The following describes the results of the tests that demonstrate meeting of the criteria — the ability to detect Earth-size transits with an end-to-end system that performs as closely as possible to the way the actual space mission will perform.

Interpretation of the Performance Plots

Baseline Test

Rotation-Translation

Bright Stars

Spacecraft Jitter of 3x Baseline

Cosmic Rays

Long-Duration Tests

Testing Summary

Conclusions

Figure 2 (and Figure 5) contain the information for the 138 stars that were measured in each test. Fifty-four of the stars are located in the crowded region representing the star density of the galactic plane.The typical test duration was about 48 hours, except for the long duration tests, which ran for 10-14 days. Figure 1 display the 1-hour to 1-hour precision versus star magnitude after the data were processed by our "standard analysis" procedure. (The long duration tests had enough data samples to compute 5-hour to 5-hour precision as in Figure 5.) The processing consists of analyzing the raw fluxes with the "optimal aperture program" (optapflux) followed by decorrelating the relative fluxes (decorr).

The fractional precision values for normal stars (round holes in the star plate) are depicted by circles, while the stars capable of transits (rectangular stars crossed with a tiny wire) are depicted by "W"s. The green "x"s depict the calculated fractional shot-noise. The red "x"s denote the instrument noise calculated from the background variations. The solid red line denotes the required limit on the fractional noise exclusive of stellar variability (compare with values on line 5a of Table 1 for 12th, 13th and 14th magnitude stars.)

A common feature seen in all of the tests was that almost all of the stars that are above the max-allowed line (the Ws) are 9th, 12th, and 14th magnitude stars with transit wires. Whereas those without wires (the Os), which includes all of the 11th and 13th magnitude stars almost always remain below the max-allowed red line. It is apparent that the wires add extra noise and can therefore be justifiably ignored when evaluating the system noise.

Prior to introducing external confounding factors, the effects of several common factors were measured in a Baseline test, since these are incorporated in the star plate. These included: dynamic range (m_v=9-14 stars), crowded field (1540 stars in one local region) and smearing (multiple stars in the same CCD columns). The photometric precision of the Baseline test run at -60°C for 46 hours are presented in Figure 2.

Figure 2. 1-Hr to 1-Hr Precision Versus Stellar Magnitude.

The fractional noise for normal stars (round holes) is depicted by circles. The noise for stars with rectangular holes crossed with a tiny wire are depicted by "W"s. The green "x"s depict the shot-noise. The red "x"s denote instrument noise calculated from background variations. The solid red line denotes the required limit on the noise shown on line 5a of Table 1 for 12th, 13th and 14th magnitude stars.

An earlier Baseline test was run at -50°C for 55 hours producing almost the same noise, indicating that -50°C was a sufficiently cold temperature (and hence, used for all subsequent testing). Sample transits from the -50°C test are shown in Figure 3. Note that although the transit signals for the fainter 14th magnitude stars were typically 10 Earth-area, the noise was sufficiently small to detect transits of a few Earth area. The Kepler Mission photometry and the projected results are based on and scaled from being able to detect a one-Earth-area transit of a 12th magnitude star at 4 sigma. The center column of transit signals clearly demonstrates this.

Figure 3 Sample of Transits from Baseline Test.

Transits for 9th (left column), 12th (middle column) and 14th (right column) magnitude stars. The vertical scale is relative brightness changes in units of Earth-areas. The blue lines are the 15-min. data. The red lines are the 5 hour averages. The data have been processed using the opaptflux (optimum aperture), decorr and polynorm programs. The location of the scheduled transits are indicated by the error bars. The error bars are the plus and minus one sigma variance for the data exclusive of the transit.

