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NICMOS Data Handbook > Chapter 5: Data Analysis > 5.3 Astrometry, Pixel scales, and Geometric Distortion

5.3 Astrometry, Pixel scales, and Geometric Distortion
Accurately transforming pixel positions in NICMOS images to relative or absolute astronomical coordinates involves several considerations. Here we consider each of these in turn. For the latest information regarding these issues, consult the STScI NICMOS plate scale Web pages at: http://hst.stsci.edu/nicmos/performance/platescale.
5.3.1
With the installation of NCS, the plate scale of NICMOS has become very stable. The NICMOS arrays are slightly tilted relative to the focal plane, and therefore the NICMOS pixel scales along the X and Y axes of each camera are slightly different, i.e., projected on the sky, the pixels are actually slightly rectangular, not square. The X and Y plate scales at the central pixel of the arrays are listed in Table 5.2 and were determined from SMOV3b data as described in more detail in Section 5.3.2. The differences in X and Y pixel scale are small: the X/Y scale ratios SX/SY are approximately 1.0030, 1.0076, and 1.0032 for cameras 1, 2 and 3, respectively, in the sense that the X scale in arcseconds per pixel is larger than the Y scale in each case. It amounts to 1 to 2 pixels “extra width” in the X direction relative to Y over the field of view of the cameras, and for precision astrometry or when registering NICMOS images to data taken with other instruments such as WFPC2, it may be important to take the effect into account. This can easily be done when drizzling NICMOS images using coefficient matrices as described in Sections Section 5.3.2 and Section 5.3.3 below.
During Cycle 7, the distortion of the NICMOS dewar due to the cryogen expansion affected the optical path, pushing the cold well and cameras closer to the field divider assembly and cold mask. This caused the effective focal length, and hence the pixel scale, to change somewhat as a function of time during Cycle 7. The changes were most rapid during the orbital verification period and approximately the first 100 days of instrument operations, then slowed, with only small variation thereafter. The pixel scale was monitored regularly throughout Cycle 7. A tabular and graphical record of these measurements for all three cameras can be found on the STScI NICMOS Web pages at:
http://hst.stsci.edu/nicmos/performance/platescale.
This source should always be consulted before transforming pixel coordinates of Cycle 7 images to arcseconds.
Table 5.2: NICMOS Plate Scales at Detector Center (i.e. pixel 128, 128)
5.3.2
The distortion corrections for the NICMOS cameras are small, but for precision astrometry or when registering and coadding images (especially taken with a wide dither pattern, or when assembling mosaics covering a large field) it should be taken into account. The geometric distortion was measured using dithered observations of the astrometric field NGC1850 through all three cameras. The data analysis and results for Cycle 7 are described in detail in an instrument science report (ISR) by Cox et al. 1997 (ISR OSG-CAL-97-07). The same technique was used to determined the distortions after NCS installation, using data obtained during SMOV3b. An ISR describing analysis of these data is forthcoming, but results are listed in Table 5.3, on the NICMOS pixel scale Web page, and are incorporated in the latest drizzle coefficient files (see Section 5.3.3).
The maximum total positional deviations (in pixels), assuming zero distortion at field center, are approximately 0.9, 0.25, and 0.75 pixels for Cameras 1, 2 and 3, respectively. Cox et al. found that quadratic relations were adequate for describing the distortion given the accuracy of the observational measurements. Given a pixel position (x,y), we define new coordinates (x,y′) relative to the array center, here chosen to be at pixel 128,128:
x = x - 128,
y = y - 128.
The positions corrected for distortion, (xc,yc′), are then given by
xc = a10 x+ a11 y + a20 x2 + a21 xy + a22 y2
yc = b10 x + b11 y+ b20 x2 + b21 xy + b22 y2
where the origin of the (xc, yc′) coordinate system is chosen to be coincident with that of (x, y′), i.e. pixel (128,128) of the array. As defined by Cox et al., the distortion corrections explicitly do not account for the X and Y scale difference described above, and therefore a10 and b11 are fixed at 1. The actual plate scales at pixel (128, 128) are listed in Table 5.2 for data taken after NCS installation or can be obtained from the Web as described in Section 5.3.1. Also, a11 (the linear dependence of x on y) is held at 0, although b10 is derived in the fit. This fixes the y axis orientation, but allows for departures from orthogonality. The fitted coefficients for the three cameras are given in Table 5.3.
