What parameter would I be looking for in a datasheet (if such a parameter exists) if I want to determine how fast the op amp output responds to changes in input? I'm using an op amp as a difference amplifier to amplify the voltage across a current sense resistor. I'd like to know at least the order of the expected delay. This is for an error calculation. I'm directly sampling some voltage values, but the 'current values' are sampled only after it passes through a difference amplifier. So I'm guessing I won't be getting the value of current for the exact instance of the voltage if I sample both at the same time. Is there any such parameter specified?
Several op-amp parameters combine to indicate what the "delay time" there may be for a given circuit configuration but, in critical timing situations I would strongly consider routing the "direct" signal referred to, thru a similar amplifier configuration so that these delays largely cancel.
The single parameter I would most focus upon as an indicator would be frequency at which the gain becomes zero (also called GBWP, gain-bandwidth-product) but slew rate (the op-amps ability to change its output voltage in volts per microsecond) can also have a part and so can settling time.
Op-amps with greater GBWP will have a smaller delay at any given frequency.
The closed-loop gain is also important - the higher the closed loop gain is the more the output phase tends to lag the input by 90 degrees. 90 degrees is the natural phase angle for most open-loop op-amps due to stability circuitry within the op-amp. When the loop is closed (by feedback) the phase angle becomes dominated by the feedback components but this gets gradually eroded towards 90 degrees as frequency rises. This happens because open-loop gain falls at higher frequencies and the effect of external feedback reduces and the internal 90 degree phase shift starts to dominate.
The parameter you want is the Total Response Time:
The time between a step-function change of the input signal and the instant at which the magnitude of the output signal reaches, for the last time, a specified level range (±e) containing the final output signal level.
This definition is from Understand Operational Amplifier SpeciFfications by Jim Karki.
Another parameter that might be helpful is the phase shift through the amplifier. For signal frequencies where the open loop gain is unity this is specified as the phase margin.
Note that the output slew rate parameter is something else altogether. The slew rate of an amplifier indicates the ability of the output stage to make large voltage changes, rather than the delay from input to output.