in unit time. A series of experiments were performed with different DRDTs. Because the minimal time for absolutely closing was fixed, we changed the exposure period to get experimental results with three different DRDTs, as shown in Fig. 5. Same as section 3.2, each curve in Fig. 5 corresponds to the most sensitive performance of multiple tests.
Fig. 5. Diffractive efficiencies and transmittances before (a-b) and after (c-d) exposure correction, with DRDT from 0.1% to 10%.
It is noticed that the exposure in Figs. 5(a) and 5(b) simply presents the power-density multiplies the elapsed time. When DRDT changes from 0.1%, 1% to 10%, actual exposure time ratios are 99.9%, 99% and 90%, respectively. When exposures of Figs. 5(a) and 5(b) are adjusted to the actual received exposure, three curves become closer. However, 0.1% still give the best sensitivity. The remain difference between different DRDTs in Fig. 5(c) is more complicated, except for consistency of samples and environment, the dark reaction is also a considerable factor. A smaller DRDT is still the recommended way to approximate the real relation between exposure and diffractive efficiency. The DRDT can easily reach to 0.0001% with the current bandwidth of PDs, if the shutter2 is replaced by a Pockels cell.
3.4 Asymmetric diffraction
When shutter2 is opened, the light intensity entering PD1 is
where Tin(t) is transmittance in grating area. The first item of Eq. (14) presents the residual power in PD1 direction after deducting diffraction to PD2 direction; its second item presents the diffraction from PD2 direction.The light intensity entering PD2 is
Similar to Eq. (1), the output of PD1 and PD2 can be expressed as follows
Fig. 6. Six tests of same kind of samples have similar (a) diffractive efficiencies and (b) transmittances, but very different signals of PD1 (c).
Thus, we assume η1≠η2, and set Δη=η1-η2, from Eq. (16) can get Δη as
4. Conclusion
The real-time grating recording and diffraction detecting is a common method for evaluating polymerization. Because TDM based scheme has privilege in keeping Bragg condition always satisfactory and needs only one laser, TDM based scheme has become the mainstream. Compared to many published schemes, the improved TDM scheme in this study has the following three advantages. Firstly, we applied high-speed photodiodes as detectors to get data with high temporal resolution; secondly, we periodically blocked one beam and kept two detectors open for detection during the whole measurement process, which provided more information to monitor polymerization; thirdly, we used two different sized spots for interference to reduce requirements for consistency about samples and positioning. To cooperate this improved scheme, an algorithm was created to extract diffractive efficiencies, transmittances, and diffractive asymmetry. The performance of this improved scheme and algorithm was proved to be excellent in the presented experiments. Additionally, the algorithm could effectively eliminate the influences of different background and gain between two photodiodes, without any specifically calibration. The future work in this area is to increase effective data points per unit time to further develop sensitive photopolymers.
Funding
Science Challenge Project (TZ2016001); China Academy of Engineering Physics (CX2019006, YZJJLX2019002); National Natural Science Foundation of China (11702275, 11802289).
Acknowledgments
We acknowledge the assistance of associate professor Zhaohui Zhai in writing code of acquisition system.
Disclosures
The authors declare no conflicts of interest.
