像差這項指標所存在的價值，一直都是在光學成像系統上被列為重要的因素，因為像差的大小會直接影響光學系統成像的優劣，所以量測像差就非常重要，波前像差在多數情況下都是使用Zernike多項式來表示，傳統上在研究量測波前相位與像差的方面上，都是需要經過繁雜的數學計算，而我們實驗室先前的研究就有提出可以使用神經網路用於干涉條紋以預測像差係數，但是先前所提出的研究方法是將兩個相位的干涉條紋在輸入神經網路之前，必須要先另外做一個相除的動作，才能將兩個相位的干涉條紋合成為一個輸入，並不能直接放入神經網路進行訓練和預測像差係數。
為了解決先前的問題，本文提出了一個ConvLSTM-Xception之模型架構的新方法，而透過本身ConvLSTM的循環神經網路架構可以輸入具有時序與圖像資料的兩個相位干涉條紋，值得注意的是因為此架構能輸入帶有時序資料的能力，而藉由將兩個不同相位的干涉條紋當作序列資料，來提取時序特徵強化其關聯性，而後分別使用理想的公式以及VirtualLab光學模擬軟體來測試網路模型的效能，並與先前所研究的網路進行比較，在理想資料測試集的模型測試下，本研究模型RMSE可達到0.008，而在使用模擬光學軟體所生成的模擬資料測試集的模型測試下，本研究經過遷移式學習後模型的RMSE可達到0.077，同時也證明此方法確實有效，可以將兩個相位的干涉條紋輸入至循環神經網路進行訓練和預測像差係數。

The value of the aberration index has always been listed as an important factor in the optical imaging system. The magnitude of the aberration will directly affect the imaging quality of the optical system, it is very important to measure the aberration. Wavefront aberrations are represented by Zernike polynomials in most cases. Traditionally, in the research and measurement of wavefront phase and aberration, complicated mathematical calculations are required. While previous research in our lab has proposed that the neural network can be used for interference fringes to predict aberration coefficients, however, the previously proposed research method is that before the interference fringes of the two phases are input into the neural network, another division must be done, so that the interference fringes of the two phases can be synthesized into one input, and cannot be placed directly into the neural network for training and predicting the aberration coefficients.
To solve the previous problem, this study proposes a new method for the model architecture of ConvLSTM-Xception. Through the recurrent neural network architecture of ConvLSTM, the interference fringes of two phases with time series and images data can be input. It is worth noting that the architecture has the ability to input the time series, and by treating the two different phase interference fringes as series data, to extract the time-series features to strengthen their correlation, and then use the ideal formula and the VirtualLab optical simulation software to test the network model respectively. The performance of the model is compared with the previously studied network. Under the model test of the ideal data test set, the RMSE of the model in this study can reach 0.008, and under the model test of the simulated data test set generated by the simulated optical software, the RMSE of the model can reach 0.077 after transfer learning in this study, and it is also proved that this method is indeed effective, and the interference fringes of two phases can be input into the recurrent neural network for training and predicting the aberration coefficients.

[1] 　J. Li et al., "Study on Aberration Correction of Adaptive Optics Based on Convolutional Neural Network," Photonics, vol. 8, no. 9, Sep 2021, Art no. 377,
doi: 10.3390/photonics8090377.
[2] J. L. Bentley, C. Olson, and R. N. Youngworth, " In the era of global optimization, the 　understanding of aberrations remains the key to designing superior optical systems," Optical Design and Testing IV, Proceedings Volume 7849, November 2010,
doi: 10.1117/12.871720
[3] P. Li, F. Tang, X. Z. Wang, and J. Li, " High NA objective lens wavefront aberration measurement using a cat-eye retroreflector and Zernike polynomial," Optics Express, vol. 29, no. 20, pp. 31812-31835, Sep 2021, doi: 10.1364/oe.437816.
[4]　 H. Jing, B. Fan, S. Wu, F. Wu, and T. Fan., "Measurement of optical surfaces with knife edge method," in 3rd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment, vol. 6723, p. 67235L: International Society for Optics and Photonics. January 2008.
[5]　 J. Siv, R. Mayer, G. Beaugrand, G. Tison, R. Juvénal, and G. Dovillaire, "Testing and 　characterization of challenging optics and optical systems with Shack Hartmann wavefront sensors," in EPJ Web of Conferences, vol. 215, p. 06003: EDP Sciences, September 2019, doi: 10.1051/epjconf/201921506003.
[6]　 K. Seong and J. E. Greivenkamp, "Chromatic aberration measurement for transmission interferometric testing," Applied Optics, vol. 47, no. 35, pp. 6508-6511, Dec 2008,
doi: 10.1364/ao.47.006508.
