Researchers are developing an optical heterodyne densitometer with the potential to measure optical density over an unprecedented dynamic range with high accuracy and sensitivity. This device uses a Mach-Zender interferometer configuration with heterodyne detection to make direct comparisons between optical and RF attenuators. Researchers expect to attain measurements of filter transmittance down to 10 to the minus 12th power with better than 1 percent uncertainty. In addition, they intend to extend the technique to the problem of measuring low levels of light scattering from reflective and transmissive optics

Hardis, J.

Migdall, A. L.

Snyder, J. J.

Zheng, Ying Cong

English

NASA Technical Reports Server

N89-13323
AN OPTICAL HETERODYNE DENSITOMETER
A.L. Migdall, Zheng Ying Cong', J. Hardis and J.J. Snyder +
National Bureau of Standards, Gaithersburg MD 20899
Abstract -- We are developing an optical he_:erodyne densitometer with the
potential to measure optical density over an unprecedented dynamic range
with high accuracy and high sensitivity. This device uses a Mach-Zender
interferometer configuration with heterodyne detection to make d_rect
comparisons between optical and RF attenuators. We expect to attain
measurements of filter transmittance down to 10 -12 with better than 1%
uncertainty. In addition we intend to extend this technique to the
problem of measuring low level of scattering of light from both
reflective and transmissive optics.
I Introduction
We have developed a system to measure optical density over an
unprecedented dynamic range with high accuracy and high sensitivity.
Using the ultra-sensitive technique of optical heterodyne detection, we
have been able to measure optical attenuations of 107, 10 I° , and i0 Iz at
633 nm with standard deviations of 0.5%, 2.5% and 20% respectively.
Optical heterodyne detection I uses a strong reference laser beam, or
local oscillator, to amplify very weak signals above the noise inherent
in the detector. In this way, the shot noise of the strong reference
beam can be made to dominate the measurement rather than the detector
noise. Our setup (Fig. i) uses a laser split equally into two beams, one
of which is sent through the filter to be measured and then frequency
shifted by an acousto-optic modulator. The two beams are then recombined
and sent to a detector which sees a beat signal at the difference
frequency. The amplitude of the beat signal is proportional to the
square root of the filter transmittance. It is this square root
dependance that, in part, gives heterodyne detection its increased
dynamic range over ordinary densitometry measurements that depend
linearly on transmittance.
This method makes possible measurements that cannot be made any
other way, the most obvious being accurate single frequency measurements
of high attenuation absorbing glass filters. Also, since this method is
not limited to a specific frequency, a tunable laser source can be used
to measure the transmission profile of an interference/blocking filter
far out into the wings. In addition, very low level scattering by
optical components can be quantified.
II Theory
Heterodyne detection, described as follows, uses a light wave of one
frequency to detect a signal at a second slightly different frequency.
The photocurrent i(t) from a photodetector is proportional to the ligILt
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intensity l(t) incident on the device at time t. Intensity is the square
of the sum of the electric fields of the two beams E 0 and E I . So if two
beams are combined, l(t)=IE0(t ) + E1(t) J2 . If the two beams have
different optical frequencies, u and w+A, then when l(t) is averaged over
many optical cycles, a cross term at the difference frequency A will
arise in addition to a constant term. This term at the difference
frequency is proportional to E0E I or (1011) 1/2, where I 0 and 11 are the
intensities of the two individual beams. The square of the amplitude of
the beat signal is proportional to the intensity of each beam. One can
see that if the two beams differ in intensity, the more intense beam
effectively amplifies the signal due to the weak beam.
When averaged over the detector area, the signal current from the
detector may be written as:
i(t) = K [ 1 + 2(TP1/P0)11Zcos(A t) ]
where K = P0e_/_, P0 and P1 are the laser powers in the two beams, e is
the electron charge, _ is the detector quantum efficiency, h is Planck's
constant over 2_, _ is the optical angular frequency, A is the difference
frequency, and T is the transmittance (assumed to be <<i) of an optical
filter inserted into the PI beam path. Thus, the optical attenuation is
found by taking the square of the ratio of the beat signal with and
without the filter inserted.
An important point to note about this technique is that extreme
requirements on detector llnearity are not necessary. This results
because the unattenuated beam effectively biases the photodetector. One
can see that as the filter transmittance changes from full transmission
to total attenuation the intensity on the detector changes by only a
factor of two.
The sensitivity of this technique may be defined as that
transmittance that will produce a signal amplitude Just equal to the
noise in the system (le. slgnal/noise = i). If the unattenuated laser
beam is powerful enough, its shot noise will dominate the detector noise,
so the noise current squared may be written as:
<in2> = 2P0e2_B/_,
where B is the bandwidth of the measurement. The sensitivity is found Oy
setting this equal to the heterodyne signal current squared written as:
<i, 2> = 2e272Tp 0PI/(_)2
and solving for T. This gives a transmittance sensitivity T=_B/_pI.
For a HeNe laser power of I mw in each beam and a 1 Hz bandwidth this
minimum detectable transmittance is 3x10 "Is
III Experimental Technique
Our optical setup is based on a simple Mach-Zender interferometer
where a I mw HeNe laser beam is split into two beams and subsequently
recomblned. The filter of interest is placed in one of the beams. The
beam transmitted by the filter is then frequency shifted by an acousto-
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optic modulator (AOM) driven at 36 MBz. The unattenuated beam and the
