A systematic approach to the calibration of a photomultiplier array spectrometer is presented. Through this approach, incident light radiance derivation is made by recognizing and tracing gain characteristics for each photomultiplier tube

Bailey, Steven A.

Piazza, Charles R.

Wright, C. Wayne

English

NASA Technical Reports Server

I 
NASA Technical Memorandum 100739 
Calibration of a Photomultiplier 
Array Spectrometer 
._ _ _  
Steven A. Bailey 
C. Wayne Wright 
Charles R. Piazza 
Wallops Flight Facility 
Wallops Island, Virginia 
National Aeronautics and 
Soace Administration 
Goddard Space FllgM Center 
Wallops Flight Facility 
Wallops Island, VA 23337 
1989 
https://ntrs.nasa.gov/search.jsp?R=19890017258 2020-03-20T02:18:29+00:00Z
Summary 
A systematic approach to the calibration of a photomultiplier 
array spectrometer (PAS) is presented. Through this ap- 
' proach, incident light radiance derivation is made by recog- 
nizing and tracing gain characteristics for each photomulti- 
plier tube (PMT). 
Introduction -. 
Calibration of any instrument is fundamental to its proper 
operation. Without calibration, an instrument provides data 
which is of little use. Calibration of a spectrometer involves 
relating a known input light source to spectrometer output 
signal levels. Gain adjustments are usually made by increas- 
ing or decreasing the integrating time of the sensor with 
respect to light. 
Calibration of aPAS, as found in the Airborne Oceanographic 
Lidar (AOL), involves making the relationships described 
above. However, since the integrating time of this particular 
device is held constant through discrete components, another 
means is used to adjust gain; device voltage. This paper 
describes how those voltages are adjusted to achieve calibra- 
tion. A study of gain characteristics as voltage changes is also 
presented. Finally, a process is described whereby true 
radiance measurements can be made with a PAS using any 
calibrated voltage combination. 
AOL 
AOL was a joint effort by NASA and AVCO Everett Research 
LABS (AElU). It was built by AERL and delivered to NASA 
in 1977. AOL is installed on a NASA P3-A research aircraft 
based at NASA/GSFC - Wallops Flight Facility, Wallops 
Island, Virginia. In its present configuration, AOL supports 
three modes of operation: Fluorosensing, Passive, and 
Bathymetry. The Fluorosensing mode resolves laser induced 
fluorescence' spectrally. The Passive mode resolves incident 
light spectrally. The Bathymetry mode resolves laser backscat- 
ter23 temporally with transient digitizers. 
Components of Calibration 
The spectrometer used in the Passive and Fluorosensing 
modes of AOL consists of a single array of 36 PMTs. The 
efforts of this paper are solely concerned with the Passive 
mode of this dual active-passive device'. Preceding the array 
is a transmission diffraction grating with 11.25 nm channel- 
adjustment for wavelength calibration and translation. 
- to-channel separation. An input beam-split-mirror provides 
* The PAS power source is a LeCroy HV4032 32 channel 
programmable high voltage power supply. It contains an on- 
board microprocessor used to maintain regulated output volt- 
ages. Programming of high voltage arrays is via RS-232. 
A multiplexed Analogic 10 bit analog to digital converter 
(ADC) is used to digitize signals received from the passive 
side of the spectrometer. This ADC and support circuitry rest 
on a camac card. 
Our calibration source is a 30 inch integrating sphere. It is 
illuminated by an external 200 watt tungsten halogen lamp 
with 6 removable apertures. Calibration (traceable to the 
National Bureau of Standards) of the sphere was done in 
house for each aperture. Light emitted is measured in mi- 
crowatts/sq.cm/nm/steradian. Sphere calibration measure- 
ments are made from 400 nm to 1 100 nm in 50 nm increments. 
Calibration Method 
Preparations 
For our purposes, we need the capability of changing power 
supply voltages in flight while maintaining calibration. To 
arrive at a calibrated array of voltages, a common numerical 
method is employed. However, before this is done, we need 
to define at which wavelength each channel is centered. 
We first position a sodium light ( with a peak at 589 nm ) 
between a set of given channels. This is done because the 
sodium peak is narrower than the channel separation of 11.25 
nm. Onceourbearn-split-mirror has been adjusted for sodium 
light placement, it is locked in place. We now calculate at 
what wavelength all other channels reside. Using this infor- 
