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Design Considerations for Optical Heterodyne

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Design Considerations for Optical Heterodyne DESIGNCONSIDERATIONS FOR OPTICAL HETERODYNERECEIVERS: A RFXIEW John J. Degnan Instrument Electro-optics Branch NASA GoddardSpace Flight Center Greenbelt,Maryland 20771 ABSTRACT By its verynature, an optical heterodyne receiver is both a receiver and anantenna. Certain fundamental antenna properties ofheterodyne receivers are describedwhich set theoretical limits on the receiver sensitivity for the detectionof coherent point sources, scattered light, and thermal radiation. In order to approachthese limiting sensitivities, the geometry of the optical antenna-heterodyne receiver configurationmust be carefully tailored to the intendedapplication. The geometric factors which affect system sensitivity includethe local osciliator (LO) amplitudedistribution, mismatches between the signaland LO phasefronts,central obscurations of the optical antenna, and nonuniformmixer quantum efficiencies. The current state of knowledge in this area, which rests heavilyon modern concepts of partial coherence, is reviewed. Following a discussion of noiseprocesses in the heterodyne receiver and the manner in which sensitivity is increasedthrough time integration of the detectedsignal, we derivean expression for the mean squaresignal current obtained by mixing a coherent local oscillator with a partially coherent, quasi- monochromaticsource. We thendemonstrate the manner in which the IF signal calculationcan be transferred to anyconvenient plane in the optical front end ofthe receiver. Using these techniques, we obtain a relativelysimple equation forthe coherently detected signal from anextended incoherent source and apply it to theheterodyne detection of an extended thermal source and to theback- scatter lidar problem where the antenna patternsof both the transmitter beam andheterodyne receiver mustbe taken into account. Finally, we considerthe detectionof a coherentsource and, in particular, a distantpoint source such as a star or laser transmitter in a longrange heterodyne communications system. 461 1. INTRODUCTION Heterodyne or coherent detection can beadvantageous in a variety of applications.Heterodyne receivers have at least two features which are quali- tativelydifferent from incoherent(or direct detection) receivers (ref. 1). First of all, the receiving bandwidth is determined by the IF bandwidthwhich, in principle, canbe varied at will to give very high spectral resolution. Secondly,information related to the phase of the radiation signal is retained in the IF output and the outputs of two or more receivers can be correlated to make coherence measurements comparable to the aperturesynthesis techniques of radio astronomy. To achieve high spectral radiation with incoherent or direct detection systems, radiation filters or spectrometers mustbe utilized and thecombination ofvery narrow bandwidth and high sensitivity (low loss) is usually difficult to realize. In general, a heterodynereceiver will be more sensitivethan a direct detectionreceiver with an equivalentnoise equivalent power (NEP) for spectral resolutions below a cutoff bandwidth which depends on the NEP and the infrared wavelength (refs. 1, 2). The sub-Doppler spectralresolution of heterodyne receivers can be exploited to study the molecular constituents and kinematics ofremote sources yielding specific information such as altitude profiles of absoluteabundance of the species, vertical temperature profiles, and wind velocities(ref. 3). In detectingextraterrestrial thermal sources, the infor- mation is gathered by passiveheterodyne spectrometers whereas, in our own atmo- sphere or in planetary atmospheres visited by spacecraft, active backscatter lidars canbe employed. In contrastto the above applications where theradia- tionsignal is totallyincoherent or only partially coherent, the signal from thelaser transmitter in a heterodyne communicationsystem (ref. 4) is coherent exceptas modified by atmosphericeffects (ref. 5). Thisarticle attempts to present a unified theory of heterodyne receivers which addresses the optical design considerations for all of these applications. A representativeheterodyne receiver is illustrated in Figure 1. Signal radiation is collected by an optical antenna and focused,along with a local oscillator beam, onto a square-lawfrequency mixer operating at the radiation frequency. The latter beams have centerfrequencies Vs and VL andpowers Ps and PL. Thetwo frequencies mix togive an outputspectrum centered at the intermediatefrequency VIF = VS - VL where VIF is much smallerthan the infraredfrequencies VS and VL and typically on theorder of a GHz orless. The resultingsignal current is amplified by an IF amplifier ofbandwidth BIF and rectified by a nominally square-law detector to