During the mission the spacecraft is rotated 90° about the photometer axis every three months to maintain the side of the spacecraft with the solar panels pointed towards the Sun and the opposite side with radiator panels pointed to deep space. In between these rotations the spacecraft attitude remains fixed with the solar-vector slowly rotating through only a single quadrant of the spacecraft. This provides for a very slowly changing and otherwise benign thermal environment. The effect of the rotation on the operations is to move the star field image to different CCDs within the focal plane every three months and then begin a new three-month period with the stars imaged on a new fixed set of pixels. This causes only a small loss of transit data during the time of the rotation and restabilization (about a day). There is no requirement for the trend lines before and after the rotation to match. To demonstrate that the noise and ability to detect transits is not dependent on any one unique set of pixels or location on the CCD, the image was translated from one end of the CCD furthest from the readout registers to the end nearest the readout registers. The resulting performance, which was actually better than the Baseline test. For the remainder of the tests the image was shifted back to the far end of the CCD.

For the large star field viewed during the Kepler Mission there are 15 stars as bright as 4th to 6th magnitude. To test the impact of these bright stars, a 4th magnitude bright star was introduced into the test image. The bright star only adversely affected a few columns of the CCD and thereby increased the noise slightly for only a few nearby stars. However, one star that was particularly close to the column containing the bright star not only had significantly more noise, but its apparent brightness was about one stellar magnitude brighter. Aside from a few stragglers, the overall noise was still well below the max-allowed as defined in Table 1. The general performance was similar to the Baseline test.

Based on previous spacecraft performance data and engineering modeling done by Ball Aerospace & Technologies Corporation for the Kepler Mission, a conservative estimate of the three-sigma pointing stability of ±0.1 arcsec has been derived. We define this to be the baseline jitter. The PZTs in the Testbed were driven at the frequencies and at three times the baseline amplitude prescribed by this attitude control system model. Except for a few stragglers, the overall noise was still well below the max-allowed even at three times baseline spacecraft jitter.

Cosmic ray hits have nearly always been detrimental to photon detectors. They cause both radiation damage and deposit energy. Over an extended period of time, CCDs produce traps, hot pixels, increased dark current and reduce the charge transfer efficiency (CTE). They also deposit unwanted charge when they interact. Radiation damage is a common problem for all CCD uses, has been a topic of continual study and may be mitigated to some extent by charge injection sometimes called a "fat zero". The fat zero also adds extra shot noise, which is an issue in low-flux situations. For the Kepler Mission, there is no shutter. Hence, the smearing of stars acts like a fat zero and has the beneficial side effect of keeping the traps filled. Long-term radiation damage was not incorporated into this Testbed.

Charge deposited by cosmic rays is particularly problematic when using a CCD to measure very low fluxes. A cosmic ray may deposit more charge in one instant than is normally expected for a long exposure of a faint object. However, to achieve the low shot-noise level for the Kepler Mission, >3x10⁸ electrons per five hour integration are required for even the faintest star (m_v=14), so that cosmic rays do not appear to be a major source of additional noise.

To test this, the equivalent of a Baseline test was run in which simulated cosmic rays were injected into the 3-second readouts but not rejected (Figure 1), based on a model for the comic ray flux seen in the LASCO/SOHO instrument. The cosmic-ray flux corresponded to 6 /cm²/sec with 2500 e^- on average deposited in a pixel. Again, aside from a few stragglers, the overall noise for this test was still well below the max-allowed.

Another cosmic-ray test was done in which a simple threshold algorithm was used to reject all 3-sec. integrations for any star that exceeded a threshold by more than a preset amount (e.g. 4x the sigma of the threshold value) and the flux for each star was corrected for the deleted data. The results were better than the case without rejecting the cosmic rays. However, when later tests were performed, in which image motion was introduced, this simple algorithm caused far too many false detections. The good results without cosmic ray rejection demonstrates that it is probably not necessary to delete the cosmic ray events.

After performing the various tests to identify any adverse effects of any individual source of noise, several long-duration tests were performed. First a 14-day Baseline test was performed. Then two tests were run incorporating all of the confounding factors. That is, in addition to those incorporated in the Baseline test, the tests included a bright star at 4th magnitude, spacecraft jitter and cosmic rays. In these tests the cosmic rays were injected but not removed.

