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.