Input analog voltage between -3 and 3V obtained with a laser sensor

Hello everyone,
I'm new to using Arduino and making electronics as well, so it is complicated for me to understand electronic schematics and I need advice.
With a Arduino Uno, I made a PID controller (see the "image" of circuit below) to control a peltier to heat water. There is a MAX31855 (thermocouple amplifier) to measure the temperature of the water and a h-bridge with a low pass filter to control the peltier for heating.
This is just the heating part of my set-up.

But in my experiment, I need to measure the displacement of a sample during the heating. Here I use a laser sensor LC-2440. I want to access to the voltage output of the sensor (1V=1000 µm displacement) with my Arduino Uno. But the range measured is between -3V and 3V, and I know that Arduino Uno cannot accept negative voltage. I read on different posts here, that we can use a voltage divider at the VCC and also at the AO pin. Like it is described here : https://www.electroschematics.com/precision-full-wave-rectifier-circuit/
But I didn't understand how to do it and what I need (because I'm not good for reading electronics schematics).
Maybe someone can help me to understand better what make the electronic circuit between the output of the laser and the Arduino Uno.
For example, this is a useful comment written here : Analog input - positive/negative voltage - #3 by Wawa

But I didn't understand how to convert the 0-1024 obtain into the voltage measured at the end.

Thank you for your answer,
I hope my message is clear :slight_smile:

-3 to +3 is 6V so you will need to shift AND scale the voltage.
You will need a precision op-amp to do it , if you wish to preserve the LC2440 precision and accuracy.

Jim is quite right, you need to do this with good quality operation amplifiers.
This link will tell you how to do it
Op amp DC offset correction design pdf download

I've used a voltage divider resistor set like the OP posted. Offsets and scales simultaneously. However going full scale on a 5v device like the Uno will require an op-amp.