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In 1994, the National Science Foundation (NSF) awarded California State University, Los Angeles funds for the creation of a Fiber Optics (FO) laboratory. The funds were made available through the Advanced Academic Research Infrastructure Program of NSF under grant# ECS-9413705. This three year project which was extended to four years in the 1996-97 academic year, culminated by the end of August 1998 in the creation of a first rate research facility for conducting R&D in the general areas of sensory applications of fiber optics and optical information processing. Many undergraduate and graduate students have already benefited greatly from their experience in this laboratory throughout its development phase, many of whom are already employed and working in the industry.
During the 1997-1998 academic year, additional research funds were provided by NSF under grant# ECS-9729224 in order to test a novel idea for analog transmission of images though multi-mode optical fiber cables. This idea (US patent number 5,469,519) constitutes a new analog technique for transmitting an image through a multi-mode optical fiber. The technique is intrinsically interesting and is of considerable practical importance, as well as being a suitable topic for student/faculty/industry collaboration. The key innovation is that the Fourier transform of the image, rather than the image itself, will be input to the fiber. In that case, modal dispersion does not hinder reconstruction of the image at the output end of the fiber. Construction and inversion of the Fourier transform are performed optically; no digital encoding or decoding is required.
While theoretical analysis had indicated that such a transmission scheme was indeed possible, to the best of our knowledge, there have been no experimental demonstration of the feasibility of the technique.
Currently, when an optical image is to be transmitted via a waveguide of circular cross-section, the image is first spatially discretized into picture elements (pixels). Transmission is then performed in either of two ways: pixels may be converted to digital format and transmitted in the time domain, by modulation of a carrier; alternatively, each pixel may be assigned to a single small waveguide. Because the former method requires analog-to-digital and digital-to-analog conversion, the usable data-rate is constrained by non-optical signal processing, and is much lower than optical systems in general are capable of. The latter method requires use of a large bundle of small waveguides often leading to cost, reliability and cross-talk problems.
Direct analog transmission by a single multi-mode fiber is also plausible, and allows better utilization of the optical data-rate capability. Unfortunately in a homogeneous fiber waveguide, the different propagation velocities of different modes result in scrambling of the image send down the fiber. Hence, prior attempts to transmit an image down a single fiber in an analog fashion have required the use of inhomogeneous gradient index fibers, which behave like a series of coaxial lenses, focusing and defocusing the image as it travels through the fiber. These devices are difficult and expensive to manufacture.
The proposed system, shown in Fig. 1, does away with these disadvantages.
Figure 1: Analog optical image transmission system. Processing
proceeds from left to right.
Each lens performs an Optical Fourier Transform (OFT) on the radiation
field. The effect of the first OFT, with subsequent coupling into a waveguide,
is to cause each input pixel to excite a certain subset of normal modes
of the waveguide. The 
and 
fields associated with each mode of that subset propagate, with a characteristic
longitudinal phase velocity, to the remote end of the fiber, where the
second OFT reassembles them back into a single spot. Since the number of
available pixels is of the order of the number of allowed modes supported
by the fiber (and can be as large as 
),
the resolution is selectable over a wide range.
Theoretically, based on the OFT theorem and the field configurations of normal modes in a step-index cylindrical fiber, the optical waveguide image transmission system is a doable project. Expressions can be derived for the amplitudes at various points in the optical system, and at the output plane (details are presented under theoretical analysis). By examining the sensitivity of these expressions to irregularities, one can obtain estimates of the required tolerances. Results include the following:
and 
image spaces, is approximately
Here 
and 
are focal lengths of the input and output lenses, and z is the length
of the fiber. The longitudinal phase velocity associated with each pixel
causes introduction of a position-dependent phase shift 
into the light constituting the image; this detail in unimportant, because
the attribute of interest in an optical image is its intensity. The image
has also been rescaled and inverted; the presentation is unimportant for
most applications.
The details of the experimental setup and the preliminary experimental
results obtained are provided under the experiment bullet of this
web page.
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