This page introduces how to calculate the relative stimulation of ipRGCs with blue and red stimuli.
Prof. Tsujimura defines ipRGC stimulation using a unit of luminance. One ipRGC stimulation was defined as the level of ipRGC stimulation produced by an equal energy spectrum of luminance 1 cd/ m2. The ipRGC stimulation is the sum of the converted spectral values of the sensitivity curves with adjusted luminance.

And Luminance is defined as a sum of L and M cone stimulations from the sensitivity curves for cones defined by CIE(http://www.cvrl.org).

The procedures are as the followings:

Get spectral values of the blue and red light stimuli
Calculate the stimulation of ipRGCs based on the the sensitivty curves of ipRGC developed by Prof.Tsujimura
adjust the luminance of blue and red light
adjust the ipRGC stimulation based on adjusted luminance

# settings
setwd("~/R/stimulation") # switch directory to the file directory
library(xlsx)
data <- read.xlsx(file = "ReceptorStimulationsSpectrumData_YehLab.xlsx", sheetIndex = 1, header = FALSE)
# get data of spectral sensitivity function & the luminance data of blue and red light.s
raw_data <- data[4:101,1:10]
names(raw_data) <- c("lambda", "L", "M", "S", "ipRGC", "L*0.69284", "M*0.349","lambda", "blue-average", "red-average" )
rownames(raw_data) <- NULL
indx <- sapply(raw_data, is.factor)
raw_data[indx] <- lapply(raw_data[indx], function(x) as.numeric(as.character(x)))
raw_data <- raw_data[, -6:-8]
head(raw_data) # check data

##   lambda           L          M          S       ipRGC blue-average
## 1    392 0.000604713 0.00053623 0.00901661 0.001732121    6.461e-27
## 2    396 0.001283400 0.00116572 0.01923470 0.003639591    5.256e-27
## 3    400 0.002540730 0.00237208 0.03963080 0.007538417    4.645e-27
## 4    404 0.004623700 0.00443021 0.07693230 0.015167795    4.176e-27
## 5    408 0.007896340 0.00775260 0.13804400 0.028698221    4.110e-06
## 6    412 0.012260700 0.01259490 0.22509100 0.050063873    2.907e-05
##   red-average
## 1   2.271e-07
## 2   3.178e-07
## 3   5.283e-07
## 4   5.097e-07
## 5   3.475e-07
## 6   9.981e-08

# data frame used to calculate stimulation of blue and red light
sensitivity_data <- matrix(0, 98, 8)
sensitivity_data <- as.data.frame(sensitivity_data)
colnames(sensitivity_data) <- c("BLUE-L", "BLUE-M", "BLUE-S", "BLUE-ipRGC", "RED-L", "RED-M", "RED-S", "RED-ipRGC")
rownames(sensitivity_data) <- NULL

lamba –> wave length L, M, S –> spectral values of L, M, S-cones on the standard sensitivity curves (from CIE 2006) ipRGC –>spectral values of ipRGC on Prof Tsujimura’s ipRGC sensitivity curves blue-averaged –> spectral values of the blue light stimuli red-averaged –> spectral values of the red light stimuli

Take a glance at what the sensitivity curves look like.

matplot(raw_data[,"lambda"], cbind(raw_data[,"L"], raw_data[,"M"], raw_data[,"S"], raw_data[,"ipRGC"]), xlab = "wave length(nm)", ylab = " ", type = "l", col = cbind("red","green", "black", "blue"), lty = 1)

legend("topright", legend=c("L-cone", "M-cone", "S-cone", "ipRGC"), pch=1, col=c("red","green","black","blue"), horiz=FALSE)

Plot of the spectral values of blue and red light presented in experiments.

matplot(raw_data[,"lambda"], cbind(raw_data[,"blue-average"], raw_data[,"red-average"]), xlab = "wave length(nm)", ylab = "cd/m2", type = "l", col = cbind("blue","red"), lty = 1)
legend("topright", legend=c("blue average", "red average"), pch=1, col=c("blue","red"), horiz=FALSE)

Then start coverting spectral values of blue and red light to ipRGC stimulation.

Also calculate luminance of the blue and red stimuli for adjusting the luminance. Luminance is defined as a sum of L and M cone stimulations.To calculate luminance, time the coefficient weights of L and M (0.69 & 0.34) cones to the to the values of L and M cones of the spectral sensitiivity functions.

lcone_lum <- raw_data["L"]*0.69284
mcone_lum <- raw_data["M"]*0.34967

To calculate stimulation of the actural stimuli, spectral values of blue and red light are mutipled by the spectral value of ipRGC sensitivity curves. Similiarly, the spectral values of blue and red light are mutipled by the spectral values of L and M-cones of sensitivity curves to evaluate the luminance.

sensitivity_data["BLUE-L"] <- lcone_lum * raw_data["blue-average"] 
sensitivity_data["BLUE-M"] <- mcone_lum * raw_data["blue-average"]
sensitivity_data["BLUE-S"] <- raw_data["S"] * raw_data["blue-average"]
sensitivity_data["BLUE-ipRGC"] <- raw_data["ipRGC"] * raw_data["blue-average"]
sensitivity_data["RED-L"] <- lcone_lum * raw_data["red-average"]
sensitivity_data["RED-M"] <- mcone_lum * raw_data["red-average"]
sensitivity_data["RED-S"] <- raw_data["S"] * raw_data["red-average"]
sensitivity_data["RED-ipRGC"] <- raw_data["ipRGC"] * raw_data["red-average"]
sensitivity_data[is.na(sensitivity_data)] <- 0 # convert NA to 0
head(sensitivity_data) # quick check of the sensitivity data

