Teich M C, Prucnal P R, Vannucci G, Breton M E, McGill W J
J Opt Soc Am. 1982 Apr;72(4):419-31. doi: 10.1364/josa.72.000419.
We have carried out a series of frequency-of-seeing experiments similar to those performed by Hecht, Shlaer, and Pirenne [J. Gen. Physiol. 25, 819-840 (1942)], using an Ar+ laser operated at 514.5 nm as the source of light. In certain blocks of trials, our subjects were encouraged to report as seen those trials in which the stimulus might have been present. It was determined that sensitivity and reliability were traded against each other over a broad range: for our subjects, the detection of 147 photons at the cornea with 60% frequency of seeing entailed, on the average, a 1% false-positive rate (FPR), whereas the detection of 34 photons at the cornea with 60% frequency of seeing was accompanied by a 33% FPR. A new neural-counting model has been developed in the framework of signal-detection theory. It combines Poisson stimulus fluctuations with additive and multiplicative neural noise, both of which are known to be present in the visual system at threshold. The resulting probability-of-detection curves, derived from the Neyman Type-A counting distribution, are in good accord with our experimental frequency-of-seeing data for sensible values of the model parameters. We deduce that, on the average, our four subjects are able to detect a single photon at the retina with 60% frequency of seeing, at the expense of a 55% FPR. In Part 2 of this set of papers [P.R. Prucnal and M.C. Teich, Biol. Cybern. 43, 87-96 (1982)], we use the normalizing transform, together with probit analysis, to provide improved estimates of threshold parameters, whereas in Part 3 [M.C. Teich, P.R. Prucnal, G. Vannucci, M.E. Breton, and W.J. McGill, submitted to Biol. Cybern.], we consider the effects of non-Poisson quantum fluctuations.
我们进行了一系列类似于赫克特、施莱尔和皮雷纳[《普通生理学杂志》25, 819 - 840 (1942)]所做的视见频率实验，使用波长为514.5 nm的氩离子激光器作为光源。在某些试验组中，我们鼓励受试者报告那些可能存在刺激的试验中他们所看到的情况。结果确定，在很宽的范围内，灵敏度和可靠性是相互权衡的：对于我们的受试者，在角膜处检测到147个光子且视见频率为60%时，平均假阳性率（FPR）为1%，而在角膜处检测到34个光子且视见频率为60%时，假阳性率为33%。在信号检测理论的框架内开发了一种新的神经计数模型。它将泊松刺激波动与加性和乘性神经噪声相结合，这两种噪声在阈值时已知存在于视觉系统中。从奈曼A类计数分布导出的检测概率曲线，对于模型参数的合理值，与我们的实验视见频率数据非常吻合。我们推断，平均而言，我们的四名受试者能够在视网膜处检测到单个光子，视见频率为60%，代价是假阳性率为55%。在这组论文的第2部分[P.R.普鲁克纳尔和M.C.泰希，《生物控制论》43, 87 - 96 (1982)]中，我们使用归一化变换以及概率单位分析来提供阈值参数的改进估计，而在第3部分[M.C.泰希、P.R.普鲁克纳尔、G.万努奇、M.E.布雷顿和W.J.麦吉尔，已提交给《生物控制论》]中，我们考虑了非泊松量子波动的影响。