mation along with given sphere calibration radiance con- 
stants, radiance constants are calculated for every channel vs 
aperture combination. Figure 1 is a block diagram of dataflow 
during calibration. 
Spectrometer 
I I 
Figure 1. Calibration data flow. 
1 
Past technique 
At this point, for any aperture used in thecal sphere, we know 
the center wavelength and corresponding radiance value for 
each channel of the PAS. The next procedure involves 
choosing a particular channel as key channel. This key 
channel becomes our reference point from which all channels 
are compared. We put an arbitrary voltage on that channel; so 
gain on that PMT supplies signal enough to register counts 
from the A X .  Generally. a red channel is used as the key 
because thecal spheres output is much higher in the red region 
as shown in Figure 2. 
17e MO u e  4.90 475 MO me eso em 1 4 ~  me ew 07e 700 n e  
Wovdmgth (nm) 
Figure 2. €4 sphere spectra using aperture 0. 
In the past, calibriition was done at selected voltages. When a 
spectrometer sensitivity change was needed, one of those pre- 
selected voltages was chosen. If a desired sensitivity was not 
found, a compromise was made. Sensitivity was accepted or 
calibration files were manually cut and pasted together to 
achieve desired sensitivity in the chosen channels. This led to 
considerable work by the user, not to mention storage and 
documentation requirements for the various voltage combina- 
tions. 
Current technique 
The secant method5 is the numerical technique used to gener- 
ate calibrated voltage arrays. This technique quickly finds the 
root of a function. In this application, the root we are 
searching for is a voltage which causes desired counts from a 
particular channel. We set a key channel voltage and note the 
counts read back. This key is our reference point. The count 
value read from this key channel is linearly related to the 
appropriate radiance value. In doing this, we relate known 
radiance values for all other channels to desired count values. 
We now iterate ( using the secant method ) on all other 
channels to achieve desired counts. Once these count values 
are found, calibration for that set of radiance constants is 
complete. Figures 3 and 4 represent spectra before and after 
calibration has been applied. 
2 
Channel number 
Figure 3. Uncalibrated spectra using constant voltage across 
all channels. 
o z 4 o 8 to 12 14 in  i n  20 za 24 20 18 m 
Chonn.( nurnbw 
Figure 4. Calibrated spectra using root voltages. 
Real world problems force us to modify straight forward 
numerical techniques such as the secant method. In our case, 
we must window our iteration limits. If the secant method 
were left to run unaltered, calibration would probably never 
occur. We are restricted by limited dynamic range in our 
digitizer along with upper and lower limits in our power 
supply. 
At present, we perform 6 complete calibrations; all using the 
same key channel, but with different key voltages. Within the 
6 cals. 3 different apertures are used. Apertures are needed 
to keep key channel signal levels at a reasonable level while 
adjusting voltage. The reason we use 3 apertures instead of 6 
will be discussed in the section on radiance derivation. 
We perform 6 cals so a least squares 4th order polynomial5 can 
be passed through each set of non-key channel voltages vs 
key channel voltages. When any key voltage is chosen, a 
calibrated voltage for any non-key channel can be accurately 
calculated. Since 1 of the 32 power supply channels is 
designated key, we must generate 3 1 polynomials to account 
for all other channels. As seen in Figure 5 ,  this is necessary 
because of non-uniform gain characteristics for each PMT. 
- 
- 
The result is a 'best' fit through this system of 6 points 
whereby: 
y[i] = aO[i] + al[i]x + a2[i]xz + a3[i]x3 + a4[i]x4 
In this case, 'x' is equal to the key voltage and 'y[i]' is equal to 
Using our calibrated voltage arrays, we generate coefficients 
'aO[i]' through 'a4[i]' for all channels using the least squares 
a .  technique. When selected channels require a sensitivity 
change, we simply apply a new key voltage to the appropriate 
polynomials. By applying our set of polynomials to channels 
that need change, calibrated adjustments to the system sensi- 
tivity become a trivial matter. 
\ the resulting non-key voltage where 'i' is the channel number. 
2100 
' I  
Figure 5. Lines represent calibrated voltage arrays for each 
channel. 
Calibration limits 
