MicroWave Spectroscopy Laboratory

Instruments RAD Spectrometer  Detailed description

Submillimeter-Wave Spectrometer with a BWO and the Acoustic Detector (RAD)

Spectrometer Classification

All existing spectrometers may be divided into two main classes (Fig. 1) according to two methods of obtaining the signal from the spectral lines of the sample investigated. The first method involves registering the change in microwave radiation power after passage through the sample; the second involves registering the change in one or more sample parameters under the action of the radiation. Considering the region of spectrometer operation close to the sensitivity limit, one may assume that the fraction of power absorbed by the sample Ps is small, i.e., Ps<<P0 , where P0 is the microwave radiation source power. Thus, in the first class of spectrometers the useful signal Ps must be observed in the presence of a large (noninformative) background P0, and this is the main source of sensitivity-decreasing phenomena (including the increase of noise, appearance of false signals, etc.).

The microwave spectrometers commonly used are devices of the first class and the above circumstances limit their absorption coefficient sensitivity to a value of the order of 10-10 cm-1 at a time constant of 1 sec, and limit the allowed power to a value of 10-3 W. Spectrometers of the second class look more promising since the null signal detection principle for the microwave power is intrinsic to them, and only the useful signal Ps is registered. The detector noise in the absence of spectral lines does not depend on the radiation power passing through the sample and the absorption coefficient sensitivity increases at a rate proportional to the radiation power up to power levels causing transition saturation or breakdown in the gas.

The absence of detector reaction outside the spectral lines also eliminates false signals. As a result, the absorption coefficient sensitivity of microwave spectrometers of the second class (when powerful enough radiation sources are used) may significantly exceed the aforementioned figure of 10-10 cm-1 at a time constant of 1 sec.


General description

In the RAD (Fig. 2) the radiation of the primary monochromatic submillimeter source the BWO passes through one or several successively placed cells containing the gases investigated and is then directed to the mixer-multiplier of the BWO stabilization and frequency measurement system. When the radiation frequency coincides with the frequency of the spectral line the gas absorbs the power, heats, and produces a pressure increase in the cell (gas sounding when absorbing modulated radiation was discovered at the end of the nineteenth century).


The amplitude or frequency of the BWO radiation is modulated with an audio range modulation frequency. The spectral component of the gas pressure variations at the modulation frequency is the signal from the absorption line registered by the sensitive microphone placed in the cell. After amplification and synchronous detection the signal is recorded. The BWO radiation frequency may be scanned electronically by approximately an octave, which permits making a record of the absorption spectrum of the gas. According to the classification given above, the RAD belongs to the second class of spectrometers because of the manner of signal formation from the line.

This leads (besides the aforementioned possibility of a sensitivity increase) to the following properties important in practice: (i) the use of high power radiation sources without an increase in receiver noise opens new perspectives in nonlinear spectroscopy; (ii) the thermal volume "null" signal detection provides independence of the sensitivity on the radiation frequency and the absence of false signals from interference effects, which in conjunction with electronic control of the BWO frequency permits carrying out automatic records of broad parts of the spectrum; (iii) the signal formation (for the majority of spectral lines) from a small fraction of the radiation power passing through the cell permits making simultaneous independent records of several gas spectra in several absorption cells with microphones, and the utilization of the full radiation power passing through the cells in the system for stabilization and measurement of the BWO frequency.

Cell and detector (receiver)

Device 004

The gas cell, microphone, and electronic detector circuit (Fig. 3) must provide the maximum signal-to-noise ratio for weak lines (g l < < 1) for given resolving power of the spectrometer and radiation power passing through the cell circuit.


The conditions for maximum condenser microphone output signal by the microphone placed in the cell are:

wMt cell 1    (1)

m = ppR4/8VT* 1   (2)

Equation (1) relates the angular modulation frequency (wM) and the time constant of the thermal processes tcell, and provides maximum amplitude of gas pressure variations. Equation (2) relates the gas and membrane elasticities and provides the most effective transformation of the pressure variations into membrane displacements. Calculations are made for the real case in which the membrane elasticity is defined by its initial tension and the frequency of free oscillations of the membrane in vacuum is much greater than the modulation frequency. Here p is the gas pressure, V is the cell volume, R and T* are the radius and initial tension of the membrane (T* is the force per unit edge length). Analysis of these matching conditions and the expression for the signal strength obtained in this case permit the following conclusions: (i) When the matching conditions are fulfilled, the signal increases slowly with decreasing modulation frequency. The minimum modulation frequency is then defined by environmental noise. (ii) The operating pressure is sufficiently strictly defined by the desired resolving power of the spectrometer. Hence from Eq. (1) we obtain the value of the smallest (transverse) dimension of the cell. (iii) For given membrane parameters the signal strength increases with increasing cell length only up to a value defined by Eq. (2). Upon further increasing the cell length, the signal strength is saturated. (iv) The dependence of the matching Eqs. (1) and (2) on the gas pressure leads to the dependence of the output signal on pressure.

