---
title: "Photon Counting"
author: "Glenn Davis"
date: "`r Sys.Date()`"
output: 
  rmarkdown::html_vignette:
    toc: true
    number_sections: false
    fig_caption: true
bibliography: bibliography.bib
csl: personal.csl    
vignette: >
  %\VignetteIndexEntry{Photon Counting}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---


This **colorSpec** vignette is a response to the question:

> Is there any program that given the lumen and the colour spectrum (relative
> intensity at any wavelength) of a light source and it outputs the total amount
> of photons per wavelength?

that was asked on a stackexchange forum, see @174314.
Featured functions in this vignette are: `actinometric()` and `photometric()`.

```{r, echo=TRUE, message=FALSE}
library( colorSpec )
```

<br>

## Read Relative Radiant Power and Scale to Specified Luminous Flux

Read the SPD for a domestic LED bulb from the
**Lamp Spectral Power Distribution Database**, see @LSPDD.
The unique ID is
`LED_A19_dim_domestic-use_softwhite-color_CREE-brand_6W_120V_75Lum_2700K_bernard`.

```{r echo=TRUE, fig.cap='Figure 1.  Energy Spectrum of a Domestic LED Bulb, manufactured by Cree', fig.align="center", fig.width=7, fig.height=4, dev='png' }
wave = 275:899
path = system.file( "extdata/sources/Cree-LED.txt", package="colorSpec" )
bulb = readSpectra( path, wavelength=wave )
par( omi=c(0,0,0,0), mai=c(0.6,0.8,0.1,0.1) )
plot( bulb, main='' )
```
The energy unit is unknown.
But it does not matter, because we are now going to scale
so that the luminous flux of the SPD is 75 lumens,
as specified by the manufacturer.

```{r, echo=TRUE, message=FALSE}
luminous.flux = photometric( bulb ) ; luminous.flux
```
The unit is lumen, but the first one - `photopic1924` - is the
appropriate official standard.
Scale spectrum to have 75 lumens.
```{r, echo=TRUE, message=FALSE}
bulb = multiply( bulb, 75/luminous.flux[1] ) ; bulb
#   check that the luminous flux is now 75 lumens
photometric( bulb )
```
From the **man** page for `photometric()` we know that the unit for `bulb` is
$\textrm{watt} * \textrm{nm}^{-1}$.
```{r fig.cap='Figure 2.  Energy Spectrum of a Domestic LED Bulb, manufactured by Cree', fig.align="center", dev='png', fig.width=7, fig.height=4,  fig.show='hold', message=FALSE}
par( omi=c(0,0,0,0), mai=c(0.6,0.95,0.1,0.1) )
ylab = expression( 'Radiant Power'  ~~~  '[watt * ' ~ nm^-1 ~ ']' )
plot( bulb, main='', ylab=ylab )
```

<br><br>

## Convert from an Energy-Based to a Photon-Based Spectrum

The unit is currently energy-based (energy of photons, aka _radiometric_),
but we need photon-based (number of photons, aka _actinometric_).
From the **man** page for `actinometric()` we know that the output unit is
$\mu \textrm{mole} * \textrm{sec}^{-1} * \textrm{nm}^{-1}$.
```{r fig.cap='Figure 3.  Photon Flux of a Domestic LED Bulb, manufactured by Cree', fig.align="center", dev='png', fig.width=7, fig.height=4,  fig.show='hold', message=FALSE}
bulb = actinometric( bulb )
par( omi=c(0,0,0,0), mai=c(0.6,0.9,0.1,0.1) )
ylab = expression( 'Photon Flux'  ~~~  '[' ~ mu ~ 'mole * ' ~ sec^-1 ~ nm^-1 ~ ']'  )
plot( bulb, main='', ylab=ylab )
```

This plot looks similar but note that $\lambda_{max}$ has moved slightly higher.
For the total number of photons/sec from this bulb, compute the integral
over $\lambda$.
```{r, echo=TRUE, message=FALSE}
bulb
```
So the total photon flux of the bulb is
$1.102559 ~ \mu \textrm{mole/sec}$.
To convert this to exaphotons, multiply by 
$0.602214 ~ \textrm{exaphotons/} (\mu \textrm{mole of photons} )$
to get $0.663976 ~ \textrm{exaphotons/sec}$.

## References

<div id="refs"></div>

<br><br>

## Session Information

<pre>
```{r, echo=FALSE, results='asis'}
sessionInfo()
```
</pre>