  An ultrafast single-pixel optical 2D imaging system using a single multimode
fiber (MF) is proposed. The MF acted as the all-optical random pattern
generator. Light with different wavelengths pass through a single MF will
generator all-optical random speckle patterns, which have a low correlation of
0.074 with 0.1nm wavelength step from 1518.0nm to 1567.9nm. The all-optical
random speckle patterns are perfect for compressive sensing (CS) imaging with
the advantage of low cost in comparison with the conventional expensive
pseudorandom binary sequence (PRBS). Besides, with the employment of photonic
time stretch (PTS), light of different wavelengths will go through a single
capsuled MF in time serial within a short pulse time, which makes ultrafast
single-pixel all-optical CS imaging possible. In our work, the all-optical
random speckle patterns are analyzed and used to perform CS imaging in our
proposed system and the results shows a single-pixel photo-detector can be
employed in CS imaging system and a 27 by 27 pixels image is reconstructed
within 500 measurements. In our proposed imaging system, the fast Fourier
transform (FFT) spatial resolution, which is a combination of multiple
Gaussians, is analyzed. Considering 4 optical speckle patterns, the FFT spatial
resolution is 50 by 50 pixels. This resolution limit has been obtained by
removing the central low frequency components and observing the significant
spectral power along all the radial directions.
