104 lines
4.3 KiB
Python
104 lines
4.3 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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from scipy.interpolate import InterpolatedUnivariateSpline
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# ------------------------------------------------
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# 1. 可见光区 PDMS 折射率数据（题目给定）
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# ------------------------------------------------
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wl_visible = np.array([
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0.3500,0.3535,0.3570,0.3605,0.3640,0.3675,0.3710,0.3745,0.3780,0.3815,
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0.3850,0.3885,0.3920,0.3955,0.3990,0.4025,0.4060,0.4095,0.4130,0.4165,
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0.4200,0.4235,0.4270,0.4305,0.4340,0.4375,0.4410,0.4445,0.4480,0.4515,
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0.4550,0.4585,0.4620,0.4655,0.4690,0.4725,0.4760,0.4795,0.4830,0.4865,
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0.4900,0.4935,0.4970,0.5005,0.5040,0.5075,0.5110,0.5145,0.5180,0.5215,
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0.5250,0.5285,0.5320,0.5355,0.5390,0.5425,0.5460,0.5495,0.5530,0.5565,
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0.5600,0.5635,0.5670,0.5705,0.5740,0.5775,0.5810,0.5845,0.5880,0.5915,
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0.5950,0.5985,0.6020,0.6055,0.6090,0.6125,0.6160,0.6195,0.6230,0.6265,
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0.6300,0.6335,0.6370,0.6405,0.6440,0.6475,0.6510,0.6545,0.6580,0.6615,
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0.6650,0.6685,0.6720,0.6755,0.6790,0.6825,0.6860,0.6895,0.6930,0.6965,
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0.7000
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])
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n_visible = np.array([
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1.4585377,1.45761865,1.456730118,1.455870728,1.455039187,1.454234276,1.453454840,
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1.452699788,1.451968089,1.451258766,1.450570894,1.449903597,1.449256044,1.448627445,
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1.448017051,1.447424151,1.446848069,1.446288159,1.445743811,1.445214441,1.444699493,
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1.444198438,1.443710771,1.443236009,1.442773692,1.442323382,1.441884657,1.441457118,
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1.441040380,1.440634076,1.440237854,1.439851378,1.439474326,1.439106388,1.438747267,
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1.438396681,1.438054357,1.437720031,1.437393455,1.437074386,1.436762592,1.436457851,
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1.436159948,1.435868677,1.435583840,1.435305247,1.435032713,1.434766062,1.434505122,
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1.434249731,1.433999730,1.433754966,1.433515292,1.433280566,1.433050651,1.432825415,
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1.432604730,1.432388473,1.432176524,1.431968770,1.431765097,1.431565400,1.431369574,
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1.431177518,1.430989136,1.430804333,1.430623017,1.430445102,1.430270501,1.430099132,
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1.429930914,1.429765771,1.429603626,1.429444407,1.429288044,1.429134467,1.428983610,
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1.428835410,1.428689802,1.428546727,1.428406125,1.428267940,1.428132115,1.427998598,
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1.427867334,1.427738274,1.427611368,1.427486568,1.427363827,1.427243100,1.427124343,
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1.427007511,1.426892565,1.426779463,1.426668165,1.426558634,1.426450831,1.426344720,
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1.426240266,1.426137434,1.426036190
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])
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# ------------------------------------------------
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# 2. 插值构建连续 n(λ)
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# ------------------------------------------------
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interp_n = InterpolatedUnivariateSpline(wl_visible, n_visible)
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# ------------------------------------------------
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# 3. 红外区 n,k 数据（示例，可替换为真实数据）
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# ------------------------------------------------
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def pdms_nk(lambda_um):
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"""
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示例：构建红外折射率 n,k（实际请替换 refractiveindex.info 数据）
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"""
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n = 1.385 + 0.015 * np.exp(-(lambda_um - 10)**2 / 20)
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k = 0.15 * np.exp(-(lambda_um - 10)**2 / 5) # 红外区 PDMS 有吸收峰
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# 可见光区用插值得到的 n
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n[lambda_um < 0.7] = interp_n(lambda_um[lambda_um < 0.7])
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k[lambda_um < 0.7] = 0 # 可见光透明
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return n + 1j*k
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# ------------------------------------------------
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# 4. TMM 计算发射率
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# ------------------------------------------------
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def layer_matrix(n_complex, d_um, lambda_um):
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k0 = 2 * np.pi / (lambda_um * 1e-6)
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delta = k0 * n_complex * (d_um * 1e-6)
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q = n_complex
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M11 = np.cos(delta)
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M12 = 1j / q * np.sin(delta)
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M21 = 1j * q * np.sin(delta)
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M22 = np.cos(delta)
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return np.array([[M11, M12], [M21, M22]])
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def emissivity(lambda_um, d_um):
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n0 = 1.0 # 空气
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ns = 1.0 # 基底（可修改）
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nk = pdms_nk(lambda_um)
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M = layer_matrix(nk, d_um, lambda_um)
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M11, M12 = M[0,0], M[0,1]
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M21, M22 = M[1,0], M[1,1]
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numerator = M11 + M12*ns - M21/n0 - M22*ns/n0
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denominator = M11 + M12*ns + M21/n0 + M22*ns/n0
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R = np.abs(numerator/denominator)**2
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T = (ns/n0) / np.abs(denominator)**2
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return 1 - R - T
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# ------------------------------------------------
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# 5. 计算发射率与绘图
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# ------------------------------------------------
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lambda_range = np.linspace(0.35, 20, 2000)
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d_pdms = 10 # 10 μm 厚度
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eps = emissivity(lambda_range, d_pdms)
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plt.figure(figsize=(10,5))
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plt.plot(lambda_range, eps, label=f'd = {d_pdms} μm')
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plt.xlabel("Wavelength (μm)")
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plt.ylabel("Emissivity")
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plt.title("PDMS Thin-film Emissivity Spectrum")
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plt.grid(True)
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plt.legend()
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plt.show()
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