##         BLUE-L       BLUE-M       BLUE-S   BLUE-ipRGC        RED-L
## 1 2.706961e-30 1.211460e-30 5.825632e-29 1.119124e-29 9.514794e-11
## 2 4.673587e-30 2.142437e-30 1.010976e-28 1.912969e-29 2.825849e-10
## 3 8.176683e-30 3.852773e-30 1.840851e-28 3.501595e-29 9.299767e-10
## 4 1.337775e-29 6.469090e-30 3.212693e-28 6.334071e-29 1.632816e-09
## 5 2.248540e-08 1.114160e-08 5.673608e-07 1.179497e-07 1.901138e-09
## 6 2.469410e-07 1.280260e-07 6.543395e-06 1.455357e-06 8.478563e-10
##          RED-M        RED-S    RED-ipRGC
## 1 4.258205e-11 2.047672e-09 3.933648e-10
## 2 1.295408e-10 6.112788e-09 1.156662e-09
## 3 4.381959e-10 2.093695e-08 3.982546e-09
## 4 7.895821e-10 3.921239e-08 7.731025e-09
## 5 9.420209e-10 4.797029e-08 9.972632e-09
## 6 4.395691e-10 2.246633e-08 4.996875e-09

Visualize the stimulation of ipRGC with blue and red stimuli

matplot(raw_data[,"lambda"], cbind(sensitivity_data[,"BLUE-ipRGC"], sensitivity_data[,"RED-ipRGC"]), xlab = "wave length(nm)", ylab ="cd/m2", type = "l", col = cbind("blue","red"), lty = 1)
legend("topright", legend=c("blue ipRGC", "red ipRGC"), pch=1, col=c("blue","red"), horiz=FALSE)

Obviously stimulation with blue light stimuli is larger than red stimuli.

Sum up receptor stimulation

Calculate total stimulation of L-, M-, S-, and ipRGCs in blue red light from sensitivity functions.

senFunSums <- colSums(sensitivity_data) 
stimulations <- matrix(0, 2, 5)
rownames(stimulations) <- c("BLUE", "RED")
colnames(stimulations) <- c("L", "M", "S", "ipRGCs", "Luminance")
# creating a table of pre-adjusted stimulations 
for (i in 1 : length(senFunSums)) {
    # assign row index 
    if (i <= length(senFunSums)/2) {
        rowIndex <- 1 
    } else rowIndex <- 2
    
    # assign col index
    if (i %% 4 !=0) {
        colIndex <- i %% 4
    } else colIndex <- 4
    
    # calculating pre-adjusted stimulations 
    # and fill adjusted data into the new data frame
    if (i%%4 == 1 | i%%4 == 2 ){
        stimulations[rowIndex, colIndex] <- senFunSums[i]*683
    } else if (i %% 4 == 3) {
        stimulations[rowIndex, colIndex] <- senFunSums[i]*1466
    } else if (i %% 4 == 0) {
        stimulations[rowIndex, colIndex] <- senFunSums[i]*872 
        #683, 1466, 872 are the constants to calculate the luminance 
        # from the spectrum and sensitivty curve, so called "Km".
        #  and its unit is lm/W
    }
}
stimulations

##             L         M          S    ipRGCs Luminance
## BLUE 2.653317 2.0261725 42.6447173 19.431430         0
## RED  2.671399 0.4579188  0.1529893  0.283531         0

Adjust receptor stimulation according to luminance

Prof. Tsujimura assumes that neither the S cones nor the ipRGC affect the photopic luminance efficiency function (i.e., luminance), therefore lumiance equals to (L-cone + M-cone) in both blue and right.

stimulations[1, 5] <- stimulations[1,1]+stimulations[1,2]
stimulations[2, 5] <- stimulations[2,1]+stimulations[2,2]
stimulations

##             L         M          S    ipRGCs Luminance
## BLUE 2.653317 2.0261725 42.6447173 19.431430  4.679489
## RED  2.671399 0.4579188  0.1529893  0.283531  3.129318

Prof. Tsujimura assumes that that red and blue stimuli were isoluminant, so adjust the stimulation according to the ratio of blue- and red- luminance.

#  adjust to same luminance 
stimulations[2,] <- stimulations[2,] * (stimulations[1,5]/stimulations[2,5])
stimulations

##             L         M          S     ipRGCs Luminance
## BLUE 2.653317 2.0261725 42.6447173 19.4314297  4.679489
## RED  3.994731 0.6847581  0.2287756  0.4239838  4.679489

# calculate the relative stimulations by dividing all values 
stimulations[1, ] <- stimulations[1,]/stimulations[2,]
stimulations[2, ] <- stimulations[2,]/stimulations[2,]
# check the relative stimulation 
stimulations

##              L        M        S  ipRGCs Luminance
## BLUE 0.6642041 2.958961 186.4041 45.8306         1
## RED  1.0000000 1.000000   1.0000  1.0000         1

Result

The stimulation of ipRGC with blue light is about 46 times larger than red light.

Introduction of calculating receptor stimulation based on cone- and ipRGC sensitivity functions.

Sung-en Chien

2016.10.24

Visualize the stimulation of ipRGC with blue and red stimuli

Sum up receptor stimulation

Calculate total stimulation of L-, M-, S-, and ipRGCs in blue red light from sensitivity functions.

Adjust receptor stimulation according to luminance

Result