[fitswcs] Distortions

[Thompson, William T. (GSFC-671.0)[ADNET SYSTEMS INC]]

Mark:

Actually, I think I figured it out.  I was getting confused by the discussion of the auxiliary variables, which I now realize isn't relevant.  I believe the correct formation would be

DPDIS3 = 'Polynomial'
DP3.NAXES = 2
DP3.AXIS.1 = 1
DP3.OFFSET.1 = i0
DP3.AXIS.2 = 3
DP3.OFFSET.2 = j0
DP3.NTERMS = 1
DP3.TERM.1.COEFF = d1
DP3.TERM.1.VAR.1 = 1
DP3.TERM.1.VAR.2 = 1

Is this correct?

Thanks,

Bill Thompson

On 6/5/19, 4:54 PM, "Thompson, William T. (GSFC-671.0)[ADNET SYSTEMS INC]" <william.t.thompson at nasa.gov> wrote:

    Mark:
    
    I'm actually having a little trouble understanding this paper, and I was wondering if you could help me.  The distortion I'm trying to encode is given by the expression
    
    	j_correction = d1 * (i - i0) * (j - j0)
    
    Where i, j are axes 1,3 respectively, and i0,j0 are the reference pixels along those axes.  I've worked out that the first keywords would be
    
    DPDIS3 = 'Polynomial'
    DP3.NAXES = 2
    DP3.AXIS.1 = 1
    DP3.OFFSET.1 = i0
    DP3.AXIS.2 = 3
    DP3.OFFSET.2 = j0
    
    But I'm not really sure where to go from there.  There's also a more complicated correction along axis 1, but I figure that if I can understand this example, I can work out the rest.
    
    Thanks for any help you can give me.
    
    Bill Thompson
    
    On 5/9/19, 9:56 PM, "Mark Calabretta" <mark at calabretta.id.au> wrote:
    
        Hi Bill,
        
        WCSLIB implements Paper IV and all of the conventional distortion
        functions that I know of.  See
        
          https://urldefense.proofpoint.com/v2/url?u=http-3A__www.atnf.csiro.au_people_mcalabre_WCS_wcslib_dis-5F8h.html&d=DwIFaQ&c=ApwzowJNAKKw3xye91w7BE1XMRKi2LN9kiMk5Csz9Zk&r=4qrOT2Lux_0sXV9XNPmKKlSxaCYiFna5mbzVK8hbN2E&m=MKgwL0KKdQR-qMtR3FwMp86fMOsqwvomGgIbWhXdm_8&s=qky39bBSDec3axL0twQDI9s6sLhm_19wftCCP8IOd6c&e=
        
        I recommend using the TPD distortion.  It conforms to the Paper IV
        formalism, can handle 1-D as well as 2-D distortions, is a superset of
        TPV, SIP, DSS, TNX, & ZPX, and is optimized for speed.
        
        Regards,
        Mark Calabretta
        
        
        
        On Wed, 8 May 2019 14:50:44 +0000
        "Thompson, William T. (GSFC-671.0)[ADNET SYSTEMS INC]" <william.t.thompson at nasa.gov> wrote:
        
        Folks:
        
        It’s been a while since I’ve heard any chatter about WCS.  What’s the status of Paper IV on distortions?  Are distortions handled in any of the software packages, such as WCSLIB?
        
        It appears that we may need to use distortions for an upcoming mission.  Ray tracing for a spectrometer for the Solar Orbiter mission shows that the relationship between the pixel positions I,J and the real-world coordinates have significant second-order terms.  Our plans are to provide data in two formats, one in the original detector pixel space, and one where the data have been interpolated to linearize and rectify the data.  The latter is no problem, but I would like to accurately describe the coordinates in the former.
        
        Second order effects show up in two places.  The most significant is that the plate scale in arc seconds increases linearly with wavelength.  In other words
        
        S = a0 + a1 * J * (1 + a2*I)
        
        where S is the spatial dimension along the slit, J is the pixel dimension associated with the spatial dimension, and I is the pixel dimension associated with the spectral dimension.  Here, the second order effect comes from the J*I term.
        
        The other second order effect comes from the fact that the slit images are slightly bowed, so that the wavelength has a dependence on J^2.
        
        Thanks,
        
        Bill Thompson