Method and apparatus for testing optical fiber by using biorthogonal codes and Moore-Penrose generalized inverses

A method for measuring a state of an optical fiber by means of biorthogonal codes and a Moore-Penrose inverse matrix, the method comprising the steps of:

• (a) setting i to 1 and setting a final measured value to 0;
• (b) coding optical pulses according to an ith codeword of the n-bit biorthogonal code matrix (2n*n matrix), injecting the coded optical pulses into an optical fiber, measuring an ith optical signal generated when the coded optical pulses are reflected from the optical fiber, and storing the ith optical signal in a memory;
• (c) multiplying the ith optical signal to each of n elements of an ith column in the Moore-Penrose inverse matrix (n*2n matrix) for the n-bit biorthogonal code matrix, thereby restoring n signals which are partially decoded from the ith optical signal;
• (d) shifting the n signals along the time axis to remove timing differences among the n signals;
• (e) averaging the time-shifted n signals, obtaining an ith measured value;
• (f) updating the final measured value by adding the ith measured value to the final measured value, storing the updated final measured value in the memory, and deleting the ith optical signal and the ith measured value which are intermediately generated in the ith measurement;
• and
• (g) comparing whether i is equal to 2n or not, adding 1 to i and returning to step (b) if i is smaller than 2n, or employing a value finally stored in the memory as the final measured value if i is equal to 2n.

An apparatus for measuring a state of an optical fiber by means of a biorthogonal codes and a Moore-Penrose inverse matrix, the apparatus comprising:

• a processor for generating the n-bit biorthogonal code matrix, decoding optical signals reflected from the optical fiber by means of the Moore-Penrose inverse matrix for the n-bit biorthogonal code matrix, performing an average operation for the decoded signals;
• and obtaining a final measured value;
• a pulse generator for generating an electrical pulse according to a codeword received from the processor;
• an electrooptic converter for converting the electrical pulses generated by the pulse generator into an optical pulse;
• an optoelectric converter for receiving the optical signals reflected from the optical fiber, and generating electrical signals proportional to the optical signals, thereby converting the optical signals into the electrical signals;
• an optical coupler for injecting the optical pulses generated by the electrooptic converter into the optical fiber, and transferring the optical signals reflected from the optical fiber to the optoelectric converter;
• and
• an analog-to-digital converter for converting the voltage inputted from the trans-impedance amplifier into sampled digital values.