How to design a transimpedance amplifier that can adjust to large voltage swings?
It's can be described as a log-responding AGC linear-optical TIA PD detector.

AGC: Automatic gain control
TIA: Transimpedance Amp.
PD: Photo Diode   

The negative feedback voltage controls the collector current to shunt the PD current and increase the gain when the output (pin 7) rises above  2.5V then Vbe is reduced with Ic shunt and thus higher gain.

The inputs are all biased to Vref=Vcc/2.

The PD's have a negative linear gain but the output is integrated towards the the average voltage of Vcc/2.  Q1 has a log Ic vs Vbe response.  

Thus the TIA has a wide dynamic range with a long time constant (R1C5=5.6ms) and a linear response at fast response (R2C1=125ns) for small signals.