Detection of deep-red low-level light pulses

Ralph Burnham and Donald Scarl

Detection of light pulses with high reliability (missed and false pulse probabilities of <10-4) by the bestavailable detectors is shown to require detector current pulses containing at least thirty-three electrons. Fordeep-red (900-nm) light, this requires light pulses containing at least 660 photons. A large area (5.1-cm2)avalanche photodiode has been evaluated and has been found to be comparable with photomultipliers fordeep-red pulse lightwave communication.

1. Introduction

The detection of low-level light pulses can best bedescribed in terms of single photon events. A singlephoton striking a detector can produce at most a singleelectron. This electron, after amplification, gives riseto a current pulse; the number of current pulses isproportional to the number of photons in the originallight pulse. Detection can be done either by countingsingle-photon pulses or by collecting all the chargeproduced by the light pulse, in which case the amountof charge is proportional to the number of photons inthe original light pulse. Commercial amplifiers, dis-criminators, and pulse height analyzers designed formeasuring gamma ray spectra are optimized for chargepulses with lengths near 1 is and are useful for theanalysis of low-level light pulses. We have calculatedthe minimum size of microsecond light pulse requiredfor a dark noise limited lightwave communication sys-tem with a given missed pulse probability and falsepulse probability. We have measured the noise pulseheight spectrum of a large area avalanche photodiodeand have shown that it can be used to detect with highreliability deep-red microsecond light pulses contain-ing -2900 photons.

II. Missed Pulse Probability for Noiseless Detectors

Light pulses that contain, on the average, (n) pho-tons, will show fluctuations in the actual number ofdetected photons per pulse. The photon number perpulse will follow a Poisson distribution, extendingfrom zero photons to a large number of photons. Thenumber of detector electrons produced per pulse willfollow a Poisson distribution with a lower average.

The authors are with U.S. Naval Research Laboratory, LaserPhysics Branch, Washington, DC 20375.

Received 19 November 1985.

There is a finite probability of having zero electrons ina pulse whose average electron number is (ni. Forexample, to have the zero electron probability be<10-4, the average electron number must be >9. ThePoisson distribution sets a lower limit on the averagepulse size, given a fixed missed pulse probability andan ideal detector.

Ill. False Pulse Probability

If there is background light or if the detector hasnoise or works into an amplifier with noise, the noiseelectrons set a new lower limit on the average numberof photons per usable pulse. Usually, a detectionthreshold is set to eliminate some of the noise pulses.Since signal pulses producing fewer than the thresholdnumber of electrons will be missed, a given missedpulse probability can be maintained only by increasingthe mean number of electrons per signal pulse.

If the signal pulse repetition rate is R, and the de-tected noise pulse rate is Rn, the false detection proba-bility per signal pulse, P1, is R/R,. For example, witha pulse repetition rate of 100/s and an acceptable falsedetection probability of 10-4, the noise detection ratemust be <10-2/s.

Since most detectors have single-electron noisepulse rates of at least 102/s, single noise electrons mustalways be discriminated against. Worse, pairs, trip-lets, and so forth, of noise electrons generated withinthe detector system time constant T can force thediscrimination threshold still higher. For a Poissondistribution of noise electrons with mean value RT pertime interval (RT<< 1), the single-electron noise rate isapproximately R, the two-electron noise rate is ap-proximately R2T/2, and the three-electron rate is ap-proximately R3T2/6. For example, with a signal pulserate of 102 /s, a noise rate of 2 X 102/s, and a timeconstant of 1 gs, the probability of two-electron noisepulses is 2 X 10-2/s, so that to maintain a 10-4 falsedetection probability, the detection threshold must beat least at the three-electron level.

1514 APPLIED OPTICS / Vol. 25, No. 9 1 1 May 1986

If the detection threshold is set at D electrons, signalpulses producing 0,1,2,. .. D - 1 electrons will not bedetected. For pulses containing an average of (n)electrons, the missed pulse probability is

D-1

Pm = I P(n),0

where P(n) is a Poisson probability distribution with amean of (n). Figure 1 shows, for various values of themissed pulse probability Pm, the minimum requiredaverage pulse size n) plotted as a function of detec-tion threshold D. For example, if the probability ofzero-, one-, and two-electron signal pulses is to be<10-4, an average of fourteen electrons per signal pulseis necessary. If the detector has a quantum efficiencyof 5%, the original light pulse must contain an averageof 280 photons.

The photoelectron and noise electron Poisson distri-butions are converted by the amplification process tosmooth continuous distributions. Although thisspreads the original distributions somewhat, itchanges very little the probabilities calculated fromthe original distributions.

