I would like to know if the equation of taper space (edges) of reflector, which is defined by ratio f/D , is an estimation of Side lobe level of the aperture D of the reflector?
I guess not directly - the 10 dB taper rule implies you dont want to get too much energy spilled over the reflector, in case the edges'level is less than 10 dB spillover losses are big. If the edges receive lets say 20dB or more than the center that would mean your reflector ended up too large. Take a look into Balanis book its well covered - spillover and taper losses.
SLL will decrease though if the edges receive lesser power - that means a larger diameter reflector will provide smaller SLL figures.
There used to be simple graphs in most antenna design books showing sidelobe level as a function of edge illumination. This is not only due to space attenuation, but also due to the beam-shape of the feed. See Volakis Antenna Engineering Handbook 4th Ed page 15-22. for example.
A rule of thumb from the graph there is (for a circular aperture) no taper = 17 dB sidelobes, 10 dB taper = 24 dB sidelobes, 15 dB taper = 30 dB sidelobes, 25 dB taper = 40 dB sidelobes. The beam gets wider for more edge taper.
Space taper is due to the reduction in power density at longer distances from the feed. For a parabolic dish with f/d ratio of 4 (the focus is level with the edges of the dish) the edge is twice as far away from the feed as the middle is, and the power density reaching it is 1/4 the power density reaching the centre of the dish. Reflection at the middle, and in the 45 degree reflector at the edge, doesn't change the power density in either case, so there is a 6 dB space taper at the edge of the aperture even if the feed pattern is uniform in all directions.
You have to work it out yourself using simple geometry - using the distance from the feed to the part of the reflector you want to know about - to calculate the power density arriving at the reflector, and then using the arrival angle and the angle of the surface to the main beam direction to get the power-density per unit area on the projected area of the reflector.