Incoherent optical heterodyne detection and its application toair pollution detection

Yoichi Fuji!, Jun-ichiro Yamashita, Susumu Shikata, and Shigebumi Saito

Fundamental problems of incoherent optical heterodyne detection are analyzed. Output of the heterodynedetection depends on the spatial and temporal coherences of incoming incoherent signal light on the photo-detector surface. The directivity of optical heterodyne detection is concluded to be the same as with thatof direct detection in an ideal case in which the image of the object is well focused on the photodetector sur-

face. This incoherent heterodyne detection is applied to air pollution monitoring. In the laboratory, theabsorption spectra due to NH 3, Freon, and SF6 are measured using an incoherent light source, and the con-centrations of each gas were determined by using the least-squares method.

Introduction

The spectroscopic air pollution detection methodusing a passive radiometer has been reported by manyauthors.1-1 0 It is a simple and practical method to re-alize.

Optical heterodyne detection of coherent light hasbeen studied by Siegman," Yura,12 and ourselves13since 1966, and its properties have been analyzed indetail. Incoherent heterodyne detection is applied tothe ir radiometer as mentioned before, but its opticaland electrical properties are not yet known. Quanti-tative agreement between theory and the experimentdoes not exist.

In this paper, the properties of incoherent heterodynedetection are analyzed, and an explanation of theproperties, considering diffraction and aberration of theoptical system, is obtained.

A radiometric system using the incoherent hetero-dyne signal, including a tunable CO2 laser and ascanning telescope, is realized. In this system, we madeuse of triple optical chopping, which compensates forthe error due to the shot noise of the signal and thecurrent noise of the photodetector.

Several kinds of pollutant gas were analyzed byscanning the frequency of the tunable laser as a localoscillator. The measured absorption spectra were

The authors are with University of Tokyo, Institute of IndustrialScience, 22-1, Roppongi 7 Chome, Minato-ku, Tokyo 106, Japan.

Received 11 March 1978.0003-6935/78/1101-3444$0.50/0.© 1978 Optical Society of America.

processed by the least-squares method, and concen-trations of each gas were obtained.

Analysis of Incoherent Heterodyne Detection

Theory of Incoherent Heterodyne Detection

First assume a small area on the photodetector sur-face. Signal amplitude is a random signal as(rt), whilethe local oscillator radiation is sinusoidal aL(r) exp(iwt).Defining the heterodyne detection amplitude h(r,t) asa product of as and aL,

h(r,t) = as(rt)aL(r) exp(iwt). (1)

The ac photocurrent from this small area i (r,t) is pro-portional to the heterodyne detection amplitudeh(r,t):

i(rt) ?hl rA, (2)

where X7 is the quantum efficiency of the photodetector.The total photocurrent I from the output terminal ofthe photodetector is given by the surface integral ofphotocurrent from the small area

I(t) = r i(r,t)d2r,fSD

(3)

where SD is the area of the photodetector. The timeaveraged i.f. power P is defined as

P = lim TSf TRLI2(t)dt

=K lim 1 T [f h(r,t)d2r 2 dt,2T .J-TLSS 6

(4)

where K is a photodetection constant including the loadresistance RL. This integral reduces to a double inte-gral if the signal is ergodic as

3444 APPLIED OPTICS / Vol. 17, No. 21 / 1 November 1978

P=KfJ' lim- h (rit)h(r2,t)dtd 2rid2r2

= K J C(r1,r2)d2rid2r2, (5)

where the spatial correlation function C(rl,r2) has beendefined as

C(rl,r2 ) = lim T h(rj,t)h(r2,t)dt. (6)T-__2T iT

This correlation function depends only on the spatialdistribution of the random signal h(r,t) and not upontime. This function is determined from the spatialcoherent properties of the source and the characteristicsof the optical system, such as diffraction and aberration.Since it is impossible to calculate C(r1,r2) in general,we shall restrict ourselves to some special cases.

The coherent area of the blackbody source is assumedto be 2. Because its exact image is usually muchsmaller than X2, the source can be divided into the piecesof the coherent area of source X2. In a practical opticalsystem, the image of the coherent area of source X2 is nota point on the detector surface but defocused to an areaAP. Meanwhile, a coherent area on the detector Ac,which is defined as an area in which the functionC(r1 ,r2 ) is stationary in time and constant, is not equalto AP, but Ac _ AP in general.