[7] E. P. Goodwin and J. C. Wyant, "Field guide to interferometric optical testing," 2006: 　　 　　　
SPIE Bellingham, WA. doi:10.1117/3.702897.
[8] J. H. Wang and Y. X. Yang, "Triple N-Step Phase Shift Algorithm for Phase Error
　Compensation in Fringe Projection Profilometry," Ieee Transactions on Instrumentation 　
and Measurement, vol. 70, 2021, Art no. 7006509, doi: 10.1109/tim.2021.3116306.
[9] J. Y. Wang and D. E. Silva, "Wave-front interpretation with Zernike polynomials," Applied Optics, Vol. 19, pp. 1510-1518, 1980, doi: 10.1364/AO.19.001510
[10] K. T. Yan, L. Chang, M. Andrianakis, V. Tornari, and Y. J. Yu, "Deep Learning-Based
Wrapped Phase Denoising Method for Application in Digital Holographic Speckle Pattern Interferometry," Applied Sciences-Basel, vol. 10, no. 11, Jun 2020, Art no. 4044, doi: 10.3390/app10114044.
[11] Y. Sun, Y. X. Bian, H. Shen, and R. H. Zhu, "High-accuracy simultaneous phase extraction and unwrapping method for single interferogram based on convolutional neural network," Optics and Lasers in Engineering, vol. 151, Apr 2022, Art no. 106941, doi: 10.1016/j.optlaseng.2021.106941.
[12] F. Zhang, R. Zhao, W. Wang, and Y. Liu, "Phase Extraction of Electronic Speckle Interference Fringe Image based on Convolutional Neural Network," ICCAI 2021, pp. 138–145, September 2021,doi: 10.1145/3467707.3467727
[13] S. N. Khonina, P. A. Khorin, P. G. Serafimovich, A. P. Dzyuba, A. O. Georgieva, and N. V. Petrov, "Analysis of the wavefront aberrations based on neural networks processing of the interferograms with a conical reference beam," Applied Physics B-Lasers and Optics, vol. 128, no. 3, Mar 2022, Art no. 60, doi: 10.1007/s00340-022-07778-y
[14] E. Z. Omar, "A refined denoising method for noisy phase-shifting interference fringe patterns," Optical and Quantum Electronics, vol. 53, no. 8, Aug 2021, Art no. 464,
doi: 10.1007/s11082-021-03106-4
[15] S. J. Ma, R. Fang, Y. Luo, Q. Liu, S. L. Wang, and X. Zhou, "Phase-aberration compensation via deep learning in digital holographic microscopy," Measurement Science and Technology, vol. 32, no. 10, Oct 2021, Art no. 105203,
doi: 10.1088/1361-6501/ac0216.
[16] Y. H. Chen, W. T. Lin, and C. W. Liu, "Image recognition of interference fringes in polishing by convolutional neural network with data augmentation by deep convolutional generative adversarial network," Optical Engineering, vol. 61, no. 4, Apr 2022, Art no. 045102, doi: 10.1117/1.Oe.61.4.045102.
[17] A. J. W. Whang et al., "Prediction technique of aberration coefficients of interference fringes and phase diagrams based on convolutional neural network," Optics Express, vol. 28, no. 25, pp. 37601-37611, Dec 2020, doi: 10.1364/oe.402850.
[18] A. J. W. Whang, Y. Y. Chen, T. H. Yang, C. T. Lin, Z. J. Jian, and C. H. Chou, "Zernike Coefficient Prediction Technique for Interference Based on Generation Adversarial Network," Applied Sciences-Basel, vol. 11, no. 15, Aug 2021, Art no. 6933,
doi: 10.3390/app11156933.
[19] B. Tong, X. Wang, J. Y. Fu, P. Chan, and Y. He, "Short-term prediction of the intensity and track of tropical cyclone via ConvLSTM model," Journal of Wind Engineering and Industrial Aerodynamics, vol. 226, Jul 2022, Art no. 105026,
doi: 10.1016/j.jweia.2022.105026.
[20] X. L. Li, J. H. Zhang, Y. Xue, and L. Qiu, "Classification of hops image based on ResNet-ConvLSTM and research of intelligent liquor picking system," Measurement, vol. 194, May 2022, Art no. 110955, doi: 10.1016/j.measurement.2022.110955.
[21] Y. L. Qiao, Y. Y. Guo, K. P. Yu, and D. J. He, "C3D-ConvLSTM based cow behaviour classification using video data for precision livestock farming," Computers and Electronics in Agriculture, vol. 193, Feb 2022, Art no. 106650,
doi: 10.1016/j.compag.2021.106650.
[22] A. Agga, A. Abbou, M. Labbadi, and Y. El Houm, "Short-term self consumption PV plant power production forecasts based on hybrid CNN-LSTM, ConvLSTM models," Renewable Energy, vol. 177, pp. 101-112, Nov 2021, doi: 10.1016/j.renene.2021.05.095.
