Supersampling

The photometric datapoints we're dealing with are always integrations over time. If the exposure time is long, such as with Kepler long cadence data, the light curve features are smeared, and we need to include the effect from the long exposure time into the light curve model. This can be done easily by supersampling the model (that is, calculating the model for several time samples inside each exposure and averaging the results).

PyTransit implements a basic supersampler in pytransit.supersampler.SuperSampler to facilitate transit model supersampling. You don't generally need to initialize or call the supersampler manually, since the transit model uses it automatically, but knowing how to use it may come handy in some more advanced situations.

SuperSampler is initialized as SuperSampler(nsamples, exptime), where nsamples is the number of subsamples to create per exposure, and exptime is the exposure duration.



In [28]:

    
%pylab inline
from pytransit.supersampler import SuperSampler









    



Populating the interactive namespace from numpy and matplotlib



In [29]:

    
sampler = SuperSampler(nsamples=5, exptime=1)

The subsample positions are calculated as $$s_i = t + \mathbf{s} \times t_e$$ where $\mathbf{s}$ are the subsample positions normalized to [-0.5, 0.5], and can be accessed from the sampler



In [30]:

    
sampler.sample_positions









    Out[30]:





array([-0.4, -0.2,  0. ,  0.2,  0.4])

After the initialization, the SuperSampler offers two methods

sample(times[npt]) $\rightarrow$ array[nsamples*npt]
average(flux[nsamples*npt]) $\rightarrow$ array[npt]

Sample is used to create a set of supersampled time stamps where times is an 1D array storing the exposure center times and expdur is the exposure duration. After the model has been evaluated for the supersampled time stamps, average is used to compute the per-exposure averaged model.



In [31]:

    
time_o = arange(0,3).astype('d')
time_s = sampler.sample(time_o)



In [34]:

    
plot(time_o, full_like(time_o, 0.99), 'o')
plot(time_s, full_like(time_s, 1.01), '.')
ylim(0.98,1.03);



In [56]:

    
def lcfun(time):
    return (time > 1.1).astype('d')

plot(time_o, lcfun(time_o), 'o')
plot(time_s, lcfun(time_s), '.')
plot(time_o, sampler.average(lcfun(time_s)), 'ko', ms=10)









    Out[56]:





[<matplotlib.lines.Line2D at 0x112a91da0>]