What resistance should be used with a phototransistor to have fast rise/fall time?

Question

I am trying to accurately capture the video latency and response time curve of an LCD display from a black image to a white image for the purpose of reviewing the accuracy of a couple of video latency measurement tools. I am using a digital storage oscilloscope and a phototransistor. This is the spec sheet for the phototransistor. I would like the values of the curve captured by the oscilloscope to be delayed no more than 100 microseconds or so. What resistance should I use to capture a luminosity curve that has this accuracy of timings?

Here is more background on my progress so far:

I have created a circuit that is similar to the "Testing principle diagram" on page 3: I have a Vcc of 4.5 V (3 AA batteries) and the oscilloscope is wired to measure the voltage across the resistor that connects to the phototransistor and ground. When using the LCD screen that I would like to measure, I get a maximum of about 60 µA through the circuit.

I have noticed that the phototransistor's rise and fall times are affected by the resistor that I use in the circuit. To demonstrate this effect clearly in a controlled manner, I have placed the phototransistor in front of an LED that is switched on using a debounce circuit. Here are some screenshots that show the voltage change across the resistor when different resistors are used:

1.3 kΩ

7.8 kΩ

140 kΩ

It seems that as resistance increases, the rise time of the phototransistor also increases. Does this mean that a resistance that approaches 0 is the most accurate? I have noticed that the signal to noise ratio decreases as I reduce the resistance. What is a good resistance that will keep the curve accurate to within 100 microseconds while also keeping the voltage across the resistor high enough to not be problematically noisy?

UPDATE:

After reading Andy's answer, I took the advice to consider using a photodiode instead of a phototransistor for this project. I actually had a couple on hand, but when I first tried them out I didn't understand anything I was doing and disregarded them after the phototransistor seemed to be "easier" for me to get visible on my oscilloscope. To be honest, I'm not sure why I initially struggled with the photodiodes.

Here is the voltage across a 194 kΩ resistor that is in a short circuit with a BPX 61 photodiode when turning on the same LED that was used in the previous examples:

This shows the LED reaching full luminosity in only 90 microseconds. When I reduced the resistance to 37 kΩ, the time to reach full luminosity decreased to 19 microseconds. That's one fast LED!

I also realized that I have an audio device with S/PDIF coax and optical toslink output that I have previously measured using an optical receiver to find that the coax and optical outputs were aligned to within less than 100 nanoseconds of each other. With this in mind, I thought it would be good to compare the voltage from my photodiode circuit when measuring the optical output of this audio device with the coax electrical output of the audio device. Here are my findings (blue is optical through my photodiode circuit and yellow is electrical S/PDIF output from the audio device):

I can see from this that the upwards and downwards changes of the optical signal are aligned with the upwards and downward changes of the electrical signal. This seems to show that the photodiode circuit's rise/fall time is not fast enough to keep up with the S/PDIF optical signal, but it does respond immediately to a change, which is the most important thing for me.

Here's a 100Ω with the same optical and electrical S/PDIF signal (I switched channels, so this time blue is electrical and yellow is optical through my photodiode):

This "works" for this optical S/PDIF signal, but is way too noisy for my use, so I'll go with a higher resistance.

I suspect I would be able to get an even better result with a transimpedance amplifier, but at this point I might just play around a bit with the resistance I am using with this specific photodiode and that might be good enough for my purposes.

Answer 1

It's the self-capacitance of the phototransistor that is the problem. It's a problem with photodiodes too but to a significantly smaller degree. So, consider using a photodiode instead of the "notably slow" phototransistor.

However, if you want to stay with the phototransistor, you can use a common base NPN BJT circuit where the phototransistor is connected from emitter to 0 volts. This keeps the voltage across the phototransistor at an almost constant level thus, its internal capacitance cannot produce negative feedback inside the device that "hits" rise and fall times so badly.

An alternative circuit is the TIA (transimpedance amplifier). These are often used with photodiodes for very fast response times (sub 10 ns) but, there's no reason why a phototransistor cannot also benefit from the same circuit (with a volt or so of bias): -

The above picture came from Pullup vs. transimpedance amplifier and it explains the mechanisms behind why a phototransistor with pull-up resistor is basically slow.