Radiometric Calibration of MVIC
Jessica R. Lovering
October 17, 2007
ABSTRACT
Using the MVIC filter functions, Beam Splitter reflectance, Aluminum mirror
reflectance, and the product of quantum efficiency and filter function
(product QE), I calculate the final transmission (CHI) for each CCD array.
CHI is the product of quantum efficiency, filter function, beam splitter
reflectance, and the AL mirror reflectance cubed. To calculate the full
response, I multiply the final transmission by a spectrum, both from
observations of various solar system bodies and a calculated black body.
1. Calculating the Quantum Efficiency
1.1. Comparing Measured and Calculated Filter Functions
There are two sets of filter functions for each filter, measured and
calculated. The calculated transmission data covers the full wavelength scale
(350-1100 nm), and the measured transmission data only covers the wavelength
range where the filter has a non-zero transmission percentage. Figure 1
compares the two data sets to confirm that they match. Both sets of filter
functions are in 1 nm steps.
1.2. Calculating the Quantum Efficiency
The product QE is measured on a grossly sampled wavelength scale, 400-1100 nm
in 50 nm increments. The filter transmission, beam splitter transmission, and
mirror reflectance are measured on a larger wavelength scale in 1 nm
increments. To calculate the true Quantum Efficiency we must first down
sample the filter functions to the product QE wavelength scale, then divide
the product QE by the filter function to get the QE. To downsample the filter
functions, I take the average of 50 points centered on the product QE
wavelength scale. The results are shown in Figure 2. The product QE and the
downsampled filter function for each filter are provided in Table 1. Where
both values are non-zero, I divide the product QE by the filter function. I
then interpolate this true QE for each filter to the whole wavelength range.
To calculate the endpoints for the color arrays, I fit a polynomial to the
Pan1 and Pan2 QEs and use their x-intercept for all other filters. The final
QE function is presented in Figure 3
[RADIOCALMVIC_TABLE1.PNG]
Table 1: The downsampled filter function and the product QE for each filter.
We can only calculate the QE where both the product QE and the filter
function are non-zero (in bold).
Fig. 1. Filter Transmission
2. Calculating CHI
2.1. Pan Frame Transmission and Beam Splitter Reflectance
Both the Pan Frame filter function and the Beam Splitter reflectance were
measured in 1 nm steps over the full wavelength scale. The Pan Frame
transmission data measures the percentage of light that transmits through the
clear filter over the two pan frame CCDs. Both functions are shown in Figure
4.
2.2. AL Mirror Reflectance
The reflection of the mirror is measured on the product QE wavelength scale.
I interpolated the points to the full wavelength scale (400-1100 nm in 1nm
steps). The reflectance is cubed since there are three mirrors.
[RADIOCALMVIC_FIGURE2.PNG]
Fig. 2. The filter transmission data downsampled to the QE wavelength scale
is given by asterisks. The original, full scale, filter function is
represented by a solid line for comparison.
2.3. Putting It All Together
Now that I have every transmission function on the same scale, I can
calculate CHI using Equation 1.
[RADIOCALMVIC_EQUATION1.PNG] (Equation 1)
Every step of the CHI calculation is shown in Figure 5, and the final CHI for
each filter is shown in Figure 6. F1 and F2 are the transmissions of Pan1 and
Pan2 without the clear filter on top,calculated using a grossly sampled
product QE. The CHI calculated from grossly sampled arrays is overplotted
with asterisks.
[RADIOCALMVIC_FIGURE3.PNG]
Fig. 3. Quantum Efficiency of each filter
[RADIOCALMVIC_FIGURE4.PNG]
Fig. 4. The Pan frame transmission, and the Beam Splitter Reflection
[RADIOCALMVIC_FIGURE5.PNG]
Fig. 5. The arrays that are multiplied to get CHI.
[RADIOCALMVIC_FIGURE6.PNG]
Fig. 6. CHI for each filter. The lines represent the finely sampled arrays,
and the asterisks are grossly sampled arrays.
3. Ball Aerospace Response Ratio
Dennis Reuter employs the measured QE from Ball Aerospace to calculate a
ratio with his calculated CHI. I will calculate the same ratio between the
finely sampled CHI for each array with the associated value from Ball
Aerospace. The values measured by Ball are provided in Table 2. To calculate
the ratio, I sum the finely sampled CHI for each filter over the significant
wavelength range (where CHI > 0), then I divide this sum by the value given
in Table 2. I will refer to this value as the QE ratio.
4. Including the Source Spectrum
4.1. Black Body Spectrum
Using the planck function, Equation 2, I calculate the black body flux over
our wavelength range for 5900 degrees Kelvin. I then multiply the black body
flux by CHI to get the full response, which I sum and multiply by the QE
ratio to calulate the final values given in Table 3.
[RADIOCALMVIC_TABLE2.PNG]
Table 2: Measured QE values from Ball Aerospace.
[RADIOCALMVIC_EQUATION2.PNG] (Equation 2)
[RADIOCALMVIC_FIGURE7.PNG]
Fig. 7. The black body function for 5900 K and the full response of the CCDs
including the black body function.
4.2. Including Spectra of Solar System Bodies
Following the method employed for the black body function, I calculate the
final response using observed spectra from Pluto, Charon, the Sun, Pholus,
and Jupiter. The spectra used for this calculation I acquired from *****. The
summed and scaled values are provided in Tables 3 - 8.
[RADIOCALMVIC_TABLE3.PNG]
Table 3: Final response including black body function, compared to Dennis
Reuter's calculated values.
[RADIOCALMVIC_TABLE4.PNG]
Table 4: Final response including Pluto's spectrum.
[RADIOCALMVIC_TABLE5.PNG]
Table 5: Final response including Charon's spectrum.
[RADIOCALMVIC_TABLE6.PNG]
Table 6: Final response including Solar's spectrum.
[RADIOCALMVIC_TABLE7.PNG]
Table 7: Final response including Pholus' spectrum.
[RADIOCALMVIC_TABLE8.PNG]
Table 8: Final response including Jupiter's spectrum.