The blue end of the spectrum is calibrated with a lower 
number of counts compared to that of the red end. This is 
because blue light is less intense from the cal sphere. Lower 
counts are nearer to the noise of the ADC than higher counts. 
To keep calibration errors to a minimum, lo0 counts was 
found to be the lower limit for any blue channel. Problems 
also arise on the red end of the spectrum. Counts read from 
any PMT are a product of gain and incident light. On the red 
end of the spectrum, there is more incident light. As power 
supply voltageincreases, so does gain. Small voltage changes 
then produce large changes in counts read back. Because of 
this large count change, a desired count number may not be 
reached. Calibration then becomes impossible. 
To insure calibration, an upper limit of 700 counts was found 
to be the cut off point for red channels given any aperture. 
known for its high gain characteristics. As seen in Figure 6, 
the line representing the largest aperture for this PMT has the 
greatest slope. Also note the exponential relationships for 
each of these lines. As voltage increases, counts read back 
.) This is a number found after observing a PMT in the red region 
increases at an exponential rate. When light and voltage 
(gain) are at their greatest, the exponential rate is also greatest. 
1000 
900 
600. 
a* 1 I I 
4d 
too 
loo0 I025 I 050 1075 1100 1125 
Valtag8 
Figure 6. Exponential relation of calibrated voltage arrays vs 
counts for AOL ch. 28 ( 690 nm ). 
Radiance Determination 
Radiance preparations 
In our calibration, we linearly related counts to radiance. If 
calibration were made to 0 percent error, this relationship 
wouldcontinue. However, due toa 5 percent error in calibrat- 
ing, aquadratic relationship was found to be more appropriate 
when making radiance determinations. It was found as 
voltage changes on a PMT, the relationship of counts vs 
radiance also changes. Due to this change, a quadratic 
representing counts vs radiance must be found for every 
desired voltage. Figure 7 is an example of lines representing 
quadratic relationships at various voltages. 
1 .o 
0.0 
t 0-0 
5 0.7 
e 
c 
0 0.6 
N - 
E O-' 
I" 0.4 
0.3 
0.2 
74 174 274 374 474 574 674 774 674 974 
Dlgitizrr aountm 
Figure 7. Quadratic relation of counts vs normalized radiance 
for AOL ch. 28 ( 690 nm ). 
3 
Radiance derivation a quadratic for any voltage. This is easily done using least 
squares again. 
Using data collected from calibration, we relate counts vs 
radiance quadratically with an equation of the form: 
y[i] = aO[i] + al[i]x + a2[i]xz 
Coefficients ‘aO[i]’ ...‘a2[ i]’ represent the gain vs incident light 
characteristics for channel ‘i’ at a particular voltage setting. 
Variable ‘x’ is equal to counts read and ‘y[i]’ is equal to 
calculated radiance. For every key voltage selected, we need 
to generate an appropriate quadratic. Once we have a quad- 
ratic for each key voltage, we can pass a least squares 4th order 
polynomial through each set of coefficients. Then, given a 
desired voltage, we can calculate the appropriate quadratic. 
However, before these quadratics can be generated, at least 3 
data points of counts vs radiance for each key voltage must be 
found. Since we use 6 key voltages, a total of 18 data points 
are needed for every channel. 
Due to limitations of hardware, we take 6 data points per 
channel instead of 18. Again, we are limited by inadequate 
dynamic range. This is the reason for 6cals. using 3 apertures; 
2 cals per aperture. A relationship must be found between 
counts vs voltage for all apertures used. This relationship 
implies a cerrain gain. By direct study, it was found that gain 
from a PAs~an  be expressed exponentially. Therefore, it will 
take a minimum of 2 data points to determine the appropriate 
exponential fit of the form: 
In y[i] = In b + mx or y[i] = b[i]@b 
By taking the natural log of both ‘y[i]’ and the y-intercept ‘b, 
this function can be treated as linear. Again, the least squares 
technique is used. The importance of this is we can now 
accurately predict, given a voltage and known radiance (aper- 
ture), what the resulting counts will be. 
As discussed, for every key voltage, there is an appropriate 
quadratic that relates counts to radiance. To produce one of 
these quadratics, a minimum of 3 points is needed for every 
key voltage. By using 2 key voltages per aperture, we are 
able to exponentially determine counts found at the other 4 
key voltages. Using 3 different apertures, we are now able 
