Derivation of the probability of joint detection in Hong-Ou-Mandel interferometer

I read the Hong, Ou, Mandel. "Measurement of Subpicosecond Time Intervals between Two Photons by Interference", from PRL 59, 2044.

Where the – now known as – Hong-Ou-Mandel interferometer was presented

And I don’t understand the derivation of Eq. 7, for the probability of a joint detection at detectors D1 and D2.

$P_{12}(tau)=K|G(0)|^2 left( T^2 g(tau)^2 + R^2|g(2deltatau-tau)|^2 -RT[g^*(tau)g(2deltatau-tau)+c.c.] right)$

Where $R$ and $T$ are the reflectivity and transitivity of the beam-splitter, $G(tau)$ is the Fourier transform of the coefficients of the input state, $g(tau)=G(tau)/G(0)$, and $K$ is a constant characteristic of the detectors.

What is the step by step derivation of Eq. $7$?

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They say it follows from Eqs $3$ – $6$.

— Eq. $3$ gives a general expression for the coefficients of the two-photon state $|Psirangle$ in the frequency basis

— Eq. $4$ gives the general expression of quantum optics for the probability of a joint-detection $P_{12}(tau)$

— Eqs $5$–$6$ give the expressions of the electrical field operators at detectors D1 and D2

I understand where each of the Eqs $3$–$6$ comes from, but I don’t understand how they combine to yield Eq. $7$.

I am familiar with quantum mechanics and have a basic knowledge of quantum optics.

See all the equations in their context: