TUNABLE DIODE LASER SPECTROSCOPY
In its simplest form the tunable laser spectrometer consists of a diode laser that shines a
beam of tunable radiation through the sample. The light impinges on a photo-detector
that produces a current proportional to the intensity of the light. However, this is too
simple to be useful. Some of the principles of operation must be considered in more
detail:
1. The aperture of the diode laser is small; this implies that diffraction from the laser
aperture may be large. So a lens of some sort must be placed in front of the laser to
collimate the light. In the infrared the divergence angle of the laser beam is given by
 = 1.22 /D radians. In the infrared the aperture may be just 10 microns or so. So, 
is big and the lens must be close to the laser to capture all of the light diffracting from
the laser.
2. The diode may not emit a single frequency. Light is emitted in modes and there may
be several modes that operate simultaneously. So, some care must be taken to ensure
that single modes are emitted. This can be accomplished by using lasers with
gratings etched internally or by using an external cavity with a grating.
3. The frequencies emitted by the lasers depend on the current flowing through them
and their temperature. I guess that these control the band gap. However, the tuning
range may be short depending on their construction. They may tune only over a cm-1
or so before jumping to a new mode. The short wavelength lasers (near 1.6 microns)
may tune continuously for 10’s of cm-1.
4. The general tuning range is controlled by the lasers chemical constitution. Some
common IR lasers are made from lead salts; e.g. PbSnTe, PbSnSe, …
The laser spectrometers, as described above, would produce a transmission spectrum.
But, they are hardly ever operated in this manner. Besides the advantage of producing
radiation far more monochromatic than the width of the lines being measured TDL
spectrometers can provide extremely high sensitivity. This is accomplished by measuring
the absorption directly instead of by analysis of the direct transmission spectrum. The
transmission spectrum allows the deduction of absorption by subtracting two large
numbers from each other to produce a number that may be small compared to either one.
This small number may be obscured by the normal fluctuations in the intensity of the
laser that occurs normally with a 1/f characteristic. The solution to the noise problem can
be accomplished in principle by looking at the derivative of the spectrum. The laser is
scanned in frequency slowly and dithered in frequency rapidly with respect to the 1/f
fluctuations; this eliminates a great deal of the noise problems. This is a good approach,
but there are some complications that deserve some examination. In fact, it is the second
derivative of the spectrum that is ordinarily observed. The second derivative is used to
eliminate (more or less) the slope in the first derivative that occurs because of changing
power of the radiation as the varying current tunes the laser.
1. The derivative spectrum is very sensitive to line shape. For illustrative
purposes, consider a Lorentz shape. The analytic expression for the
transmission is given by (ignoring some irrelevant factors):
T() = exp(-/[()2 + 2]  /[()2 + 2]
The peak of the second derivative occurs at  = 0. At that frequency the second
derivative varies as:
d2T/d2  3
The spectrum is produced by slowly scanning the laser frequency through the absorption
line while simultaneously dithering the laser frequency. This produces an AC signal as
the laser frequency tunes through the line. The second derivative is deduced by looking
at the first harmonic of the dither frequency. This is how that works: consider a function
y = f(x).
x = xo +  sin (t).
Expand y in a power series:
y = f[xo +  sin (t)] = f(xo) + (df/dx) x + (½) (d2f/dx2) (x)2 + …
x =  sin (t)
x2 = [ sin (t)]2 = 2 cos (2t)
In practice the derivative of the spectrum is not observed, but something closely related
to it is.
2. The second derivative could be observed by slowly scanning the laser
frequency, all the while dithering the frequency with a very small amplitude. But, this
would produce a very small AC signal that would strain the data processing part of the
spectrometer. So, instead the laser frequency is dithered by a large amount while
scanning the laser frequency. This produces a large amplitude signal that looks like the
second derivative, but isn’t. In order to connect the observed second derivative-like
signal to the desired transmission properties it is necessary to calibrate. There are ways
to do this using auxiliary absorption cells with known amounts of gas. However, we note
that the amplitude of the 2nd derivative signal is very sensitive to line shape. So, in order
to get accurate results it is important to calibrate with cells that represent the conditions
accurately. Are there other ways to get a calibration?