Introduction
The CCD detector of the C1 instrument is a 1024 x 1024 pixel array upon which is formed an image of the solar corona out to about 3 solar radii. The plate scale of the LASCO C1 instrument is the angular distance observed by one pixel. In what follows, the term "p" (one pixel unit) will refer to the length of one pixel (about 0.021 mm) while a "pixel" will be used as a unit of area (1 pixel = 1 p2).
Wavelength Method of Measuring Plate Scale
The Fabry-Perot (FP) interferometer and the blocking filters in the C1 instrument transmit only light of a particular wavelength. The wavelength of the light transmitted depends upon the separation of the FP plates and the angle of the light ray with respect to an axis normal to the FP plates. This axis is called the optical axis of the FP, and the point at which it intercepts the detector is the optical axis intercept (FPAI). The relationship between the transmitted wavelength of a normal ray and that of a ray passing through the FP at some other angle is given by:
w = w0 cos(a p) Eq(1)
where w0 is the wavelength passed by a normal ray, and p
is given by:
p = sqrt((px-px0)2+(py-py0)2) Eq(2)
where p is
the distance (in pixel units) from the point where the ray strikes the detector
([px,py])
and the location of the FPAI
([px0,py0])
and a is the "plate scale" in angular units per pixel unit.
The plate scale may be measured by taking a scan of a closed door image, which will consist almost entirely of "Fraunhofer" radiation characteristic of the solar disk. Using the NSO[1] tabulation of the solar irradiance convolved with the known instrument profile of the C1 instrument allows the wavelengths of solar features on a C1 scan to be assigned a wavelength. The set of wavelengths so measured may be fitted in a least squares sense to Equation 1 using a, px0, and py0 as fitting parameters
The plate scale for the LASCO C1 instrument has been measured by this method to be a=5.62 "/p in any direction. The position of the FPAI has been measured to be at px0=577.9 p, py0=378.46 p. Note that for even the most extreme case, the product of a and p is so small that the Taylor expansion of Equation 1 may be used quite accurately:
w ~ w0(1-(ap)^2/2) Eq(3)
The alpha Leo Method of Measuring Plate Scale
The second way of measuring the C1 plate scale is to observe the transit of a star across the C1 field of view. Knowing the angular rate of transit from orbital parameters will allow the plate scale to be determined. Only a few stars are bright enough to be visible in C1. One such star is alpha Leo (Regulus) which transits the C1 field of view every August 22-23. Using the transit of 1997, it was determined that the rate of transit was 24.814 pixels per hour. Making the simple assumption that the star transits 360 degrees every year, the plate scale can be estimated at 5.958 "/p. Correcting for the eccentricity of the earth's orbit, and the orbital motion of SOHO about the Lagrangian point, a more accurate estimate of the plate scale is 5.826 "/p.
It is not presently known why the plate scale as derived by the above two methods disagree. The expected error in each is not nearly enough to explain the difference. For purposes of wavelength calculation, the wavelength-derived values should be used, but for positional determination on an image, the second should be used.
[1] Kurucz, R.L., Furnlid, I., Brault, J., Testerman, L, ``Solar Flux Atlas from 296 to 1300 nm'', National Solar Observatory Atlas No. 1, June 1984.