[23] M. Moishin, R. C. Deo, R. Prasad, N. Raj, and S. Abdulla, "Designing Deep-Based Learning Flood Forecast Model With ConvLSTM Hybrid Algorithm," Ieee Access, vol. 9, pp. 50982-50993, 2021, doi: 10.1109/access.2021.3065939.
[24] H. Huang, Z. N. Zeng, D. Y. Yao, X. Pei, and Y. Zhang, "Spatial-temporal ConvLSTM for vehicle driving intention prediction," Tsinghua Science and Technology, vol. 27, no. 3, pp. 599-609, Jun 2022, doi: 10.26599/tst.2020.9010061.
[25] S. K. Yadav, K. Tiwari, H. M. Pandey, and S. A. Akbar, "Skeleton-based human activity recognition using ConvLSTM and guided feature learning," Soft Computing, vol. 26, no. 2, pp. 877-890, Jan 2022, doi: 10.1007/s00500-021-06238-7.
[26] S. Y. Lu, Y. Tian, Q. N. Zhang, X. X. Lu, and J. D. Tian, "Dynamic quantitative phase imaging based on Ynet-ConvLSTM neural network," Optics and Lasers in Engineering, vol. 150, Mar 2022, Art no. 106833, doi: 10.1016/j.optlaseng.2021.106833.
[27] E. Cicek and S. Goren, "Smartphone power management based on ConvLSTM model," Neural Computing & Applications, vol. 33, no. 13, pp. 8017-8029, Jul 2021,
doi: 10.1007/s00521-020-05544-9.
[28] M. L. Bai, Y. X. Chen, X. Y. Zhao, J. F. Liu, and D. R. Yu, "Deep attention ConvLSTM-based adaptive fusion of clear-sky physical prior knowledge and multivariable historical information for probabilistic prediction of photovoltaic power," Expert Systems with Applications, vol. 202, Sep 2022, Art no. 117335, doi: 10.1016/j.eswa.2022.117335.
[29] Y. Feng, Z. Tang, Y. Xu, S. Krishnamoorthy and Q. Hu, "Predicting vacant parking space availability zone-wisely: a densely connected ConvLSTM method," 2021 IEEE Vehicle Power and Propulsion Conference (VPPC), pp. 1-6, October 2021,
doi: 10.1109/VPPC53923.2021.9699140
[30] H. X. Ge, S. T. Li, R. J. Cheng, and Z. L. Chen, "Self-Attention ConvLSTM for Spatiotemporal Forecasting of Short-Term Online Car-Hailing Demand," Sustainability, vol. 14, no. 12, Jun 2022, Art no. 7371, doi: 10.3390/su14127371.

[31] D. Wang, Y. Yang and S. Ning, "DeepSTCL: A Deep Spatio-temporal ConvLSTM for Travel Demand Prediction," 2018 International Joint Conference on Neural Networks (IJCNN), pp. 1-8, July 2018, doi: 10.1109/IJCNN.2018.8489530.
[32] M. Majd and R. Safabakhsh, "A motion-aware ConvLSTM network for action recognition," Applied Intelligence, vol. 49, no. 7, pp. 2515-2521, Jul 2019,
doi: 10.1007/s10489-018-1395-8.
[33] M. Konnik and J. De Doná, "Waffle mode mitigation in adaptive optics systems: A constrained Receding Horizon Control approach," 2013 American Control Conference IEEE, pp. 3390-3396, August 2013, doi: 10.1109/ACC.2013.6580355.
[34] Y. Li, Y. Y. Yang, C. Wang, Y. K. Chen, and X. Y. Chen, "Point diffraction in terference detection technology," Chinese Optics, vol. 10, no. 4, pp. 391-414, Jul 2017,
doi: 10.3788/co.20171004.0391.
[35] B. F. Cao, C. F. Liu, L. J. Qin, and X. Q. Li, "Electroplating solution concentration detection based on interference principle and balanced detector," Optik, vol. 240, Aug 2021, Art no. 166903, doi: 10.1016/j.ijleo.2021.166903.
[36] K. T. Yan, Y. J. Yu, C. T. Huang, L. S. Sui, K. M. Qian, and A. Asundi, "Fringe pattern denoising based on deep learning," Optics Communications, vol. 437, pp. 148-152, Apr 2019, doi: 10.1016/j.optcom.2018.12.058.