These arguments hold for pulse height distributionsin a system in which microsecond electrical pulses arecreated by charge integration as well as for pulse num-ber distribution in a photon counting system. In fact,they are valid no matter what the signal processingmethod.

IV. Light Pulses

The light pulses to be detected are assumed to have awidth of -1 s. They are centered at a wavelengthnear 900 nm with little wavelength spread. They cov-er a large area so that the detected signal is proportion-al to detector area. The pulse repetition rate is -100pulses/s.

V. Dark Noise

Dark noise can be divided into two categories: (1)detector input noise: noise generated by the detectorbefore any amplification within the detector. (2) am-plifier noise: noise generated by the detector afterinternal amplification or by the amplifier following thedetector.

Detector input noise consists of thermally generatedsingle electrons and electron bursts generated by ions,cosmic rays or detector radioactivity. Amplifier noiseconsists of thermally generated electrons from photo-multiplier dynodes, shot noise generated by dark cur-rent through a detector pn junction, Johnson noise atthe amplifier input, and actual amplifier input noise.

In the case of single-electron noise, amplifier noise,shot noise, and Johnson noise, the noise pulse heightdistribution has a Poisson or Gaussian shape. On thehigh side of this distribution the noise pulse rate is asharply dropping function of pulse height. Since thedetection threshold is always set on the high side of thenoise distribution, a small increase in detection thresh-old leads to a large decrease in noise rate for this type ofnoise.

50

30

.n)20

0 2 4 6 e 10 12 14 10 1 I Threshold

Fig. 1. Required average number (n) of detected electrons perpulse in order to assure a missed pulse probability of 10-3, 10-4, 10-5,

and 106, as a function of the electron detection threshold.

For the larger ion, cosmic ray, or radioactivity noisepulses in photomultiplier tubes, the noise pulse heightdistribution is often wider than the single-electronnoise distribution. For this type of noise, the noisepulse rate falls somewhat more slowly with detectionthreshold.

VI. Detectors

The two candidate detectors for deep-red low-levellight pulse detection are photomultipliers and largearea avalanche photodiodes (LAAPDs). Photomulti-pliers, with their internal amplification of 106 or more,allow a following amplifier with very relaxed noiserequirements. LAAPDs, with internal amplificationof several hundred, place more stringent requirementson the following amplifiers.

A. Photomultipliers

Photomultipliers have high internal gain (>106) butlow quantum efficiency (QE) for deep-red light. Atypical extended red multialkali (ERMA) cathode canbe expected to have a QE of -1% near 900 nm. Themore exotic GaAs cathodes can have quantum efficien-cies of 10% near 900 nm but deteriorate with time andwith photomultiplier operating current. They mustbe cooled to near -20'C to decrease their dark currentto acceptable levels (500 electrons/s). At this tem-perature, the deep-red QE of GaAs cathodes drops toless than half of its room temperature value.

With a QE of 5% and a three-photoelectron thresh-old, a photomultiplier can reliably detect light pulsescontaining an average of 280 photons which produce anaverage of fourteen detector electrons. However,most photomultipliers show a small number (10/s) ofmuch larger noise pulses originating from ions acceler-ated from the dynodes back toward the cathode, fromradioactivity in their glass envelope, and from flashesof light produced by cosmic rays striking the envelope.1These pulses often necessitate a detection threshold inthe neighborhood of fifteen electrons. Taking theselarge pulses into account, with a detector threshold offifteen electrons, a missed pulse probability of <10-4requires an average number of photoelectrons of 33, orfor a 5% QE cathode, an average of 660 photons/pulse.The fast time response of photomultipliers (1 ns) al-