attenuated and frequency shifted beam are recombined by a beam splitter
and focused onto a detector/amplifier. The detector produces a DC signal
plus the AC component at the difference frequency of the two beams. The
amplitude of the beat signal depends on the intensity of the recombined
beam and thereby on the transmittance of the filter.
LASER j-'j ][NTENS][TY
_UTTI_ _
FILTER r---.
CDHPUTER
\
t
CEIHPUTI_R
_,_---
I \
I_
%
\
DET
,\
Figure 1 Schematic of Experiment
The AC output of the detector/amplifier is put into a computer
controlled 0-127 db RF attenuator followed by two 35 db gain RF
amplifiers. The signal along with the AOM drive frequency is then fed
into a 50 MHz lock-in amplifier. This produces two DC signals, one
proportional to the beat signal in phase with the drive frequency and the
other proportional to the signal in phase with the drive frequency
shifted by 90 degrees. These inphase and quadrature signals are recorded
by the computer which calculates the magnitude of the beat signal.
When the filter is removed from the optical path, the RF attenuator
is increased to maintain a nearly constant signal at the lock-ln. By
alternately recording the beat signal (including the RF attenuation) with
the filter in and out, any problems due to slow changes of the RF gain
are eliminated. The computer also monitors the laser power and the power
of the frequency shifted light exiting the AOH to normalize the beat
signal. An optical shutter placed in the frequency shifted arm and
controlled by the computer is used to zero the electronics.
This precise arrangement of components was chosen to minimize
ordinarily small effects that become important at our high detection
sensitivities. We found that the exit surface of the AOM backscattered
light at the i0 -_ level. This produced a beat signal even with the
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frequency shifted beam blocked, indicating that light backscattered by
the output surface of the AOMreached the laser and was reflected into
the unshifted beam. To prevent this, the test filter was placed upstream
of the AOM so that the backscattered and frequency shifted light is
reduced twice by the filter attenuation. Several measures are taken to
make the optical phase difference of the two beam paths stable to allow
for very narrow bandwidth settings on the lock-in amplifier, and thus
reduce the noise. The optical apparatus is enclosed in a box to reduce
air turbulence, and the optical table is placed on vibration isolation
legs.
Measurements are typically made with 1 s integration times on the
outputs of the lock-ln and the laser power monitors. A I0 second wait
time is used to allow for these signals to settle after changing the
shutter or filter position. These delays and the time to repositlon the
filter (currently via a very slow translator) result in a single
measurement taking about 1.5 minutes.
IV Results
Our initial tests were made to characterize the noise and drifts
associated with the technique. We found that we could make measurements
with 1.5% standard deviation of individual measurements once the
interferometer had stabilized. This was accomplished only after
correcting for a systematic error of 10% in the lock-in response varying
with input phase angle. This correction was able to reduce this problem
to approximately i%. We hope to reduce this further by designing and
constructing our own lock-in.
We have made initial tests of the dynamic range and found that
measurements of attenuations as great as 10 -12 could be made with a
standard deviation of 20% between individual measurements. This implies
a sensitivity in the 10 -13 range, leaving 3 orders of magnitude, before
running up against the theoretical limit using our current experimental
parameters.
While most of our initial tests were made using a frequency
stabilized HeNe laser, we have successfully run a test using a multimode
Ar + pumped dye laser, demonstrating the tunabllity of the technique.
V Conclusion
Our tests thus far have succeeded in demonstrating the extraordinary
dynamic range and sensitivity of heterodyne measurement of optical
density. This range far exceeds the capabilities of the ordinary
attenuation measurements presently in use at NBS. Since the current
measurements are not at the fundamental limits of the technique, further
work should allow us to push the sensitivity at least an order of
magnitude better.
Planned improvements to this system include construction of new
lock-in amplifier to reduce systematic errors with respect to phase angle
to below the current 1% level. We intend to shift our beat frequency to
30 MHz, where RF attenuators can be calibrated by an available service at
NBS in Boulder. This will allow us to complete the traceability of our
optical measurements to high precision RF electrical standards and to
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produce accurate, absolute optical standards. When this is done, we will
compare our heterodyne measurements to conventional measurements where
the dynamic ranges overlap. In addition, tests will be done to verify
the linearity of our technique. Work is also underway to extend this
technique to the infrared using a CO 2 laser at 10.6_m.
We intend to measure transmittance versus angle to allow the total
transmittance of a filter to be measured. In addition, this will enable
us to characterize the distortion of the transmitted wavefront. Another
application where this high dynamic range technique should prove useful
is in measuring the low angle scattering of both transmissive and
reflective optics. This should be particularly useful in the case of the
low scatter super-polished mirrors now becoming available.
We greatfully acknowledge support for this work by the U.S. Army
Strategic Defense Command.
i. R.W. Boyd, Radiometry and the Detection of Optical Radiation, p. 195,
John Wiley & Sons, New York, 1983.
* Permanent address National Institute of Metrology, BeiJing, People's
Republic of China
+ Present address Lockheed M. S. C., Palo Alto, CA
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An optical heterodyne densitometer

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