# How are the structure functions in Deep inelastic scattering measured?

I've been reading lots of different textbooks on the parton model and deep inelastic scattering and the discovery of quarks, and most of the time whenever I see a plot, it's about the measurement of the structure functions, like $$G_E, G_M$$ or $$F_1, F_2$$. I can understand how they come up with the cross section (by dividing the number of particles shot vs the number detected perhaps?), but I can't see how derive the value of the structure functions, which live within the formula for the cross section. For example:

$$\frac{\mathrm{d} \sigma}{\mathrm{d} \Omega}=\left(\frac{G_{E}^{2}+\tau G_{M}^{2}}{(1+\tau)}+2 \tau G_{M}^{2} \tan ^{2} \frac{\theta}{2}\right) \cdot\left(\frac{\mathrm{d} \sigma}{\mathrm{d} \Omega}\right)_{0}$$ where $$\left(\frac{\mathrm{d} \sigma}{\mathrm{d} \Omega}\right)_{0}=\frac{\alpha^{2}}{4 E^{2} \sin ^{4}(\theta / 2)}\left(\frac{E^{\prime}}{E}\right) \cos ^{2} \frac{\theta}{2}$$ or hell, even \begin{aligned} \frac{d \sigma}{dE' d \Omega} &= \sum_{i} \int_{0}^{1} f_{i}(x) \frac{\alpha^{2} e_{i}^{2}}{4 E^{2} \sin ^{4} \frac{\theta}{2}}\left[\frac{2 M}{Q^{2}} x^{2} \cos ^{2} \frac{\theta}{2}+\frac{1}{M} \sin ^{2} \frac{\theta}{2}\right] \delta (\xi - x) dx \\ &= \frac{\alpha^{2}}{4 E^{2} \sin ^{4} \frac{\theta}{2}}\left[\frac{2 M}{Q^{2}} x^{2} \cos ^{2} \frac{\theta}{2}+\frac{1}{M} \sin ^{2} \frac{\theta}{2}\right]\sum_{i} e_{i}^{2} f_{i}(x) \end{aligned}

and they somehow manage to calculate the $$f_i$$ (I think?).

Can anyone maybe explain for me please? Thank you!
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