1 May 1986 / Vol. 25, No. 9 / APPLIED OPTICS 1515

. I . I , I . I I at C . I r I

rIE-8

I~

~~~~~~~~~~~~~~

. . . .0

lows discrimination against some kinds of noise pulses(radioactivity, cosmic rays) that are shorter than the 1-gs light signal pulses.

The high internal gain of photomultipliers allowsthem to be combined in large area arrays without af-fecting the performance of the noncritical followingamplifier. When combined, the width of their noisepulse height distribution does not change. The rate ofsingle electron noise pulses increases linearly with thearea of the array, and the number of two- and three-electron noise pulses increases as the square and cubeof the size of the array. By increasing the detectionthreshold the noise rate for a large array of tubes canalways be reduced to fewer than 10-2 noise electronsper second. That is, because of the sharply droppingcurve of noise rate vs pulse height, as the detector areais increased the detection threshold must be increasedonly slightly to maintain the same false pulse detectionrate.

B. Large Area Avalanche Photodiodes

The recent development of large area avalanchephotodiodes2 provides an alternative to photomulti-pliers for the detection of deep-red low-level lightpulses. In an avalanche photodiode, a conductionelectron created by an incident photon is acceleratedby the electric field to a high enough energy to createan electron-hole pair. The original electron and thecreated electron are again accelerated to create addi-tional electron-hole pairs until a charge pulse of sever-al hundred electrons is produced.

LAAPDs have modest (102) internal gain and high(>50%) quantum efficiency for deep-red light. Whileable to operate at room temperature, their optimumworking temperature is probably near -201C. Be-cause of the modest gain of LAAPDs they must befollowed by low noise amplifiers. Commercially avail-able charge sensitive amplifiers are good enough thatthe total noise is dominated by the LAAPD noise andnot by amplifier noise. However, because photodi-odes are high capacitance devices (100 pF/cm 2 ) andcharge sensitive amplifiers have noise levels that in-crease lienarly with input capacitance (see the Appen-dix), the number of LAAPDs that can be connected toone amplifier is limited.

VII. LAAPD Measurements

The measured gain vs bias voltage for a 2.5-cm diamsilicon LAAPD manufactured by RMD, Inc., Water-town, MA, is shown in Fig. 2. The points on this figurewere generated by measuring the diode output pulseheight vs voltage for a 200-,gs 880-nm input pulse con-taining 4.6 X 108 photons. The LAAPD temperaturewas -19'C for these gain measurements.

The diode quantum efficiency can be calculatedfrom the data used to generate the gain curve of Fig. 2.The constant pulse height measured for diode voltagesbetween 200 and 700 V was assumed to correspond to again of one. For this range of voltages, the incidentlight pulse, which delivered 2.3 X 1012 photons/s, pro-duced a diode output current of 2 X 10-7 A, corre-

1 - 19L

1000 1100 1200 1300

bias voltage

dark

current

(to)

400 1500

000 1100 1200 1300 1400 1500bias voltage

Fig. 2. Large area avalanche photodiode gain and dark current vsvoltage.

sponding to a LAAPD quantum efficiency of 54% at880 nm.

The measured dark current for this device at -13'Cis also shown in Fig. 2. From 1 to 1400 V the darkcurrent varies linearly from 0.5 to 1.0 MA. From 900 to1440 V the gain has increased by a factor of 150 whilethe dark current has increased by a factor of only 1.5.This component of the dark current seems not to beamplified by the device gain and may be edge leakagecurrent. It corresponds to a leakage resistance of 1.8 X109 . Above 1450 V the dark current increases as ahigh power of the bias voltage. This can be interpret-ed as ajunction leakage current of -2 nA multiplied bythe rapidly increasing gain. At gains below 150, thejunction leakage current is insignificant comparedwith the unamplified edge leakage current. However,at gains above 150, the amplified junction leakage cur-rent exceeds the unamplified edge leakage current andbecomes the dominant dark current.

The dark noise pulse height spectrum of the RMDLAAPD was measured using an Amptek charge sensi-tive preamplifier with a time constant of 1 Ms and anamplifier noise level of fewer than 300-rms electrons.Pulses from the preamplifier were analyzed by a Da-vidson model 4048 pulse height analyzer. Since thereare a very large number of small pulses (-10 6/s for anamplifier time constant of 1 Ms), the lower level dis-criminator on the pulse height analyzer rejected smallpulses to avoid operating the analyzer with dead timesabove 50%. A plot of the number of pulses per channelvs channel number (pulse height) for a total countinglive time of 10 s/curve is shown in Fig. 3. Curve (a) of

1516 APPLIED OPTICS / Vol. 25, No. 9 / 1 May 1986

T= -13C

6 .

4-

2 4 + 4 *1*

