October1959 ATMOSPHERIC STRUCTURE FROM RADIATION MEASUREMENTS 1007

applied to a broken cloud condition by a simple linearaveraging, if the fractional cloud cover is known. Forthis purpose, it would be desirable that the satellite alsotake television pictures of the cloudiness.

Only the question of sounding our own atmospherehas been discussed and that only in part. Measurementsin the 9 .6 -/u ozone band, for example, can give us boththe ozone and temperature distribution from about 25to 60 km. But the methods are equally applicable to theatmospheres of other planets.

The requirements for an adequate program outlinedhere are severe but possible. Our technical ability toproduce an adequate optical system and our knowledge

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

of the atmospheric infrared spectrum are sufficient forthe experiment. And as very careful planning is neces-sary, it is not too early to start. If we begin immedi-ately, by the time the instrument is ready it could beput into orbit.

ACKNOWLEDGMENTS

I wish to express my appreciation to Mrs. BarbaraGrant and Mr. Jack Roseman for programing the cal-culations, which were done on the digital computer atthe MIT Computation Center. The work reported inthis paper as well as the studies on which it was basedwere supported by the Office of Naval Research.

VOLUME 49, NUMBER 10 OCTOBER 1959

Background Noise Measurements at the Sea Horizon

LOUIS J. FREEU. S. Navy Underwater Sound Laboratory, Fort Trumbull, New London, Connecticut

(Received June 20, 1958)

The design of passive infrared detection systems requires a knowledge of the sea-horizon backgroundnoise. The horizontal wave-number distribution of noise from the sky immediately above and the sea im-mediately below the horizon was measured during 1956 and 1957. The measurements, which are discussedin this paper, included the range of wave numbers from 7.1 to 91 cycles/rad. The results are graphed interms of the one-dimensional angular Wiener spectrum of the background noise as a function of the horizon-tal wave number and show that both the sky and sea noise spectra are inversely proportional to the 1.7power of the wave number in the region from 14 to 91 cycles/rad. A brief discussion of the analyzing equip-ment is also included.

INTRODUCTION

IN the past, many designers of infrared systems havetaken into account the electrical noise in the de-

tectors used, but have not used specific informationabout the noise introduced into the system by thespatial variations of the radiance of the background.No natural background has a perfectly uniform radi-ance. The spatial fluctuation of the radiance about itsmean value has the effect of introducing electrical noiseinto the output of the system. The spatial fluctuationin the radiance of the background is called backgroundnoise.

This paper reports the results of measurements of thebackground noise of the sea horizon.

One of the ways to describe the background noise isto state its one-dimensional, angular Wiener spectrum,which has the dimensions of mean square radiance percycle/rad. The Wiener spectrum may be used tooptimize the design parameters (optical-electrical) of apassive infrared detection system.

Roughly, the Wiener spectrum may be defined as thesquare of the absolute value of the Fourier transformof the radiance distribution, divided by the angularrange from which the Fourier transform was determined.

On various nights, during 1956 and 1957, the one-

dimensional angular Wiener spectrum of the sky im-mediately above and the sea immediately below thehorizon was measured.' The primary purpose of thesemeasurements was to improve the design of passiveinfrared detection systems.

INFRARED BACKGROUND NOISE ANALYZER

The measurements were performed on a 50-ft towerat the former U. S. Coast Guard Station, Ditch Plain,Long Island, New York. Figure 1 shows the tower andpart of the 100-degree clear sea sector which was used.

The infrared background noise analyzer comprisesfour major units: the scanning head, the scanner-drivecontrol unit, the main console, and the recording oscil-lograph.Y The scanner, shown in Fig. 2, which containsthe optical receiver, a double-strip low-impedanceBaird bolometer, the preamplifiers, and the motordrive, was mounted on a corner of the 3-ft catwalkatop the tower. The main console, shown in Fig. 3,consists of the main amplifiers, sequential switchingcircuits, analog components, recorder amplifiers, and

1 The measurements grew out of USL Rept No. 237 by RobertW. Mitchell and the late Oscar Imalis (May 10, 1954).

2 For a more detailed discussion of the instrumentation seeL. J. Free and F. V. Jackson, USL Research and DevelopmentRept. No. 340 (May 28, 1957).

