Path difference modulation

Consider a monochromatic beam The detected signal oscillates as the two components alternately come into and out of phase as the path difference (p) is varied and gives rise to an interference pattern, the ac portion of which is a modulated cosine wave. The simplest equation representing this is... 

Figure 1.11 Synchronisation between the collection of FTIR spectra and the potential applied to the working electrode during potential modulation techniques. It is assumed that single-sided interferograms are collected during the forward sweep of the moving mirror (ZPD = zero path difference for the two paths of the interferometer).

The sinusoidal modulation present in the spectra in the shape of small ripples with high frequency is due to the instrumental line shape (ILS) of the FTS. It has a period of 2.3 cm which corresponds to an optical distance of 4mm, this is the maximum optical path difference Smax of this simulation. 

For a given solid angle through the interferometer, each optical frequency, then, has a specific value of the optical retaradation where the sine function is zero. If the interferometer is driven beyond this path difference, the phase of the modulation for that frequency is reversed, and energy at that frequency is removed from the spectrun rather than added to it as the optical retardation continues to increase. Therefore, in order to insure that this does not occur for any frequencies within the spectral bandwidth even at maximum path difference, the absolute maximum solid angle which can be used is... 

An idealized Michelson interferometer is illustrated in Figure 3. The interferometer modulates the incident beam by changing the optical path difference of the interferometer. The optical path difference can be changed continuously or in increments, methods called rapid scanning and step scanning, respectively. 

In step scan mode the optical path difference is changed incrementally, the mirror does not scan continuously. It steps to a position, collects data, and moves to the next position. Data are collected at each step with the path difference held constant. At each step the mirror is jittered at a constant frequency, a procedure that modulates the incident beam. The ability to select a constant modulation frequency, independent of the mirror velocity and wavenumber, results in a constant probed depth over the entire spectral range. This is advantageous over the varying sampling depth observed when using rapid scanning,... 

Because of the off-center positioning of the outboard color channels, the optical paths differ from the center channel, and keystone scanning height modulation is necessary to correct for differences in optical throw from left to right The problem, illustrated in Fig. 5.119, is more severe for wide-screen formats. Variables to be evaluated in choosing among the many schemes include the following ... 

If the output of the photomultiplier is displayed on an oscilloscope, the sinusoidal envelope which contains a high frequency sinusoidal modulation is observed and as the path lengths of the two arms approach equality, the modulation depth of the higher frequency sinusoidal modulation in the envelope increases. If the interferometer is adjusted to produce a maximum modulation depth, zero path difference has been located. If a white light is then used to illuminate the interferometer, the photomultiplier should detect the expected eight to ten fringes and present the typical interferogram of a broadband source. Fig, 3. 

There are several types of measurements for which standard rapid-scanning interferometers may be inappropriate. These include hyperspectral imaging (Section 14.5), high-speed time-resolved spectrometry (Section 19.2), photoacoustic spectroscopy (Section 20.3), and sample modulation spectroscopy (Chapter 21). For these measurements it is necessary to hold the optical path difference constant while a measurement is made, after which the OPD is rapidly advanced to the next sampling position and then held constant once again for the next measurement. This process is repeated until all the data needed to obtain the interferogram are acquired. Such interferometers are called step-scan interferometers. 

The infrared beam modulated before entering the interferometer is again modulated by the interferometer with a modulation frequency proportional to wavenumber v (see Section 4.3.1). As a consequence, the interferogram F(x) as a function of the optical path difference (OPD) X is expressed as... 

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