Ocean Optics ARCoptix ANIR - Manual (Page 33)

A: How the ARCoptix ANIR Works
ARC-00000-000-02-0310 25
The intensity is thus modulated and changes with a cosine function of the grating depths x. The
period is given by the wavelengths. If the lamellar grating is illuminated with a source containing
several wavelengths of intensities A

( 

), then the interferogram is the integral over all wavelengths 

.
   
        d x A x I 2 cos ) ( Eq. A - 2
The recorded intensity I( x) contains information about the spectral composition of the incoming light
A( ) that can be extracted by using a Fourier transform.
It is useful to define the contrast (or visibility) as follows:
C( x) = I
max
( x) – I
min
( x) / I
max
( x) + I
min
( x) Eq. A - 3
An important measurement point is the zero path difference ( x = 0) when all mirrors are at the same
positions and the grating acts as a simple mirror. At this point, all intensity values A( ) are added
since the cosine term is maximum for all wavelengths. At the zero path difference, the contrast is
maximum and equal to unity. If
x is non-zero, then the broader the spectrum of the source, the
smaller the contrast. On the other hand, the narrower the spectrum (e.g. monochromatic light source),
the higher the contrast.
Reference Laser
The ARCoptix NIR contains a reference laser to precisely control the position of the movable parts in
the interferometer. The reference laser operates at about 635 nm and its spectra can be measured
depended on the light level in the measurement channel. To check the operation of the reference laser
choose the EXTREME detection gain and choose the spectral range in the graphing options.
Resolution
In Fourier spectroscopy, resolution is depending of the maximum optical path difference (i.e., phase
delay) that you can achieve with the interferometer. The longer the scanning range the higher the
resolution. Strictly speaking, the smallest spectral interval that can be discerned is defined as:
max
1
x 
   Eq. A - 4
Resolution is usually defined as the smallest spectral interval multiplied by the truncation effect of a
boxcar. This corresponds to the full width half maximum of a monochromatic radiation. If no
apodization is used, resolution is about 1.2*
 and if a triangle apodization is used, then resolution is
1.7* .
Detector Nonlinearity
If the detector response does not increase linearly with the illumination intensity the measured
interferogram will be distorted. Every detector (or analogue/digital converter) shows some non-
linearity, especially when approaching the saturation level or the detection limit of the detector.
However, if detectors are used in useful range below saturation very good linearity is obtained and
distortions are negligible. This has to be respected when the gain level is chosen. To high gain will
increase effects of nonlinearity.