# Weber achromatic contrast for the Receptor Noise Limited Model (Vorobyev & Osorio 1998) Weber achromatic contrast for the Receptor noise limited model (Vorobyev & Osorio 1998; Vorobyev et al. 1998). ```r RNLachrom(R1, R2=Rb, Rb, I, C, e, interpolate = TRUE, nm = seq(300, 700, 1)) ``` ## Arguments - `R1`: Reflectance of observed objects. A data frame with first column corresponding to wavelength values and following columns with reflectance values. `R1` must be in the same scale as `R2` and `Rb` (percentage or proportion). - `R2`: Reflectance to be compared against R1. `R2=Rb` if comparison is to be made against the background. A data frame with two columns only: first column corresponding to wavelength values and second column with reflectance values. `R2` must be in the same scale as `R1` and `Rb` (percentage or proportion). - `Rb`: Background reflectance. A data frame with two columns only: first column corresponding to wavelength values and second column with reflectance values. `Rb` must be in the same scale as `R1` and `R2` (percentage or proportion). - `I`: Irradiance spectrum. A data frame with two columns only: first column corresponding to wavelength values and second column with irradiance values. Irradiance values must be in quantum flux units. - `C`: Photoreceptor sensitivity curves, from lowest to longest lambda-max. A data frame: first column corresponding to wavelength values and following columns with photoreceptor sensitivity values (see function `photor`). - `e`: Noise of the photoreceptor. - `interpolate`: Whether data files should be interpolated before further calculations. See `approx`. - `nm`: A sequence of numeric values specifying where interpolation is to take place. See `approx`. ## Returns - **e1**: Photoreceptor noise. - **Qr1_R1**: Photoreceptor photon catch value from `R1`, after the von Kries transformation (see function `Qr`). - **Qr1_R2**: Photoreceptor photon catch value from `R2`, after the von Kries transformation (see function `Qr`). - **E1_R1**: Photoreceptor output from the stimulus (`R1`) - **E1_R2**: Photoreceptor output from R2 - **deltaS**: Euclidean distance from R1 to R2. It represents the achromatic contrast of the stimulus (`R1`) in relation to the background when `R1=Rb`. ## Details The Weber achromatic contrast for a single photoreceptor is calculated by: $$ \Delta S = |\frac{\ln(Qr_1)-\ln(Qr_2)}{e}| $$ where $Qr_1$ and $Qr_2$ are the relative photoreceptor quantum catches from stimulus 1 (`R1`) and stimulus 2 (`R2`). Noise may be dependent of the intensity, but this possibility is not implement in `colourvision` yet. Noise dependent of intensity usually holds for low light conditions only (Vorobyev et al. 1998). ## References Vorobyev, M., and D. Osorio. 1998. Receptor noise as a determinant of colour thresholds. Proceedings of the Royal Society B 265:351-358. Vorobyev, M., D. Osorio, A. T. D. Bennett, N. J. Marshall, and I. C. Cuthill. 1998. Tetrachromacy, oil droplets and bird plumage colours. J Comp Physiol A 183:621-633. ## Author(s) Felipe M. Gawryszewski f.gawry@gmail.com ## See Also `RNLmodel`, `photor`, `RNLthres`, `CTTKmodel`, `EMmodel`, `GENmodel` ## Examples ```r #1 ## Photoreceptor sensitivity spectra ##with lambda max at 350nm, 450nm and 550nm: C<-photor(lambda.max=c(350)) ##Grey background ##with 7 percent reflectance from 300 to 700nm: Rb <- data.frame(300:700, rep(7, length(300:700))) ## Read CIE D65 standard illuminant: data("D65") ##Reflectance data of R1 and R2 R1.1<-logistic(x=seq(300,700,1), x0=500, L=50, k=0.04) R1.2<-logistic(x=seq(300,700,1), x0=400, L=50, k=0.04) w<-R1.1[,1] R1.1<-R1.1[,2]+10 R1.2<-R1.2[,2]+10 R1<-data.frame(w=w, R1.1=R1.1, R1.2=R1.2) R2<-logistic(x=seq(300,700,1), x0=550, L=50, k=0.04) R2[,2]<-R2[,2]+10 plot(R1[,c(1,2)],type="l", ylim=c(0,60)) lines(R1[,c(1,3)]) lines(R2[,c(1,2)],col="red") lines(Rb,col="green") ## Run model RNLachrom(R1=R1, R2=R2, Rb=Rb, I=D65, C=C, e = 0.16) ```

RNLachrom function