In post 2 I had not much to go on. I said that i=c x de/dt. In post #8, Mr Al, abjadi said; i=c x de/dt not satisfied. That was the 'dissatisfaction'.
I like the CRO you are using; looks like a really nice little unit. The trace pic suggests the HF compensation is too much for the 'voltage' waveform.
ajbadi, according to the circuit, when the switch conducts, the rate of rise of current will be a function of the (Vout - Vin). This rate of rise of current will be supplied to the load, which presumably is resistive. As the current rises, the load voltage will rise. The capacitor current should then be C x de/dt, and is a constant.
When the switch opens, the back emf across the coil will cause a circulating current through D1 and Cout and the load current will be discharging the Cout. So what you get is not straight forward.
To measure these ripple currents/voltages, it may be necessary to use the 'AC' setting for the input probe as you have done for channel 1.
Setting up the test probes to make these measurements requires some fiddling for the best spot connecting the earth lead etc, so experiment a bit to get some nice traces.
Many of the switch mode IC manufacturers have excellent data sheets and application notes, so consult them widely.
Frankly, I think you have it pretty much under control. Well done.