The realization of the matching condition m 1 at small gas pressures is the most difficult problem in practice, even when rather thin membranes are used (a membrane is stiffer than gas, <<1). In this case the signal drops proportionally to m. The maximum close approach to fulfillment of Eq. (2) is very desirable from the point of view of requirements for the sensitivity of the electronics circuit.

The spectrometer output noise is defined by the thermal fluctuations of the microphone membrane in the gas (both due to inherent Brownian motion of the membrane and to Brownian motion of the gas) and by the inherent noise of the electronics circuit. The limiting sensitivity of the spectrometer is obtained when the thermal fluctuations of the membrane are defined preferably by Brownian motion of the gas. In this case the parameters are practically unrestricted, since the gas noise and the signal are similarly transformed into membrane displacements. Only the weak dependence on the cell length remains. The signal-to-noise ratio increases as l1/2, because the effective volume thermal noise sources do not correlate between each other, but the signal sources do. In the absence of line saturation for T = 300K, l = 10 cm, an integration time of 1 sec, and a typical gas thermal conductivity, one may obtain the following estimate for the limiting absorption coefficient sensitivity of the RAD:

g min(cm -1) 4 x 10-11/P0    (3)

where P0 is in watts. An analogous estimate may be obtained more roughly using Eq. (4) and the expression for the signal power Psg lP0 . Let us consider the possibilities of achieving this ultimate sensitivity.

The rms displacement of the center of the membrane due to fluctuations connected with Brownian motion in the gas (at wMtcell1, m<<1) in the receiver bandwidth Dwrec near the modulation frequency is equal to

sg(1/4p)(kTm Dwrec/T* Dwcell)1/2    (4)

and that due to the inherent membrane Brownian motion is

sm(1/p)(kT Dwrec/2QMWT*)1/2     (5)

Here W and QM are the resonant frequency and quality factor of the membrane as a mechanical oscillator in vacuum. For the parameter values QM 5x102, W104 sec-1,  m 10-2, and Dwrec103 sec-1, the ratio sg/sm , is nearly 2.5 and the order of magnitude of sg is 5x10-5 Angstrom.

The electronic circuit must register these rather small fluctuation displacements of the membrane with very weak tension. When the cell is evacuated and filled with the gas to be investigated, considerable displacements of the membrane may occur. These must not influence the sensitivity of the microphone and circuit in the subsequent operation. The most suitable circuit for fulfilling these conditions is the high-frequency bridge condenser microphone circuit with the microphone capacity included in one resonant bridge arm. It will be shown below that the sensitivity of such a circuit is sufficient for detection of gas fluctuations. The use of an automatic bridge balance along two coordinates (microphone capacity by electrostatic control of the membrane position, the circuit losses by an electrically controlled resistor) provides constant sensitivity of the microphone and the circuit.

When the bridge is fed by a quartz oscillator with a sufficiently pure spectrum, then the noise in the narrow sidebands Dwrec at the frequencies wqwM is caused only by thermal fluctuations in the resonant bridge arms and the circuit sensitivity is equal to

sc(1/Q)(8/p)(1/2)(kT Dwrec/Pq)1/2d     (6)

Here wq  is the quartz oscillator frequency, Q is the quality factor of the microphone resonant circuit at the frequency wq, Pq is the power dissipated in this circuit, d is the distance between the membrane and the other electrode of the microphone. The value Q is defined by the losses in the thin conductive layer on the membrane and is approximately equal to 102. The value Pq may be increased until the electrostatic attractive force between membrane and electrode is compensated by the membrane tension. The condition for membrane stability loss is

d/Pq1/2=(Q/4pwq T*)1/2      (7)

and when the value d/Pq1/2 is near the optimal from Eqs. (6) and (7), one has

sc (1/p)(2kT Dwrec/Qwq T*)1/2     (8)

Assuming membrane fluctuations to predominate over fluctuations of the circuit, one may obtain the condition for wq. In practice we require wq >=106 Hz, which is easy to fulfill.

The relatively small dimensions of the RAD absorption cells in comparison with the cells of common microwave spectrometers have some advantages for a number of investigations (free radicals, Stark and Zeeman effects, etc.). At present, the experimentally obtained RAD sensitivity is equal to

gmin(cm-1)6x10-11/P0     (9)

(with P0 in watts), which is rather close to the theoretical value in Eq. (3). In particular, at the wavelength of 0.75 mm, where the BWO power is near 10 mW, the sensitivity of 6x10-9 cm-1 is obtained.

Example of application of simplest version of RAD spectrometer (see diagram in Fig. 3 above) for broad-band high resolution spectroscopy.

Example of record demonstrating RAD spectrometer sensitivity.

Example of broadband study of molecular spectrum using submillimeter frequency synthesizer and RAD gas cell (see diagram in Fig. 2 above) - Teraherz spectrum of oxygen .

Example of lineshape, line broadening and line shifting studies with BWO based submillimeter-wave frequency synthesizer with RAD gas cell (see diagram in Fig. 2 above).

   Institute of Applied Physics of the Russian Academy of Sciences
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