EXES flat processing steps

Make Flat

Flats are generated by the top level procedure makeflat: use the card sequence to make a calibrated flat. Also run derive_tort on black cards to determine distortion parameters

Steps

  1. Calculate mean to find black frame (brightest)

    • robustmeancomb

  2. Determine photon background at given wavelength & temperature, as given by the header values WAVENO0 and BB_TEMP respectively.

  3. Calculate the RQE (Robust Quality Estimator?) for the black frame

  4. Determine the sky and shiny frames

  5. Combine all frames grouped by their label (black, shiny, sky, sky2) through direct sum

  6. Get flat values by mode

    • Determined by cardmode, initially pulled from header key CARDMODE but might be overriden by downstream logic.

    • Available values:

      • BLK

      • NONE

      • SKY

      • SHINY

      • BLKSKY

      • OBJ

      • BLKOBJ

      • BLKSHINY

  7. Check for correlation between card frames

  8. Check for saturated pixels

  9. Clean cards with clean

  10. Derive tort parameters with a 2D FFT with derive_tort

  11. Clean diff (\(diff = black - sky\)) frame with clean

  12. Calculate flat from

    \[flat = \frac{B_{\nu}(T_{card})}{black-sky}\]

  13. Calculate variance frame from

    \[variance = \frac{cardstd^2 * bnut^2}{(black-sky)^4}\]

  14. Update illumination frame with results of flat

    • Correct for tort with tortcoord

    • Mark all out-of-bounds pixels as -1

    • Mark all pixels next to a bad pixel as 0

  15. Set the first plane of cards to the second plane

  16. Tort the first card with echelon slit skewing with tort

  17. Return flat

Derive Tort

Sets distortion parameters by processing a blackbody flat frame. Identify orders and illuminated regions. Generates the illumination frame which indicates which regions of the undistored frame are illuminated.

Steps

  1. Undistort input flat data with tort

  2. For cross-dispersed data (HIGH-MED or HIGH-LOW) test and optimize distortion

    • Enhance the edges of the image

    • Generate 2D FFT of resulting image

    • Determine order spacing

    • Calculate the angle

    • If \(|angle|>0.001\) update krot and rerun distortion correction

  3. Generate illumination frame

    \[ \begin{align}\begin{aligned}power = \sum_y undistorted\\threshold = threshold\_fraction \cdot max(power)\\\begin{split}illum = \left\{ \begin{array}{c l} 1 & power > threshold \\ 0 & power < threshold \end{array} \right\}\end{split}\end{aligned}\end{align} \]

  4. Update header with the edge definition parameters determined from the undistorted flat.

    • NORDERS

    • ODRn_T1

    • ODRn_B1

    • ODRn_XR

    • ORDR_B

    • ORDR_T

    • ORDR_S

    • ORDR_E

    • EDGEDEG: Degree of the polynomial fit to order edges

    • ORDERS: Orders indentified’

    • SLTH_PIX: Slit height in pixels

    • SLTH_ARC: Slit height in arcseconds

    • SLTW_PIX: Slit width in pixels

    • SLTW_ARC: Slit width in arcseconds

    • RP: Resolving power

    • ROTATION: IDL rotate value

Tort Coord

Calculates undistorted image coordinates. Uses the array size and tort parameters from the header, along with knowledge of the instrument’s optics, to calculate x- and y-coordinates in the undistorted array that correspond the x- and y-coordinates of the raw array.

Main Parameters

HR = High Resolution XD = Cross-Dispersed

From header

  • KROT:

  • SLITROT: Slit rotation

  • HRG:

  • HRR: R number of echelon grating

  • XDG:

  • XDR: R number of cross-dispering element

  • XDDELTA:

  • PIXELWD: Pixel width

  • XDFL: Adjusted XD focal length

  • HRFL: Adjusted echelon focal length

  • DETROT: Detector rotation

  • BRL:

  • X0BRL:

  • Y0BRL:

  • XORDER1: First pixel of order 1

  • SPACING:

  • KROT: Rotation angle between chambers

Calculations

  • \(hr_{skew}\)

  • \(xk_{skew}\)

  • \(xd_{smile}\)

  • \(xd_{nonlin}\)

  • \(dxd_{skew}\)

  • \(hr_{nonlin}\)

