The temperature correction inflates the signal-to-noise ratio of the LEDs: the noise is not divided by the reduction factor

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调研方向

从 ExtinctionCoefficients.apply_temperature_correction 开始，追踪它如何更新参考强度和噪声列；然后检查 calc_and_set_coefficients 和 calc_and_set_coefficients_mp，了解 SNR 是如何形成的。添加一个测试，使用相同的提取数据分别进行温度校正和不进行温度校正，并确认传递给 calc_coefficients_of_img 的 SNR 保持不变。

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描述

ExtinctionCoefficients.apply_temperature_correction divides the reference property by the reduction factor of every value, but leaves its noise column as it was extracted:

corrected_intensities = self.calculated_img_data[self.reference_property] / factors
self.calculated_img_data = self.calculated_img_data.assign(
    **{self.reference_property: corrected_intensities})

The signal-to-noise ratio that weights the LEDs in the linear solver is then formed from the corrected intensity and the uncorrected noise (calc_and_set_coefficients and calc_and_set_coefficients_mp):

snr = single_img_array / single_img_data[self.noise_property].to_numpy()

So with a temperature correction every SNR comes out too high by 1/factor. The correction rescales the signal, it does not add any: the SNR of a measured value is I/σ before and after it. The weight min(1, SNR / snr_full_weight) is meant to be the inverse standard deviation of the optical depth -ln(I_e/I_0), and the correction does not change that either.

Effect

Only LEDs below snr_full_weight are affected, because the weight is capped at 1. With a reduction factor of 0.8 and the default snr_full_weight = 10:

true SNR weight now correct weight
8 1.0 0.8
4 0.5 0.4
1 0.125 0.1

The min_layer_weight cut-off is computed from the same weights, so layers are set to NaN later than they should be. The error grows with the reduction, i.e. with the LED temperature, which is highest where the smoke is densest and the LEDs approach the noise floor, so it hits exactly the LEDs the weighting exists for.

Runs without a temperature correction, and runs of a reference property without a noise column, are not affected.

Fix

Divide noise_sum_col_val by the same factors in apply_temperature_correction whenever self.noise_property is loaded. The moving average runs before the correction for both columns, so they stay consistent.

A test: for the same extracted data, the SNR passed to calc_coefficients_of_img should be the same with and without a temperature correction.

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