Page 195 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Stability and Tempco Issues

188 Chapter Eight

into the 200mm core diameter, 0.3 numerical aperture (NA) silica-on-silica fiber,
whose loss is 1dB/m. In order to compensate for coupled power variations of
the source, a polished fiber coupler is used to tap off one-half of the source power
to a high-quality connectorized monitor photodiode with negligibly small tem-
perature coefficient. The signal fiber is likewise connectorized and coupled to a
receptacle-mounted photodiode and transimpedance receiver. Responsivity of
both diodes at 0.88mm wavelength is 0.6mA/mW.
The distal end of the probe fiber is 10m away, immersed in the aqueous
process liquid, whose refractive index n 2 varies from 1.33 to 1.40, roughly cor-
responding to 0 to 40 percent concentration on the Brix scale. Although there
is a range of incident angles of light within the fiber core passing into the liquid
-1
(approximately ±sin (NA) =±17°), we will just use the normal-incidence Fresnel
relations, where the power reflection coefficient R is given by:
2
È n - n ˘
1
2
R @ (8.21)
Í Î n + n ˚ ˙
2
1
Hence with an average fiber refractive index of n 1 = 1.47, the power reflectiv-
ity at the fiber end varies from 0.06 percent to 0.25 percent in the different
process liquids, and the signal power can then be calculated from the double
pass through coupler and sensor fiber. We obtain for the detected signal power:
( n 2 = . ): mW ¥ . 0 5 ¥ . 0 1 ¥ . =
1 40 1
0 0006 1 5 . nW
0 5 ¥ .
0 1 ¥ .
( n 2 = . ): mW ¥ 0 5 ¥. 0 5 ¥. 0 1 ¥. 0 1 ¥. 0 0025 =. 6 25 nW
.
1 33 1
The monitor channel detector should generate a photocurrent I r ª 400mA, so
with a transimpedance amplifier load of 12k we have a voltage or 4.8V, ideal
for digitization in a 0 to 5V ADC. This channel should provide few difficulties.
The first problem with the sensor configuration is the relatively low received
power at the main signal photodiode. With 6.25nW power and 3.75nA
maximum photocurrent, we need a transimpedance of 1GW for 3.75V output.
As we don’t have any, we will use a 100MW transimpedance and a further stage
of 10¥ gain. With a minimum of 90mV at the transimpedance output, we are
likely to be just shot-noise limited.
The modulation frequency is chosen as 3892Hz, well above the main inter-
ference sources, but not so high that achieving adequate bandwidth is difficult.
The level of detected ambient light in the process chamber will be negligible,
and as the light is fiber-guided, a small, low-capacitance photodiode can be used
to capture it and achieve 10kHz bandwidth. Much more worrying is the reflec-
tion from the monitor photodiode assembly. If this is a simple polished fiber
connector butt-coupled to the photodiode, the fiber end will reflect about 3.6
percent of the incident light, contributing another received signal power of the
order of:

.
.
.
Reflected monitor power: 1 mW ¥ 0 5 ¥ 0 5 ¥ 0 036 = 9 0 m W
.
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