Digital filters underpin the performance of coherent optical receivers which exploit digital signal processing (DSP) to mitigate transmission impairments. We outline the principles of such receivers and review our experimental investigations into compensation of polarization mode dispersion. We then consider the details of the digital filtering employed and present an analytical solution to the design of a chromatic dispersion compensating filter. Using the analytical solution an upper bound on the number of taps required to compensate chromatic dispersion is obtained, with simulation revealing an improved bound of 2.2 taps per 1000ps/nm for 10.7GBaud data. Finally the principles of digital polarization tracking are outlined and through simulation, it is demonstrated that 100krad/s polarization rotations could be tracked using DSP with a clock frequency of less than 500MHz.

Digital filters for coherent optical receivers.

By inserting a microlens array into the optical train of a conventional microscope, one can capture light fields of biological specimens in a single photograph. Although diffraction places a limit on the product of spatial and angular resolution in these light fields, we can nevertheless produce useful perspective views and focal stacks from them. Since microscopes are inherently orthographic devices, perspective views represent a new way to look at microscopic specimens. The ability to create focal stacks from a single photograph allows moving or light-sensitive specimens to be recorded. Applying 3D deconvolution to these focal stacks, we can produce a set of cross sections, which can be visualized using volume rendering. In this paper, we demonstrate a prototype light field microscope (LFM), analyze its optical performance, and show perspective views, focal stacks, and reconstructed volumes for a variety of biological specimens. We also show that synthetic focusing followed by 3D deconvolution is equivalent to applying limited-angle tomography directly to the 4D light field.

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Light field microscopy

Active, optical range imaging systems collect three-dimensional coordinate data from object surfaces. These systems can be useful in a wide variety of automation applications, including shape acquisition, bin picking, assembly, inspection, gauging, robot navigation, medical diagnosis, cartography, and military tasks. The range-imaging sensors in such systems are unique imaging devices in that the image data points explicitly represent scene surface geometry in a sampled form. At least six different optical principles have been used to actively obtain range images: (1) radar, (2) triangulation, (3) moire, (4) holographic interferometry, (5) lens focusing, and (6) diffraction. The relative capabilities of different sensors and sensing methods are evaluated using a figure of merit based on range accuracy, depth of field, and image acquisition time.

Active optical range imaging sensors

The recently developed digital coherent receiver enables us to employ a variety of spectrally efficient modulation formats such as $M$ -ary phase-shift keying and quadrature-amplitude modulation. Moreover, in the digital domain, we can equalize all linear transmission impairments such as group-velocity dispersion and polarization-mode dispersion of transmission fibers, because coherent detection preserves the phase information of the optical signal. This paper reviews the history of research and development related to coherent optical communications and describes the principle of coherent detection, including its quantum-noise characteristics. In addition, it discusses the role of digital signal processing in mitigating linear transmission impairments, estimating the carrier phase, and tracking the state of polarization of the signal in coherent receivers.

Fundamentals of Coherent Optical Fiber Communications

Polarization-maintaining fibers and their applications are reviewed. The classification of high-birefringent fibers and low-birefringent fibers and their fabrication methods and characteristics are discussed in Section II. Analytical methods and numerical methods for fiber design on the birefringence are presented in Section III. Degradation factors of polarization maintenance expressed as crosstalk or mode-coupling parameters caused by internal origins such as structural imperfections, wavelength, and nonlinear effects, and by external origins such as temperature fluctuations, mechanical perturbations, and electromagnetic effects, are discussed in Section IV. Characterization methods on beat length, mode coupling, stress distribution, and mechanical strength are presented in Section V. Applications to the fiber devices and nonlinear effects, and splicing methods for the polarization-maintaining fibers are described in Sections VI and VII.

Polarization-maintaining fibers and their applications

Coherent Optical Fiber Communications

In this Letter a new method is proposed for measuring the beat length of linearly birefringent optical fibers. In this method the beat length is determined from the wavelength dependence of the phase difference between two orthogonally polarized HE(11) modes at the output end of a sample fiber. The important feature of this method is the wide range of the measurable beat length (0.4 mm-1 m:) The principle, the experimental setup, and the result of the experiment are described.

Wavelength-sweeping technique for measuring the beat length of linearly birefringent optical fibers

Research and development of coherent optical fiber communications have been accelerated mainly because of the possibility of receiver sensitivity improvement reaching 20 dB, and partly because of the possibility of frequency-division multiplexing (FDM) with very fine frequency separation. In this paper, recent advances in the research on coherent optical fiber communication systems are reviewed, with emphasis on those reported in the past two years. The bit-error rate measurements so far reported are classified and investigated in four categories: PCM-ASK, PCM-FSK, PCM-PSK, and PCM-DPSK. The states-of-the-art of polarization-state stabilization techniques is also discussed.

Recent advances in coherent optical fiber communication systems

Standard optical fiber communication systems employ intensity-modulation/direct-detection schemes. This is noise-carrier communication and in a sense is more primitive than the radio engineering in Marconi’s age. However, it has the practical advantage of system simplicity and low cost. On the other hand, some applications of optical fiber communication exist in which a long repeater separation is the primary concern; an example is submarine optical cable communication between islands, in this case, the improvement of the bit-error rate (BER) by a coherent modulation/demodulation scheme such as PCM-PSK or PCM-FSK may be advantageous even at the sacrifice of simplicity and low cost.

Heterodyne-type optical fiber communications

A new exit-radiation pattern method for measuring the refractive-index profile of a single-mode fiber is proposed and used experimentally. In this method the profile is computed from the far-field exit-radiation pattern of the HE11 mode at the end of the single-mode fiber. This method can be applied to a cabled fiber, and the propagation constant, field profile, and group delay of the HE11 mode, and the single-mode limit can be obtained as well as the index profile. The principle, computer simulations, experimental setup, and experimental results are first described. The profile obtained shows a good agreement with that obtained from the interference fringe pattern measured before drawing the fiber. Computations of the group delay of the HE11 mode and the single-mode limit from the measured exit-radiation pattern are discussed.

Takanori Okoshi

Papers

Coherent Optical Fiber Communications

Wavelength-sweeping technique for measuring the beat length of linearly birefringent optical fibers

Recent advances in coherent optical fiber communication systems

Heterodyne-type optical fiber communications

Measurement of refractive-index profile and transmission characteristics of a single-mode optical fiber from its exit-radiation pattern