Electronic – arduino – Using op-amps to read real-time resistance values over a wide range

Background

I have been using a simple inverting op-amp circuit and Arduino to measure the resistance of a photoresistor (light 5k, dark 200M), like in the schematic below. This provides linear data which is good for the calibration of light intensity.

^{simulate this circuit – Schematic created using CircuitLab}

I used -5V as the input voltage. The output voltage was reading from an Ardunio Uno (resolution 10 bits). The resistance of the photoresistor can be calculated as below.

R = - RF * Vin / Vout

The measurable resistance range is decided by the resistance RF of the reference resistor. Taking the RF = 1k in the schematic and Vin = -5V as an example, the measurable resistance of the photoresistor is from 1k (Vout = 5V) to 1.023M (Vout = 1/1023 * 5V), despite of the decreased accuracy in the large resistance range.

Question

Now I need to measure the real-time resistance change of the photoresistor over a larger resistance range (1k to 100M).

Is there a way to improve this circuit, to be able to measure the dynamic resistance values of the photoresistor over at least five magnitudes (1k to 100M)?

I read this post "Reading dynamic resistance values over a wide range"
but I still want to keep with the inverting op-amp for its linear output, which makes it easier to calibrate the light intensity for my test.

In the meantime, I also try to divide it to several ranges. I am using extra analog input ports on Arduino to read from extra inverting op-amps with shared photoresistor but different RF, i.e., op-amps in parallel. As shown in the schematic below, I planned to use a current mirror to provide the same input for these op-amps, and use different reference resistors in these op-amps. By carefully selecting these reference resistors, it should be possible to have at least one output with good resolution. However, this design may produce very high voltage to damage the Arduino…

^{simulate this circuit}

Follow up on July 29, 2019

Thanks to @GRTech 's suggestion of using a log amplifier, I simply put the photoresistor in a log amplifier as shown in the schematic below.

^{simulate this circuit}

According to the calculation:

Vout = n * VT * ln(Vin / (R * Is))

The measurable resistance range would be largely increased as shown in the picture below. I think I just need to figure out a way to make the output voltage to span from 0 to 5V to maximize the resolution on Arduino analog input.