Countsper IE 2

Channel

lE- IIt E 1 . ... ... ... .. . A .1 . 1

0 20 40 60 50 100Pulse Haight

Fig. 3. Pulse height spectrum of charge sensitive amplifier outputwith (a) no detector and (b) large area avalanche photodiode detec-tor. The left-hand side of each curve reflects the pulse height

analyzer threshold setting and not the actual noise spectrum.

Fig. 3 is the amplifier noise distribution with no detec-tor attached. Curve (b) is the noise distribution withthe LAAPD connected and biased at 1 V. The noiseincrease is caused by the -700-pF capacitance of theLAAPD loading the input of the charge sensitive pre-amplifier (see the Appendix.)

Figure 4 shows the LAAPD noise pulse height distri-butions for increasing bias voltage. Again, the count-ing live time per curve was 10 s. At the operatingvoltage of 1440 V the noise is much greater than theamplifier noise and originates in the LAAPD itself.

Figure 5 shows the LAAPD pulse height distributionwhen the diode is illuminated by light pulses contain-ing an average of 2900 photons. These pulses weregenerated by a LED driven by 1-Ms long 1.6-mA pulsesat a 100-Hz repetition rate. The 700-nm LED lightwas collected by a lens, attenuated by a ND3 (3.1 X10-3 transmission at 700 nm) filter, and focused on theLAAPD. The counting time was 100 s.

The thin lines are Gaussian curves fit to the noiseand signal pulse height distributions. The Gaussianfit to the noise pulse distribution has a peak height of 2X 107 counts per channel, is centered at channel zero,and has a halfwidth (standard deviation) of 24 chan-nels. The Gaussian fit to the light pulse distributionhas a peak height of 200 counts per channel, is centeredat channel 220, and has a width of 21.5 channels. With2900 incident photons and a quantum efficiency of-505%, 1450 photoelectrons are generated in the diode.The Poisson width of a 1450 electron curve would beonly six channels, the additional width of the measuredcurve being caused by the diode noise pulse distribu-tion.

A discriminator set at the level of channel 140 woulddetect more than 99.9% of the incident light pulses,while counting fewer than 10-2 noise pulses per second,giving a missed pulse probability of 10-4 and a falsepulse probability of 10-4.

For an array of LAAPDs, the dark current wouldincrease linearly with the area of the array, while thewidth of the noise pulse height distribution wouldincrease as the square root of the area. A small in-crease in detection threshold would compensate forthis increase in noise width.

IE

1 4 4

IE 3Counts

Channel lE 2

ElI

lE0

IE-10 100 200 300 400 500

Pulse Height

Fig. 4. Large area avalanche photodiode pulse height spectra withdetector voltages of 500, 1400, and 1440 V. The left-hand side ofeach curve reflects the pulse height analyzer threshold setting andnot the actual noise spectrum.

12 4 \ T=-28C

I E 3Counts

per 1E 2Channel

IE I

IE

IE-10 00 200 300 400

Pulse Height

Fig. 5. Large area avalanche photodiode pulse height spectrum.The detector was illuminated with microsecond light pulses contain-ing an average of 2900 photons. The points below channel 100reflect the pulse height analyzer threshold setting and not the actualnoise spectrum. The thin lines are Gaussian fits to the noise and

signal distributions.

Vill. Conclusions

The multielectron dark noise spectrum of photo-multipliers requires a high detection threshold toavoid false detection events in a pulsed lightwave com-munication system. The Poisson distribution of sig-nal photoelectrons requires an average of 33 photoelec-trons per pulse to give a missed pulse probability of<10-4/pulse. For a photomultiplier with a GaAs pho-tocathode having a quantum efficiency of 5% in thedeep-red, an average of at least 660 photons per pulse isrequired for a reliable communication system. For anERMA photocathode with a quantum efficiency of 1%,a pulse containing at least 3300 photons is needed.

Large area avalanche photodiodes provide a usefulalternative to photomultipliers in low-light level deep-red communication. We have detected 700-nm lightpulses containing an average of 2900 photons with 10-4missed pulse and 10-4 false pulse probabilities. Thesmall size, good deep-red response, and reliable opera-tion of LAAPDs will make them useful detectors forlow-level deep-red pulsed communication systems.

1 May 1986 / Vol. 25, No. 9 APPLIED OPTICS 1517

Appendix: Charge Sensitive Amplifier

The charge sensitive amplifier is an operational am-plifier (op amp) used to convert charge to voltage.The input of the amplifier remains at exactly 0 V whilethe charge to be measured produces an output voltageby charging a capacitor in the op amp feedback loop.The output voltage is V = qIC, where q is the chargeinput and C is the feedback capacitance. Typicalcharge sensitive amplifiers use a feedback capacitanceof 1 pF, giving a charge-to-voltage conversion factor of1 V/pC.