give a current output pro- portionalto the power in the IF. This is usuallyinput to a low-frequency filter or integrating circuit to further enhancethe spectral resolution and/or sensitivity and is thenrecorded. Although the present article will address most factors influencing the per- formanceof the receiver in Figure 1, it will emphasizethe design of the optica front end of the receiver for a variety of applicationsand, in particular, the manner in which the optical antenna geometry and local oscillator distribution affect system sensitivity. In Section 2 of thispaper, we reviewthe noise processesrelevant to the IF signal and discussthe system signal-to-noise in the IF in termsof an asyet undefined mean squaresignal current. Section 3 462 brieflyoutlines the sensitivity improvementachieved by time integrationtech- ’ niques.In Section 4, we addressthe calculation of the mean squaresignal current in the mixer plane for a general,partially coherent, quasi-monochromatic sourceand, in Section 5, demonstratethe manner in which the IF signalcalcula- tion can be transferred to any convenient plane in the optical front end of the receiver. InSection 6, we applythe general result to thespecific problem of coherentlydetecting an extended incoherent source. The resultsof that section are then applied to the heterodyne detection of an extended thermal source in Section 7 and to the backscatter lidar problem in Section 8 and some useful designguidelines are generated.In Section 9, we applythe results of Sec- tion 4 to the detection of a spatiallycoherent source such as a laser trans- mitter in a heterodynecommunications system or a distant point source such as a star. 2. THE SIGNAL-TO-NOISE RATIO OF A HETERODYNE RECEIVER The power signal-to-noise ratio of a heterodyne receiver is a measure of its sensitivity since setting the ratio equal to onepermits calculation of the noiseequivalent power (NEP). It is given,in most cases ofinterest, by (ref. 1) We will leave thecalculation of the mean squaresignal current <iM2> to later sections and limit our present discussion to the various noise terms in the denominator of Equation (2.1) . The localoscillator induced shot noise, or quantum noise, <is2>is oftenthe dominant noise if hV >> KTB where TB is theequivalent blackbody temperature of a thermalsource lying inside the antenna pattern of the receiver.Shot noise is due tofluctuations in the rate of arrivalof LO pho- tons. If the LO power is much greaterthan the signal power, the mean square shot noise current is given by 2- - <is > - 2BeBIFiDC - where iDc is the DC currentgenerated by the LO, e is theelectronic charge, BIF is theintermediate frequency bandwidth, and hV is thephoton energy. The integrandcontains the detector quantum efficiency nQ and the LO intensity IL which are assumed tovary over the plane of thedetector defined by the two- -+ dimensionalcoordinate rD. The parameter B equals 1 forphotoemissive mixers 463 while,for photoconductors, it equals 2 due to fluctuations in the generation andrecombination of charge carriers as described by Levinstein (ref. 6). One can rewrite Equation(2.2) in the more familiarform - if we definean average quantum efficiency nQ by and PL is the local oscillator power incidenton the detector. Radiationfrom a thermal source contained within the receiver field of view and thereceiver bandwidth BIF will becoherently detected and subjectto so-called"heterodyne amplification." In some experiments,such as inpassive heterodynespectrometry, this thermal source is theobject of study,while in others it correspondsto unwanted backgroundnoise. We will show in later sections that it can be described bythe equation where nT is 'an overallefficiency whichdepends in part on thedesign of the opticalfront end. Fluctuationsin background radiation, which spectrally is outsidethe receiverbandwidth but within the infrared response band of the mixer, will also producenoise currents, given by <iB2>inEquation (2.1) as will sourcesof radiation outside the antenna pattern of the receiver but inside the heterodyne receivingbandwidth. McLean and Putley(ref. 7) havederived expressions €or this noise componentwhich are complicated€unctions of wavelength,spectral interval,detector area andtemperature, and field of view. The latter noise is notamplified by theheterodyne process, however, and can be rendered negligible by choosing a large enough local oscillator powerand by spatially and spectrally filtering the input radiation. Two otherimportant sources of noise are Johnson orthermal noise asso- ciatedwith the mixer and the IF amplifier. The mixer noise is given by 464 <iJ2> = 4KT~B~~ %I where TM and % are the mixer's (or mixer load resistor's) temperature and resistance as seen by the IF amplifier. For most cooled mixers, this wouldbe negligible comparedwith the amplifier noise given by <iA2>
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