IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43, NO. 1, FEBRUARY 1994 86

Short Papers

Measurement of Gas Concentrations by Means of the Power Saturation Technique

in a Microwave Cavity Spectrometer

Z. Zhu, C. Gibson, A. H. Samuel, and I. P. Matthews

Abstract-The power saturation technique in microwave spectrometry, as first put forward by Harrington in 1967 [l], involves measuring a coefficient r under conditions of “power saturation.” This paper gives a general expression of r for various radiation field configurations in the gas cell. Concentrations of ethylene oxide gas were measured in a microwave spectrometer with a resonant cavity gas cell by using this technique. A relatively good linear correlation was found (to within a standard deviation of 4%) between the output signal and the concentration of ethylene oxide gas in the cavity.

I. INTRODUCTION

A straightforward method for quantitative analysis of gas species in microwave molecular rotational spectrometry is the “power satura- tion” technique [ 1.21. This technique involves measuring a coefficient r at center frequency FO of one of the absorption peaks of the analyte gas. The coefficient I? at FO is generally defined as

6Po 1 ro = -- ( P ) ’ / 2 L’

where PO is the total absorption power by the analyte gas, P is the total radiation power level exhibited in the gas cell, and L is the length of the waveguide gas cell.

The conventional absorption intensity coefficient N at FO may be generally defined as

where (YO is generally a function of position (s, y, L), Spo(.r, y. 2 )

is the absorption power density, p ( r , y, z ) is the radiation power density in the gas cell, a,,, is the unsaturated absorption intensity coefficient, I< is the power saturation coefficient, and

(3)

no is proportional to the gas concentration 9 (expressed as the number of analyte gas molecules per unit volume) [l]. From (2), the total absorption power at Fo is

6Po = Jab, 6po(x, y. 2). dsdydr

Manuscript received June 2, 1992; revised November 17, 1992. This work was suppored in part through a project grant from the Medical Devices Directorate of the Department of Health, U.K..

The authors are with the Department of Epidemiology and Community Medicine, University of Wales, College of Medicine, Cardiff, CF4 4XN, UK.

IEEE Log Number 9216496.

Fig.

and

I-a-4

, Rectangular waveguide gas cell.

where abL is the volume of the gas cell as shown in Fig. 1. Substituting (4) and (5) into (1) results in

= n . 9 . (6)

Thus, ro is factorized into two parts:

It = (nbL)‘/2no (7)

where n is proportional to the gas concentration N . For a gas cell with uniform radiation field density, i.e. p = PO,

(9)

This would lead to a constant maximum value (@cL)max = 0.5 at h y p o = 1. Please refer to the curve 9tL(X)/(@u)max shown in Fig. 2, where the abscissa is normalized with respect to Iipo = 1, and the ordinate is normalized with respect to = 0.5. Thus, from (6), we obtain

(ro)rnax = 0.5. 7 1 . (10)

where (ro)rI,ax is directly proportional to n , and hence, to the gas concentration N.

For a nonresonant rectangular waveguide gas cell, the radiation fields are (TElo mode):

E, = 0 E, = - J ~ o . sin(.rr.r/n) . e ~ ( c + J ’ )

H , = J ( / j ~ ~ / u l p ) . sin(a . r /o) . # ‘ + ‘ j Z )

Er = 0

H , = 0 H ; = ( .rrEo/wpn). cos( . rr . r /o) . e J ( “ “ - ” ’ ) ,

0018-9456/94$04.00 0 1994 IEEE

I

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43, NO. 1. FEBRUARY 1994 87

X 0 .84

0.26 0.6 1.0 2.0 4.0

Fig. 2. Plot of the normalized functions of @/amaY(l : @.,/@.,,),,,,,; 2 : Qw~/(@w),~,; 3 : @c/(@c)max) with respect to the normalized ab- scissa X = K p o / ( l i p ) r , , where S is nomalized with respect to (Zip)rL = 1 for function @'u/(@u)max. to (l ip)?& = 1.57 for function @ ' ~ . / ( @ w ) ~ ~ , ~ , . and to ( l ip) , = 1.99 for function @c/(Qc)r,,ax.

