Identification of appropriate primitive polynomials to avoid cross-contamination in multifocal electroretinogram responses

Abstract-The basis of the multifocal/electroretinogram is the use of a decimated m-sequence for simultaneous and independent stimulation of many areas of the visual pathway. The purpose of this study was to investigate the effects of cross-contamination from higher orders of the response. A series of primitive polynomials were found by construction of finite fields. The first-order ERG response was formed by cross-correlation of m-sequence with the physiological response. A second-order response was formed by investigation of particular flash sequences of the stimulation sequence and cross-correlation of a second-order m-sequence with the physiological response. Zech logarithms were used to identify cross-contamination between the various first and second-order sequences. Tables of good and bad primitive polynomials were constructed for degrees 12-16, and the effects of window length and decimation length were examined. When the sequence was decimated into 128 areas, and a window of length 16 was examined, cross-contamination occurred in all sequences generated from primitive polynomials of degree less than or equal to 12, but in only 26% of degree 14, and 5.6% of degree 16. A photodiode (artificial eye) was used in an experiment to construct trace arrays showing responses from 61 individual areas. Additional waveforms were present on the trace array when the experiment was carried out with a bad primitive polynomial. The use of finite field theory to generate primitive polynomials and Zech logarithm analysis allowed prediction of which primitive polynomials were suitable for m-sequence generation for multifocal electroretinography. Practical investigations supported the theoretical analysis. This has important implications for developers of multifocal electrophysiology systems.