Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998. Diffraction increases as aperture size Diffraction increases as aperture size If is large compared to the aperture, the waves will spread out at large angles into the region beyond the obstruction. Diffraction Video 1 Video 2
Diffraction Pattern From a Single Slit Ingle and Crouch, Spectrochemical Analysis
Diffraction Pattern From a Single Slit Ingle and Crouch, Spectrochemical Analysis For Destructive Interference: x = /2 W sin = W sin =
Diffraction Pattern From a Single Slit Ingle and Crouch, Spectrochemical Analysis For Destructive Interference: x = /2 W sin = 2 W sin = 2
Diffraction Pattern From a Single Slit Ingle and Crouch, Spectrochemical Analysis For Destructive Interference: W sin = m W sin = m m = ±1, ±2, ±3, …
Eugene Hecht, Optics, 1998. Diffraction Gratings Plane or convex plate ruled with closely spaced grooves (300- 2400 grooves/mm). http://www.olympusmicro.com/primer/java/imageformation/gratingdiffraction/index.html
Two parallel monochromatic rays strike adjacent grooves and are diffracted at the same angle ( ). Difference in optical pathlength is AC + AD. For constructive interference: m = (AC + AD) m = 0, 1, 2, 3, … Ingle and Crouch, Spectrochemical Analysis Grating Equation
m = (AC + AD) AC = d sin AD = d sin Combine to give Grating Equation: d(sin + sin ) = m d(sin + sin ) = m Ingle and Crouch, Spectrochemical Analysis Grating Equation Grating Equation only applies if: d > /2
Are you getting the concept? At what angle would you collect the 1 st order diffracted light with = 500 nm if a broad spectrum beam is incident on a 600 = 500 nm if a broad spectrum beam is incident on a 600 groove/mm grating at i = 10 ° ? For = 225 nm? For = 750 nm?
Modern infrared spectrometers are very different from the early instruments that were introduced in the 1940s. Most instruments today use a Fourier Transform infrared (FT-IR) system.
In early experiments infrared light was passed through the sample to be studied and the absorption measured. This approach has been superseded by Fourier transform methods. A beam of light is split in two with only half of the light going through the sample. The difference in phase of the two waves creates constructive and/or destructive interference and is a measure of the sample absorbance.
The waves are rapidly scanned over a specific wavelength of the spectra and multiple scans are averaged to create the final spectrum. This method is much more sensitive than the earlier dispersion approach.
A Fourier transform is a mathematical operation used to translate a complex curve into its component curves. In a Fourier transform infrared instrument, the complex curve is an interferogram, or the sum of the constructive and destructive interferences generated by overlapping light waves, and the component curves are the infrared spectrum.
An interferogram is generated because of the unique optics of an FT-IR instrument. The key components are a moveable mirror and beam splitter. The moveable mirror is responsible for the quality of the interferogram, and it is very important to move the mirror at constant speed. For this reason, the moveable mirror is often the most expensive component of an FT- IR spectrometer.
The beam splitter is just a piece of semi- reflective material, usually mylar film sandwiched between two pieces of IR- transparent material. The beam splitter splits the IR beam 50/50 to the fixed and moveable mirrors, and then recombines the beams after being reflected at each mirror.
Michelson Interferometer "Schematic of a Michelson interferometer illuminated by a monochromatic source." Dr. S. M. Condren
"Illustration s of time doamin plots (a) and (b); frequency domain plots (c), (d), and (e)." Dr. S. M. Condren
“Comparison of interferograms and optical spectra.” Dr. S. M. Condren