Direct imaging of exoplanets by reflected starlight is extremely challenging due to the large luminosity ratio to the primary star. Wave-front control is a critical technique to attenuate the speckle noise in order to achieve an extremely high contrast.

We present a phase quantization study of a spatial light modulator (SLM) for wave-front

control to meet the contrast requirement of detection of a terrestrial planet in the habitable zone of a solar-type star.
 

We perform the numerical simulation by employing the SLM with different phase accuracy and actuator numbers,which are related to the achievable contrast. We use an optimization algorithm to solve the quantization problems that is matched to the controllable phase step of the SLM.

Two optical configurations are discussed with the SLM located before and after the coronagraph focal plane mask. The simulation result has constrained the specification

for SLM phase accuracy in the above two optical configurations, which gives us a phase accuracy of 0.4/1000 and 1/1000 waves to achieve a contrast of 10^-10.

Finally, we have demonstrated that an SLM with more actuators can deliver a competitive contrast performance on the order of 10^-10  in comparison to that by using a deformable mirror.