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Michelson Interferometer Operation

Most interferometers used today for infrared spectrometry are based on the two beam type originally designed by Michelson in 1891. As such, a design employing this approach is referred to as a Michelson Interferometer.

The Michelson Interferometer divides an incoming beam of radiation into two equal (ideal) parts with each part continuing along a separate path. When the two beams are recombined, a condition is created under which interference can take place. Interference occurs when two beams of radiation are added together or combine to form one summation signal.

Since the radiation is in the form of a sinusoid, many combinations of the beams are possible. As shown in the figure below, the resultant signal can vary between zero and some maximum depending on the relative phase of the two beams. By changing the physical length of one path relative to the other path, the phase between the two beams can be varied. The difference between the two paths is know as retardation.

Description of Michelson Interferometer

The design of many interferometers used for infrared spectrometry is based on the two-beam interferometer originally designed by Michelson in 1891. Many other types of two-beam interferometers have been designed that may be useful for certain specific applications. The general idea behind all scanning two-beam interferometers is similar, and the theory of interferometry can be explained by describing the way a simple Michelson interferometer can be used to measure infrared spectra.

The Michelson interferometer is a device that divides a beam of radiation into two distinct paths and then recombines the two beams after introducing a difference in the two paths. Under these conditions, interference between the beams can occur. The interference creates variations in the output beam intensity as the difference in the path length changes. The intensity variations of the output beam can be measured with a detector as a function of the path difference.

The simplest form of Michelson interferometer is shown in the Figure below. It consists of two mutually perpendicular plane mirrors, one of which is mounted so that it can be moved along an axis perpendicular to its plane (surface). This movable mirror is normally moved at a constant velocity or could be moved and held at equally spaced points for fixed, short time periods and then rapidly stepped between points. Located between the fixed mirror and the movable mirror is a beamsplitter. The beamsplitter divides the input beam of radiation into two beams. That is, the input beam is partially reflected to the fixed mirror M1 (at point A) and partially transmitted to the movable mirror M2 (at point B).

After the beams return to the beamsplitter at O, they interfere and are again partially reflected and partially transmitted. Because of the effect of interference, the intensity of each beam, one passing to the detector and the other returning to the source, depends on the difference of path lengths in the two arms of the interferometer. The variation in the intensity of the beams seen by the detector is a function of the path difference and a graph or plot of this intensity is know as an interferogram. After mathematical manipulation, the interferogram ultimately provides the desired spectral information in a Fourier Transform Spectrometer or FTS.

To understand the processes occurring in a Michelson interferometer better, consider an ideal situation where a source of pure monochromatic radiation produces an infinitely narrow and perfectly collimated beam. Let the wavelength of the radiation be l (in centimeters) and its wavenumber be v (reciprocal centimeters)

v = 1/λ

Assume that the beamsplitter is ideal and has a reflectance and transmittance which are both 50%. Let's first determine the intensity of the beam at the detector when the movable mirror is held stationary at different positions. The path difference between the beams traveling to the fixed and movable mirrors is 2(OB - OA). This optical path difference or retardation is usually given the symbol δ. When the mirrors are held exactly perpendicular as they should be, and the beam is perfectly collimated, δ is the same for all parallel input beams.

When the fixed and movable mirrors are equidistant from the beamsplitter (zero retardation), then the two beams travel the same distances through the same materials and are exactly in phase after they recombine at the beamsplitter. At this point, the beams interfere constructively and the intensity of the beam passing to the detector is the sum of the intensities of the two beams passing to the fixed and movable mirrors. Therefore, all the light from the source reaches the detector at this retardation.

If the movable mirror is displaced a distance of λ/4, the total retardation or path difference is λ/2 (roundtrip). Therefore the path difference between the fixed and movable mirrors is exactly one-half wavelength. On recombination at the beamsplitter, the beams are 180 degrees out of phase and interfere destructively.

A further displacement of the movable mirror by λ/4 makes the total path difference or retardation λ. The two beams are once more in phase on recombination at the beamsplitter, and a condition of constructive interference again exists. This pattern of constructive-destructive-constructive..... interference repeats as the mirror moves further. For monochromatic radiation such as a laser, there is no way to determine if a particular point at which a signal maximum occurs corresponds to zero retardation or a retardation equal to an integral number of wavelengths.

Moving the mirror at constant velocity, the signal at the detector varies sinusoidally, a maximum being registered each time the retardation is an integral multiple of wavelengths, λ. The intensity of the beam at the detector, measured as a function of path difference, is given the symbol I(λ). The intensity at any point where δ = nλ (where n is an integer) is equal to the intensity of the source I (δ). At other values of , the intensity of the beam at the detector is given by:

I (δ) = 0.5 I(v) cos(2πvδ)

I (δ) as given above is the AC portion of the signal, which is the part of the interferogram we are interested in. Therefore, for a monochromatic source, the interferogram is a cosine wave of constant amplitude and a single frequency.

