Super-resolution using Barker-based array projected via spatial light modulator.

The use of a two-dimensional Barker-based array in the conventional time multiplexing super-resolution (TMSR) technique was recently presented [Opt. Lett.40, 163-165 (2015)OPLEDP0146-959210.1364/OL.40.000163]. It enables achieving a two-dimensional SR image using only a one-dimensional scan, by exploiting its unique auto-correlation property. In this Letter, we refine the method using a mismatched array for the decoding process. The cross-correlation between the Barker-based array and the mismatched array has a perfect peak-to-sidelobes ratio, making it ideal for the SR process. Also, we propose the projection of this array onto the object using a phase-only spatial light modulator. Projecting the array eliminates the need for printing it, mechanically shifting it, and having a direct contact with the object, which is not feasible in many imaging applications. 13 phase masks, which generate shifted Barker-based arrays, were designed using a revised Gerchberg-Saxton algorithm. A sequence of 13 low resolution images were captured using these phase masks, and were decoded using the mismatched arrays, resulting in a high-resolution image. The proposed mismatched array and the design process of the phase masks are presented, and the method is validated by a laboratory experiment.

Time multiplexing super resolution using a Barker-based array.

We propose the use of a new encoding mask in order to improve the performance of the conventional time multiplexing super resolution method. The resolution improvement is obtained using a 2D Barker-based array that is placed upon the object and shifted laterally. The Barker-based array is a 2D generalization of the standard 1D Barker code. The Barker-based array has stable autocorrelation sidelobes, making it ideal for the encoding process. A sequence of low resolution images are captured at different positions of the array, and are decoded properly using the same array. After removing the low resolution image from the resulting reconstruction, a high resolution image is established. The proposed method is presented analytically, demonstrated via numerical simulation, and validated by laboratory experiment.

High-resolution long-range distributed Brillouin analysis using dual-layer phase and amplitude coding.

A new, hybrid time-domain and correlation-domain Brillouin analysis technique is proposed and demonstrated, providing a large number of high-resolution acquisition points. The method is based on dual-layer hierarchal encoding of both amplitude and phase. The pump and signal waves are co-modulated by a relatively short, high-rate binary phase sequence. The phase modulation introduces Brillouin interactions in a large number of discrete and localized correlation peaks along the fiber under test. In addition, the pump wave is also amplitude-modulated by a slower, carefully synthesized, long on-off-keying sequence. Brillouin interactions at the correlation peaks imprint weak replicas of the pump amplitude sequence on the intensity of the output signal wave. The Brillouin amplifications at individual correlation peaks are resolved by radar-like, matched-filter processing of the output signal, following a recently-proposed incoherent compression protocol. The method provides two significant advantages with respect to previous, pulse-gated correlation-domain analysis schemes, which involved a single pump pulse. First, compression of the extended pulse sequence enhances the measurement signal-to-noise ratio, which is equivalent to that of a large number of averages over repeating single-pulse acquisitions. The acquisition times are potentially much reduced, and the number of resolution points that may be practically interrogated increases accordingly. Second, the peak power level of the pump pulses may be lowered. Hence, the onset of phase pattern distortion due to self-phase modulation is deferred, and the measurement range can be increased. Using the proposed method, the acquisition of Brillouin gain spectra over a 2.2 km-long fiber with a spatial resolution of 2 cm is demonstrated experimentally. The entire set of 110,000 resolution points is interrogated using only 499 position scans per choice of frequency offset between pump and signal. A 5 cm-long hot-spot, located towards the output end of the pump wave, is properly recognized in the measurements.

High-resolution long-reach distributed Brillouin sensing based on combined time-domain and correlation-domain analysis.

A new scheme for distributed Brillouin sensing of strain and temperature in optical fibers is proposed, analyzed and demonstrated experimentally. The technique combines between time-domain and correlation-domain analysis. Both Brillouin pump and signal waves are repeatedly co-modulated by a relatively short, high-rate phase sequence, which introduces Brillouin interactions in a large number of discrete correlation peaks. In addition, the pump wave is also modulated by a single amplitude pulse, which leads to a temporal separation between the generation of different peaks. The Brillouin amplification of the signal wave at individual peak locations is resolved in the time domain. The technique provides the high spatial resolution and long range of unambiguous measurement offered by correlation-domain Brillouin analysis, together with reduced acquisition time through the simultaneous interrogation of a large number of resolution points. In addition, perfect Golomb codes are used in the phase modulation of the two waves instead of random sequences, in order to reduce noise due to residual, off-peak Brillouin interactions. The principle of the method is supported by extensive numerical simulations. Using the proposed scheme, the Brillouin gain spectrum is mapped experimentally along a 400 m-long fiber under test with a spatial resolution of 2 cm, or 20,000 resolution points, with only 127 scans per choice of frequency offset between pump and signal. Compared with corresponding phase-coded, Brillouin correlation domain analysis schemes with equal range and resolution, the acquisition time is reduced by a factor of over 150. A 5 cm-long hot spot, located towards the output end of the pump wave, is properly identified in the measurements. The method represents a significant advance towards practical high-resolution and long range Brillouin sensing systems.

Experimental demonstration of localized Brillouin gratings with low off-peak reflectivity established by perfect Golomb codes.

Dynamic Brillouin gratings (DBGs), inscribed by comodulating two writing pump waves with a perfect Golomb code, are demonstrated and characterized experimentally. Compared with pseudo-random bit sequence (PRBS) modulation of the pump waves, the Golomb code provides lower off-peak reflectivity due to the unique properties of its cyclic autocorrelation function. Golomb-coded DBGs allow the long variable delay of one-time probe waveforms with higher signal-to-noise ratios, and without averaging. As an example, the variable delay of return-to-zero, on-off keyed data at a 1 Gbit/s rate, by as much as 10 ns, is demonstrated successfully. The eye diagram of the reflected waveform remains open, whereas PRBS modulation of the pump waves results in a closed eye. The variable delay of data at 2.5 Gbit/s is reported as well, with a marginally open eye diagram. The experimental results are in good agreement with simulations.

Low-noise delays from dynamic Brillouin gratings based on perfect Golomb coding of pump waves.

A method for long variable all-optical delay is proposed and simulated, based on reflections from localized and stationary dynamic Brillouin gratings (DBGs). Inspired by radar methods, the DBGs are inscribed by two pumps that are comodulated by perfect Golomb codes, which reduce the off-peak reflectivity. Compared with random bit sequence coding, Golomb codes improve the optical signal-to-noise ratio (OSNR) of delayed waveforms by an order of magnitude. Simulations suggest a delay of 5 Gb/s data by 9 ns, or 45 bit durations, with an OSNR of 13 dB.