Lock-in detection, a common measurement technique, distinguishes signals from noise by imparting periodic variation at the source and amplifying the modulated component at the detector. In optics, this is used in telemetry, free-space communications, and biomedical imaging. Imaging through scattering media, such as biological tissues or fog, is challenging due to multiple scattering of photons. Existing techniques, including time-gated, polarization imaging, and spatial modulation, have limitations in speed and wide-field application. High-frequency wide-field demodulation imaging is highly desirable for real-time applications like navigation, 3D ranging, vibrometry, and optical communications. Current methods using image intensifiers, Time-of-Flight (ToF) sensors, and lidar systems have only partially addressed the challenges of phase synchronization, timing jitters, snapshot operation, and frequency tuning. This paper introduces a new full-field all-optical single-shot technique for quadrature demodulation (FAST-QUAD) to overcome these limitations and achieve instantaneous two-dimensional image demodulation from a single camera frame.

Existing techniques for imaging through complex disordered media include time-gated methods (costly but efficient), polarization imaging (comparatively inexpensive), and spatial modulation techniques. Temporal modulation/demodulation utilizes the fact that ballistic photons (a small fraction of total photons) retain phase relationship with source modulation, while scattered diffusive light loses this relationship. High modulation frequencies (10-100 MHz for transport applications, GHz for biological tissues) are needed for effective filtering. Current modulation-based approaches in the radio-frequency (RF) range are limited to point-wise detection. Two-dimensional ballistic-light imaging techniques require post-processing (electronic, mechanical, or software), increasing complexity and processing time. The need for rapid wide-field demodulation imaging is significant for applications in navigation, 3D ranging, vibrometry, and various scientific instruments. Progress towards snapshot image demodulation at high frequencies requires overcoming challenges in phase synchronization, timing jitters, and frequency tuning.

The proposed FAST-QUAD technique performs demodulation optically in the polarization space at the receiver. It exploits the Pockel's effect in an electro-optic crystal, which introduces a phase difference between orthogonal light components proportional to the applied voltage. Suitable electrical excitation and orientation of birefringent/polarizing elements resolve light into quadrature components, achieving demodulation without source synchronization. A single camera frame, acquired over many modulation periods, provides the demodulated image. The optical setup includes a polarizer, quarter-wave plate, splitting/polarizing prisms, and a single electro-optic (EO) crystal. A periodic sawtooth electric field is applied to the EO crystal to achieve sinusoidal optical transmission. The ¼ optical path difference in the QWP is converted into a 90° phase delay between optical transmission curves, allowing for wide frequency tuning. Four quadrature images are simultaneously acquired. The average (DC) intensity, amplitude, and phase of the modulated light component can be retrieved from these four intensities at each pixel. A prototype FAST-QUAD camera was built using a lithium niobate EO crystal and a low-frame-rate high-dynamic range camera. The system was operated up to several hundred kilohertz (limited by amplifier bandwidth). Calibration and processing algorithms compensated for mechanical and optical imperfections. Experiments used an externally intensity-modulated green laser. The demodulation frequency was tunable, and frequency selectivity was analyzed by varying the frequency detuning. The system's ability to filter images based on modulation frequency was demonstrated using two objects illuminated by sources with slightly different modulation frequencies. Image encryption was also demonstrated by embedding a high-frequency modulated image within an unmodulated background. The mathematical operations for extracting the amplitude and phase from the four quadrature images are provided in the paper.

The FAST-QUAD technique successfully achieved instantaneous full-field demodulation of images from a single camera frame. Experiments validated snapshot image demodulation with good resolution (300x300 pixels) in the DC to 500 kHz frequency range, with continuous frequency tuning. The demodulated amplitude was negligible when illuminated by unmodulated light, showing effective noise rejection. Frequency selectivity of approximately 0.5 Hz (FWHM) was obtained at 5 kHz and 100 kHz with a 2-second exposure time, increasing to ~2 Hz with a 0.5-second exposure. The frequency selectivity was relatively uniform across the field of view. The continuous frequency discrimination capability was demonstrated by imaging two objects illuminated by independent sources with slightly different modulation frequencies. The ability to filter images based on modulation frequency was demonstrated, and its potential for clutter reduction and image encryption was illustrated. This technique showed its ability to filter out specific frequencies and separate objects modulated at different frequencies. Image encryption experiments showed the potential to embed information in a background by utilizing differing modulation frequencies.

The FAST-QUAD technique addresses the limitations of existing high-frequency image demodulation methods by providing a compact, portable, all-optical solution that requires no synchronization between source and observer. The continuous frequency tuning capability allows for selective filtering of images based on modulation frequency. The successful demonstration of clutter reduction and image encryption highlights the versatility of the technique. The ability to operate without source synchronization is particularly significant for applications involving relative motion between the source and receiver, such as navigation systems. The achieved demodulation bandwidth and frequency selectivity are promising for various applications. Future improvements could focus on higher frequency operation, improved image quality, and broader applicability.

The FAST-QUAD technique represents a significant advancement in high-frequency image demodulation. The all-optical approach enables instantaneous full-field demodulation from a single camera frame, offering advantages in speed, simplicity, and portability. Future work should focus on extending the operational frequency range into the MHz-GHz regime, optimizing optical design to improve resolution and minimize chromatic dispersion, and exploring applications such as high-speed vibrometry, multiplexed free-space optical communications, and ballistic photon imaging for medical diagnosis.

The current prototype is limited to a frequency range up to 500 kHz, primarily due to the bandwidth limitations of the high-voltage amplifier. The use of a narrow-bandwidth green laser illumination limited the impact of chromatic dispersion but also limited the potential for broader applications. While the frequency selectivity is relatively uniform across the field of view, minor inhomogeneities exist due to imperfections in the optical setup. Future work needs to address these limitations and also conflicting requirements on the laser illumination linewidth for good demodulation and speckle removal.