Shimadzu IRAffinity-1, Instruction Manual

Page: 25 / 134

1.1 Principle and Construction
1-3
IRAffinity-1
Assume that the light source emits monochromatic light of wavelength
λ
(cm). When the distance l
1
between
the fixed mirror and the beam splitter is equal to the distance l
2
between the moving mirror and the beam
splitter, the optical path difference between the two beams, χ = 2 (
l
1
−
l
2
), is equal to zero, and the beams are in
phase. While in phase, the beams interfere constructively with each other ( Fig. 1.2 A, B). As the moving mirror
is displaced λ /4 cm, the optical path difference becomes λ /2 cm, and the two beams are out of phase,
interfering destructively ( Fig. 1.2 A, C). Thus, the two beams interfere constructively with each other when χ =
n
λ
and destructively when
χ
= (n + 1/2)
λ
where n is an integer.
Fig. 1.2 Interference
Equation 1.1, extrapolated from the above principles, calculates the intensity I*(
χ
) of light (wavelength
λ
)
incident to the detector.
where R: energy reflected by the beam splitter
T: energy transmitted by the beam splitter
S (
λ
): radiation energy from the light source
The intensity of the light observed by the detector is a function of Equation 1.1. I( χ ) denotes the light intensity,
and the wavenumber
σ
(cm
-1
) replaces the wavelength
λ
.
The signal I(
χ
) observed by the detector is called an interferogram, and 4RT is labeled beam splitter efficiency.
If polychromatic light is emitted instead of monochromatic light, I(
χ
) is given by the integration of 1.2 with
respect to wavenumber.
Light from the
moving mirror
Light from the
fixed mirror
Light from the
moving mirror
The difference of the resultant
interfering light
bright
dark
λ light wave
2 λ light wave
......................................................................................................... (1.1) I*
χ ( )
4RTS
λ ( )
1
2
---
1
2
---
2
πχ
1
---
cos + =
............................................................................................................................ (1.2)
B
σ ( )
2
πσχ
cos =
I
χ ( )
4RTS
λ ( )
1
2
--- •
2
πσχ
cos =
where B σ ( ) 4RTS λ ( ) 1 2 ⁄ • =
.................................................................................................................... (1.3)
I χ
( )
B σ
( )
2 πσχ σ δ cos
0
∞
∫
=