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Sensitivity of an astronomical infrared heterodyne spectrometer
Infrared
Phyws.
1976. Vol
16. pp. 61 64. Pcrgamon
Press Pnntcd
111Great Britain
SENSITIVITY OF AN ASTRONOMICAL INFRARED HETERODYNE SPECTROMETER T. KOSTIW. Laboratory
M. J. MUMMA. M. M. ALWAS* and D. BUHL
for Extraterrestrial Physics. NASA,‘Goddard Greenbelt. MD 2077 I. U.S.A.
Space Flight
Center.
AbstractThe factors determining the sensitivity of a real astronomical heterodvnc spectrometer arc described. The deviation from the ideal hcterodyne system for lint dctectlon i> dcscrihed in terms of a series of degl-adation klctors A,. A discussion of degradation due to a low local oscillator power. and to line profile dctcction is prescntcd. RepresuGLtivc ~alucs fol- the A, are given. Even with the total degradation of 2 30. the hetcrod)nc spectrometer is still found to he a highly sensitive tool in i.r. astronomy.
High resolution heterodyne spectroscopy provides a powerful tool for detection and identification of molecular and atomic species through measurements of in situ line profiles of i.r. spectra from astronomical sources. It is well known that, in principle, the limiting sensitivity of a heterodyne receiver approaches the quantum detection limit (NEP = hv/y, y7= dynamic quantum efficiency of the photomixer) provided that the local oscillator power is sufficiently large. (” For practical detection of line profiles, there are a number of factors (g being one of them) which degrade the sensitivity of the system. The minimum detectable power (post-integration) for an ideal (q = 1) detector line is hv ,, B/z, and the heterodyne field of view is AR = A‘2 . (2) For most convenient detection only one side band (B) contributes signal. For convenience. we first take the width of a line at frequency vo9 bandwidth to be equal to the doppler (5 = AI,, = 7,16 x 10p7\‘0 (T/M) “’ Hz) of a molecular species at temperature T( K) and of mass M (AMU). The minimum detectable power for an integration time r can then be written as, P;,1,,
=
hi”-3!2[7.16
x 1o-7
where P:,,il, is referred to the detector. by a series of factors A;. The resulting be represented by
(T/M)“2
c3 z-l]“’
w,
This sensitivity of a real system is degraded minimum detectable source power can then
P”(Real) = Pi,i,,Ui (Ai), where P”(Rea1) refers to the total line power radiated into the heterodyne field of view. The degradation factors Ai are listed in Table 1. We will now discuss their origin and give representative values for each based on theory and current technology. 1. Degradation factor AQ = l/t1 is -just that due to the quantum efficiency of the i.r. mixer used. A typical value for good commercially available mixers is 2. HgCdTe photodiodes (widest band-width mixers available for use with low power IocaLosciilators) have a theoretical limit of A, % I.5 for uncoated chips.‘3’ mismatch between the source and local oscillator 2. Ap,l, is due to the polarization radiation. The degradation can vary from 1 to x depending on polarization and A,+, = 2 for an unpolarized source. Techniques can be devised (e.g. using polarization rotators) to recover some of this loss due to polarization mismatch. due to chopping of the source beam for elimination of 3. Achop is the degradation background noise and for obtaining a reference. &.hop = 2 for Dicke type chopping, ,’ 2 for frequency load switching, and unity for the unchopped case. * NAS/NRC II’ Ih I’
I
Resident
Senior
Research
Associate. 61
%-
1/:
Cpantum
efficiency
photomixer.