to generate the 3 required data points per key voltage. This 
gives us the 18 data points needed for each channel. Figure 8 
illustrates those 18 points and how they are determined. 
Due to calibration constraints, 6 complete calibrations are 
made using 3 apertures. The exponential relation of voltage 
vs counts is used to extrapolate count values that are outside 
the ADC range. We now can fulfill our requirement of 3 data 
points for every key voltage. A quadratic least squares fit is 
passed through these 3 points to make a ‘best’ fit. Now, with 
a quadratic for every key voltage, we need a way to generate . 
At this point, we have generated 6 quadratics for every voltage 
of the PAS. Each quadratic corresponds with a key voltage 
selected when calibrating. Since each quadratic is unique and 
possesses 3 coefficients each, we must relate all of the first 
coefficients with the key voltages. Likewise, we must relate 
all of the second coefficients with the key voltages. Finally, 
we must relate all of the third coefficients with the key 
voltages. By passing a least squares 4th order polynomial 
through each coefficient-voltage pair, quadratic generation 
for any non-key voltage is now possible. By choosing any 
voltage within bounds of the key, we can generate the correct 
coefficients which make up our needed quadratic for that 
particular voltage. Now, with this quadratic, we can solve for 
radiance given counts read from the PAS. 
’ 
‘* 
575 
550 
450 
350 
1300 
1200 
- 
0 0 
0 o 
0 0 
0 0 
0 0 
0 0 
- 
0 3 5 
Aperture 
Known count values 
Exponentially determined count volues 
Figure 8. Calibration data points for AOL ch. 30 (712.5 nm). 
Concluding Remarks 
Calibration of this particular device is a multi-step operation. 
Considerations must be made to insure both a good calibration 
for sensitivity adjustments and sound data for radiance deriva- 
tion. When radiance measurements were taken immediately 
following a complete calibration, a 5 percent error was found 
using the cal sphere as a reference. Since there is a 5 percent 
error in calibration of the sphere, our total error is 10 percent. 
Improvements in thecal sphere calibration and use of a higher 
resolution ADC should reduce this error. 
- 
I 4 
References 
1. Hoge, F. E.; R. N. Swift: Airborne Simultaneous Spectro- 
scopic Detection of Laser-Induced Water Raman Backscatter 
and Fluorescence from Chlorophyll a and Other Naturally 
Occurring Pigments, Appl. Opt., Vol. 20, No. 3197, 1981. 
2. Hoge, F. E.; W. B. Krabill; R. N. Swift: The Reflection of 
W h e t  Pulsesfrom the Ocean, Mar. Geod., Vol. 8, No. 3 13, 
1984. 
* 
'L 
3. Bufton, J. L.; F. E. Hoge; R. N. Swift: Airborne Measure- 
ments of Laser Backscatter from the Ocean Surface, Appl. 
Opt., Vol. 22, No. 2603, 1983. 
4. Hoge, F. E.; R. E. Beny; R. N. Swift: Active-Passive Air- 
borne Ocean Color Measurement, I: Instrumentation, Appl. 
Opt., Vol. 25, No. 1, 1986. 
5. Burden, R. L.; D. J. Fakes; A. C. Reynolds: Numerical 
Analysis. Prindle, Weber, and Schmidt. 1978. 
5 
Report Documentation Page 
1. Report No. 
NASA TM-100739 
2. Government Accession No. 
4. Title and Subtitle 
Calibration of  a Photomultiplier Array Spectrometer 
17. Key Words (Suggested by Author(s)) 
Spectrometer 
Calibration 
Photomultiplier array 
7. AuthorW 
Steven A. Bailey, C. Wayne Wright, 
and Charles R. Piazza 
9. Performing Organization Name and Address 
NASA Wallops Flight Facility 
Wallops Island, VA 23337 
18. Distribution Statement 
Unclassified--Unlimited 
Subject Category 6 4  
Agency Name and Address 
National Aeronautics and Space Administration 
Washington, DC 20546-0001 
19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of pages 
Unclassified I Unclassified 5 
I15. Supplementary Notes 
22. Price 
3. Recipient's Catalog No. 
5. Report Date 
June 1989 
6. Performing Organization Code 
672 
8. Performing Organization Report No. 
10. Work Unit No. 
11. Contract or Grant No. 
13. Type of Report and Period Covered 
Technical Memorandum 
14. Sponsoring Agency Code 
Steven A. Bailey, C. Wayne Wright, and Charles R. Piazza: Wallops Flight 
Facility, Wallops Island, Virginia. 
16. Abstract 
A systematic approach to the calibration of a photomultiplier array spectrometer 
(PAS) is presented. Through this approach, incident light radiance derivation 
is made by recognizing and tracing gain characteristics for each photomultiplier 
tube (PMT). 


Calibration of a photomultiplier array spectrometer

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