[37] J. Schwiegerling, "Review of Zernike polynomials and their use in describing the impact of misalignment in optical systems," in Optical System Alignment, Tolerancing, and Verification XI, vol. 10377, p. 103770D: International Society for Optics and Photonics, August 2017. doi: 10.1117/12.2275378
[38] R. J. Noll, " Zernike polynomials and atmospheric turbulence*," Journal of the Optical Society of America, vol. 66, pp. 207-211, March 1976, doi: 10.1364/JOSA.66.000207
[39] I. Gurov and M. Volynsky, "Interference fringe analysis based on recurrence computational algorithms," Optics and Lasers in Engineering, vol. 50, no. 4, pp. 514-521, Apr 2012, doi: 10.1016/j.optlaseng.2011.07.015.
[40] G. M. Dai and V. N. Mahajan, "Orthonormal polynomials in wavefront analysis: error analysis," Applied Optics, vol. 47, no. 19, pp. 3433-3445, Jul 2008,
doi: 10.1364/ao.47.003433.
[41] R. Shrestha, J. Park, and W. Kim, "Application of thermal wave imaging and phase shifting method for defect detection in Stainless steel," Infrared Physics & Technology, vol. 76, pp. 676-683, May 2016, doi: 10.1016/j.infrared.2016.04.033
[42] S. Zhang, "Composite phase-shifting algorithm for absolute phase measurement," Optics and Lasers in Engineering, vol. 50, no. 11, pp. 1538-1541, Nov 2012,
doi: 10.1016/j.optlaseng.2012.06.005.
[43] A. Bardhan et al., "A novel integrated approach of augmented grey wolf optimizer and ANN for estimating axial load carrying-capacity of concrete-filled steel tube columns," Construction and Building Materials, vol. 337, Jun 2022, Art no. 127454,
doi: 10.1016/j.conbuildmat.2022.127454.
[44] M. Lin, Q. Chen, and S. Yan, "Network In Network," Neural and Evolutionary Computing, Dec 2013 , doi: 10.48550/arXiv.1312.4400.
[45] F. Chollet, "Xception: Deep Learning with Depthwise Separable Convolutions," Computer Vision and Pattern Recognition, Oct 2016 , doi: 10.48550/arXiv.1610.02357
[46] A. G. Howard et al., "MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications," Computer Vision and Pattern Recognition, 2017,
doi: 10.48550/arXiv.1704.04861
[47] K. He, X. Zhang, S. Ren, and J. Sun, " Deep Residual Learning for Image Recognition," Computer Vision and Pattern Recognition, Dec 2015, doi: 10.48550/arXiv.1512.03385
[48] S. Hochreiter, and J. Schmidhuber, " Long Short-Term Memory " Neural Computation, vol. 9, pp. 1735–1780, November 1997, doi: 10.1162/neco.1997.9.8.1735
[49] K. E. ArunKumar, D. V. Kalaga, C. Kumar, M. Kawaji, and T. M. Brenza, "Comparative analysis of Gated Recurrent Units (GRU), long Short-Term memory (LSTM) cells, autoregressive Integrated moving average (ARIMA), seasonal autoregressive Integrated moving average (SARIMA) for forecasting COVID-19 trends," Alexandria Engineering Journal, vol. 61, no. 10, pp. 7585-7603, Oct 2022, doi: 10.1016/j.aej.2022.01.011.
[50] X. SHI, Z. Chen, H. Wang, D. Y. Yeung, W. k. Wong, and W. c. WOO, " Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting," Computer Vision and Pattern Recognition , Jun 2015, doi: 10.48550/arXiv.1506.04214
[51] K. Gavahi, P. Abbaszadeh, and H. Moradkhani, "DeepYield: A combined convolutional neural network with long short-term memory for crop yield forecasting," Expert Systems with Applications, vol. 184, Dec 2021, Art no. 115511,
doi: 10.1016/j.eswa.2021.115511.
[52] B. Karlik, A. V. J. I. J. o. A. I. Olgac, and E. Systems, "Performance analysis of various activation functions in generalized MLP architectures of neural networks," International Journal of Artificial Intelligence and Expert Systems(IJAE), vol. 1, no. 4, pp. 111-122, August 2011.
[53] D. Chicco, M. J. Warrens, and G. Jurman, "The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation," Peerj Computer Science, Jul 2021, Art no. e623, doi: 10.7717/peerj-cs.623.
[54] W. H. Zhu et al., "Advanced simultaneous phase-shifting Fizeau interferometer," Optics and Laser Technology, vol. 111, pp. 134-139, Apr 2019,
doi: 10.1016/j.optlastec.2018.09.040.
[55] K. Xie, C. Wang, and P. Wang, "A Domain-Independent Ontology Learning Method Based on Transfer Learning," Electronics, vol. 10, no. 16, Aug 2021, Art no. 1911,
doi: 10.3390/electronics10161911.
[56] A. Horé and D. Ziou, "Image Quality Metrics: PSNR vs. SSIM," 2010 20th International Conference on Pattern Recognition, 2010, pp. 2366-2369, doi: 10.1109/ICPR.2010.579.