Reduction to the Johnson Bands

The reduction of "proprietary instrumental optical bands" to a standard photometric system is not mandatory when using an astronomical imager, but it is required for comparison with measurements taken by other instruments. To understand the usefulness of the Foveon detector for astronomical studies, it is therefore important to find out if the Foveon bands Rf, Vf and Bf can be compared to the standard Johnson bands. We convolved the Foveon bands of Fig. 4 with the flux of seven blackbody spectra in the range 2000-20,000 K and compared the results to the Johnson's magnitudes obtained from the same spectra. The Johnson minus Foveon magnitudes differences are a simple monotonically increasing function with respect to the color index (Vf -Rf), therefore we could use second order polynomials to convert the data between the two systems (see Fig. 5).

Figure 5. Residuals of Johnson minus Foveon magnitudes as a function of the Foveon color index (Vf -Rf) for blackbody spectra. The lines are second order polynomial interpolations.

The rms errors are less than a few percent when using relations like the following, derived for the V band:

(V-Vf)= 0.7818(Vf - Rf)2 + 0.2571-(Vf - Rf) - 0.0051 (2)

Similar formulae can be derived for the other Foveon bands with comparable errors. Our simulations therefore show that the Foveon magnitudes can be converted into astronomical standard magnitudes with a precision comparable to the one given by classic CCD imagers with filters.

3.2 Foveon vs. CCD on a Large Telescope (8.4 m)

We compare the performance of a hypothetical Foveon camera, which we name "Energy", and a state-of-the-art traditional CCD imager with filters (see Table 1). Our test science application aims at detecting fast transient phenomena in B, V and R bands by means of fast recursive imaging of a star field. The pixel size of both imagers is set to 9 microns.

Figure 6 shows the computed ratio of the CCD and Foveon exposure times needed to reach a S/N of 100 in all three bands for a given magnitude. It is evident that Energy is better than the CCD, because the bands are sampled simultaneously and faster. This is especially true for brighter magnitudes, despite Energy's larger noise and lower QE. Above 19th magnitude, both cameras are comparable, except for the simultaneous sampling of Energy.

Table 1. Comparison of hypothetical Foveon camera and traditional CCD imager performance.

Parameter

CCD

Energy

Detector size [Mpix]

4

4

RON [e-]

5

30

Read Out Time [sec]

1

0.25

Gain [e-/ADU]

2

5

Filter change time [sec]

1

Not needed

Scale ["/pix]

0.15

0.15

f-number

1.4

1.4

11 13 15 17 19 21 23 Magnitud«

Figure 6. Exposure time ratio of CCD and Energy cameras on an 8.4-meter telescope as function of target magnitude at S/N=100. The dots represent the sampling frequency of the target using the Foveon detector.

11 13 15 17 19 21 23 Magnitud«

Figure 6. Exposure time ratio of CCD and Energy cameras on an 8.4-meter telescope as function of target magnitude at S/N=100. The dots represent the sampling frequency of the target using the Foveon detector.

3.3 Foveon GRB hunter on a small telescope (0.6 m)

The performance of the Energy camera can be also evaluated for small Schmidt telescopes that search for GRB optical counterparts of "X-ray satellite alerts", a specific but popular astronomical application. In this case, the pixel scale is 1" and the imaged field is 1/3 deg squared. Optical counterparts are sometimes as bright as magnitude V=5. If the real-time data reduction pipeline is smart enough to detect the fast optical transient then it can be monitored in all three bands with the frequencies reported in Fig. 7. Table 2 compares the Foveon detector to standard technology imagers.

The Foveon detector looks promising and it could become the leader of a new family of optical detectors for photometric studies, especially if the manufacturer could:

1. reduce the RON,

2. increase the QE (e.g., with thinning and back illumination),

3. extend the UV and IR response, with more Foveon bands per pixel.

i g 3 10 12 M 15 IS Magnitude

Figure 7. Sampling frequency vs. target magnitude at a 60 cm Schmidt telescope for S/N=100 and S/N=10 using the Energy camera.

i g 3 10 12 M 15 IS Magnitude

Figure 7. Sampling frequency vs. target magnitude at a 60 cm Schmidt telescope for S/N=100 and S/N=10 using the Energy camera.

Table 2. Comparison of a Foveon detector to standard technology imagers.

Detector

Q.E. %

Sampling

Simultaneous

Complexity

Filter Wheel

90

Good

No

Standard

Mosaic (Bayer)

20-30

Bad (Moire)

Yes

Low

Dichroic

80-90

Good

Yes

High

Foveon

30

Good

Yes

Low

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