PROCEEDINGS OF THE IRE

/TAa "OR T WxTo(X) 2(X)dX (7)

where p is the required signal-to-noise ratio. TJhe noise,N, which limits the performance of the system is frequently one of the most difficult parameters to evaluate.Operation under daytime conditions usually leads to theconclusion that the background radiation furnishes thelimiting noise, while night-time operations are limitedby detector noise. A further discussion of these factors

Paper 3.4.2

is included elsewhere in this text.QAlthough the wavelength inteival for integration in

(6) anld (7) is indicated to be O toco, inm piractice, somie ofthe quantities under the integral are zero except over a

fairly narrow wavelenigth region Sinice the integrationmust be donie either numierically or graphically, it isimportant to exami-ine the values beforehanid in orderto limit the amiount of work as imiuch as possible.

I See R. H. Genioud, "Infrared search-syste ii range perforniance."'Paper 4.4.5, this issue, p. 1581L

Range Equation for Active Devices *KENNETH V. KN-IGHTt

A CTIVE inifrared anid optical raniging can be ac-complished with the use of pulsed radiation in amanner anialogous to that of radar in pulsed RF

techniques. A very-high-intensity lamp at the focus of acollimating milrror is caused to flash, and the eniergyreflected from the target is collected in another miirrorand focused upon a photodetector. The elapsed timlebetweeni the emi.ission of the pulsed light anid the detec-tionl of its reflection from the target is, as in radar, ameasure of the range to the target. This time cani bemeasured on the face of ani oscilloscope whose sweepis triggered with the firing of the flash lamp, or it canbe measured and delivered as an analog voltage bymore sophisticated automatic electroniic techniqujes.Gating and integration techniques can be used to enhanice performanice wheini signal-to-noise ratios are low.

Greater ratige performance can presently be obtainedusing emission of flash lamps in the visual optical regionand using photodetectors senisitive in this region. How-ever, if it is desirable to operate totally within the in-frared spectrum, flash lamps equipped with in-fraredfilters can be employed together with suitably fastinfrared photodetectors.

Farrand Optical Company, Inc., New York, N. Y,has been a leader in. developing these techniques andhas applied them to a wide variety of classified militaryequipmenits.

Although pulsed-light (visible or infrared) rangiing ispresently limited in comparison with pulsed radar,

*Original mantiscript received by the IRE, June 26, 1959.t Ramo-Wooldridge Corp., a division of Thompson Ramio-

Wooldridge Inc., Los Anigeles, Calif.

there are niarly attractive features to reconeiiiiend itsconsideration- where lonig-range performance is niot re-iquired. Several of these are noted. the transmittei fieldof view canl be very small and the receiver field of viewcan be very accurately defined and made as small as oniepleases; consequently, the troublesome ground clutterof radar is n-iot experieniced in operati;ng grounidtoground. Side and rear radiationi lobes are not present.Low power, size, and weight requirements fIurther comi-mend the techniques. High-range accuracy and rangeresolution are attainable with less difficulty than inRF technology. Because of high directivity anid operation outside the RF spectrum, pullsed-light techiniquesare less susceptible to detection and jamnmin-ig thani areRF techniques. Raiigefinders employinig thLe techniiqueare rugged and require little optical adjiustlment Asso-ciated electronic circuits are usually relatively silple.The basic range equatioiis are also simnple.We recall from-n elementary physics that illumination

uponi a scenie varies inversely with the square of the dis-tanice, R, from the illuminatineg source. If we place acollimating mirror behind a source in such a way thatthe target "sees' the iiirror full of light, we have thefam-aiiliar relationship

BsDT21T = (1

(igniorinig atmospheric attenuation) whereIl irradiance of the target,Bs-radiance of the source, an-idDT-=diameter of the transmitting rriirmor

1490 o'eptfember

()

3.4.2 Knight: Range Equation for Active Devices

If the target is a perfectly diffuse reflector of reflec-tance r, its radiance can be expressed as

PT= k2ITr (2)

and by substitution from (1)

BsDT2rPT=k3 R (3)

We are interested, of course, in the reflected energycollected at the receiver mirror. This is expressed as

size and reflectance; background radiance; receiver fieldof view; and range.

Tacit in the development above is the assumptionthat the receiver field of view is larger than the anglesubtended by the target, admitting background noiseoutside the target area. If we have a case where theangle subtended by the target is larger than the field ofview, the effective target can be expressed as

ST = OR (10)

and, upon substitution in (9) we can obtain the result

S/N-=kg BsBDTDRSTrR3BB 12

where

DR-diameter of the receiver mirror andST=diameter of the target.