where the meaning of each parameter may be obtained from any standard text on microwave engineering. The radiation power density may be determined from the Poynting theorem and is a function of s:

where PO is the maximum power transmitted along the z-axis (po is the maximum power density). It should be mentioned that the second term, JE,J . JH,J, should be taken into account here, since it is a part of the total radiation power exhibited in the gas cell (Harrington ignored this term in his work [ l ] ) . From (8), we obtain

By using numerical methods, it was determined that ( @ w ~ ) , , , ~ ~ M 0.452 at lip0 M 1.57 (noting that we chose: n = 1.0668 cm, b = 0.4318 cm, and FO = 24.923 GHz). See @W ( X ) / ( @ W ) " , , ~ in Fig. 2, where the abscissa is normalized with respect to lip0 = 1.57, and the ordinate is normalized with respect to (@w )may = 0.452. Thus, for a nonresonant rectangular waveguide gas cell,

(rO)max = 0.452. n. (13)

Therefore, the "power saturation" technique involves searching for (ro ),,,, and this is achieved in practice by adjusting the incident power to the gas cell while monitoring the signal from the crystal detector S (which is proportional to r [I , 3]), until a maximum signal S,,, is obtained.

Since the power saturation coefficient li varies with the mean time between molecular collisions T (which itself varies with very many factors including the partial pressure of each gas in the gas mixture), so will @(lip, 1. Thus, it is generally necessary to search for (ro )max at each measurement. However, provided that the variation in the power saturation coefficient, li, is such that @(lipo) remains approximately constant, it is unnecessary to search for a maximum signal at each measurement. This would greatly simplify the operation of a microwave spectrometer employing this technique, as it would enable the instrument calibration to remain independent of variations in T.

11. FUNCTION * ( l i p o ) IN A RESONANT

The radiation fields in a resonant rectangular waveguide cavity of RECTANGULAR WAVEGUIDE CAVITY

length L are (TElo9 mode):

E, = 0 E, = Eo. sin(.rri/n). ?in(q.rrz/L) E; = O H , = - j (qEo /wpL) . sin(.rrs/a). cos(q.lrz/L) H , = 0 H , = j ( E o ~ / ~ p a ) ' c o s ( x s / a ) . s in(qnz/L) .

The radiation power density is then a function of I and 2:

p(s, z ) = { [po . sin2(.rrs/n). s i n ( 2 q n z / ~ ] *

+ [(poL/qn). sin(2.rrx/a) . sinZ(qnz/~)12}1'2

{ ( I E Y I . lHr1)2 + (IEYl. lH*1)2}1/2

. sin2 ( q . r r z / ~ ) I ) ' I 2

ix { [ P O . sin2(n.r/n) . s i n ( 2 q . l r z / ~ ] ~ + [ (PoL/qn) . s in(2sr /a )

(14)

where PO is the maximum power transmitted along the z-axis @O is the maximum power density). From (8), we obtain

@ =

By using numerical methods, it was determined that (@r)max M 0.43 at l i p , M 1.99. See @c(X)/(@c)n,ay in Fig. 2 (noting that in the practical system we chose: q = 20 and length L M 14.58 cm), where the abscissa is normalized with respect to l i p 0 = 1.99, and the ordinate is normalized with respect to (@c)max = 0.44. This illustrates that peak @< ( l ipo) is slightly broader than the peaks @,(l<po) and *w(lipo), and across the range of X x 0.7 to 1.8, i.e. l i p 0 M 1.4 to 3.6, the value of (+c)max remains approximately constant given that it varies by less than 3%) across that range. As stated earlier, provided that the variation in K is such that this range is not exceeded, then it would be unnecessary to search for ( (equal to 0.44. n in this case) at each measurement.

111. SPECTROMETER SYSTEM

Fig. 3 shows a schematic diagram of the cavity spectrometer system which employs a triple modulation technique. A varactor-tuned Gunn oscillator is used as the radiation source, and its power output is varied by a precision attenuator. The microwave source is frequency-double- modulated by means of a sweeping signal (of frequency f l = 300 Hz) and a relatively high-frequency sinusoidal dither signal (of frequency f2 = 200 kHz), such that the microwave frequency is swept around a preselected cavity gas cell resonant frequency F, which is contained within the profile of one of absorption peaks of the analyte gas. At the same time, a low-frequency modulation such as Stark [4] or cavity modulation (of frequency f3 = 30 Hz) is applied in the cavity gas cell. Thus, the electrical signal from the crystal detector comprises low-frequency components (around f l and around A) and high frequency components (around f 2 ) in addition to a d.c. component. It is the high-frequency components, i.e. those resulting

88 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT. VOL. 43, NO. 1, FEBRUARY 1994

mvaguide - pipe line --t signal/control line

air-I-1 filter cylinder pk control

Ilicrocoquter

*msignal 1 Fig. 3. A schematic diagram of the cavity spectrometer system.