oi
4. &,.,,i,, = l/x is the effect of total optical transmission of the system, 2. but not including losses in the beam splitter. 5. APhaqeis the deg~dat~o~l caused by the misalignment and mismatch of the phase fronts and spot sizes of the local oscillator beam and the source beam at the photomixer. These problems have been considered by Cohen. “) Fink.“’ and Degnan and Klein.“” For optimum matching and ~~ligll~~ei~tof an airy signal and Gaussian local oscillator APll,lW- 1.2. 6. AFF = .4’““,!.4, is a beam tilling factor 2 1 and is determined by how much the source area. il,, fills the diffraction limited heterodyno field of view, A’“r”. 7. A,) is deg~d~~tion due to the noise generated in the mixer and preampli~er and the effect of the impedance mismatch between the two. The signal to noise ratio of a heterodyne receiver is given by”’
s IV: = g;;+
(“/Piin-)P;J,, (BIT)’ ,2 f&R
i
2k( 7;,, + 7-i,) BGdi2y’
where Pi is the source power. GCj,,,is the equivalent admittance of the mixer; IO the shot noise current generated by the local oscillator: I, is the dark current, k is Boltzmann’s constant, T,,, is the mixer t~tni~~ratLlre and T;, is the effective preamplifier input noise temperature and includes the effect of impedance mismatch between the mixer and the IF amplifier. The denominator includes two noise ~ontriblltions. shot noise and thermal noise. For sufficiently large local oscillator powers. i. is the dominant noise term and the signal to noise reduces to the well known shot noise limited case
For low local oscillator powers (such as those available with diode lasers) a considerable degradation A,, can be introduced. It can bc minimized by careful selection of the mixer ( a junction device such as the HgCdTe photodiode) and low noise preamplifier and careful impedance matching of the two. The reflection to transmission ratio of
Astronomical
infrared
0.1
hctcrodync
0.5
1
63
spectrometel-
2
345
1of1Gdq Fig. 1. Degradation
A0 as a function of mixer-preamplifier parameters. local oscillator powers (II = O.?mA).
7;,,
, G,,.,.for several
the beam splitter must also be optimized in order to obtain maximum signal to noise ratio. If /I is the transmission of the beam splitter, the LO power on the detector is P t,o = /I PLO0(Pf, = LO power output) and the source power on the detector is P‘ = (IL/#';,. The degradation factor An can then be written as
wherer = P(I,/I,) and T,fr = T, + For large local oscillator powers
T,..
and A,, approaches unity when the dark current is small compared to the local oscillator induced current (~4 0) and p is made sufficiently small. One finds that for large LO powers, small E and low thermal noise the optimum /3 becomes small. For low LO powers maximum signal to noise is obtained with p - 04-0.5. powers is given A plot of A0 as a function of T‘,,., Gdrq for several local oscillator in Fig. 1 (Id = 0.2 mA). The degradation can be high for typical HgCdTe mixers (e.g. AD of - 2 can be T<‘II Gdeq- 0.5, AD - 5). With 1 mW local oscillators a minimum obtained, Care must be taken in minimizing T,,,,, Gdrqby impedance matching since the system IF bandwidth is a function of the impedance and thus can be significantly reduced by the matching. 8. AL is due to the line shape distribution of signal power in our detection bandwidth. Previously we considered heterodyne detection of spectral lines with the smallest resolving element in our receiver equal to the Doppler width (Av,) of the line. In astronomical spectroscopic observations one would like to cover the entire line profile simultaneously at a resolution much smaller than the linewidth and thus study the line profiles (kinetic
63
T. KOS~I~~IC.M. J. MLIPVI~$A. M. M. ARHAS and D. BUII
temperatures. turbulence etiects. gross vclocit! shifts. etc.) characterizing the source. The smallest resolving element in the heterodyne line receiver’“’ can be an r.f. filter and the number of resolving elements the numbcr of filters in the fixed IF bandwidth. A,. can bc calculated”) as a function of B/AY,~ for Doppler lines. It can be shown that minimum A,. occurs when B = 1.2 AY,) for which AI, t 1.3. The measurement of line profiles with B/A,, c 0.17 gives a A,_ = 2.6. WC can sum the total degradation for a system using a HgCdTc photodiode as a mixer and a tunable diode laser as a local oscillator (having an output of - 700~1W single mode at - X.5 /m-) with the result, Alo, ,,, - 150. A hetcrodync spectrometer with a LO input of several milliwatts has a minimum achievable degradation of - 30. In the latter case. the minimum detectable power of an infrared heterodyne spectrometer is - 4 x IO- ” W in one second integration (B = SOMHz at IO /Im). and for I .‘3 hr integration (B/AL.,, - 0.17) high signal to noise ratios can bc obtained on some astronomical sources (e.g. S,‘N 2 50 for SIV emission line from NGC -7027)“” This high sensitivity. ultra-high spectral resolution and high spatial resolution make the i.r. hcterodyne spectrometer a potentially powerful tool in i.r. astronomy.
