I am looking for a level shift which shifts an analog circuit with a variable ( tunable) DC level.
means for example I can change the analog voltage with 15volt once, and next time may be -10. the range of change for the DC is (-20 to 20).
Another solution could be adder; to add the analog voltage to the tunable DC voltage.
Here is a good place to start, about 1/2 way down the page is the basic theory (and maths) and simple circuit (showing a generic op-amp) showing a +-1 V signal transposed to 0 to 2 VDC (for, say, feeding to a ADC which only has a 0V to 2V input range):
Of course, your specific application will need to know actual voltage levels to be shifted to, and your frequency response is probably not actually the 'speed of light' but rather some more reasonable rate-of-change like several kilo Hertz to perhaps a couple MegaHerz depending on the source creating the light energy (how rapidly it turns on and off, rather than the fact it is 'light' energy as a photodetector diode provides an output voltage proportional light amplitude, and the output will roughly 'follow' the enevelope of the light that is shined on it).