Optical direct analog-to-digital conversion for microphones

Hitoshi Mada and Katsuo Koide

Acoustic pressure is directly converted to a parallel 3-bit binary code using optical interference. Since thediaphragm deforms sinusoidally when pressure is applied, the interference is different from point to pointon the diaphragm. We simultaneously detected the interference intensity at an adequate sampling of threepoints. A quantized bit plane is produced in parallel without scanning. The dynamic range is ±240 Pa, andgood linearity is obtained. This method can be used to measure other quantities such as temperature andvoltage.

1. Introduction

The optical sensor using a fiber or an electroopticdevice is becoming a useful tool in the field of metrology.Its usefulness is based on the fact that an optical signalis not influenced by electromagnetic noise. In mostcases the data so obtained are processed by computer.The signal must be converted to the digital mode usinga conventional electronic analog-to-digital converter(ADC). If the sensor incorporates the function of A/Dconversion, a separate converter is not needed and thecost is reduced. On the other hand, in the field ofspeech recognition and so-called digital audio, a high-rate ADC is necessary and a low-cost digital microphoneis available.

Recently, optical A/D conversion was reported.1 2

King and Cebulski achieved A/D conversion using aguided-wave Mach-Zehender interferometer.2 Byconnecting the optical ADC to the optical sensor, apurely optical-digital sensor is created. This sensor canbe connected directly to the digital computer. How-ever, such a sensor is difficult to construct, and, to thebest of our knowledge, practical models have not yetbeen made.

In this paper we propose as a more practical approachthe optical direct A/D conversion of acoustic pressureand report a preliminary study of its application to themicrophone. Since the structure of the microphone isvery simple, construction cost is considerably reduced.Such a digital pressure sensor or microphone should beuseful not only for metrology but also for audio andspeech recognition.

The authors are with Tokyo University of Agriculture & Technol-ogy, Faculty of Technology, Department of Electronic Engineering,Koganei, Tokyo 184, Japan.

Received 3 June 1983.0003-6935/83/213411-03$01.00/0.© 1983 Optical Society of America.

II. Principle of Optical-Direct A/D Conversion

Figure 1 shows the schematic optical system for directsensing and A/D conversion of acoustic pressure. Anexpanded and collimated laser beam projected throughthe half-mirror is reflected from the reference plane andthe diaphragm. The reflected beams interfere witheach other and are detected by the photodiode array.The diaphragm is deformed by applied acousticalpressure. If the pressure is small enough, the dis-placement of the diaphragm is sinusoidal. We repre-sent the unperturbed gap between diaphragm and thereference plane as d. The displacement of the dia-phragm un is different from point to point. The in-terference intensity I,, is given by

ri+ r2 - 2rir2 COS - (d - un)In = Io, (1)

1+rr2- 2r1r2cos - (d - u.)

where Io and X are the intensity and wavelength of theincident light; r1 and r2 denote the amplitude reflec-tivity of the diaphragm and the reference plane, re-spectively. To apply this repetitive function of un toA/D conversion, the repetition must be equiperiod atadequate threshold level. If the threshold is taken ashalf of the maximum intensity, finesse = 2. Therefore,the reflectivity must be -27%3 taking some absorptioninto account.

The maximum displacement ul, (n = 1) occurs at thecenter of the diaphragm. The quantities u2 and U3 arethe displacement at the respective points where a halfand a quarter of the displacement of ul occurs. Theinterference intensity In at each point is given ap-proximately in Fig. 2 for r2 = r2= 0.27. If we quantizethem with the threshold level at half the maximum in-tensity, a parallel binary-coded signal is obtained(dashed line in Fig. 2). The signal I1 behaves as theleast significant bit.

1 November 1983 / Vol. 22, No. 21 / APPLIED OPTICS 3411

D

Pressure

U 2 X

12

LI1

Fig. 1. Optical system for direct analog-to-digital conversion formicrophone: HM, half mirror; RP, reference plane; D, diaphragm;

Det, detector (photodiode array).

i ) 1 I

I I I I

L~~~~~~~~~~~~~~~K ~~~~~~~~~~~~II

I ~~~~~~~~~~~~I

I II d I I I I -\ /ll

I I I Il''l'-l

0 1 2 3 4 5 6 7 8 9 10

Displacement of center (A/4)Fig. 2. Displacement of the diaphragm and the interference lightintensity. Solid lines and dashed lines are light intensity and quan-

tized value, respectively.

I11. Experimental

We used the bulk optical system for certification ofthe A/D conversion. The light source, 632.8 nm of aHe-Ne laser, is expanded and collimated. The half-mirror with 30% reflectivity is used as the referenceplane. The diaphragm, a glass cover for a microscopeslide, is 0.16 mm thick and 20 mm in diameter with a20% reflective coating. The detector has thirty-twophotodiodes with parallel output. The sinusoidal in-terference light was converted to the electric signal andquantized by a Schmitt trigger circuit. For simplicity,we measured static pressure to evaluate linearity andresolution of this system.