Upon substitution from (3), (4) becomes

BsDT2DR2ST2rPR =k5 (5)

This is the basic equation for pulsed-light systemsexpressing the energy available for processing intoelectronic signals. Unfortunately, we must also recog-nize the existence of noise accompanying S and exam-

ine the familiar S/N ratio.Pulsed-light systems are particularly affected by

external noise, the principal source of which is randomfluctuations in the level of energy received from thebackground in daylight operation, when sun reflectionsmay be expected to occur in the background. Noisepower can be expressed, assunming a typical exponent,

N = k6PB1/2 (6)

where PB=background radiation collected by the re-

ceiver.But

PB = k7BB02DR2 (7)

where

BB =background radiance at the receiver, and

0=field of view of the receiver.

Comnbining (6) and (7), we have

N = kSODRBB'12. (8)

Combining (5) and (8), we have the S/N ratio for a

pulsed-light system operating against a perfectly diffusetarget reflector.

BsDDT2DRST2r

OR4BB 12

Pulsed-light system performance, therefore, is de-pendent upon the parameters: source radiance; aper-tures of the transmitter and receiver mirrors; target

which indicates that, for a condition where the receiverfield of view is adjusted to encompass the target pre-

cisely, performance varies as the inverse third, ratherthan fourth, power of range.

The simplest control of background noise is to reducethe receiver field of view until it receives energy onlyfrom the target itself. Many targets are of such extent,

however, that they subtend sizeable angles at theranges at which pulsed-light systems operate best, andthe problem is not severe. However, for targets of smallangular extent, such as aircraft at a distance, reductionin the field of view establishes a requirement for a highdegree of pointing accuracy.

Another source of external noise is the backscatteringof the pulsed-emitted light from dust and other particu-late matter between the transmitter and receiver. Ordi-narily this is of less consequence in daylight than isbackground noise, but at night, when background noiseis at a miniimum, backscattered light may equal or ex-

ceed the signal energy at the longer ranges possible indarkness. However, as in RF techniques, electronicprocessin-g can extract signals which are considerablybelow noise.There are many interesting and useful applications

of pulsed-light techniques in which the "target" can beprovided with a specular reflector. With r in the equa-

tions above increased considerably, S/N is similarlyincreased and range limits become greater. A flat mirror,suitably oriented, will returii the projected pulse to thetransmitter. In practice, however, corner reflectors, or

triple mirrors, are used to obviate the need for accurateorientation of the target reflector.

Coaxial mounting arrangement of transmitter and re-

ceiver mirrors is preferable if a triple-mirror reflectoris used as a target; otherwise, the reflected energy may

be partially or wholly lost. Coaxial arrangements are

generally used, however, even in the case of diffuse re-

flectors, to facilitate aiming the rangefinder.In the case of a perfect triple-mirror target, the ex-

pression for S/N can be developed as

S/N k1o BsASm2 (12)OR2A R1/2BBI,2

DR2PTST2PR = k4 _

R2(4) (11)

1959 1491

PROCEEDINGS OF THE IRE

where

Sm=diameter of the triple mirror,A area of receiver mirror intercepting energy re-

flected from the triple mirror, aidA=whole receiver area which accepts background

noise.

This equation should be compared with (9) for the simi-lar case of a diffuse reflector smaller than the receiverfield of view. Note that range affects S/N to the inverse

second, rather than fourth, power. Range performanceis markedly increased by this fact.

Atmospheric attenuation has not been treated in theforegoing development. It is a formidable factor affect-ing S/N, but it does not affect the relationship shown toexist between the parameters above.Thus far, we have conisidered only the external optical

characteristics of the pulsed-light systemni Many of theurnique advantages of optical pulse ranging derive fromthe fact that extremely shoort pulses of optical energyare generated and are detected on reflection and processed by even faster photodetectors

Capacitors are discharged through pulse lamups ofspecial design to insure that a maximum of the stocredenergy is dissipated in a single flash. This single flashmay be of less than a half-microseconid duratioin with a

rise time of less than tenth of a microsecond.Since optical energy is propagated at the same

velocity as RF energy (3 X 108 meters per second, or 300meters per microsecond), a microsecond delay ir detec-tioIn of an optical pulse corresponds to 300/2, or 150,meters in range. With modern electroiiic techniques,time resolutions are possible, permitting range measuremnents to an accuracy of less than oiie meter.

1492 September