The following special cases will be considered:(1) When Ac < AP << SD, as in an ideal optical sys-

tem, the two heterodyne detection amplitudes h (rl,t)and h(r 2 ,t) do not correlate with each other. Then,

C(rir2) = (PSPL)/(SD), (7)

where PL is the total local oscillator power, and theuniform distribution of the signal and the local oscillatorpower are assumed. Thus, the i.f. power P is

P = KPSPL. (8)

In this case, all signals focusing on the detector aretransformed into i.f. power as in coherent heterodynedetection. This photodetector detects the total signalon the photodetector, as in conventional photodetec-tion. Optical detection of the signal in this heterodynedetection is the same as direct detection.

(2) When AP SD and Ac < SD, as in the focusingoptics used in the experiment described below, spatialcorrelation exists across the detector surface, but it hasrandom phase distribution. So C(r,,r2 ) is expressed bya product of two independent phase functions:

C(ri,r2) = (PSPL)/SD) exp[iO (ri) -io(r)]- (9)

The i.f. power P is given by

P = K(PsPL/(S2)D I' SSD exp [i 0 (ri)] exp [-i0(r2 )]d2rjd2r2

2= K(PSPL)/(SD) DS exp [i 0 (r)]d2r , (10)

Since r1 and r2 are independent variables. The integralof Eq. (10) can be estimated when exp [ik(r)I is assumedto be constant within the coherent area Ac as

CrI\1J~2_2 Ac S| EDexp [i (r)] d2r -D-

p SDe I SD

Thus, iUf power P is

(11)

P = KPSPL (AC/SD). (12)

(3) When AP > SD and Ac > SD, the i.f. power be-comes the coherent heterodyne detection case, afterreducing the effective signal power to PSSD/Ap.Then,

P = KPSPL(SD/AP)- (13)

(4) When AP < SD and Ac << SD, Ac has minimumvalue due to the dipole interaction of the detectormolecules, which is assumed to be X2; then,

P = KPSPL(X2/Ap). (14)

This is the case of phase misadjustment of the localoscillator light.

(5) When AP > SD and Ac << SD, it reduces to case(4), after correction for vignetting. Then,

P = KPSPL (SD/AP) (X2 /SD) = KPSPL ( 2/Ap). (15)

These results are summarized in Table I.

Effect of Aberration and Diffraction of the OpticalSystem

In the previous discussion, the coherent area Ac isdetermined only by the diffraction of the aperture.Assuming a single lens, the radius of the Airy disk rdis

rd = 0.61 fX/a, (16)

where f is the focal length, and a is the aperture radius.However, the defocusing area AP is approximately givenby

AP - 7E (r' + r), (17)

where r is the radius of the circle of confusion due toaberration:

a3 n(4n - 1)f2 32(n - 1)

2(n + 1)

(18)

where n is the index of refraction of the lens.The heterodyne output is schematically shown in Fig.

1, taking into account the effect of aberration and dif-fraction of the optical system. In this experiment, APL 1.4 X 10-2 mm2, Ac 6.9 X 10-3 mm 2 , and SD +X 10-2 mm2 . Thus case (2) gives the best approxima-tion. Experimental results for a Ge lens, with focallengths 50 mm and 10 mm, agree well with the theo-ry.

Air Pollution Monitoring by Incoherent Heterodyne

Experimental Heterodyne Detection System

In the experimental system, schematically shown inFig. 2, the local oscillator is a tunable CO2 laser (GTESylvania model 950), and a HgCdTe photovoltaic de-tector (SAT PV-1130), with 50-MHz bandwidth is used.The i.f. amplifier has 70-dB gain, 2.5-dB noise, and500-MHz bandwidth (Avantek AD 502 and GPD 401X 3).

1 November 1978 / Vol. 17, No. 21 / APPLIED OPTICS 3445

I

41-i

u)

0H H

E-

.,4

4J

Cd 0

u

rH 0 rH

ci) 0

14

cia)

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a,

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0 0

4-,

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a, .r-4

0

o

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U)U

0_ ) ., ..

