Description

Assumptions

This correction is currently only implemented for MIRI data and is only for integrations after the first integration (i.e. this step does not correct the first integration). It is assumed this step occurs before the dark subtraction, but after linearity.

Background

The MIRI Focal Plane System (FPS) consists of the detectors and the electronics to control them. There are a number of non-ideal detector and readout effects which produce reset offsets, nonlinearities at the start of an integration, non-linear ramps with increasing signal, latent images and drifts in the slopes.

The manner in which the MIRI readout electronics operate have been shown to be the source of the reset offsets and nonlinearities at the start of the integration. Basically the MIRI reset electronics use field effect transistors (FETs) in their operation. The FET acts as a switch to allow charge to build up and to also initialize (clear) the charge. However, the reset FETS do not instantaneously reset the level, instead the exponential adjustment of the FET after a reset causes the initial frames in an integration to be offset from their expected values. The Reset Switch Charge Decay (RSCD) step corrects for the slow adjustment of the FET output to its asymptotic level after a reset. This correction is made for integrations > 1 and is based on the signal level in the last frame of the previous integration in the exposure. Between exposures the MIRI detectors are continually reset; however for a multiple integration exposure there is a single reset between integrations. The reset switch charge decay has an e-folding time scale ~ 1.3 * frame time. The affects of this decay are not measurable in the first integration because a number of resets have occurred from the last exposure and the effect has decayed away by the time it takes to readout out the last exposure, set up the next exposure and begin exposing. There are low level reset effects in the first integration that are related to the strength of the dark current and can be removed with an integration-dependent dark.

For MIRI multiple integration data, the reset switch decay causes the the initial groups in integrations after the first one to be offset from their expected linear accumulation of signal. The most significant deviations occur in groups 1 and 2. The amplitude of the difference between the expected value and the measured value varies for even and odd rows and is related to the signal in the last frame of the last integration.

The MIRI reset electronics also cause a zero-point offset in multiple integration data. Subsequent integrations after the first integration start at a lower DN level. The amplitude of this offset is proportional to the signal level in the previous integration. Fortunately this offset is constant for all the groups in the integration, thus has no impact on the slopes determined for each integration.

Algorithm

This correction is only applied to integrations > 1. The RSCD correction step applies an exponential decay correction based on coefficients in the reset switch charge decay reference file. The reference files are selected based on READOUT pattern (FAST or SLOW) and Subarray type (FULL or one of the MIRI defined subarray types). The reference file contains the information necessary to derive the scale factor and decay time to correct for the reset effects. The correction differs for even and odd row numbers.

The correction to be added to the input data has the form:

corrected data = input data data + dn_accumulated * scale * exp(-T / tau)  (Equation 1)

where T is the time since the last group in the previous integration, tau is the exponential time constant and dn_accumulated is the DN level that was accumulated for the pixel from the previous integration. Because of the last frame effect the value of the last group in an integration is not measured accurately. Therefore, the accumulated DN of the pixel from the previous integration (last group value) is estimated by extrapolating the ramp using the second to last and third to last groups.

In the case where the previous integration does not saturate the \(scale\) term in Equation 1 is determined as follows:

\(scale = b{1}* [Counts{2}^{b{2}} * [1/exp(Counts{2}/b{3}) -1] \; \; Equation \; 2\)

The terms \(b{2}\) and \(b{3}\) are read in from the RSCD reference file. The following two additional equations are needed to calculate the \(b{1}\) and \(Counts{2}\) terms:

\(b{1} = ascale * (illum_{zpt} + illum_{slope}*N + illum2* N^2) \; \; (Equation \; 2.1)\) \(Counts{2} = Final \, DN \, in \, the \, last \, group \, in \; the \, last \, integration \, - Crossover \, Point \; \; (Equation \; 2.2)\)

In equation 2.1, N is the number of groups per integration and \(ascale\), \(illum_{zpt}\), \(illum_{slope}\), and \(illum2\) are read in from the RSCD reference file. The \(Crossover \, Point\) in equation 2.2 is also read in from the RSCD reference file.

If the previous integration saturates, the \(scale\) term in Equation 1 is found in the following manner:

\(scale_\text{sat} = slope * Counts{3} + sat_\text{mzp} \; \; (Equation \; 3)\)

where \(Counts{3}\) is an estimate of what the last group in the previous integration would have been if saturation did not exist. The \(slope\) in equation 3 is calculated according to the formula:

\(slope = sat_{zp} + sat_{slope} * N + sat_2*N^2 + evenrow_{corrections} \; \; (Equation 3.1)\).

The terms \(sat_\text{mzp}\), \(sat_{zp}\), \(sat_2\), \(evenrow_{corrections}\) are read in from the reference file.

All fourteen parameters \(tau\), \(b{1}\), \(b{2}\), \(b{3}\), \(illum_{zpt}\), \(illum_{slope}\), \(illum2\), \(Crossover Point\), \(sat_{zp}\), \(sat_{slope}\), \(sat_2\), \(sat_{scale}\), \(sat_\text{mzp}\), and \(evenrow_{corrections}\) are found in the RSCD reference files. There is a seperate set for even and odd rows for each READOUT mode and SUBARRAY type.

Subarrays

Currently the RSCD correction for subarray data is the same as it is for full array data. However, we anticipate a separate set of correction coefficients in the future.