linpol: Calculate polarization frames and Stoke’s parameters

Package: nproto

Usage

linpol input output

Parameters

input

A list of input images. There must be either three or four input images taken with the polarizer at even multiples of a 45 degree position angle.

output

The output data cube which will contain as separate bands the fractional linear polarization and angle frames, and optionally the Stokes parameter frames.

degrees = yes

Report the polarization angle in degrees? If degrees = no, the polarization angle will be reported in radians.

stokes = yes

Output the Stokes parameter images? If stokes = yes, the three linear Stokes parameters, I, Q, and U, will be included in the output data cube as separate bands. If stokes = no, only the fractional linear polarization and angle frames will appear in the output.

normalize = no

Normalize the Q and U frames? This is appropriate when using a tool such as VELVECT to plot the polarization vectors. If normalize = yes, the Q and U Stokes parameter frames will be normalized by dividing by the I parameter frame. This parameter has no effect on either the fractional polarization or angle frames.

keyword = "polangle"

This must be set to the name of a header keyword that contains the polarizer angle for each of the input images. LINPOL will only accept polarizer angles at even 45 degree separations. Either four such frames, at 0-45-90-135 degrees, or three frames with any one of the 0-45-90-135 degree frames omitted, may be specified.

Description

LINPOL calculates the pixel-by-pixel fractional linear polarization and polarization angle for a set of either three or four images taken with polarizer set at even multiples of a 45 degree position angle. At least three different frames with the header keyword set to one of 0, 45, 90, or 135 degrees must be specified in the input list.

If degrees = yes, the output polarization angle band of the image will be in units of degrees, if degrees = no, the angle will be reported as radians. If stokes = yes, the output image will consist of five separate bands, one each for the pixel-by-pixel fractional linear polarization and the corresponding polarization angle, and one for each of the I, Q, and U pixel-by-pixel Stokes parameters. If stokes = no, only the fractional polarization and the polarization angle will be saved in the output.

The normalize parameter is useful for plotting purposes. If normalize = yes, the Q and U Stokes parameter frames will be normalized by dividing by the I parameter frame. This may be appropriate when using a tool such as VELVECT to plot the polarization vectors. This parameter has no effect on either the fractional polarization or angle frames.

Each input image must contain the corresponding polarizer angle in the header keyword specified by the parameter keyword Linpol will only accept polarizer angles at even 45 degree separations. Either four such frames, at 0-45-90-135 degrees, or three frames with any one of the 0-45-90-135 degree frames omitted, may be specified.

The output image header will include information describing the particular input images that went into its generation and the particular nature of each band of the output.

Examples

An observer obtained four exposures of a particular field through a polarizer set at a position angle of 0-45-90-135 degrees. The first step in producing a good map of the polarized light from (extended or point-like) sources in the field is always to register these frames very precisely. A slight mismatch in the positioning of each pixel relative to the shoulders of nearby sources or extended emission will result in large errors in the determination of the polarization quantities.

Another preprocessing step that may be desirable is to match the PSFs (Point Spread Functions) of the various frames. Ideally, these are stable in the raw data (i.e., the seeing at the telescope was constant), but if not they must be matched to avoid the same errors as above. Note that it may also be a good idea to "smooth" the raw images before applying linpol to increase the signal-to-noise of the output.

After guaranteeing the integrity of the input images, the image header keyword must be created to contain the position angle. The hedit task can be used to do this:

hedit im.00 polangle 0 add+
hedit im.45 polangle 45 add+
hedit im.90 polangle 90 add+
hedit im.135 polangle 135 add+

At this point, the input images are ready to be processed by linpol.

To generate an output image containing the fractional linear polarization and polarization angle in separate bands, along with the pixel-by-pixel Stokes parameter frames:

np> linpol im.*.imh polar

To omit the Stokes parameter frames:

np> linpol im.*.imh polar stokes-

To represent the pixel-by-pixel polarization angle in radians, rather than degrees:

np> linpol im.*.imh polar degrees-

To normalize the Q and U Stokes frames and plot the result with velvect:

np> linpol im.*.imh polar normalize+
np> imhead polar lo+
polar[100,100,5][short]: Linear polarization image
    No bad pixels, no histogram, min=unknown, max=unknown
    Line storage mode, physdim [100,100,5], length of user area 2147 s.u.
    Created Wed 10:15:05 29-Apr-92, Last modified Wed 10:15:05 29-Apr-92
    Pixel file 'ursa!/ursa/scr3/iraf/seaman/polar.pix' [ok]
    ...

    POL0    = 'im.00.imh'
    POL45   = 'im.45.imh'
    POL90   = 'im.90.imh'
    POL135  = 'im.135.imh'
    POLAR   = 'Band 1 is the percent polarization'
    ANGLE   = 'Band 2 is the polarization angle'
    I-STOKES= 'Band 3 is the Stokes I parameter'
    Q-STOKES= 'Band 4 is the normalized Stokes Q parameter'
    U-STOKES= 'Band 5 is the normalized Stokes U parameter'
np> velvect polar[*,*,4] polar[*,*,5]

Note that the current version of the velvect task is not particularly appropriate for this use. It has no support for reducing the pixel resolution of the output plot: each pixel will generate a plotted vector so that to produce an uncrowded (and low "noise") plot, the input images or output bands must be manually block averaged or otherwise smoothed. In addition, the plotted vectors are directed (little arrows) not undirected line segments, and the length of the vectors are not easily adjusted.

See also

velvect, imalign, hedit