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.i uC *

UU

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3446 APPLIED OPTICS / Vol. 17, No. 21 / 1 November 1978

S Ua

U,

U,

C.

Q

-

-

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_ oper ment o /theory- -

... Ic 1

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len pre.

f-5Om

- tpe Imet

Since the i.f. output contains the heterodyne detectionoutput, shot noise from the signal and the local oscillatorand the noise from the photodetector itself follows therelation:

PSI = T - Phet + YPI,

PIII = Phet + YPIV,

(19)

(20)

0 20

len pre.

Fig. 1. Incoherent heterodyne detection output as a function of thelens aperture.

Fig. 3. Photograph of the experimental radiometer by incoherentheterodyne detection.

'from chopper

Fig. 2. Experimental incoherent heterodyne detection radiometer.

In the laboratory, the 1200-K gas heater is used as thelight source. The i.f. output is detected by a lock-inamplifier (NF LI 573) (Fig. 3).

Triple Chopping to Compensate for Current Noise in thePhotodetector

The noise output from the HgCdTe photodetector,including shot noise from the incident light and currentnoise in the semiconductor, varies nonlinearly with thetotal detector current as shown in Fig. 4. To compen-sate for this noise and also the shot noise in the signal,a new chopping system, in which signal, local oscillator,and bandpass filter in the signal circuit are chopped isproposed. The i.f. power in four phases of the choppingoutput are given as:

PI : Only the signal with a narrow bandpass ir filtercentered at 10.6 Aim;

PI, : the signal with the filter and the local oscilla-tor;

PI,,: the signal without the filter and the local os-cillator;

