The predominant reason why the waveform becomes distorted is the photodiode ( and also the transistors and LEDs) have small amounts of capacitance which I hope you know by now tends to slow down a change in voltage to a change in current.
THis part is educative indeed. I didnt make the link in my mind exactly as you explain it here, i tell you sincerely. Though I am aware of the fact that EVERY component has it's own capacitance and resistance in a certain procentage, but usually is very-very low. For example, a capacitor has an internal resistance, and a resistor has an internal capacitance, and the other components for example a diode has a bit of both, a bit of resistance and a bit of capacitance when is working. Basically, nothing is perfect flowing the current through them. THat part I knew it already. But the way you put it is good for me to know "small amounts of capacitance tends to slow down a change in voltage" for each component. The thing is, I am a bit overlooking this little detail because the impact or effect is so small, it is insignificative in the big circuit.
For example, if I was stumble over each of these details in my big wings circuit, I would never had make it, or at least push it until this stage is right now.
I respect the fact that you want to teach me something new ! All the help I want from you is to assist me, as well as you can, and if you can, along the road I am already with this projekt.
When I was a youngster knowing little I would write down all the technical terms I did not know or understand and then look them up in books or ask my uncle to explain them.
That is a very smart thing to do. I do it very rarely, "write down the problem". THough as you mentioned, if I have a problem, with today internet I kind of understanding everything i put my mind to. If not 100% then it will be in a big percentage. It will be better than I knew nothing anyway. Haha.
To respond to your question, which is a bit intriguing but is a part of a bigger problem, from what I can see between the lines: about "impulse response". I just read about it. It is very new concept to me. It refers to frequncies, or oscilations. It is basically a shock or a bang. It is containing all the frequencies at once in the impulse part. Then the response part, from what I understand, is based on the component structure to reflect back. It is like a light red filter for example, when you shine white light over it, but under it, you obtain only the red light. THat is because it absorbs the other frequncies of the light but let pass only the red through it. THat is the response part. But it is applied not for a piece of glass like in my example, but to active components like diodes, or your experimental photodiodes that you measured with that fancy osciloscope which I like very much. Haha