SMTN-003: Trailing Losses for Moving Objects

  • Lynne Jones

Latest Revision: 2017-04-18

Solar system objects move across the image during an exposure. If the movement is significant, the signal to noise ratio of the object decreases compared to an equivalent stationary object.

_images/trailing_losses.png

Figure 1 Trailing losses in 0.7” seeing for 30 second exposures. The blue dotted line (SNR loss) indicates the losses due to simply spreading the light from a moving source over more background pixels. The red line (Detection loss) indicates the losses due to detection algorithms assuming a stellar PSF instead of a trailed PSF. With additional work in the source detection software stage, detection losses can be mitigated to the level of SNR losses.

_images/trailing_losses_fast.png

Figure 2 Trailing losses in 0.7” seeing for 30 second exposures, as above, but with a wider range of velocities.

_images/dmag_trailing_X.png

Figure 3 Trailing losses as a function of “X” = velocity(deg/day) * exposure time(s) / seeing(”) / 24.0.

def trailing_losses(velocity, seeing, texp=30.):
   """Calculate detection-based and SNR-based trailing losses.

   Parameters
   ==========
   velocity : float
       The velocity of the moving object, in deg/day.
   seeing : float
       The seeing in the image, in arcseconds.
   texp : float, opt
       The exposure time, in seconds.

   Returns
   =======
   dict
       dmag['trail'] and dmag['detect'] - detection and SNR losses.
   """
   a_trail = 0.761
   b_trail = 1.162
   a_det = 0.420
   b_det = 0.003
   x = velocity * texp / seeing / 24.0
   dmag = {}
   dmag['trail'] = 1.25 * np.log10(1 + a_trail*x**2/(1+b_trail*x))
   dmag['detect'] = 1.25 * np.log10(1 + a_det*x**2 / (1+b_det*x))
   return dmag

Note

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Calculating trailing losses for moving objects.