Microwave-Free Optical Readout of NV- Spin States via Magnetic Modulation for Probing Picomolar Paramagnetic Ions

Microwave-free optical readout of nitrogen-vacancy (NV-) centers based on magnetic-field-dependent photodynamics and magnetic modulation provides a route for sensing without microwave excitation, yet its use in calibrated trace paramagnetic-ion analysis remains underdeveloped. In this work, we combine DOTA-functionalized silica-coated fluorescent nanodiamond (FND@SiO2-DOTA) probes, low-frequency magnetic modulation, UNet-ConvLSTM-based signal-pixel identification, and pixelwise lock-in-amplitude analysis to detect weak paramagnetic effects without microwave excitation or frequency sweeping. Using Gd3+ as a model paramagnetic ion, the lock-in readout achieves a detection limit of 51.8 pM, which is lower than that obtained from optically detected magnetic resonance contrast measurements under the same probe system and comparable to T1 relaxometry. By distinguishing modulated FND pixels from the optical background and extracting a lock-in signal, this approach provides a streamlined workflow for Gd3+-referenced trace paramagnetic-ion sensing.