The output noise of a charge sensitive amplifierdepends on the capacitance from its input to ground.The input noise V,, generated by the input transistor,is very small (it can be as little as the equivalent of 5-rms electrons in a 1-gs pulse). However, the feedbackimpedance Z1 and the input impedance to ground Z2form a voltage divider between the output and theinput of the op amp. When the amplifier output at-tempts to cancel the input noise voltage by producingan output signal V0, only the fraction Z2/(Z2 + Z1)reaches the input. Therefore the output must pro-duce a signal of Vo = -(Z 1 + Z2)Vn/Z2 to cancel theinput noise, leading to an output noise much greaterthan the input noise. For a charge sensitive amplifier,Z1 and Z2 are inversely proportional to the feedbackcapacitance C and the capacitance from input toground C2, respectively. The output noise voltage isthen

V l/cl + /C2 V C1 + C2 V1/C2 C

1

In a typical charge sensitive amplifier, C1 I pF and C2= 50 pF, leading to an output noise voltage 51 timesthat of the intrinsic FET input noise.

When a detector is connected to the input of a chargesensitive amplifier, its capacitance C3appears in paral-lel with the amplifier input capacitance C2, leading toan output noise voltage of

V C + C2 + C3 V.C1

For a charge sensitive amplifier with a V, of oneelectron, a C1 or 1 pF, a C2 of 50 pF, and a detectorcapacitance C3 of 700 pF, the RMD LAAPD wouldcause an output noise voltage equivalent to -750 elec-trons. For a LAAPD with a gain of 100, this wouldcorrespond to a detector input noise of 7.5 electron-s/pulse.

Donald Scarl also holds an appointment with Poly-technic Institute of New York.

References1. R. Burnham and D. Scarl, "Photomultiplier Dark Pulses," Appl.

Opt. 24, 293 (1985).2. G. Entine, G. Reiff, M. Squillante, H. B. Serreze, S. Lis, and G.

Huth, "Scintillation Detectors Using Large Area Silicon Ava-lanche Photodiodes," IEEE Trans. Nucl. Sci. NS-30, 431 (1983).

Patents continued from page 1366

4,548,502 22 Oct. 1985 (Cl. 356-358)Ultra-high sensitivity interferometer.S. CHANDRA and R. S. ROHDE. Assigned to U.S.A. as represent-ed by Secretary of the Army. Filed 20 Dec. 1984. Continuation ofSer. 398,179, 14 July 1982, abandoned.

This patent describes a method for increasing the sensitivity of a Michelsoninterferometer. The usual movable mirror is replaced by (see the figure) atwo-mirror wedge in which only one mirror (16) moves. The sensitivity isincreased by the number of bounces in the wedge, but the useful aperture isreduced. G.D.

-PHOTO DETECTOR 22

4,549,788 29 Oct. 1985 (Cl. 350-354)Intensity of a light beam applied to a layered semiconductorstructure controls the beam.D. S. CHEMLA. Assigned to AT&T Bell Laboratories. Filed 3Jan. 1983.

Polarized radiation is directed to one of two detectors, depending on theinput beam's intensity. The switch is a nonlinear optical device having bothsmall and large energy gap materials in a planar array normal to the E field ofthe input radiation. The angle of incidence is greater than the critical anglefor low intensity light and less than the critical angle for high intensity light.It is claimed that the switching speed "potentially is very high," but no data orcalculations are given, describing exactly what these speeds are. A.B.

4,550,987 5 Nov. 1985 (Cl. 350-454)Small size telephoto lens.S. TACHIHARA. Assigned to Asahi Optical Co., Ltd. Filed 6 May1983 (in Japan 13 May 1982).

Four examples are given of an 80% telephoto lens consisting of six airspacedelements. The system covers +6.3' at f/4 and is suitable for manufacture in afocal length of 200 mm for an SLR camera. The positive front component hasthree elements (+-+); it is followed by a positive element and a two-elementnegative component (-+). The design is controlled by six conditions. R.K.

4,553,253 12 Nov. 1985 (Cl. 378-084)Plane-grating monochromator.H. PETERSEN. Assigned to Berliner Elektronenspeicherring Ge-sellschaft. Filed 20 June 1984 (in Fed. Rep. of Germany, 5 Dec.1980). Continuation of Ser. 327,657, 4 Dec. 1981.

A plane grating monochromator is claimed to be satisfactory, particularlyfor wavelengths in the 1-15-nm range. An ellipsoidal mirror is utilized forimaging at the exit slit. The inventor states that the image falling on the slit isvirtually free from distortion in the dispersion axis but he ignores distortiondue to nonparallelincidence of the optical bundle on the grating and also dueto the use of the ellipsoidal mirror. This distortion could presumably reduceresolution by producing a slit image of nonuniform width over the slit length.

J.J.J.S.

Fl. F2

F1

4,553,823 19 Nov. 1985 (Cl. 350-463)Large relative aperture objective lens.M. KATO and S. -IASHIMOTO. Assigned to Canon K. K. Filed 6May 1982 (in Japhn 25 May 1981).

A compound double-Gauss lens is described, covering +23' at 1/2. Three

1518 APPLIED OPTICS / Vol. 25, No. 9 / 1 May 1986