Table 5.3: NICMOS Geometric Distortion Coefficients
a10
a20
a21
a22
b10
b11
b20
b21
b22
After applying this distortion correction, remember to add 128 to each of the xc and yc values to transform the origin back to pixel position (128,128).
Also remember that the above solution does not correct the X/Y scale differences described above. The preferred way to do this would be to multiply all the a coefficients in the expression above by the square root of the pixel scale ratio, √(SX/SY), and the b coefficients by the reciprocal value, √(SY/SX), using the scale ratios given above. This will correct all pixels to square geometry, preserving the area of a pixel located at array center. This is the approach used in the distortion coefficients used by the drizzle algorithm (see Section 5.3.3).
Cox et al. also solve for the detector y axis orientation relative to the telescope V3 axis. The beta angles (Bx and By), shown in Table 5.4, indicate the angle of the +x and +y axes from the telescope +V3 through +V2 in degrees (see Fig 6.1 in the NICMOS Instrument Handbook).
Table 5.4: Beta Angles for all Three NICMOS Cameras
5.3.3
One way to apply the geometric distortion correction when combining dithered NICMOS images is to use the drizzle software, which is incorporated into the package stsdas.analysis.dither. This software was written to allow geometric distortion corrections to be applied during drizzling. In order to do so, it is necessary to specify a coefficient file with the parameter drizzle.coeffs. Geometric distortion coefficient files in a format suitable for use with drizzle are available from the STScI NICMOS Web pages and are also provided with the stsdas.analysis.dither package. In these, the coefficients from Cox et al. have been multiplied by the square root of the pixel scale ratio so that the output images will have square pixels with uniform X and Y scales, as described above. The absolute pixel scale (arcseconds per pixel) is not set by the drizzling procedure, and should be determined by using or by consulting the NICMOS pixel scale Web page, as explained above. The appropriate value to use with the drizzled images is the geometric mean of the X and Y scales specified by the Web pages, i.e. √(SX SY).
The latest version of MultiDrizzle, available in stsdas.analysis.dither now fully supports NICMOS observation and is to date the easiest way to apply geometric correction to NICMOS observations. MultiDrizzle applies the same corrections described above when using drizzle. However, the distortion coefficient files for all three NICMOS detector are now available as part of the routine NICMOS calibration files and these will be used automatically by MultiDrizzle. Users should refer to the NICMOS example of the MultiDrizzle Cookbook for a much more detailed example of how using MultiDrizzle with NICMOS data.
5.3.4
As with all HST instruments, determining the absolute astrometry in NICMOS images to good accuracy requires precise astrometry from some external source for at least one object within the field of view. The absolute pointing reference given by world coordinate system (WCS) information encoded in NICMOS image headers is derived from the HST Guide Star Catalog (GSC) positions for the stars used to guide the observations. Although the GSC positions, and hence the WCS astrometry, are generally good, deviations by as much as 2 arcseconds from an absolute celestial reference frame (e.g., FK5) are not uncommon. The WCS information provided with NICMOS images does account (at least to first order) for the nominal pixel scale, camera orientation, and even the X and Y pixel scale differences of the cameras. It does not, however, include any higher order corrections for geometric distortion. Therefore relative positions measured using the WCS (e.g., with the IRAF tasks imexam or rimcur) are fairly accurate, even if the absolute pointing reference may not be exact.
Finally, it is important to note that precise astrometry with NIC3 can be complicated by three effects. First, for data taken outside the January or June 1998 refocus campaigns, focus effects may affect the geometry of the focal plane. Second, data taken prior to January 1998 was usually vignetted (see Section 4.7.4), which can also distort the geometry. Finally, intrapixel sensitivity variations (see Section 5.2, and NICMOS ISR-99-005, Storrs et al.) can affect centroiding for undersampled point source images.

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