MicroWave Spectroscopy Laboratory

Instruments Resonator spectrometer Detailed description of the spectrometer

Resonator spectrometer for atmospheric studies and absolute radiation absorption measurements in dielectrics

The block-diagram of the apparatus is presented in Fig. 1. The Fabry-Perot resonator (Device 011) uses fundamental TEM (00q) mode, where q is longitudinal mode number, i.e., number of halfwavelengths between mirrors. The quality factor of Fabry-Perot resonator, 25-42 cm long, spherical silver-plated mirrors 12 cm in diameter and 24 cm curvature radius, coupled with source and detector by 6 micrometer teflon film, placed 45 degrees to the resonator axis, is determined by unavoidable reflection losses (silver is the best reflecting material in millimeter wave range).

Fig. 1. Block - Diagram of the experimental setup of the resonator millimeter-wave spectrometer. Radiation source is BWO with frequency controlled by PLL including slow MW and fast RF reference synthesizers. The sensor is a high-Q Fabry-Perot resonator. The Schottky diode is the detector of the radiation passed through the resonator. Computer performs control of synthesizers, data acquisition and processing.

It is known that the width of the resonance can be written as

D f = cPtotal / 2p L ,

where c is the light velocity in a substance, L is the resonator length and Ptotal are total relative losses of radiation energy during one traversing of the resonator. The length L is defined in our case as

where l - wavelength in the substance, R mirrors radius of curvature, q - number of halfwavelengths between mirrors.

Total losses in the Fabry-Perot cavity Ptotal consist of:

Ptotal = Preflection + Pcoupling + Pdiffraction + Patmosphere ,

and one needs some additional procedure to separate the loss to be measured. Expressions for all the losses are known with higher or lower accuracy: losses in the atmosphere filling the resonator can be calculated using MPM program written by H. Liebe and its updates; diffraction coupling and reflection losses can be calculated using expressions from classical books.

The synthesized frequency radiation source is based on a Backward Wave Oscillator (BWO) which is stabilized by Phase Lock-in Loop (PLL) with the use in this case of two reference synthesizers: one microwave (MW) synthesizer (8-12 GHz), determining central frequency of the BWO and fast radio frequency (RF) synthesizer (20-40 MHz) for precision fast scanning of the BWO frequency around the chosen central frequency.

Radio frequency synthesizer provides frequency scanning without loss of the phase of oscillations (without phase jumps). Both synthesizers are computer-controlled. As a result, BWO frequency is defined as

fBWO = n fMW 10 fRF ,

where n varied from 4 to 20, and factor 10 before fRF appears because phase detection is done at 10 times digitally divided intermediate frequency (IF) which was 350 MHz. The main source of error in measurement of the resonance width is the drift of the central frequency of resonance during the measurement. To minimize this error one has to measure the resonance curve as fast as physically possible. Response time of the resonator itself t ~ 1/p D f~2 microseconds. For precision measurement the observation time should be increased, say, ten times, i.e., up to ~20 microseconds. Microwave and millimeter-wave synthesizers commonly used for spectroscopy, employ indirect frequency synthesis and so have ~ 10  50 millisecond switching time, thus preventing fast scanning of the resonance curve. Fast direct radio frequency synthesizer with switching time ~200 nanoseconds and time between switching 58 microseconds was used in this work as a source of reference signal for phase detector in the lock-in loop. Thus precision and fast scanning of the BWO radiation frequency within ~200 MHz around the central frequency defined by microwave frequency synthesizer was achieved. Extension of the scanning range up to the full BWO frequency range is possible [Ref. 2 (2006)]. Scanning without loss of phase permits the physical limits of the resonance observation time to be approached and reduces the source phase noise. The passed through resonator radiation was received then by low-barrier Schottky diode detector. The precision frequency control, signal acquisition and processing were done by computer as it is shown in Fig. 1 and will be explained below. Results of each scan were recorded and processed separately.