References
1. F. H. Mok, M. C. Tackitt, and H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3 crystal,” Opt. Lett. 16(8), 605–607 (1991). [CrossRef]
2. M. Ortuño, E. Fernández, R. Fuentes, S. Gallego, I. Pascual, and A. Belendez, “Improving the performance of PVA/AA photopolymers for holgoraphic recording,” Opt. Mater. 35(3), 668–673 (2013). [CrossRef]
3. P. Liu, L. Wang, Y. Zhao, Z. Li, and X. Sun, “Holographic memory performances of titanocene dispersed poly (methyl methacrylate) photopoymer with different preparation conditions,” Opt. Mater. Express 8(6), 1441–1453 (2018). [CrossRef]
4. Y. Liu, F. Fan, and Y. Hong, “Volume holographic recording in Al nanoparticles dispersed phenanthrenequinone-doped poly (methyl methacrylate) photopolymer,” Nanotechnology 30(14), 145202 (2019). [CrossRef]
5. K. Curtis and D. Psaltis, “Characterization of the Dupont photopolymer for three-dimensional holographic storage,” Appl. Opt. 33(23), 5396–5399 (1994). [CrossRef]
6. F. Bruder, S. Hansen, and T. Kleinschmidt, “How to integrate volume holographic optical elements (vHOE) made with Bayfol® HX film into plastic optical parts,” Proc. SPIE 11030, 110300C (2019). [CrossRef]
7. C. Li, L. Cao, Z. Wang, and G. Jin, “Hybrid polarization-angle multiplexing for volume holography in gold nanoparticle-doped photopolymer,” Opt. Lett. 39(24), 6891–6894 (2014). [CrossRef]
8. P. Liu, X. Sun, Y. Zhao, and Z. Li, “Ultrafast volume holographic recording with exposure reciprocity matching for TI/PMMAs application,” Opt. Express 27(14), 19583–19595 (2019). [CrossRef]
9. S. Vyass, Y. Chia, and Y. Luo, “Volume holographic spatial-spectral imaging systems,” J. Opt. Soc. Am. A 36(2), A47–A57 (2019). [CrossRef]
10. Z. Shen, Y. Zhang, A. Liu, Y. Weng, and X. Li, “Volume holographic waveguide display with large field of view using a Au-NPs dispersed acrylate-based photopolymer,” Opt. Mater. Express 10(2), 312–322 (2020). [CrossRef]
11. D. Yin, H. Pu, B. Gao, H. Dai, and J. Liu, “Analytical rates determinations and simulations on diffusion and reaction processes in holographic photopolymerization,” Appl. Phys. Lett. 94(21), 211108 (2009). [CrossRef]
12. K. Omura and Y. Tomita, “Photopolymerization kinetics and volume holographic recording in Zro2 nanoparticle-polymer composites at 404 nm,” J. Appl. Phys. 107(2), 023107 (2010). [CrossRef]
13. T. Mikulchyk, S. Martin, and I. Naydenova, “N-isopropylacrylamide-based photopolymer for holographic recording of thermosensitive transmission and reflection gratings,” Appl. Opt. 56(22), 6348–6356 (2017). [CrossRef]
14. D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part I: Short exposure,” Opt. Commun. 330, 191–198 (2014). [CrossRef]
15. H. Li, Y. Qi, C. Guo, R. Malallah, and J. T. Sheridan, “Holographic characterization of diffraction grating modulation in photopolymers,” Appl. Opt. 57(22), E107–E117 (2018). [CrossRef]
16. K. Tsuchida, M. Ohkawa, and S. Sekine, “Holographic characteristics of two different films using methyl violet dyes in polyvinyl alcohol matrices,” Opt. Eng. 46(1), 015801 (2007). [CrossRef]
17. F. Zhai, G. Yang, K. Yang, and M. Huang, “Two dyes co-sensitized photopolymer for multi-wavelength holographic recording,” J. Polym. Mater. 31(2), 225–232 (2014).
18. V. V. Shelkovnikov, E. V. Vasil’ev, V. V. Russkikh, L. V. Ektova, V. N. Berezhnaya, and E. F. Pen, “Monochrome and two-color holograms in layered photopolymer materials,” Optoelectron.Instrument.Proc. 52(4), 404–412 (2016). [CrossRef]
19. M. Ohkawa, K. Osabe, and T. Sato, “Evaluation of polymerization and diffusion times in holographic recording for acrylamide-based photopolymer film,” Proc. SPIE 10558, 1055812 (2018). [CrossRef]
20. Y. Liu, F. Fan, Y. Hong, J. Zang, G. Kang, and X. Tan, “Volume holographic recording in irgacure 784-doped PMMA photopolymer,” Opt. Express 25(17), 20654–20662 (2017). [CrossRef]
