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org/q1.py

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