The demand for rapid and accurate surface profile imaging of micro- and nano-scale devices is increasing due to advancements in microelectromechanical systems (MEMS) and three-dimensional integrated circuits (3D-ICs). Current methods like interferometry and confocal microscopy have limitations in measurement range and speed. Similarly, while coherent and white-light interferometers offer nanometric axial resolution, their ambiguity range and slow video rates hinder the study of high-speed vibrations. Laser Doppler vibrometers (LDVs) can measure high-speed vibrations but only at a single point. The study of complex dynamic behaviors in micro- and nano-mechanical resonators, including anharmonic vibrations and pulsed optomechanics, necessitates real-time, multi-dimensional imaging with improved resolution and speed. This research addresses this need by developing a novel line-scan TOF camera capable of capturing both static and dynamic properties with high dynamic range.

Existing surface metrology techniques, including interferometry and confocal microscopy, face challenges in achieving both high dynamic range and high speed over large areas, particularly when characterizing the static properties of advanced MEMS and 3D-ICs. For dynamic properties, coherent and white-light interferometers, while offering nanometric axial resolution, suffer from limitations in ambiguity range and speed, making them unsuitable for high-speed vibration analysis. Laser Doppler vibrometers, though capable of GHz bandwidth measurements, provide only out-of-plane vibration data at a single point. Therefore, characterizing vibrations and mechanical motions often relies on combining multiple techniques or using stroboscopic methods, limiting real-time observation of complex dynamics. The authors highlight a gap in real-time multi-dimensional imaging of fast mechanical motions to fully understand dynamic behaviors in microscale devices.

The researchers developed a line-scan TOF camera utilizing space-to-wavelength encoding with a mode-locked Er-fiber optical frequency comb. The frequency comb's spectrum is spatially dispersed by a diffraction grating, encoding spatial coordinates into wavelengths. This creates a line-scan illumination with few-micrometer lateral resolution over several millimeters. Each sub-pulse experiences a different time-of-flight (TOF) corresponding to the sample's surface profile. An electro-optic sampling-based timing detector (EOS-TD) is employed for parallel detection of the TOFs of numerous sub-pulses, overcoming limitations of previous frequency comb-based methods. The EOS-TD measures the relative timing and TOF changes between optical pulses and frequency-locked periodic electric waveforms (derived from a modified uni-traveling carrier (MUTC) photodiode), converting TOF variations into spectral intensity variations. A 1024-pixel InGaAs line-scan camera analyzes the EOS-TD output, reconstructing the TOF profile of multiple positions simultaneously. Despite the sub-pulses' relatively long pulse width (>90 ps), the EOS-TD achieves sub-nanometer precision. Axial and lateral resolutions were analyzed using overlapping Allan deviation, measuring TOF precision under varying bias voltages. Lateral resolution was assessed using a resolution test target. 3D surface profile imaging was accomplished by synchronously scanning the target perpendicular to the line scan, and step height measurements were performed on gauge blocks and a complex silicon structure.

The line-scan TOF camera demonstrated remarkable performance characteristics: * **Pixel rate:** Up to 260 megapixels/s * **Axial resolution:** Down to 330 pm * **Dynamic range:** Up to 126 dB * **Lateral resolution:** ~4.38 µm * **Field of view (FOV):** >4.4 mm The system accurately measured step heights of gauge blocks with high repeatability (e.g., 31 nm repeatability for a 300 µm step height at 10 kHz line-scan rate). Measurements on structures made of different materials also demonstrated high accuracy, though repeatability slightly decreased due to variations in reflectance. The camera successfully imaged a complex silicon structure with high resolution, accurately measuring step heights and surface profiles. High-speed 3D imaging was achieved, capturing a 6.4 mm x 2.4 mm region in 3.47 ms with 1024 x 882 pixels resolution, resulting in a frame rate exceeding 120 Hz in FHD resolution.

The developed line-scan TOF camera overcomes the limitations of existing techniques by providing a unique combination of high speed, high resolution, and large dynamic range. This allows for real-time, multi-dimensional imaging of complex surface structures and dynamic mechanical motions, which is crucial for advancing the understanding of micro- and nano-scale devices. The high accuracy and repeatability of the step height measurements demonstrate the system's potential for precise metrology. The ability to image structures with varying reflectances showcases its versatility. The results significantly enhance the capabilities for studying complex dynamic phenomena in micro- and nanomechanical systems.

This research presents a novel line-scan TOF camera that achieves unprecedented performance in terms of speed, resolution, and dynamic range for surface profile imaging. The technique combines space-to-wavelength encoding with high-speed electro-optic sampling, enabling real-time, multi-dimensional imaging of micro- and nano-scale devices. Future work could explore the integration of acousto-optic deflection for vibration-free high-speed scanning, enhancing the system's capabilities further.

The current system's scanning speed is limited by the mechanical limitations of the motorized stage used for target scanning. While high-speed imaging was demonstrated, utilizing acousto-optic deflection could further improve the speed and eliminate motor vibration-induced uncertainty. The precision and dynamic range can be non-uniform when the optical spectrum is non-uniform. The accuracy of measurements may be affected by the reflectance properties of the material being imaged, as seen in the slightly degraded repeatability when measuring structures with varying reflectances.