If you’re like me, and not an optical engineer, the most interaction you'll have with optics is with either an aspheric collimating lenses or multielement imaging lenses. This post is going to focus on the later while informing on the former. We will briefly discuss the fundamentals of optical design, followed by a discussion of lens specification by defining Image Circle, Focal Length, Aperture, and Resolution.
Imaging lenses, be it for a telescope or a camera, can be designed using either mirrors which work by the reflection of light, or glass which work by refraction of light. Reflective optical systems have the ideal quality that all light reflected by the surface bends at the same rate, and thus are inherently achromatic. They also follow simple trigonometric rules where the excidence angle is equal but opposite in sign to its corresponding incidence angle. These ray angles are referenced from the normal line which is perpendicular to the surface tangent at the particular point of incidence. The only knob the designer has to turn is the mirror element shape and clever mechanical design. These designs are quite large, and are ideal for systems which require long focal lengths; however they are unreasonable for designs which require small compact lenses. Refractive optical systems are more conducive to smaller systems, which is why they are much more prevalent, yet their designs are more complex.
If you are one of the aforementioned optical engineers, back in the day one would do the entire design by hand using Snell’s law and a list of available glasses with their frequency dependent index of refractions; nowadays one would use an optical ray tracing software package like ZEMAX or Code V (pronounced "code 5") to aid in the design. The advent of computer aided optical design opened the industry up for much more advanced, reduced distortion, achromatic lens designs. However, to pay our respects to the past – Snell’s law states that the excidence angle of an incidence ray is proportional to the index of refraction of the two materials.
Where 'θi' represents the angle off perpendicular to the surface tangent at the point of incidence, 'θe' represents the excidence angle while 'ni' and 'ne' represent the index of refraction of the two materials. Note: index of refraction is defined as how much faster or slower light travels through a medium as compared to vacuum where the refractive index of vacuum = 1 while air ≈ 1. Refractive index is also wavelength dependent which means that light bends at different rates when entering and exiting a medium, thus braking up into its component wavelengths. There are graphs which can be found for different optical materials which plot their index of refraction vs. wavelength. Snell’s equation gives the designer two knobs they can turn to develop their design - element material, and shape. However, the fact that refractive index varies with wavelength adds complexity in producing an achromatic design.
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.
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.