The experiment to demonstrate the feasibility of analog image transmission in a fiber was conducted in the fiber optic laboratory of the California State University, Los Angeles. In table 2 a complete list of the used equipment is reported. In the preliminary phase of the experiment the goal was to implement the transmission of a fixed image through the fiber by sending the Fourier transform of the image itself at the fiber input.

The scheme of the setting is depicted in figure 2.

table settimg
Figure 2

The light of a monochromatic laser with wavelength  is used to generate an enlarged beam by a beam expander implemented with a pair of lenses; the beam coming out from the laser source is deflected with a system of mirrors mounted on holders with micrometric regulations so that the position of the beam is easily adjustable, while keeping the beam parallel to the table.

The two lenses of the beam expander are chosen so as to obtain after the second lens a parallel beam, indeed, the first is a biconcave lens while the second is bi-convex. The beam expander used enlarges the input beam by a factor of 10. The frame of each lenses  was  mounted on a micrometric positioning system so that the position of the two lenses is precisely under control.

The input image was obtained cutting a desired shape on a screen put on the path of the
enlarged laser beam. The dimension of the shape is quite smaller than the diameter of the whole enlarged beam so that the shaped beam after the screen can be accurately considered to be parallel to the table, allowing us to neglect the border effects.

The shaped beam was then passed through the lens (L3) that performs the desired spatial Fourier Transform of the image to be transmitted in the fiber. Again the actual position of the lens is controlled by micrometers.

The most delicate part of the experimental setup was then the positioning of the near end of the fiber exactly at the focal point of the L3. In fact, the fiber has to be positioned exactly at the focal point of L3, with the with the beam focused on the core of the fiber. Not only the position of the fiber is important, but, in order to avoid undesired distortion of the image, the flat end of the fiber has to be completely perpendicular to the incoming beam. The extreme flatness of the fiber causes severe reflections problems that were not considered in the original analytical study. Another problem is that the beam cannot be made to be perfectly perpendicular to the flat end of the fiber. 
To control the correct positioning and alignment, the power of the beam coming out from the fiber was monitored and compared to the incoming power. Using micrometers, the coupling was precisely adjusted in order to obtain the maximum output power corresponding to the best coupling of the light inside of the fiber. This power is constantly under observation and some further adjustment are required if the coupling loss increases.

A lens (L4) is put at the output of the fiber to operate the inverse Fourier transform, and the image is then collected onto a screen.


Table 2: Equipment used for the analog image transmission experiment in a multimode optical fiber

The Test Image

The chosen test image is a square of size . With this size, the image
could be easily coupled into the core of the test fiber, with a negligible distortion due to the finite size of the core. In fact, according to the propagation equation, the square shaped beam after the lens L3 in the focal plane can be expressed as,

  where

and  are the variables in the space domain that span the actual support of the image in the focal plane that is related through the expressions 2 to the Fourier transform of the test image. Consider for example the first zero of the (2) located at  that corresponds to ; substituting , ,  we obtain; considering that the smallest fiber core considered has a diameter  we are assured that a minimum percentage of  of the total energy is put in the core. It can be remarked that with larger image and with larger core diameter the distortion due to truncation of the optical Fourier transform in the spatial domain due to coupling is even more negligible.

The fibers

Fibers with different features has been tested, all of them matching the general requirements derived from the theoretical analysis for the flatness of both ends, but with different dimensions of the core. Due to the requirements on flatness customize fibers were purchased used. The relevant characteristics of the fibers that were tested are as follows:

Cable 1

Cable 2

Cable 3

Cable 4


 
 

The idea of using a fiber whose end is not exactly flat, but have a small curvature, was due to the fact that with a small radius the coupling of the light inside is made easier primarly via reduction of reflection at the ends of the fiber.

Conclusion and future work

The preliminary experimental results are encouraging and the overall experiment was partially successful. In particular, the best possible image obtained at the output of the fiber corresponded to the use of Cable-4 and is sketched in Fig. 8. The multiple peaks in the spatial domain and the rounding effect at the edges could be partially explained as an effective low pass filtering of the input image due to cutoff of the modes due to inadequate coupling in the core of the fiber.

Several outstanding issue that must be addressed and were not known prior to the actual experimentation are:
 

  1. analytical results seem to suggest that the endface flatness within 0.1  is sufficient for proper image reconstruction from its Fourier transform. Our experimental results suggest that the endface flatness within 0.1  seems to be unsatisfactory to transmit the image with acceptable distortion, even if this value is the best that can be actually guaranteed from semi-custom fiber manufacturing practices. A broader investigation is necessary using fibers with a flatnesswhich is guaranteed to be within 0.01. Such fibers can only be obtained with very special polishing and processing techniques;
  2. the reflection problem due to fiber flatness has not been considered in the theoretical analysis. This problem becomes more and more severe as the endfaces of the fiber are made more and more flat. Hence, there is significant power loss due to reflection. A natural experimental line of pursuit would be to consider the use of different coupling techniques that differ from the simple coupling between the free-space media and the fiber itself. A possible solution may be to use a microlens touching the core. The theoretical investigation of how much distortion such coupling will introduce is required, and if necessary, predistortion techniques may have to be employed to correct for the induced coupling distortion;
  3. there is a possibility of multiple light reflections inside the fiber itself at both ends of the fiber changing the effective optical path length that various modes may travel while experiencing multiple reflections. This influences both the effective intensity and phase of the signal associated with a given mode at the fiber output. Once again, the effect of this phenomena has not been analytically studied;
  4. experimental results suggest that there is significant light coupling in the fiber cladding which is clearly an undesirable effect. Just how this effect can be reduced must be experimentally investigated;
  5. The required fiber flatness of better than 0.01 imposes additional requirements in particular in connection with the laboratory environment itself in order to avoid problems with dust and particulate in the air whose diameters are generally much larger than 0.01.

Figure 8: Sketch of the observed output