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You need a way to see the light with a very fast response.
The LED probably has 10nS response time so you need a detector with 2nS response time.
No photo transistor will do that.
Some photo diode will do that fast.
Do you have a driver that will drive the LED from 0 to 10mA in 2nS?
Do you have a 500mhz oscilloscope?
i am trying to understand the behaviour of the waveforms..
i drive the LED directly with the function generator(with 85 ohm series resistance for 20mA current).The photodiode is connected to the oscilloscope with the BNC connector cable.
for 1khz square wave frequency i can see the waveforms across LED is same as the waveform across the photodiode.
but when the increase the frequency to 10Khz,the (electrical signal)waveform across LED is square but the electrical signal from the photodiode is kind of looks like sawtooth waveform..i wonder why..maybe the photodiode is not fast enough when compared tot the LED ?
White LED's are really UV LED's that cause a phosphor dome to excite. This causes them to be much slower in light output response time. Light output may degrade some over lifetime as the phosphor degrades.
Can you use a red LED for a test. Red should be much faster.
Depending on what type of white LED you have.....The current becomes UV light with 10nS delay. The UV light charges up a mixture of phosphors that glows white. (each type of phosphor has a different color and by mixing you can get about any color (of white)) The phosphor has a response time that I don't know. Probably about the same as phosphor used in CRT monitors.
You might be testing the phosphor decay time and not the LED response time.
Because you chose white, you are measuring the response time of phosphors not the LED. So your tests are not what you thought.
Back when I designed CRT monitors and TV sets I could find out the response time of each type of phosphors.
In LEDs (white) there are many types of white. Blue-white, Red-white, warm, natural, etc. Each have a different mix of phosphors. There is more than one way to mix up "warm white". The LED companies will not tell me what mix they are using. In a CRT the response time was important. Because no one is using white LEDs 'fast' to send data, the response time is not important and not measured and certainty not in the data sheet.
Phosphors materials turn on pretty fast, but they turn off much much slower. For radar displays we used some that had a decay time of 6 seconds. For data terminals I have used as slow at 100mS to typically 5mS. CRT phosphors is refreshed 60 times a second. It has been a long time scene I thought about phosphors response time, I know I have used fast phosphors I do not remember their time but I can't believe they are much faster than 0.1mS.
Where are you measuring? Directly next to the LED, or at the input end of a length of wire feeding the LED? If the latter, then the current through the LED (hence the brightness) may not be a square-wave because of the wire inductance/capacitance.
some white LEDs use a UV diode and a white phosphor. the phosphors introduce some lag in the response of the LED. ideally, you want a white LED that consists of a combination of red, green, and blue LEDs on the same chip. since they use no phosphors, their response time will be faster. the limiting factor of an LED is it's junction capacitance. on most LED spec sheets, their response time isn't usually listed. you might want to look at TOSLINK transmitters and receivers which can operate up to 8Mb/s.