14Apr/104

When one talks about quantitative qualities of a light source, you generally subscribe to one of two schools of thought - Radiometric in SI units of Watts or Photometric in SI units of lumens, candelas or lux. In this post i am going to discuss these two different approaches.

Photometric
Photometric units are quasi-quantitative hand-wavey units; they are an attempt to quantify the qualitative aspects of a light source i.e. how bright a light source appears to the human eye. These units are useful for things like home lighting, vehicle headlights, or photography light meters.

A COTS Sylvania SoftWhite 100W incandescent light bulb advertises that it produces 122 candelas. If we were to convert that value into watts using the standard conversion factor of 1 lumen = 1/683 Watt (at 555nm as that is the accepted wavelength of peak sensitivity of the human eye), we get:

$122\left[cd\right]\cdot 4\pi\left[sr\right]=1530\left[cd\cdot sr\right]=1533\left[lm\right]\cdot\frac{1\left[W\right]}{683\left[lm\right]}=2.24\left[W\right]$

This tells us that a 100W incandescent bulb is only about 2.25% efficient in producing visible light and the rest of the power is wasted in producing NIR through LWIR (heat) photons.

Radiometric units are scientific in nature - absolute units based solely on the physical photonic quantities. Radiometric units address the entire spectral transmission of a light source regardless of detector. These units are useful for scientific applications like spectroscopy, detector characterization, optical communications, etc., essentially anything scientific that deals with light.

24Mar/100

## MS257 output divergence

the MS257's spec sheet calls out the input F/# in order to match the source to the monochrometer however it doesn't specify the output F/# or divergence which is extremely important to couple the monochromatic light into an optical system.  The spec sheet does instead specify the input and output focal lengths which we can use to back calculate the output divergence.
We first must find the F/# at the output, which is only possible if we assume the input and output apertures are the same. This is a reasonable assumption for a monochrometer as the instrument requires matching input and output slits to function properly. Using the definition of F/# we first solve for d:

$F/\#=\frac{fl}{d}\;\therefore \;d=\frac{fl}{F/\#}$

Once we have this standard equation, we plug it back into the F/# equation with the different focal lengths:

${F/\#}_o=\frac{fl_o}{d}=\frac{fl_o}{\left(\frac{fl_i}{{F/\#}_i}\right)}$

This equation can be rewritten to show that the ratio of the output F/# to the input F/# is equal to the ratio of the output focal length to the input focal length.

Now that we have a close form solution, we can plug-in the constants - the MS257 specification states the instrument has an input focal length of 220mm and an output focal length of 257.4mm; when we plug those values into the equation with the original input F/3.9 we get an output of F/4.56, and by using the equation from the previous post, that translates to a divergence of 12.51° from the exit slit.

26Jan/104

## MODTRAN

This post is going to discuss two pitfalls that i encountered while using MODTRAN via the PLEXUS GUI.  First is the conversion between Wavenumber to Wavelength, the second is using PLEXUS to perform night time lunar models.

Background:
The atmosphere, through its six layers, contains various particles and gases which attenuate impinging solar radiation.  The particles which contribute the most to this attenuation are water (H2O) in the troposphere (0-11Km), carbon dioxide (CO2) also in the troposphere, and ozone (O3) in the stratosphere (11-50Km).  While there is relatively little solar absorption through the visible bands (380nm - 750nm), there are strong absorption bands in the UVC and LWIR attributed to ozone, while H2O and CO2 absorb intermittently throughout the rest of the solar spectrum.  A Transmittance vs. Wavelength graph for two generic scenarios can be seen below.  Note: For larger absorption bands, the contributing particles are shown; the full Raytheon infrared wall chart can be found below under references. MODTRAN (MODerate spectral resolution atmospheric TRANSmittance algorithm and computer model) is an atmospheric spectral radiance modeling code developed by the Air Force Research Lab, Space Vehicles Directorate.  This code has been combined with several others (MODTRAN4 V2R1, SAMM 1.1, SAMM 1.82, FASCODE3 with HITRAN2K, SHARC Atmosphere Generator (SAG) V1 & V2, and Celestial Background Scene Descriptor (CBSD) V5) into a single software suite called PLEXUS (Phillips Laboratory EXpert-assisted User Software) which provides the user with an easier to use GUI for these atmospheric codes.  The most  recent version as of the publishing of this post is Release 3 Version 3A.  More information on PLEXUS as well as its constituent codes can be found on the AFRL software information page.