Steps

  1. Calculate parameters to characterize skew, echelon smile, and whatever xdnlin is.

  • For cross-dispersed modes

    \[ \begin{align}\begin{aligned}hr_{skew} &= 2 * HRG * HRR * \tan(\theta_{slit})\\xk_{skew} &= 2 * XDG * XDR * \tan(\theta_{rot})\\xd_{smile} &= \frac{-XDR * PIXELWD}{XDFL}\\xd_{disp} &= \frac{XDFL * \left(XDR - XDDELTA \right)}{HRFL * HRR}\\xd_{nonlin} &= -\left(XDR + \frac{1}{2 * XDR}\right) * \frac{PIXELWD}{2 * XDFL}\\dxd_{skew} &= \left(XDG + \frac{xd_{disp}}{2 * XDR}\right) * \left( 1 + XDR^2 \right) * \frac{PIXELWD}{XDFL}\\hr_{nonlin} &= -\left( HRR + \frac{1}{2 * HRR}\right) * \frac{PIXELWD}{2 * HRFL}\\xorder_0 &= xorder_1 - \frac{spacing}{2}\end{aligned}\end{align} \]

  • For longslit modes

    \[ \begin{align}\begin{aligned}xd_{skew} &= 2 * XDG * XDR + \tan(\theta_{slit})\\xd_{smile} &= \frac{-XDR * PIXELWD}{XDFL}\\xd_{nonlin} &= -\left(XDR + \frac{1}{2 * XDR}\right) * \frac{PIXELWD}{2 * XDFL}\end{aligned}\end{align} \]

  1. Apply skew, smile, and nonlinearity corrections

  • Generate coordinate arrays with the same shape as a data frame, where \(x\) has values of the distance along the x-axis and \(y\) has values of the distance along the y-axis

  • Distance from each pixel to center

    \[ \begin{align}\begin{aligned}x_{dist} = x - \mbox{mean}(x)\\y_{dist} = y - \mbox{mean}(y)\end{aligned}\end{align} \]

  • For crossdispersed modes

    • If handling skew

      \[ \begin{align}\begin{aligned}order = \frac{x - xorder_0}{spacing}\\y_{dist} = y_{dist} + hr_{skew} * spacing * \left(order - round (order)\right)\end{aligned}\end{align} \]

    • Correct for nonlinearity of echelon spectrum

      \[y_{cor} = y_{dist} + hr_{nonlin} * \left( y_{dist}^2 - y_{mid}^2 \right)\]

    • Correct for skewing due to cross dispersion, k mirror, and smile

      \[x_{cor} = x_{dist} + xd_{disp}*y_{dist} + xd_{skew}*y_{cor} + dxd_{skew}*x_{dist}*y_{cor} + xd_{smile}*y_{cor}^2\]

    • Correct for nonlinearity of xd spectrum

      \[x_{cor} = x_{cor} + xd_{nonlin}\left(x_{cor}^2 - x_{mid}^2 \right)\]

  • For longslit mode, only correct distortions along x-axis

    \[ \begin{align}\begin{aligned}y_{cor} = y_{dist}\\x_{cor} = x_{dist} + xd_{nonlin} \left(x_{cor}^2 - x_{mid}^2 \right)\end{aligned}\end{align} \]

  1. Apply barrel distortion correction

\[ \begin{align}\begin{aligned}barrel = 1 - BRL * \frac{(x_{cor} - X0BRL)^2 + (y_{cor}-Y0BRL)^2}{x_{mid}^3}\\x_{cor} = x_{cor} * barrel\\y_{cor} = y_{cor} * barrel\end{aligned}\end{align} \]

  1. Rotate by detector rotation angle (DETROT).

    \[ \begin{align}\begin{aligned}u = -x_{cor}\cos(DETROT) + y_{cor}\sin(DETROT) + x_{mid}\\v = -y_{cor}\cos(DETROT) - x_{cor}\sin(DETROT) + y_{mid}\end{aligned}\end{align} \]

Tort

Corrects image for optical distortion. Uses tortcoord to generate undistorted coordinates from raw pixel coordinates and distortion parameters in the header. The image is then interpolated onto the undistorted coordinates. If the variance is provided, it is also interpolated onto undistorted coordinates.

Main Parameters

Steps

  1. Convert raw coordinates to undistorted coordinates with tortcoord

  2. Loop over each frame of the image

  3. Interpolate each frame of the image onto new undistorted coordinates

  4. Do same for variance

  5. Return undistorted image