LOUIS J. FVRPiVo

" operations and scan reversal. During the 100-deg live7M: t clog sector the analyzer is in one of its three possible modes

of operation, namely, background noise, system noise,or calibrate. The background noise mode is what itsname implies; the analyzer is irradiated by the back-ground. During the system noise mode the bolometeris shielded from the background by a shutter so thatthe analyzer records only its intrinsic noise. The cali-

~ brate mode merely monitors the stability of the elec-tronic components of the system.

Some pertinent data concerning the analyzer are asfollows: a. The measurements were performed only at

FIG. 1. Site of sea horizon background noise measurements. night, the night limitation being imposed by thesilver chloride window on the bolometer capsule. b.

power supplies; it was installed inside the hut along with the scanner-drive control unit and the recordingoscillograph.

Figure 4 shows a simplified flow diagram of the

one strip; radiation from the sea below the horizon isfocused on the other. The electrical signals generatedby the incident radiation are, in separate channels, Psuccessively amplified and shaped, squared (in themathematical sense), integrated, amplified again, andArecorded. The recorded data are then manually reducedto yield the Wiener spectrum of the horizon backgroundnoise.

The scanning head sector-scans a 340-deg horizontalfield, of which only a 100-deg segment contributes in-formation. The 240-deg segment is used for switching

FIG. 3. Main console for infrared background noise analyzer.

The minimum radiation fluctuations which can be de-P", ~~~~~~~~~tected by the complete system are approximately

3 X10~ w. The radiation fluctuations are defined hereas [((P - )) 1 ,where P is the instantaneous radiation(in watts) incident on the analyzer. c. The sensitivityof each bolometer strip is approximately 0.50 rmsv/rms w. d. The analyzer detected radiation in thespectral region transmitted by silver chloride, that is,approximately to 24 A. e. The receiving mirror is anastronomical quality paraboloid with a 12-in, focal/ ~ ~~~~~~~~~~~length and an 18-in. diamn. f. Each of the two bolometerstrips subtends a -degree vertical field and a -degree

horizontal field. g. Background noise was measured atthe wave numbers, 7.1, 14, 27, 53, and 91 cycles/rad.

FIG 2 Scanning head for infrared background noise analyzer. (These wave numbers correspond approximately to ,

10.08 Vtol. 49

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October1959 BACKGROUND NOISE MEASUREMENTS AT SEA

-I 2X 1, and 1 cycles/degree.) The lower wave-numberlimit is determined by the mechanical design of thescanning head; in fact, mechanical difficulties reducedthe number of measurements performed at 7.1 cycles/rad. The upper wave-number limit is determined bythe physical dimensions of the bolometer, that is, theresolution of the optical system. h. The signal ampli-fiers have a peak frequency of 10 cps.

Before proceeding further the reader may find it in-teresting to note some of the major difficulties encoun-tered with the analyzer design. Noisy slip-rings pre-sented the first problem. This was finally solved byeliminating the slip-rings and sector-scanning the op-tical receiver. Another problem was microphonism. Ahigh-gain transformer (1: 300 turns ratio) was requiredto match the low-impedance bolometer to the pre-amplifier input. Bolometer-biasing current flowing inthe transformer primary made it very sensitive tomechanical vibration. Minimum microphonism resultedonly after the biasing current flowing in the two halves

BRUSHRECORDER

FIG. 4. Simplified flow diagram of infraredbackground noise analyzer.

of the primary winding was carefully balanced. Thatubiquitous trouble-maker, hum, was reduced to negli-gible proportions by using a 400 cps line frequency forthe signal amplifier and bolometer-bias power supplies.The final and most difficult problem was that of elimi-nating cross talk between the two channels of theanalyzer. A polarity coincidence correlator helped im-measurably in determining the electrical common config-uration which gave the least cross-channel interference.

