Data Timestamp

The timestamp of the data obtained by Tomo-e Gozen is synchronized by the GPS clock. Since Tomo-e Gozen obtains an image in a rolling shutter mode, the exposure starting time of each pixel may differ. A careful treatment is required for the reduction of time-critical observations. This page provides a guide to calculate the timestamp of each pixel in an image cube. The FITS header contains several keywords related to timing and interval. The table below lists important keywords for observation.

Keyword	Explanation
`UTC`	Timestamp when the exposure of the first pixel started in UTC.
`EXPTIME`	Total exposure time in seconds.
`TELAPSE`	Total elapsed time to obtain the data cube in seconds.
`EXPTIME1`	An exposure time for a single frame in seconds.
`TFRAME`	An interval between to successive frames in seconds.
`TRLSTEP`	An interval of the reset line feeding in seconds.

The meanings of the keywords are illustrated in the figure below. The horizontal arrow indicates the elapsed time for a pixel.

The red rectangles show the intervals when the pixel accumulates photons, corresponding to EXPTIME1. The grayed rectangles show the duration when the pixel is insensitive to photons, corresponding to TFRAME. TELAPSE is the total-elapsed time required for the observation. Instead, EXPTIME is the net exposure time defined by

\[ \text{EXPTIME} = \text{NAXIS3} \times \text{EXPTIME1}. \]

The detector controlling signal is synchronized with a GPS clock installed in Tomo-e Gozen. Tomo-e Gozen sends a trigger signal to the GPS clock when the first photosensitive pixel starts integration. The GPS clock records the time in UTC by the trigger, which is recorded as UTC or GPS-UP in the FITS header. The timestamp is as accurate as 0.2 ms (see, Kojima et al., 2018).

The integration timing of each pixel can be calculated using the information above. Define the pixel coordinates as \(\text{NAXIS1} = i\), \(\text{NAXIS2} = j\), and \(\text{NAXIS3} = k\).¹ The midst-point of the integration timing of the \((i,j,k)\)-pixel is provided by

\[ t_{i,j,k} = \text{UTC} + 0.5\,\text{EXPTIME1} + (k - 1){\times}\text{TFRAME} + \left\lfloor \frac{j - 1}{4} \right\rfloor{\times}\text{TRLSTEP}, \]

where \(\lfloor \cdot \rfloor\) is the floor operator. The first term is the GPS timing. The second term corresponds to half of the exposure time per frame. The third term accounts for the elapsed time of the past frames. The fourth term provides the time shift due to the rolling shutter. Since the detector of Tomo-e Gozen samples 4 rows at once, \(t_{i,j,k}\) depends only on \(\lfloor (j-1)/4 \rfloor\).

Caution

Headers may contain wrong timestamp if the GPS clock malfunctions, although the validity of the timestamp is checked in the automated data reduction process. Please inform the Tomo-e Gozen team if you find something wrong in the timestamp.

Info

The intervals (EXPTIME, TELAPSE, etc.) written in the header are calculated from a clock pattern that drives the detectors. The clock pattern relies on the crystal oscillator equipped on a digital I/O board. Thus, the intervals may suffer from the stability of the crystal oscillator, that has not been evaluated. Assuming the stability is about 100 ppm, the intervals may have the uncertainties of about 0.01 %. The exposure timing can differ by about 10 ms when TELAPSE is about 100 s. This uncertainty may matter in some science cases (e.g., cross-correlation analysis against X-ray observations).

The pixel coordinates are defined in the 1-origin format. ↩