If the moving mirror is scanned at a constant velocity V then d = 2 V t. Substituting into equation above we now have:

I (δ) = 0.5 I(v) cos(2πv ⋅ 2 V t)

The frequency of this cosine wave is given by:

f = 2v V

The above description shows how the interferometer when operating at a constant velocity modulates each wavelength into a unique frequency. If the source is made up of many wavelengths, then the interferogram is the sum of all these sine waves.

Passive Standoff FTIR Sensing

Spectrometers are designed and used to measure radiation over a specified spectral bandwidth. All objects at a temperature greater than absolute zero emit radiation according to Planck's Law.

By operating the spectrometers with cooled detectors and in the 7 to 14 µm (IR) spectral band, the self emission of backgrounds and targets can be exploited. In the IR spectral band, all objects radiate some level of photon flux proportional to the objects temperature (above absolute zero) and its emissivity. It is the detection of this self radiation (emission) due to its temperature that is termed Passive Detection.

In the figure below, the sensor is viewing a background at temperature TB through the atmosphere at temperature TA, and also a chemical cloud at temperature TC . The goal of passive sensors is to detect the presence of the chemical cloud using only the naturally occurring (passive) radiance.

For passive detection to be successful there must be a difference in temperature between the target cloud and the background. The temperature differential can either positive (cloud warmer than background) or negative which results in the cloud being seen in emisssion or absorption. The temperature difference can be as small as a fraction of a degree. The larger the difference (delta temperature), the easier the detection process.

As seen from the figure, the final signal that must be evaluated is a complex combination of radiation from the background, the chemical cloud and atmosphere.

In contrast, an active measurement requires some kind of hot source placed behind some of the cloud and within the spectrometers field of view. This is not always convenient or possible. Successful passive detection generally demands very high sensitivity from the spectrometer which requires a very high quality detector (for 7-13.5mm, a HgCdTe detector cooled to 80K), whereas an active system can use an uncooled detector combined with a very hot source to get the desired signal-to-noise or sensitivity.

FTIR Technology

FTIR (Fourier Transform Infrared) or FTS (Fourier Transform Spectroscopy) is a sensor technology based on the Michelson interferometer. Historically the Michelson interferometer consists of two flat mirrors located at 90° to each other with a beam splitter mounted on the 45° line which separates the two mirrors (see below).

Generally one of the mirrors is fixed and the other mirror is mounted such that it can be translated while maintaining the precision alignment relative to the fixed mirror.

The Michelson interferometer modulates the incoming optical radiation by changing the optical path difference (OPD) between the two possible paths in the interferometer in a smooth(some FTIR sensor do use a step scan approach) continuous fashion. As described above, the interferometer is made up of two mirrors oriented 90° to each other and separated by a beam splitter/compensator pair.

A change in path difference (called retardation) is accomplished by moving one of the two mirrors at a constant velocity over a fixed distance. When the mirror has traveled the required distance, which is governed by the required spectral resolution, it is quickly returned to the start position to begin the next scan.

During the motion of the moving mirror each wavelength of the collected radiation is modulated at a unique frequency that is a function of the wavelength of the radiation and the velocity of the moving mirror.

As an example, if a laser (10 µm CO2) was used as the source of radiation and the interferometer mirror was moving at 10 cm/sec (optical), the signal generated would be a sine wave of constant amplitude and constant ( { 1/10 µm} X 10 cm/sec = 10 kHz) frequency. Assuming a broadband source such as a blackbody, taking into account all the wavelengths which make up the target radiation and adding together all these sinusoids produces what is called an interferogram.

Therefore, the interferogram is a coded representation of the target spectrum. The Fourier Transform or decoding of the interferogram provides the spectrum of the target radiation. These sensors are used primarily in the infrared portion of the spectrum, where the detectors require their sensitivity advantage; they are therefore called Fourier Transform Infrared Spectrometers.

Why FTIR?

Why deal with the complexity created by encoding the data and then having to decode it with the Fourier Transform? Michelson interferometers provide a significant sensitivity advantage over grating, prism, and circular variable filter (CVF) spectrometers.

There are two significant reasons for the sensitivity advantage. The first can be described as a multiplex advantage. The Michelson interferometer's single detector views all the wavelengths (within the sensor passband) simultaneously throughout the entire measurement. This effectively lets the detector "dwell" on each wavelength for the entire measurement time, measuring more photons. This improvement is called the multiplex advantage and, in effect, increases the integration time.

The second advantage is due to the light gathering capability or larger throughput. The interferometer is not limited in aperture (slit width or height) as severely as dispersive or CVF instruments. This translates into a much higher throughput or light gathering capability. Both of these advantages enable the Michelson FTIR to provide superior sensitivity over other spectrometers over the infrared portion of the spectrum.