December 2002
Volume 2, Issue 10
OSA Fall Vision Meeting Abstract  |   December 2002
Non-linear analysis of the contrast paradox for vernier acuity
Author Affiliations
  • Anthony M. Norcia
    Smith-Kettlewell Eye Research Institute, San Francisco, CA, USA
  • Chuan Hou
    Smith-Kettlewell Eye Research Institute, San Francisco, USA
Journal of Vision December 2002, Vol.2, 89. doi:
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      Anthony M. Norcia, Chuan Hou; Non-linear analysis of the contrast paradox for vernier acuity. Journal of Vision 2002;2(10):89.

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      © ARVO (1962-2015); The Authors (2016-present)

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Stereo-acuity increases with increasing contrast. However, if contrast is increased in one eye, but not the other, acuity “paradoxically” decreases. Analogous contrast paradoxes exist for vernier acuity and two-frame motion (Stevenson and Cormack, 2000; Vision Research). Here we used non-linear analysis of the Visual Evoked Potential and simulations to learn more about the underlying neural mechanisms. By analogy to psychophysical studies, we measured vernier acuity as a function of contrast with targets whose elements were equal in contrast (5–80%), compared to targets where one set of elements varied in contrast (5 to 80%), while the other elements were fixed (20% contrast). Our stimuli were comprised of several abutting panels of square wave gratings that were oscillated sinusoidally. One set of panels was oscillated at F1=3.76 Hz and the inter-digitated panels were oscillated at F2=6.01 Hz. The phasing of the oscillations was such that the total pattern alternated between collinear and non-collinear at the difference frequency. Responses at combination frequencies (nF1+ mF2) are associated with vernier position sensitivity and reflect the non-linear pooling of the constituent elements. The intermodulation spectrum is dominated by second- order terms (1F+1F2) with additional, small fourth-order terms (2F1+2F2). Vernier thresholds for these components in the matched contrast condition systematically improve with increasing contrast and were ca. 2 5 arc sec at the highest contrast. In the mis-matched condition, thresholds were best for the matched contrast condition (20%/20%). Reduced psychophysical performance with mismatched contrasts may reflect the reduced intermodulation responses that occur under mismatched conditions. Simulations indicated that the sensitivity of the intermodulation components to mismatched contrast is a general property of systems containing sigmoidal non-linearities. Such non-linearities, in addition to their role in gain control, may serve to veto the combination of mis-matched stimulus elements in spatial tasks.

Norcia, A. M., Hou, C.(2002). Non-linear analysis of the contrast paradox for vernier acuity [Abstract]. Journal of Vision, 2( 10): 89, 89a,, doi:10.1167/2.10.89. [CrossRef]

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