DATA ANALYSIS

The analysis of background noise data would not bedifficult if it were possible to construct a system tomeasure the radiance at infinitesimal points of thebackground. Practical radiance-measuring devices, how-ever, "see" a small but finite area, and what they ac-tually measure when scanning the background is thebackground radiance modified by the spatial filtercharacteristics of the optical receiver. Mathematicallythis amounts to convolving the background radiance

FIG. 5. Over-all averageof background noise data,(The average Wiener spec-trum for the years 1956 and1957 plotted against wavenumber. The solid curve isfor scans made just abovethe horizon; the dashedcurve is for scans made justbelow the horizon.)

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function with the aperture response function of theoptical receiver. In addition, such devices present theirinformation in terms of some electrical parameter.

In order to tie these diverse quantities together,Jones3 developed a theory of background noise. Hisformulation assumed that the irregularities in back-ground radiance could be specified in either a two-dimensional spatial domain or a two-dimensional wave-number domain and that these two domains trans-formed into one another by means of the Fourier in-tegral. Given this mathematical basis, a relation be-tween the electrical output of the measuring device andthe background noise wave-number spectrum can befound. Since the electrical output is a one-dimensionalfunction, however, it is not possible to determine ex-plicitly the two-dimensional background noise spectrum.

By scanning uniformly along one of the two spatialcoordinates and assuming that the optical receiver'saperture response function can be separated into two

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FIG. 6. Comparison of average background noise data for 1956with average data for 1957. (Wiener spectrum plotted againstwave number. The solid curve is for scans made just above thehorizon; the dashed curve is for scans made just below thehorizon.)

I This theory is presented by R. Clark Jones, in "Sky noise:its nature and analysis," Polaroid Corporation Research Depart-ment Rept. No. 480 (September 15, 1953), second edition.

LOUIS J. FREE

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FIG. 7. Background noise data for March, April, and June, 1956.(Wiener spectrum plotted against wave number. The solid curveis for scans made just above the horizon; the dashed curve is forscans made just below the horizon.)

independent one-dimensional functions, another rela-tion between the background noise spectrum and theelectrical output can be found. In this equation thebackground noise spectrum is a one-dimensional func-tion of the wave number associated with the scannedspatial coordinate. The electrical output of the meas-uring device now gives enough information to determineexplicitly this one-dimensional background noise spec-trum. Jones4 derived just such a relationship, an equa-tion relating the noise power at the output of a linearamplifier to the noise power of the one-dimensional,angular Wiener spectrum of the background.

Application of this equation to the output signal ofthe analyzer demanded an intimate knowledge of theanalyzer characteristics. Conventional calibration pro-cedures yielded the following necessary information:a. The aperture response function of the optical re-ceiver. b. The gain as a function of frequency of thesignal amplifiers and the analog circuits. c. The bolom-eter responsivity as a function of frequency. d. Thesolid angle field of view and the aperture area of theoptical receiver. e. The linearity and dynamic range ofthe analyzer.

RESULTS

Twenty-three nights of data were collected, 12 during1956 and 11 during 1957. In addition to the backgroundnoise measurements, general weather information wasobtained. This information contained qualitative dataconcerning daylight visual range, cloud cover, cloudtype, wind velocity, wind direction, and sea state; andquantitative data concerning temperature, relativehumidity, and barometric pressure.

The general weather conditions for the 23 nights wereas follows: a. Sixteen and a half, or approximately 70%,

4 R. Clark Jones, Polaroid Corporation Research DepartmentRept. No. 489 (September 22, 1953).

of the nights were clear, 5 were hazy, and 1 werefoggy. (A night was considered clear if the horizon wassharply defined, and hazy if poorly defined. On thefoggy nights the horizon was completely obliterated byfog banks.) b. 50% cloud cover occurred one-third ofthe time. c. Two-thirds of the time the wind blew froma westerly direction. d. Half the time the wind velocitywas less than 10 miles per hr. e. A sea state of less than2 was noted two-thirds of the time. f. The average tem-perature during the measurements was 560 F. Tempera-tures covered the range, 280 to 690F. (The mediantemperature was 590F.) g. The relative humidity rangedfrom 47 to 100% and averaged 83% (The median rela-tive humidity was 83%.) h. The average barometricpressure was 1017 mb. The lowest pressure recordedwas 1011 mb and the highest, 1026 mb. (The medianpressure was 1016 mb.)

