Non-contact Sub-nanometer Displacement Sensing Based on Optical Digital Coherent Detection Using Frequency-Domain Filters

We have introduced a sub-nanometer non-contact displacement sensing method using phase-diversity optical digital coherent detection. The initial work achieved 0.62 nm displacement sensing with a 0.21 nm resolution using a temporal domain filter. However, optimizing the filter for a sharp transition band and low order posed challenges, limiting noise filtering. To overcome this, frequency-domain filter is proposed and investigated in this work. Employing a frequency-domain bandpass filter improved resolution to 0.07 nm at 0.62 nm displacement, resulting in an 18.5 dB signal-to-noise ratio—8 dB higher than temporal domain filtering. This advancement enhances precision for applications in precision instruments without any additional cost.