Phyws.
1976. Vol
16. pp. 61 64. Pcrgamon
Press Pnntcd
111Great Britain
SENSITIVITY OF AN ASTRONOMICAL INFRARED HETERODYNE SPECTROMETER T. KOSTIW. Laboratory
M. J. MUMMA. M. M. ALWAS* and D. BUHL
for Extraterrestrial Physics. NASA,‘Goddard Greenbelt. MD 2077 I. U.S.A.
Space Flight
Center.
AbstractThe factors determining the sensitivity of a real astronomical heterodvnc spectrometer arc described. The deviation from the ideal hcterodyne system for lint dctectlon i> dcscrihed in terms of a series of degl-adation klctors A,. A discussion of degradation due to a low local oscillator power. and to line profile dctcction is prescntcd. RepresuGLtivc ~alucs fol- the A, are given. Even with the total degradation of 2 30. the hetcrod)nc spectrometer is still found to he a highly sensitive tool in i.r. astronomy.
High resolution heterodyne spectroscopy provides a powerful tool for detection and identification of molecular and atomic species through measurements of in situ line profiles of i.r. spectra from astronomical sources. It is well known that, in principle, the limiting sensitivity of a heterodyne receiver approaches the quantum detection limit (NEP = hv/y, y7= dynamic quantum efficiency of the photomixer) provided that the local oscillator power is sufficiently large. (” For practical detection of line profiles, there are a number of factors (g being one of them) which degrade the sensitivity of the system. The minimum detectable power (post-integration) for an ideal (q = 1) detector line is hv ,, B/z, and the heterodyne field of view is AR = A‘2 . (2) For most convenient detection only one side band (B) contributes signal. For convenience. we first take the width of a line at frequency vo9 bandwidth to be equal to the doppler (5 = AI,, = 7,16 x 10p7\‘0 (T/M) “’ Hz) of a molecular species at temperature T( K) and of mass M (AMU). The minimum detectable power for an integration time r can then be written as, P;,1,,
=
hi”-3!2[7.16
x 1o-7
where P:,,il, is referred to the detector. by a series of factors A;. The resulting be represented by
(T/M)“2
c3 z-l]“’
w,
This sensitivity of a real system is degraded minimum detectable source power can then
P”(Real) = Pi,i,,Ui (Ai), where P”(Rea1) refers to the total line power radiated into the heterodyne field of view. The degradation factors Ai are listed in Table 1. We will now discuss their origin and give representative values for each based on theory and current technology. 1. Degradation factor AQ = l/t1 is -just that due to the quantum efficiency of the i.r. mixer used. A typical value for good commercially available mixers is 2. HgCdTe photodiodes (widest band-width mixers available for use with low power IocaLosciilators) have a theoretical limit of A, % I.5 for uncoated chips.‘3’ mismatch between the source and local oscillator 2. Ap,l, is due to the polarization radiation. The degradation can vary from 1 to x depending on polarization and A,+, = 2 for an unpolarized source. Techniques can be devised (e.g. using polarization rotators) to recover some of this loss due to polarization mismatch. due to chopping of the source beam for elimination of 3. Achop is the degradation background noise and for obtaining a reference. &.hop = 2 for Dicke type chopping, ,’ 2 for frequency load switching, and unity for the unchopped case. * NAS/NRC II’ Ih I’
I
Resident
Senior
Research
Associate. 61
%-
1/:
Cpantum
efficiency
photomixer.