I 4.##_(

2.w

6.86

-2. OH

I I I 1

H 8.25 16.5 21.75 33

A time-domain representation of the AM signal. T i n e (IS)

Fig. 4.

from the application of the high-frequency (f~) dither signal, which are of interest; therefore, a band-pass filter is used to extract those frequency components. The output of the band-pass filter is an AM signal with a carrier frequency f2, as in Fig. 4. A Fourier analysis of this AM signal shows that the signal consists of the following frequency components, fz, fz * f 1 , f2 f f l f f3, fz f f l f 2f3, . . ., and so on. Only components fz f f~ f fs are of interest, since these contain the relevant information regarding the amount of power absorbed by the analyte gas in the cavity gas cell. In other words, the fs (30 Hz) signal bearing the salient information of gas absorption is carried by the f2 (200 kHz) camer signal. This salient information is then extracted by means of a series of demodulators and tuned amplifiers.

1200-

PO0 -

600 -

40 60 60 70 80 pressure (Pa.)

Fig. 5. outlet pressure of the cavity (note: EO = ethylene oxide).

This shows the output signal with respect to various values of the

More detailed description of the operation of the spectrometer system has been given somewhere else [5, 61.

IV. EXPERIMENT

In order to construct the resonant cavity gas cell, we adapted a piece of waveguide by inserting a diaphragm and adding a tunable short circuit to form a cavity (of total length N 14.58 cm). For ease of gas cell construction and accurate radiation field configuration in the gas cell, we have chosen cavity modulation in our initial experiments. The cavity modulation is implemented by oscillating the position of the tunable short circuit, and hence, its resonant frequency F,. This is achieved by means of a piezoelectric positioning translator (mounted between the short circuit and a screw micrometer) which converts applied high voltages into mechanical displacements.

In order to measure the coefficient r at the center frequency of one of the absorption peaks of ethylene oxide gas, i.e. at FO = 24.923 GHz, the resonant frequency of the cavity was centred upon a single position at F j % 24.943 GHz (i.e. 20 MHz from the center of the absorption peak) by carefully adjusting the position of the short circuit using the screw micrometer. The cavity resonant frequency was then oscillated (at f3 = 30 Hz) about F, over a range of f 2 0 MHz which covers approximately half the profile of the absorption peak through the action of the piezoelectric positioning device. As a result, the output signal from the crystal detector is proportional to the coefficient r [ l , 31.

Pure ethylene oxide gas was introduced into the gas cell while the outlet pressure of the cavity gas cell was set to 50 Pa, and the incident microwave power to the cavity was adjusted between approximately 0.1 mW and 2 mW (measured outside the cavity and 709, coupled into the cavity at F, ), until a “range” was observed over which the output from the lock-in amplifier remained approximately constant. The incident power was subsequently fixed at an appropriate value within this range (approximately 0.5 mW in this case). Two procedures of the experiment were undertaken: (1) increasing the pressure of the sample by adding air, and (2) increasing the pressure of the sample by adding pure ethylene oxide while recording the signal from the lock-in amplifier, as shown in Fig. 5, i.e. the signal from the lock-in amplifier with respect to various values of the outlet pressure of the cavity. In the former case, as was expected, the signal remains approximately constant. In the latter case, the signal is approximately linearly proportional to the pressure, and hence, gas concentration, N. Having analyzed the data, it was found that there was a linear relationship between the output signal and the concentration to within a standard deviation of 4%.

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43, NO. 1 , FEBRUARY 1994 89

V. CONCLUSION

The objective of the first phase of the work, namely, to test the feasibility of applying the power saturation technique in a microwave cavity spectrometer, has been achieved. A relatively good linear correlation between the output signal and the concentration of ethylene oxide gas to within a standard deviation of 4% was found. Further work is being carried out in order to expand the dynamic range of the measurement and determine the detection limits of the spectrometer.

