Using triple extrapolation method to estimate entropy rate, RS, noise entropy rate, RN, and information transfer rate, R, of photoreceptor output to 20 Hz bursts. (A) Mean (black) and 30 voltage responses (light gray) of a photoreceptor to a 2-s-long bursty light intensity time series. (B), The responses were digitized to 2–20 voltage levels, ν; shown for 20 levels. Entropy, HS, and noise entropy HN, are calculated for T-letters-long words, in which each 1-ms-long letter is a voltage level, ν, as explained previously (Juusola and de Polavieja, 2003). (C) first extrapolation to infinite data size. Entropies of the 10 letter words (top) and five letter words (bottom) for 5–10 voltage levels fitted with linear trends. Thus, HSTT = 10,ν and HSTT = 5,ν (black and blue ■, respectively, for ν = 5–10) are obtained from extrapolation of HSTT = 10,ν,size and HSTT = 5,ν,size for size → ∞ (1/size → 0). Here, the probability of 5 letter words is similar for 50–100% of data so size corrections in HSTT = 5,ν are minute, but for 10 letter words size corrections impact HSTT = 10,ν slightly more. (D) second extrapolation to infinite voltage levels. HST,v is shown for words of 1–10 letters, each fitted with its linear trend. HST (gray ■s for T = 5–10) is obtained from the extrapolation of HST,v when ν → ∞ (1/ν → 0); HST = 5 = blue ■; HST = 10 = black ■. (E) third extrapolation. Entropy rates obtained from extrapolations to infinitely long words. The total entropy rate, RS (red ■), is obtained from a linear extrapolation when T → ∞ (1/T → 0). RN (red ●) for the same data. Both RS and RN collapse to 0 when the data are inadequate to provide a satisfactory extrapolation of HST and HNT for long words and high voltage resolutions. The graph, however, shows enough linearly aligned points for good estimations of RS, RN, and R. (F) Effect of the number of voltage levels v used in the second extrapolation on R. For v ≥ 8, the first point for the second extrapolation is the fifth voltage level. Linear fits (red) and second-order Taylor series (black) give similar estimates (<10% difference) when v = 10–20 for these data. (G) Average R estimates obtained from linear (red) or second-order Taylor series (black) fits by the triple extrapolation method (Eq. 4) and from Shannon equation (Eq. 1). These estimates for data in (A) are similar. For 20 voltage level data (B), the mean Shannon capacity estimate is only ∼2–5% less than the mean estimates for the full response waveforms with n = 30 trials or when extrapolated to infinite data (1/n → 0), implying consistency in these estimation methods.