Automation system consisted of IBM PC and module containing RF synthesizer and data acquisition system. For minimization of ground-to-ground static the module is connected with PC by optically coupled interface. The core of the module is microprocessor with external memory. RF synthesizer is based on Direct Digital Synthesizer (DDS) microcircuit AD9850 of Analog Devices Inc. and it is able to generate harmonic signal in 20-40 MHz range with 0.03 Hz discreteness and without phase jumps at the switching. Data acquisition (digitizing of preamplified detector signal) is done by 12-digits ADC. Data are stored in a data memory. Microprocessor controls frequency of synthesizer and synchronizes the data acquisition process with frequency steps. Parameters of the synthesizer frequency tuning - starting frequency, value of frequency step, time of the next frequency step, number of points, frequency change law and number of scans - the microprocessor receives from PC. Time between frequency changing was chosen for our purpose as 60 microseconds per point. Frequency was changed by triangle law meaning forward and backward scan. Maximum number of points per scan was 512. In each frequency point microprocessor several times collects data from ADC, averages the obtained results and put the result of averaging into data memory. In such a way 32 of 512 points triangle scans may be put into local memory. The number of scans which could be put into local memory increases proportionally with reducing the number of points per scan. So process of registration of 32 scans with 512 points per scan takes 0.98 sec. After the recording of ordered number of scans into local memory the data are transferred to PC for further processing.

The processing consists of least squares fitting of the results of each scan to Lorentzian with added linear (practice showed no necessity in quadratic term) and constant terms representing effects of interference in the tract in the vicinity of resonance, level of noise on detector and bias voltage of amplifier:

As a result of the fit the width of the resonance D f and position of the center f0 are obtained. The time necessary for the fitting of one scan depends primarily on the scan size and type of the PC processor. With P120 processor and 1024-points scan this time varies from split second to several seconds depending on the noise level. This time is defined for one single scan without use of the results of the processing of previous scan. The next scan processing time can be reduced down to some tens of milliseconds by use of the previous scan processing result as initial fitting parameters. It is clear that some of non-physical time losses can be reduced, e.g., just by the change of the processor.

The basic procedure in resonator spectroscopy is measurement of width of the resonance. The example of experimentally observed resonant curve of the Fabry-Perot resonator at 85 GHz is presented in Fig.2.

Fig. 2. Resonance curve of Fabry-Perot resonator record (500 centered scans). Residual of the fit to the Lorentzian curve multiplied by 100 is presented below. Measured width of the resonance (FWHM) at the frequency 85.139 GHz is equal to D f = 164 728 (20) Hz.

The curve is a combination of 500 scans with a duration of 30 ms each, i.e., corresponds to the summary averaging time 15 s. Each fast scan was processed separately, then resonant curves were combined so that their centers coincided, and so was obtained the averaged curve in Fig. 2. Residual of the fit, presented in the lower part of the figure indicates adequacy of the fitting model. The increased noise on the line slopes corresponds to transformation of phase noises of radiation into amplitude ones. The width of the resonance (FWHM) was defined then as D f = 164 728 (20) Hz. Of course, to obtain only averaged value of the width one can just average values of the widths obtained by processing each scan.

Fig. 3. Convergence of measured width of the resonance curve of Fabry-Perot resonator with the number of measurements. Results of forward (curve F) and backward (curve B) scans are presented separately, demonstrating existence of the fast drifts of the center resonance frequency even at scan times as short as 30~ms. Average of back and forth scans is shown (medium curve).

In Fig. 3 some inside story of obtaining the resonator width value by means of averaging each single scan processing result is shown. The width is plotted vs. the number of averaged measurements: thin curves depict results of only forward (F) and only backward (B) frequency scans; thick curve depicts the mean value of these two. Every point corresponds to twenty times averaged value of width obtained from processing of 30 ms duration single scans. The curves in Fig. 3 show not only the effect of measurement accuracy increase with data accumulation - after 340 averaging the mean value of back and forth scans varies within 10 Hz - but also the significance of the fast frequency scan introduced by us for faster obtaining of the data as well as for lessening the measurement errors arising from the resonance center frequency drift. The difference between width values measured with opposite directions of the scan reaches 400 Hz due to the drift of the center frequency of the resonance during the time of the scan even for scans as fast as 30 milliseconds. The change from slower scans used earlier (10 s) to the 30 ms scan is in some sense equivalent to the change to modulation method (with 30 Hz modulation frequency) leaving behind most part of flicker type drifts and perturbations.

The sensitivity of the spectrometer in terms of the absorption coefficient determined from 20 Hz resonance width measurement accuracy constitutes ~ 4  10-9 cm-1 (or 1.8  10-3 dB/km).

For more details and the spectrometer applications see the paper [Ref. 11 (2000)].

Examples of the spectrometer use for "in situ" observation of atmoshperic lines.

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