# Echo and DFE in the SIS: How to Correct Them

--by Chiko Otani, Tadayasu Dotani, ISAS

## Echo

"Echo" is the phenomenon where some specific fraction of a pixel's pulse height (PH) is added to the PH of the neighboring right-hand side pixel (next read-out pixel). Because an event's PH and grade is calculated using the PHs of the event's 3x3 pixels, echo affects both the grade and energy of each photon event in a non-linear fashion. Echo is thought to occur in the video filter of the Analog Electronics (AE). The echo fraction has different values for SIS-0 and SIS-1. Echo ratios among the different chips in the same sensor are the same. The echo ratio has neither positional dependence on the chip nor PH dependence between at least 200Ð2000 Analog to Digital Convertor Units (ADU). The echo values for each sensor are listed in Table 1. As seen in the table, echo ratio shows secular increase. Therefore, the appropriate echo ratio should be used in the data analysis. The reason of this secular increase is not known.

Table 1: Time-dependence of echo ratio

### Method of Correction

Suppose that we know the value of echo ratio, we can easily correct the grade and PH of each event, provided that the event data is in Faint mode. The real PH of each pixel is calculated by a simple formula: (real PH) = (observed PH) - (real PH of previously read-out) x (echo ratio). We don't need to be concerned about the propagation of echo, because the added amount is determined from the "real" PH of its left-hand pixel.

In the case of bright mode, we cannot correct the echo for each event. Instead, echo should be included in the response matrices.

### Uncertainty and Systematic Error

Because the PH value of an event is usually converted into an integer after the echo correction, about 0.5 ADU (approx. 2 eV) uncertainty is always present in each event energy. This is at least 10 times smaller than fluctuation of PH value of one pixel.

## Dark Frame Error

"Dark Frame Error" (DFE) is the difference between the real "zero level" of pixels and that estimated by the onboard software. Onboard software calculates "zero level" (referred to as Dark Frame by the hardware team) for each 16 x 16-pixel subsection by averaging the PH of pixels whose PH lies between Ð40 ADU and 40 ADU (1 ADU approx. 3.5 eV). DFE mainly arises from asymmetric distribution of PH around zero, and is influenced by the charges generated by X-ray photons, charged particles, and optical light leakage on the CCD chips. This means DFE depends on the accumulation time (1-, 2- or 4-CCD mode).

When the satellite is in orbital night, where the light leakage does not exist, the amount of DFE is typically Ð2 to Ð3 ADU for 4-CCD mode. For 1- or 2-CCD mode, the absolute value of DFE is closer to the real "0 level" than 4-CCD mode, because of shorter accumulation time (4 or 8 sec compared to 16 sec in 4-CCD mode). During the night time of the satellite, DFE is stable with typical standard deviation of 1 ADU (approx. 3.5 eV). During the satellite day time, DFE behavior becomes very different from the night time because of the optical light leakage. Though the mean DFE values are almost same as at night, the amplitude of fluctuation is typically doubled. When the angle between SIS FOV and Bright Earth edge is less than 25 degrees, DFE can be a few tens of ADU. Such data should not be used because they exceed the limit of the DFE correction possible now. Similarly, those data when DFE values are highly variable should not be used.

Absolute Dark level is different between satellite night and day. This causes a sharp jump of DFE during the night-day terminator. The amount of this jump is well correlated with the angle between the FOV and the Sun (qzs), and ranges from a few ADU (theta zs <90 degrees) to approx. 20(10) ADU for S0(S1) (theta zs approx. 70 degrees). After this jump, DFE returns exponentially to almost the same DFE level as the night time, because the onboard software updates the Dark Levels using the data in the previous exposures. When this jump is large and/or a precise correction is needed, the data in this transition zone should not be used. Especially, when theta zs < 70 degree, telemetry for S0C2 and S0C3 is easily saturated at the transition from night to day time by the instantaneous increase of the amount of light-leakage. The typical timescale to restabilize the DFE is approximated by (50-60)n seconds where n is the number of readout (1, 2 or 4) CCD chips (e.g. 200-250 seconds for 4-CCD mode).

A similar situation occurs when the satellite leaves the South Atlantic Anomaly (SAA). This is because the analog electronics of SIS is turned off in SAA by the Radiation Belt Monitor (RBM) flag, and the Dark Level is held at the values it had before the RBM flag fired. As the charges produced by particles and light in the SAA fill the CCD chips, the Dark Levels of first several read-outs after the SAA are incorrect. Jumps similar to those at the night/day transition occur in the DFE after the SAA passage.

### Method of DFE Corrections

The PH distribution of the corner pixels of each 3 x 3- pixel event is useful to estimate the DFE values. We use only events in grade 0, 2, 3, and 4 for DFE calculation because the corner pixels of these events are considered to be free from charges from X-rays or charged particles. After the selection, we consider that the peak of PH distribution of corner pixels represents "real 0 level." Because DFE is variable with time, we have to calculate so-called DFE light-curve. Empirically, more than about 100 events (including hot pixels) are needed to determine the peak value of the corner pixel distribution within an accuracy of 1 ADU. The typical integration time for 100 events is 64 second for the faintest sources.

### Uncertainty of DFE correction

The typical uncertainty of PH after DFE correction in night time is less than 1 ADU in the lower energy band and 1.5 times larger in the higher energy band. In the daytime, the uncertainty becomes 2Ð3 times larger than during nighttime. There is also a 0.5 ADU (approx. 2 eV) uncertainty due to the conversion from real number into integer.

DFE correction becomes less precise and such data must be removed, when the variation of DFE is faster than integration time, such as day-night terminator. So far we ignored positional dependence of DFE over the chip. Position dependence of DFE may be present especially on S0C2 and S0C3 where the light leak is serious. However, currently available software does not calculate positional dependence of DFE; this may slightly increase the uncertainty of the DFE for the two chips.

In addition, there is no method to detect instantaneous DFE variation within 10 ADU. Though the probability to get such large DFE is very small, such DFE causes unusually large offset in photon energy, especially for the spectra with short accumulation time. As large DFE is always positive, large energy shift in spectrum also occurs in this direction systematically. Accordingly, typical uncertainty or systematic error in energy is within 10 eV and instantaneous maximum systematic error may be about 30 eV.

### Treatment of Bright mode data

As the DFE effect cannot be corrected for bright mode, we need to include it in the response matrices. Because DFE is variable, we had better select the time region where DFE is stable enough. After such selections, we can make spectral analysis by using the response matrices in which the typical DFE value is included. All the nighttime data except day-night terminator show stable DFE as we can see for the faint mode data. Accordingly, the selection is essentially important only for the daytime data.

One of the easiest way to select relatively stable DFE data in bright mode is to use number of pixels above threshold (this parameter is available in the MKFILTER). Both the pixel number and DFE depend on the amount of light leakage, so the pixel number can be an indicator of DFE, although it is not a very good one. If you select time intervals where the pixel number is stable, that period corresponds to where the DFE does not show large variations.

### Secular variation of PH distribution

It is known that PH distribution around zero show secular time variation. Asymmetry of PH distribution becomes more prominent with time in 4-CCD mode. However, time variation is not clear in 1-CCD mode. This secular variation is considered to be related with the increase of the flickering pixels.

The nature of this secular variation is now under investigation. The DFE correction program uses a template PH distribution to search the peak of the distribution. Because the secular variation is not included in the template, DFE correction for recent 4-CCD mode data may suffer from additional systematic error. The amount of error is estimated to be 1Ð2 ADU. The method to adapt this secular variation is under development.