oi
4. &,.,,i,, = l/x is the effect of total optical transmission of the system, 2. but not including losses in the beam splitter. 5. APhaqeis the deg~dat~o~l caused by the misalignment and mismatch of the phase fronts and spot sizes of the local oscillator beam and the source beam at the photomixer. These problems have been considered by Cohen. “) Fink.“’ and Degnan and Klein.“” For optimum matching and ~~ligll~~ei~tof an airy signal and Gaussian local oscillator APll,lW- 1.2. 6. AFF = .4’““,!.4, is a beam tilling factor 2 1 and is determined by how much the source area. il,, fills the diffraction limited heterodyno field of view, A’“r”. 7. A,) is deg~d~~tion due to the noise generated in the mixer and preampli~er and the effect of the impedance mismatch between the two. The signal to noise ratio of a heterodyne receiver is given by”’
s IV: = g;;+
(“/Piin-)P;J,, (BIT)’ ,2 f&R
i
2k( 7;,, + 7-i,) BGdi2y’
where Pi is the source power. GCj,,,is the equivalent admittance of the mixer; IO the shot noise current generated by the local oscillator: I, is the dark current, k is Boltzmann’s constant, T,,, is the mixer t~tni~~ratLlre and T;, is the effective preamplifier input noise temperature and includes the effect of impedance mismatch between the mixer and the IF amplifier. The denominator includes two noise ~ontriblltions. shot noise and thermal noise. For sufficiently large local oscillator powers. i. is the dominant noise term and the signal to noise reduces to the well known shot noise limited case
For low local oscillator powers (such as those available with diode lasers) a considerable degradation A,, can be introduced. It can bc minimized by careful selection of the mixer ( a junction device such as the HgCdTe photodiode) and low noise preamplifier and careful impedance matching of the two. The reflection to transmission ratio of
Astronomical
infrared
0.1
hctcrodync
0.5
1
63
spectrometel-
2
345
1of1Gdq Fig. 1. Degradation
A0 as a function of mixer-preamplifier parameters. local oscillator powers (II = O.?mA).
7;,,
, G,,.,.for several
the beam splitter must also be optimized in order to obtain maximum signal to noise ratio. If /I is the transmission of the beam splitter, the LO power on the detector is P t,o = /I PLO0(Pf, = LO power output) and the source power on the detector is P‘ = (IL/#';,. The degradation factor An can then be written as
wherer = P(I,/I,) and T,fr = T, + For large local oscillator powers
T,..
and A,, approaches unity when the dark current is small compared to the local oscillator induced current (~4 0) and p is made sufficiently small. One finds that for large LO powers, small E and low thermal noise the optimum /3 becomes small. For low LO powers maximum signal to noise is obtained with p - 04-0.5. powers is given A plot of A0 as a function of T‘,,., Gdrq for several local oscillator in Fig. 1 (Id = 0.2 mA). The degradation can be high for typical HgCdTe mixers (e.g. AD of - 2 can be T<‘II Gdeq- 0.5, AD - 5). With 1 mW local oscillators a minimum obtained, Care must be taken in minimizing T,,,,, Gdrqby impedance matching since the system IF bandwidth is a function of the impedance and thus can be significantly reduced by the matching. 8. AL is due to the line shape distribution of signal power in our detection bandwidth. Previously we considered heterodyne detection of spectral lines with the smallest resolving element in our receiver equal to the Doppler width (Av,) of the line. In astronomical spectroscopic observations one would like to cover the entire line profile simultaneously at a resolution much smaller than the linewidth and thus study the line profiles (kinetic
63
T. KOS~I~~IC.M. J. MLIPVI~$A. M. M. ARHAS and D. BUII
temperatures. turbulence etiects. gross vclocit! shifts. etc.) characterizing the source. The smallest resolving element in the heterodyne line receiver’“’ can be an r.f. filter and the number of resolving elements the numbcr of filters in the fixed IF bandwidth. A,. can bc calculated”) as a function of B/AY,~ for Doppler lines. It can be shown that minimum A,. occurs when B = 1.2 AY,) for which AI, t 1.3. The measurement of line profiles with B/A,, c 0.17 gives a A,_ = 2.6. WC can sum the total degradation for a system using a HgCdTc photodiode as a mixer and a tunable diode laser as a local oscillator (having an output of - 700~1W single mode at - X.5 /m-) with the result, Alo, ,,, - 150. A hetcrodync spectrometer with a LO input of several milliwatts has a minimum achievable degradation of - 30. In the latter case. the minimum detectable power of an infrared heterodyne spectrometer is - 4 x IO- ” W in one second integration (B = SOMHz at IO /Im). and for I .‘3 hr integration (B/AL.,, - 0.17) high signal to noise ratios can bc obtained on some astronomical sources (e.g. S,‘N 2 50 for SIV emission line from NGC -7027)“” This high sensitivity. ultra-high spectral resolution and high spatial resolution make the i.r. hcterodyne spectrometer a potentially powerful tool in i.r. astronomy.