LASCO C1 Radiometry
Questions? call (202) 767 2263 ask for the LASCO C1 Calibration Person

Introduction

In a previous note (Three-image Method of Calculating LASCO C1 Emission Images) the method of extracting the emission line signal from a C1 image was outlined. It remains to convert this signal into the corresponding intensity of the solar emission corona which produced it. An IDL program fpc1_2img.pro is available to convert a line emission signal image to intensity. The program takes as input the signal image (DN/pixel/sec), the lower left corner position on the detector [ix,iy] (pixel units), the binning of the image, and the particular closed door dataset used to derive the calibration image. The corresponding intensity image (erg/sec/cm²/sr/A) is returned.

The radiometric calibration of the C1 instrument is accomplished by using a model which has been found to be accurate to within a few percent:

	S(w,p) = R(p)I(w) + L(p) + E(w,p)		Eq(1)

where w is wavelength, p is position (in pixel units) on the detector, S(w,p) is the signal (corrected for offset bias and exposure time), I(w) is the disk-averaged solar "Fraunhofer" intensity, E(w,p) is the emission line signal, and R(p) and L(p) are model parameters.

For closed door images, the sun illuminates a translucent screen at the entrance aperture of the instrument, which swamps any coronal radiation E(w,p). The solar intensity I(w) may be estimated from the NSO[1] solar irradiance. Since the signal S(w,p) is measured, this leaves only the model parameters R(p) and L(p) to be determined. These parameters are found by a least squares fit to Equation 1 above.

Relative Radiometry

Equation 1 may be restated using radiometric parameters as:

	S(w,p) = C g(p) [q(p)I(w) + IL(w) + IE(w,p)]	Eq(2)

were q(p) specifies the variation of Fraunhofer radiation over the detector relative to the nominal value I(w), g(p) is the dimensionless relative radiometric correction and C is the average radiometric conversion factor which converts signal (DN/pixel/sec) to intensity (erg/sec/cm²/sr/A). The relative radiometric calibration will consist of determining the value of g(p) in Equation 2.

Since we are dealing only with closed door scans, the emission term I_E(w,p) may be dropped. Also, the closed door illuminates the detector rather evenly except for the region of the occulter, the occulter rolloff, and the outer vignette region. This region of constant illumination will be referred to as region U. Over U, q(p) will be practically a constant (q_c). For any pixel in U, then we may write:

	S(w,p) = C g(p) [qcI(w)+IL(w)]			Eq(3)

The pixel average of any quantity over U will be the sum of that quantity over all pixels in U divided by the number of pixels in U. Denote this average by brackets < >. A condition which will be imposed on the relative calibration image g(p) will be:

	< g > = 1					Eq(4)

It follows from Eq 1, 3, and 4 that g(p) is given by:

	g(p) = R(p)/< R >				Eq(5)

which completes the relative radiometric calibration.

Absolute Radiometry

The absolute radiometric calibration will consist of determining the value of C in Equation 2. This is done with the door open, using a star of known magnitude, in this case alpha Leo. From Equation 2, subtracting two images containing alpha Leo will isolate the signal due to alpha Leo:

	Sa(w,p) = C g(p) Ia(w)				Eq(6) 

where S_a is the pure alpha Leo signal and I_a is the (effective*) intensity of alpha Leo which may be obtained from the literature [2,3]. It can be seen that:

	C = Sa(w,p)/g(p)Ia(w)				Eq(7)

As it turns out, the value of C measured in this manner is equal to 0.7991 DN/pixel/erg/cm²/sr/A, which completes the absolute radiometric calibration of the C1 instrument.

In order to convert a signal image to intensity, it need only be divided by the Cg(p) calibration image. The calibration image derived from the 06/Mar/1998 closed door data is shown below:

The image looks very much like a closed door image, as it should, since it is, in a sense, a very refined and averaged closed door image. Note the rings which are present in the image. These are apparently due to diffraction effects in the telelens part of the instrument. As regards radiometric calibration, they would be no problem at all if their position were independent of wavelength, but since they are in fact a diffraction phenomenon, the positions of the rings vary slightly with wavelength. This is a small but not negligible effect (a few percent) which cannot be accounted for by the model equation (Equation 2). In order to accurately account for these rings, a new model must be developed in which the relative radiometric image g(p) becomes a function of wavelength as well as position.

* - Since a pixel responds to the average intensity over the field that it "sees", the effective intensity of alpha Leo will be the irradiance of alpha Leo as given in References [2,3] divided by the square of the plate scale.

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References

[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.

[2] Knyazeva, L.N., and Kharitonov, A.V., Astron. Zh. 68, 323-331, March-April 1991. (English Translation in Sov. Astron. 35(2), March-April 1991.)

[3] Knyazeva, L.N., and Kharitonov, A.V., Astron. Zh. 68, 501-511, May-June 1991. (English Translation in Sov. Astron. 35(3), May-June 1991.)

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PR Oct 31, 1999