IV. Results and Discussion

The interference intensity and quantized signal weremeasured by applying static pressure on the diaphragm.Figure 3 shows the pressure dependence of the lightintensity. The interference periods 12 and I3 are twoand four times that of I,. This agrees qualitatively withFig. 2. However, the visibility decreases with increasingpressure. This is particularly true for I3 and can beexplained as follows: when the diaphragm deforms, thereflected beam from the diaphragm shifts from the re-flected beam from the reference plane shown in Fig. 4.If the shift s goes outside the photodiode width (0.585mm), we cannot detect and measure the interference atthe point.

The displacement of the diaphragm is given by

U = Umaxos X,2r

(2)

where r is the radius of the diaphragm. Then shift sis

s = (L-u) tanO = (L-u) tan V rj7- 12r M 21 (3)

where L is the distance between diaphragm and detec-tor. When u is much smaller than L and also 0 << 1, Eq.(3) becomes

Z

D °

C)54

anj01 -3_0

0

150.0

41-2 i.. . :.1-

1 * . . .n~~~~~~_

40 80 120 160 200 240 280Pressure ( Pa)

Fig. 3. Pressure dependence of the interference light intensity.

S = Lr V-U7- _

Incidentbeam

Position of.-detector

Diaphragm

Umax

0

L

-Shift sHJ

flectedbeam

L -x r

Fig. 4. Shift of the beam reflected from the diaphragm.bols are in the text.

3412 APPLIED OPTICS / Vol. 22, No. 21 / 1 November 1983

I. \

(4)

The sym-

l l By

. ,L

l

I

I I

I .. 1% -\-I\-

.V

v(

ll110

, 101- 100.i- 011

01c 001

C 000I

Mwof

. Ir

WI1-1

eL l

) 40 80 120 160 200 240Pressure ( Pa)

Fig. 5. Linearity of the 3-bit binary code.

Assuming n-bit resolution, umax can be replaced by2nX/4 and u by X/4. The intensity corresponding to thepoint u is the most significant bit. Finally, the shiftis

LirXLar Adnd 1 (5)8r

To measure the correct signal the shift must be smallerthan the width of photodiode w. Thus we obtain thefollowing condition:

LirXW > s =~ 2 8 (6)

8r

In our setup the distance L was -50 cm, r = 10 mm, w= 0.585 mm, and X = 632.8 nm. Substituting thesevalues into the above condition, one obtains 2n < 47.The maximum resolution is 5 bits in the conditions ofthis experiment.

The initial phase of each interference beam is notcompletely in phase with the others because, in thepresent setup, the glass cover is not sufficiently flat.

The quantized binary 3-bit data are shown in Fig. 5.The pressure dependence remains linear up to 240 Pa,and the minimum detectable pressure is 30 Pa. In thepresent data the measurable pressure range is higherthan the acoustic pressure range (-10-3 - 10 Pa). Thesensitivity is restricted by the characteristics of the di-aphragm: material, thickness, and stiffness. One caneasily change the measurable range by using a dia-phragm made of another material. The bit numberdetermines the dynamic range (or resolution); theacoustic dynamic range is 104 (80 dB) as describedabove. Thus, we need to apply at least 10 bits (corre-sponding to 60 dB) to the actual microphone. To ob-tain the 10-bit resolution, distance L must be <23 mmaccording to Eq. (6). It is possible to obtain a distanceof <23 mm.

In this preliminary experiment we measure the staticpressure. But for acoustical sensitivity the frequencycharacteristic must be considered. The acousticalsensitivity of a conventional stiffness-controlled mi-crophone is expressed as

V F U VP P F U

where the quantities P, F, U, and V are pressure, driv-ing force, displacement of the diaphragm, and voltage.

The first term denotes an acoustic-mechanical con-version and does not depend on the frequency f. Thesecond term is also independent of f below the me-chanical resonance frequency of the diaphragm fo. Sothe final term, which is a mechanical-electrical con-version must not depend on f.

The acoustic sensitivity of our optical microphone canbe

V. F U., I V.P P F U,, I,,

(8)

The first and second terms are the same as Eq. (7) anddo not depend on f. The third term is given by Eq. (1)and is also independent. The upper limit of responseis governed by the time it takes for light to pass throughthe diaphragm to the detector. The frequency char-acteristics of the final term depends on those of thephotodiode and Schmitt trigger circuit. These re-sponses are sufficiently higher than fo. The frequencyresponse of this microphone depends only on the me-chanical properties of the diaphragm. Flat frequencycan be obtained ranging from static pressure to o.

We used multibeam interference in this experiment.This method restricts the reflectivity of the diaphragmand the reference plane, as mentioned before. A Mi-chelson interferometer more conveniently upgrades theresolution: (1) the reflectivity of the diaphragm can beset at unity; and (2) the distance between the diaphragmand the detector is shortened.

This A/D conversion can be used for sensing tem-perature, voltage, and any other quantities whichsinusoidally deform a diaphragm.

V. Conclusion

We have proposed and demonstrated a new type ofpressure sensor applied to a microphone using opticaldirect A/D conversion. The linearity holds to ±240 Pawith the glass-cover diaphragm, and a 3-bit binary codewas developed. More effort is necessary to improve thesystem, especially the resolution.

References1. A. Armand, A. A. Sawchuk, T. C. Strand, D. Boswell, and B. H.

Soffer, Opt. Lett. 5, 129 (1980).2. G. D. H. King and R. Cebulski, Electron. Lett. 18,1099 (1982).3. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford,

1975), Sec. 7.6.

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