Photodiodes: Measuring Low Optical Power vs Dark Current Contradiction
The concern when your dark current approaches your photocurrent is SNR. The three big noise components you are likely to encounter are dark current shot noise, photocurrent shot noise, and noise from your readout circuit. The first two can be easily calculated as:
\$S=2qI\$
Where \$S\$ is the input referred noise power spectral density in A2/Hz. The third is something you may have to measure, unless you have good noise models in your simulator. Sum all of these components, multiply by your bandwidth, and take the square root to get a measure of your expected noise in A.
If you wanted to measure photocurrents below the dark current, you can do so using a capacitive TIA, which is just a regular TIA with a capacitor in feedback, also known as an op-amp integrator. Adjusting the integration time allows you to increase the signal strength proportional to integration time, but the noise only increases as the square root of integration time. Increase integration time to obtain whatever SNR you need. Be sure to size your integration capacitor to account for the dark current. You will additionally need to calibrate your particular detector as dark current varies between detectors.