ACKNOWLEDGMENT

The authors express their gratitude to the Medical Devices Direc- torate of the Department of Health, U.K., who supported part of this project although the views expressed in this paper are those of authors and not necessarily those of the Medical Devices Directorate.

REFERENCES

H. W. Harrington, “On the separation of the broadening-relaxation time and molecular concentration from pure-rotational spectroscopic intensity data,” The Journal of Chemical Physics, vol. 46, pp. 3698-3703, 1967. H. W. Harrington, “Intensity law for microwave spectroscopy: theoret- ical and experimental,” The Journal of Chemical Physics. vol. 49, pp.

G. F. Crable and J. C. Wahr, “Power saturation of microwave line intensities,” The Journal of Chemical Physics, vol. 5 1, pp. 5 181-5 182, 1969. C. H. Townes and A. L. Shawlow, Microwave Spectroscopy, New York: Dover, 1975, ch. IO, pp. 248-283. Z. Zhu, C. Gibson, A. H. Samuel and I. P. Matthews, “Microwave cavity spectrometer for process monitoring of ethylene oxide sterilization,” Review of Scientific Instruments,ol. 64, pp. 103-108, 1993. Z. Zhu, C. Gibson, A. H. Samuel and I. P. Matthews, “Triple modulation technique applicable to microwave spectrometers with cavity gas cell,” in IEEE Proc.-H Microwave. Antenpropagat., vol. 140, pp. 141-143, 1993.

3023-3035, 1968.

A Microcomputer-Based Video-Pattern Generator for Binocular Vision Test

M. S . Obaidat, Senior Member, IEEE, and D. S. Abu-Saymeh

Abstract-This paper presents a hardware and software system for the generation of video patterns that can be used for various vision tests, particularly depth perception. Among the capabilities of the system is generation of static and dynamic random dot stereograms that can be used to test depth perception. The system generates the patterns in real time which provides the capability of moving the objects in the stereogram. This feature is very useful in testing depth perception among infants and noncommunicative people by correlating the movement of the eye with the movement of the object. The other patterns am the checkerboards, vertical and horizontal bars with a capability to sweep the size of the checkers and bars. These latter patterns are useful for testing vision acuity. The system is based on the TMS34010 graphics processor and is connected to a host computer through an RS-232C serial communication port. It has an RGB video output for connection to an RGB color video monitor to display the various video patterns. The application and system software is written in assembly language which is efficient for real-time applications.

I. INTRODUCTION

The eye is one of the most important parts of the human commu- nication sensors. In fact, it determines more than 50% of the data captured by the human being. The eye is responsible for recording images that surround the human being which are further analyzed by the brain to recognize various objects in the image. A person with normal vision can perceive depth from the difference in the view of the two eyes (stereoscopic vision or stereopsis). However, some people with certain visual defects lack the ability to perceive depth. It is essential that such a defect be discovered early for corrective surgery to be possible [1]-[4].

Previous studies used computer-generated images to test the vision system. Julesz and Hesse [5] studied the inability of some people to perceive the direction of rotation movement of line segments. Fox et al. [6] described a simple and primitive system which is used to test stereoscopic depth perception. The method is based on attracting the infants’ attention through movement of a stereoscopic contour formed from a dynamic random-element stereogram. Tessman [7] discussed the methods to form stereo perspective projections and how to implement them in software on a very high-speed and costly workstation.

The study of stereogram generation has been attractive to re- searchers. Julesz and Johnson [8] devised an algorithm to generate a single stereogram for two or more surfaces. Julesz [9] described a method to scramble text. When the images are viewed monocularly, text is seen clearly, while when they are viewed binocularly, nothing is seen. Furthermore, he discusses the suppression of monocu- larly perceivable symmetry during binocular fusion. Wixson [IO] proposed a stereoscopic workstation for visualizing transparent three- dimensional volumes of data. Mizuno [ l l ] described a system in which the stereogram images were displayed on two CRT oscillo- scopes (each eye views one of the images). This system is not efficient

Manuscript received May 19, 1992; revised March 19, 1993. This work was supported by Transoft 32 Ltd. and MRAA under grants Nos. C-6-29645 and MRAA #202.

The authors are with the Department of Electrical Engineering, The City University of New York, The City College, New York, NY 10031.

IEEE Log Number 9216617.

0018-9456/94$04.00 0 1994 IEEE