[PIPE2D-302] 1d skysb: model fit approach Created: 23/Oct/18  Updated: 08/Jan/20

Status: Open
Project: DRP 2-D Pipeline
Component/s: None
Affects Version/s: None
Fix Version/s: None

Type: Story Priority: Normal
Reporter: Masayuki Tanaka Assignee: sogo.mineo
Resolution: Unresolved Votes: 0
Labels: None
Σ Remaining Estimate: Not Specified Remaining Estimate: Not Specified
Σ Time Spent: Not Specified Time Spent: Not Specified
Σ Original Estimate: Not Specified Original Estimate: Not Specified

Issue Links:
Blocks
is blocked by PIPE2D-455 Fit multigaussian to cauchian Open
is blocked by PIPE2D-456 Find a good optimizer Open
Relates
relates to PIPE2D-346 Provide a method for determining the ... Done
Sub-Tasks:
Key
Summary
Type
Status
Assignee
PIPE2D-455 Fit multigaussian to cauchian Sub-task Open sogo.mineo  
PIPE2D-456 Find a good optimizer Sub-task Open sogo.mineo  
Story Points: 6
Epic Link: 1D sky subtraction
Sprint: 2DDRP-2019 J, 2DDRP-2019 K

 Description   

As I (Sogo) understand Masayuki's suggestion:
 
Let s_α(λ) the sky spectrum from the α-th fiber.
We first decompose s_α(λ) = sd_α(λ) + sc_α(λ),
where sd_α(λ) is a discrete spectrum and sc_α(λ) is a continuum.
 
Somehow we model sc_α(λ).
 
The discrete spectrum sd_α(λ) will be reconstructible as
    sd_α(λ) = Σ_i a_i P(λ - λ_i; θ_{αi})
if we have a perfect dictionary of emission lines

{λ_i\} and a PSF model at each emission line P(λ - λ_i; θ_\{αi}

).
 
After we represent the sky spectrum as
    s_α(λ) = sc_α(λ) + Σ_i a_i P(λ - λ_i; θ_{αi}),
we then somehow tweak sc_α(λ), a_i and θ_{αi} before subtracting
s_α(λ) from an object spectrum, in a way that the sky spectrum
will be removed neatly. This subtraction also includes a
subtle transformation λ ↦ λ', which is almost identity, in order
to absorb errors in wavelength calibration.

edit (2018-11-09)

To be more correct:

0. We assume that all fibers in an exposure share a single, common sky spectrum.

1. From arc exposure(s) we construct a 1-D PSF model for each fiber f:

PSF = PSF(λ - λ_p; f, λ_p).

The PSF depends on the fiber_id f and the peak position λ_p.

We save this PSF model as one of calibration data, just as they save flat and fibertrace.

2. To process spectra (mixture of sky spectra and object spectra),
we first load the PSF model that has been constructed beforehand.
Then, assuming a sky spectrum of fiber f can be expressed as a sum of PSFs:

sky_f(λ) ~ skymodel(λ; (A_p)) = Σ_p A_p PSF(λ - λ_p; f, λ_p),

we determine A_p by minimizing the difference between lhs and rhs.
Note the amplitude A_p depends only on the peak position p.
It does not depend on the fiber f, in accordance with the assumption 0.

3. We subtract the same skymodel(λ; (A_p)) from every object spectra.

Note:

  • In 1., we need arc spectra with continua subtracted.
  • In 2., we have to separate continua from sky spectra.
    If an upstream module can do this separation, we will just use it.
    Otherwise we have to do it for ourselves.


 Comments   
Comment by hassan [ 01/Nov/18 ]

sogo.mineo or Masayuki Tanaka: for my information could you clarify what you mean by the parameter θ_{αi} for the 1-D PSF model? Thanks.

Comment by sogo.mineo [ 01/Nov/18 ]

> could you clarify what you mean by the parameter θ_{αi} for the 1-D PSF model?

I have not determined what model to use, but if I were simply to use the gaussian (quite unlikely, though) θ would be the standard deviation σ of the gaussian.

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