At last!
You shouldn't place things for "convenience", but for electrical behaviour, including "parasitic" resistance and inductance.
There are lots of wires and "joints" with variable resistance all over that board.
You have different probe's shields connected to different points. That can introduce noise due to currents flowing through resistance (and inductance) not shown in your schematic (nor your thinking).
You should look at the time domain oscilloscope waveforms, to assess any correlation between "noise" on each channel. Only after that is acceptable should you look at the XY plots.
Try connecting two probes to the exactly the same strip on the solderless breadboard. What do you see?
Try connecting two probes's shields to the exactly the same strip on the solderless breadboard. What do you see?
I understand your point and I at least to some extent understand the issue with the breadboards. I think I mis-asked and/or mis-explained the reason of my question or this post, also I should have put another title I think. Maybe because of English as my second language.
I am probably going to repeat myself, so excuse me for that.
I am not looking a way to improve the situation on the breadboard using only a sense resistor (I already have a current sense amp solution which gives me more than I need). I am already trying different things (using a current sense amp was one), just to make the trial a bit better. However, this is not going to live on the breadboard. If I want to carry on a proper experiment, I am going to have it on a proper PCB. Naturally I cannot share every step I am taking neither every waveform I am seeing, this would be too much time consuming.
The scope channel and the probe (actually a coax + adapter) is the same for current sense amp output measurement and the sense resistor voltage measurement. Hence I dont think that can be the reason. It may not be 100% correct, but I think the effect of breadboard's imperfectness should be more pronounced with current sense amp because it involves more wiring.
There are old research, and the ones I saw is not the same element values as they can be calculated differently but the circuit topology is the same, that is using only the sense resistor for measuring the current passing through L, and it is a bit difficult to judge but it seems like it was OK (at the moment, I see it as not OK on my prototype). Naturally it was not a circuit on the breadboard, possibly a PCB.
Coming back to my actual question that it seems I couldnt manage to ask, in other words, taking the breadboard out of the picture; if I have this circuit (with only the sense resistor) on a PCB, can I have the same current measurement that I do with the current sense amp in terms of less noise ? would they be of equal or not very different quality ? in other words, is the noise I see without the current sense amp only due to breadboard ? I understand if the answer can be we cannot know without trying.
I understand you want to see actually what is going on, the circuit, the wiring etc., but my question was more broad -I should have been more clear about this-, that is why I didnt want to mention details of the circuit at first. This is not the only circuit I want to measure the current with similar properties.
Basically my question is this. I have a project, I have to bidirectionally measure current, a few tens of kHz bandwidth is more than enough. I can use 1 ohm (or less) sense resistor (but not more), either low side or high side not important, and high side is 9V max, and the current is around 1mA. When I say measure, I mean measuring voltage with the scope I have (20MHz, input sensitivity minimum 2mV/div, 45uV noise on 10mV range, 12-bit ADC). These are the things I cannot change, but I can change anything regarding to power supply (for convenience I am using a 5V to +-9V DC-DC converter here, I can also use a split rail linear regulator if it matters), and I can use other ways to 'sense' the current (e.g. using a current sense amp, and I will actually need a differential amp as well to shift the level) as long as the effect on the circuit is the same as merely having the sense resistor. So the question, given these above, is it OK to measure the current just as a single ended voltage measurement on a 1 ohm current sense resistor at low side ? or is it not and I need another way (which probably involves using a current sense amp) ?