An unsuccessful attempt was made to correlate this

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FIG. 8. Background noise data for July, August, and October,1956. (Wiener spectrum plotted against wave number. The solidcurve is for scans made just above the horizon; the dashed curveis for scans made just below the horizon.)

information with the analyzed data. Neither the am-plitude nor the shapes of the curves seemed to have anyrelation to the weather conditions which were observed.

An average of all the data obtained during the two-year period 1956 and 1957 is given in Fig. 5. The plotsare log-log; the solid line is the one-dimensional angularWiener spectrum of the background noise immediatelyabove the horizon; the dashed line is the spectrum ofthe background noise immediately below the horizon.Straight lines which fitted the points of these log-logplots most closely were determined. These lines allowthe Wiener spectra to be stated in terms of an exponentof the wave number. For both of the background noisecurves shown, the Wiener spectra are inversely pro-portional to the 1.7 power of the wave number.

In Fig. 6 the data for 1956 and 1957 are compared.It also shows the average of those nights in 1956 whenmeasurements were made at the wave number, 7.1cycles/rad. Again, straight lines were fitted to the

1010 Vol. 49

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October1959 BACKGROUND NOISE MEASUREMENTS AT SEA HORIZON

points. The three plots of the sea background noise areconsistent; the Wiener spectrum is inversely propor-tional to the 1.7 power of the wave number. However,the sky background plots present a different story; for1956 the exponent of the wave number is 3.4, for 1957the exponent is 1.2, and for the partial data of 1956 theexponent is 2.7.

The characteristics of the background noise averagedover monthly periods are shown in Figs. 7, 8, and 9.Figure 7 shows March, April, and June, 1956. Thepoint of interest here is that for March and April thesea background noise is higher than the sky backgroundnoise. In June the sea noise has fallen below the skynoise. (The wave-number exponents vary between-2.5 and -3.5 for the sky background noise and be-tween -1 and -1.5 for the sea background noise.)Figure 8 shows that in July, August, and October, 1956,the sea noise remained below the sky noise. In Octoberthere is a considerable spread between sky noise andsea noise. In fact, the sea background noise was notmeasurable. (The wave-number exponents vary be-tween -2.5 and -3.5 for the sea background noiseand are -3 for the sky background noise.) Figure 9shows the same July-August-October period during1957. Again, the sea noise is slightly lower for July andAugust, and considerably lower for October. (Thewave-number exponents vary between 1 and 3 for boththe sky and the sea background noises.)

On the basis of the 1956 and 1957 tests, the followingconclusions may be drawn: (1) The average of all thedata collected during 1956 and 1957 shows that boththe sky and sea background noises have one-dimen-sional angular Wiener spectra which are inversely pro-portional to the 1.7 power of the wave number in the

JULY 1957 AUGUST 1957 OCTOBER 1957

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FIG. 9. Background noise data for July, August, and October,1957. (Wiener spectrum plotted against wave number. The solidcurve is for scans made just above the horizon; the dashed curveis for scans made just below the horizon.)

region from 14 to 91 cycles/rad; (2) the amplitude ofthe Wiener spectrum of the sky is about three timesthat of the sea; (3) general weather information didnot correlate with the background noise data; and(4) background noise, when considered on a monthly

basis, had Wiener spectra proportional to a wavenumber, whose exponent varied between - and -3.5.

ACKNOWLEDGMENTS

Acknowledgments are made to the members of theInfrared Branch at the Underwater Sound Laboratorywho assisted in this work and, in particular, to the lateFred V. Jackson, who developed the electronic circuitry.

1011