PIV only the signal without local oscillator (see Fig.5).

~~~~~1 ~~~~~~o / ~ ~~~~ i .. -ee

I o~~~~~~~~- ...

IInis

TOTAL CURRENT OF DETECTOR

Fig. 4. Total noise from the HgCdTe photodetector as a functionof the total current including the biasing current and photocurrent

A NEW TRIPLE CHOPPING SYSTE

WHICH CHOPS

1. SIGNAL

2. LOCAL

3. BANDPASS FILTER TO THE SIGNAL

Helero- Shtoise Shot.oise E cess|dyne i signa in locO Nise

PI

ITO

_ - Y

het III PIV PI-TFPlI _-FO 1V

re Tf i tantAac of the fiZt.r at 10.6 pm

y i ooeffiient

Fig. 5. Four phases of the triple chopping system.

1 November 1978 / Vol. 17, No. 21 / APPLIED OPTICS 3447

E

I

110-

1o-4

lo0-6

where Phet is the i.f. heterodyne detection output, Tfis the transmittance of the filter at 10.6 gim, and y is acoefficient depending on nonlinear excess noise char-acteristics as shown in Fig. 4.

-Y = (P1 - TfPii,)/Pi - TfPlv), (21)

then the i.f. output of heterodyne detection Phet is ob-tained by properly designed electronics

Phet = PIN - YPIV. (22)

10.2 10.3 10.4 10.5 10.6 10.7 l0.8WAVELENGTH (pm)

Fig. 6. Spectra of SF6 , CCl2F2 (Freon), and NH3 gases.

SF6

10 - 10Ojj) 0-- 0o

I I) - 10

1 1 ) , - I0

Vul

R2P R 0

2 2

300

300

7H

700

ppm-m

pp.-.

pp. -.

P0 P20 P30 (Branch)

10.2 10.3 10.4 10.5 10.6WAVELENGTH Gpm)

10.7 10.8

Fig. 7. Spectra of the gas mixture.

(a)

SE6

K0 0 '/0

F reon,/

/ NH3 //

*1

(b) (c)

Experimental Results

Using the experimental setup shown in Fig. 2, theconcentrations of SF6, Freon (CCl2 F2 ), ammonia (NH3 ),and their mixed gases are measured.

The measured absorption coefficient of each gas isshown in Fig. 6. An example of the spectrum of themixed gases is shown in Fig. 7. Most probable valuesof the concentration of each gas are calculated by theleast-squares method.

In this experiment, the test gases are sealed in a cellwith a polyethylene window, with 0.3-m optical path atatmospheric pressure. Gas concentration values by theleast-squares method agree well with the partial pres-sure of the gas content. And no value is affected by theexistence of other gases. However, when the spectraof the component gases have high correlation, consid-erable error occurs. Figure 8 shows the normalizedconcentration. For each of the cases in Fig. 7, Fig. 8(a)shows the interference error due to the correlation be-tween spectra. Figures 8(b), 8(c), and 8(d) show theresults of the same calculation assuming the gas, whichis not shown in the figure, does not exist. Because thespectra of NH3 and Freon gases have high correlation,the error appears, for example, in Fig. 8(c) of case (2).

Finally, the linearity of this measurement is not jeo-pardized by the interference of the coexisting gas, asshown in Fig. 7.

Conclusion

The effect of spatial correlation of the incoherentheterodyne is analyzed, taking aberration and diffrac-tion into account. This theory agrees with the experi-mental results. Novel triple optical chopping is pro-posed to eliminate shot noise in the signal and currentnoise from the photodetector. The experimental ra-diometer, with incoherent heterodyne detection, canmeasure thermal radiation of 38 C. This system isapplied to air pollution gas measurement. Concen-

(d)

Fig. 8. The effect of the interference due to thecoexisting gas in the gas mixture. The figure on theleft shows the results of the calculation of the con-centration of each gas taking into account threegases. The three figures on the right show the re-sults when only two kinds of gases mentioned in the

figure are taken into account.

(EFFECT OF INTERFERENCE ERROR)

Freon ' *--. -/X

/, I'I

'NH' 3. 0.0

A_ _ _ - _X

I) II) iII) I) ii) III) I) II) III) I) ii) IIi)

G A S M I X T U R E S C A S E N U M B E R

3448 APPLIED OPTICS / Vol. 17, No. 21 / 1 November 1978

-: lo'

t!

,, I

S

I:

I1 -

Io-2

-

1.0

0.0

I 1 1.

,__ __ I -r-I

I

/

400 -

5 300

c

200 -I

2 00

I:

01

0

0

0 100

STO t CH I OMETR I C

E

,4 0 '

IsI

I

-2 0 tlII2IIII

200 300 400 500

FREON CONCENTRATION (Ip-m)

Fig. 9. The effect of the coexisting gas on the results of the concen-tration, for example, CCl2 F2 (Freon), while the concentration of SF 6

is kept constant.

trations of the gas mixture, for example, 800 ppm-m ofNH3 , 10 ppm-m of SF6 , and 300 ppm-m of Freon, weredetermined separately using the least-squares methodwith 10% error.

References1. R. T. Menzies, Opto-electronics 4, 179 (1972).2. R. T. Menzies, Appl. Phys. Lett. 22, 592 (1973).3. R. T. Menzies and M. S. Shumate, Conference on Laser Engi-

neering and Applications (CLEA) (OSA/IEEE, Washington, D.C.,1975).

4. J. H. McElroy, Appl. Opt. 11, 1619 (1972).5. B. J. Peyton, A. J. DiNardo, S. C. Cohen, J. H. McElroy, and R.

J. Costes, IEEE J. Quantum Electron. QE-il, 569 (1975).6. J. Gay, A. Journet, B. Christophe, and M. Robert, Appl. Phys.

Lett. 22,448 (1973).7. B. Christophe and D. Camus, Conference on Laser Engineering

and Applications (CLEA) (OSA/IEEE, Washington, D.C.,1975).

8. S R. King, D. T. Hodges, T. S. Hartwick, and D. H. Barker, Appl.Opt. 12, 1106 (1973).

9. H. J. Raterink, H. v. d. Stadt, and H. J. Frankena, "RemoteHeterodyne Detection Techniques to Measure Air Pollutants,"International Council of Quantum Electronics, 1976.

10. M. C. Teich, Proc. IEEE 56, 37 (1968).11. A. E. Siegman, Proc. IEEE 54, 1350 (1966).12. H. T. Yura, Appl. Opt. 13, 150 (1974).13. Y. Fujii and H. Takimoto, "Imaging Properties due to the Optical

Heterodyne and its Application to Laser Microscopy," Inter-national Council of Quantum Electronics, 1976.

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continued on page 3481

1 November 1978 / Vol. 17, No. 21 / APPLIED OPTICS 3449

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