The Wikipedia webpage "Delayed choice quantum eraser" offers a simplified explanation of this experiment.
"In the basic double slit experiment, a beam of light (usually from a laser) is directed perpendicularly towards a wall pierced by two parallel slit apertures. If a detection screen (anything from a sheet of white paper to a CCD) is put on the other side of the double slit wall, a pattern of light and dark fringes will be observed, a pattern that is called an interference pattern. ... The emergence of an interference pattern suggests that each particle passing through the slits interferes with itself, and that therefore in some sense the particles are going through both slits at once. This is an idea that contradicts our everyday experience of discrete objects. ... in 1982, Scully and Drühl found a loophole around this interpretation. They proposed a "quantum eraser" to obtain which-path information without scattering the particles or otherwise introducing uncontrolled phase factors to them. Rather than attempting to observe which photon was entering each slit (thus disturbing them), they proposed to "mark" them with information that, in principle at least, would allow the photons to be distinguished after passing through the slits. Lest there be any misunderstanding, the interference pattern does disappear when the photons are so marked. However, the interference pattern reappears if the which-path information is further manipulated after the marked photons have passed through the double slits to obscure the which-path markings.".
"A simple quantum eraser experiment
A simple version of the quantum eraser can be described as follows: Rather than splitting one photon or its probability wave between two slits, the photon is subjected to a beam splitter. If one thinks in terms of a stream of photons being randomly directed by such a beam splitter to go down two paths that are kept from interaction, it would seem that no photon can then interfere with any other or with itself.
However, if the rate of photon production is reduced so that only one photon is entering the apparatus at any one time, it becomes impossible to understand the photon as only moving through one path, because when the path outputs are redirected so that they coincide on a common detector or detectors, interference phenomena appear.".
So that explains what is going on, refer to Kim's paper on page 4. Particles which were detected without which-path information form a fringe pattern (Figures 3. and 4.) and particles which were detected with which-path information form a particle pattern (Figure 5.), D4 is unused
That is further demonstrated in this YouTube video: "#1 - Delayed Choice Quantum Eraser", and verbally explained in this YouTube video: "#2 - Delayed Choice Quantum Eraser".
In the paper Taming the Delayed Choice Quantum Eraser, Figure 2 shows a plot of the bits of Equation 4.7.
The paper your question refers to, "Taming the Delayed Choice Quantum Eraser" (7 Nov 2017), by Johannes Fankhauser, on page 1 says:
"The delayed choice experiment conceived by Wheeler [Wheeler, 1978] has formed a rich area of theoretical and experimental research, as evidenced in the literature ([Eichmann et al., 1993], [Englert and Bergou, 2000], [Englert et al., 1999], [Mohrhoff, 1999], [Kim et al., 1999], [Walborn et al., 2002], [Kwiat and Englert, 2004], [Aharonov and Zubairy, 2005], [Peres, 2000], [Egg, 2013]). From the results of the original delayed choice experiment Wheeler concluded that ‘no phenomenon is a phenomenon until it is an observed phenomenon’, and ‘the past has no existence except as it is recorded in the present’ (ibid.). I shall discuss a modified version of Wheeler’s delayed choice experiment, one which was first proposed by [Scully and Drühl, 1982] and later realised in the experiments of [Kim et al., 1999].
Kim's paper is called "A Delayed Choice Quantum Eraser" (13 Mar 1999), on page 1 it says:
"This paper reports a "delayed choice quantum eraser" experiment proposed by Scully and Drühl in 1982.".
That paper is called: "Quantum eraser: A proposed photon correlation experiment concerning observation and "delayed choice" in quantum mechanics" Marlan O. Scully and Kai Drühl Phys. Rev. A 25, 2208 – Published 1 April 1982.
How do they obtained these plots? For each of them, what is the corresponding function derived from Equation 4.7? From the caption of the figure, it is not clear at all.
How these plots are generated and recorded is explained above.
The functions for those plots and the image included in your question (specifically with respect to the paper you quoted) are on the bottom of pages 6 and 8.
I'm asking this because I would like to get those plots also pictured differently, as we graph usually a function (and get the waves). However I don't see how they got the plots, since I cannot derive the desired functions.
I have included two YouTube videos showing the graphed functions and also included the images from Kim's paper.
Quantum erasure is discussed in many papers, I suggest "Causality and Quantum Theory", there's an easy to read explanation on pages 2-4.