For the 14-day Baseline test, the overall noise level is somewhat higher than in any other test with several stars deviating above the max-allowed line. However, these few stragglers did not raise the ensemble average above the max-allowed line.

A ten-day test was conducted with the all the confounding noise factors: 4th magnitude bright star, spacecraft jitter at 1/3 the baseline value (best estimate of performance) and cosmic rays added but not deleted. The overall noise level is somewhat higher than in any other test with several stars deviating above the max-allowed line. However, these few stragglers did not raise the ensemble average above the max-allowed line. Sample transits from this test are shown in Figure 4.

Figure 4 Transits from Long Duration Test (10 Days) with a Bright Star, 1/3 Spacecraft Jitter and Cosmic Rays. Star 5 (upper left) has a 12 hour transit. All others are 5 hour transits. The locations of the scheduled transits are indicated by the error bars. The green error bars are the plus and minus one sigma variance for the data exclusive of the transit.

The final long duration test was a six-day test with the 4th magnitude star, spacecraft jitter at one-times baseline and cosmic rays added but not deleted. The precision versus stellar magnitude plot, Figure 5, shows that the performance was generally within the required limits. The average measured noise was well below the required level at all star magnitudes. This test demonstrates the ability to achieve the required precision photometry in a realistically simulated space environment.

Figure 5 5-Hour to 5-Hour Precision for the 6-Day Test with 1x Baseline Spacecraft Motion, Cosmic Rays and a 4th Magnitude Star.

All of the usual disturbances were also present throughout this 6-day test. The precision was within the requirement for all 9th, 13th and 14th magnitude stars (Table 1 line 5). The average precision for 11th and 12th magnitude stars is very close to the required limit. Note that W stars were inherently more noisy due to the presence of the wire.

In all of the tests performed, the noise level was at or below the maximum allowed, with the exception of those stars that had transit wires. A tabular summary of the average fractional measured noise in units of 10^-5 is given in Table 3 for 5-hour binning. The max allowed noise is from Table 1 line 5, except that the required value for stars brighter than 12th magnitude is taken to be no better than that for 12th. The 13th mw and 14th mw are those stars that are in the crowded region representative of the star field density in the Milky Way where the Kepler Mission observes.

The Kepler Mission is designed to detect hundreds of Earth-size planets by looking for transits. To demonstrate the technology to be utilized, a Testbed Facility was built and operated with a flight-type CCD. The facility simulates all of the features of the sky and the spacecraft/photometer that are important for the success of the mission. Optimum operating conditions for the PSF, photometric aperture size versus stellar brightness and maximum operating temperature were measured. Proto-flight software necessary for processing the data was used throughout. The required photometric precision was demonstrated while operating without a shutter during readout, having some saturated pixels in the brightest stars, working in a crowded field with a star density the same as planned for the mission, inclusion of spacecraft jitter and over a dynamic range of five stellar magnitudes. Additional tests of comic-ray hits and field rotation also did not have detrimental effects. Transits were injected and detected at the required statistical significance under all operating conditions during all tests.

In long duration tests the Camera was simultaneously subjected to normal tracking errors, uncorrected cosmic ray hits, a 4th magnitude star in the CCD field and all of the other confounding factors expected under realistic operating conditions. These tests demonstrated that SNRs of 4.6 are achievable for Earth-size transits of 9th to 12th magnitude stars without stellar variability, permitting SNRs of 4.0 when stellar variability is included. For 13th and 14th magnitude stars the SNRs (including variability) are 2.3 and 1.1, respectively, due to the higher level of shot noise.

While the achievement of 10^-5 precision had already been demonstrated in earlier tests, the results presented here provide ample evidence for the ability of existing commercially available CCDs in an end-to-end test with realistic operating conditions to consistently achieve a fractional precision of better than 1x10^-5 and to consistently detect simulated Earth-size transits at the require SNR. The very successful test results should greatly reduce any perceived risk in the Kepler approach to planet detection.