OSIRIS

A Technical Note on Level 1 Wavelength Calibration

Raisa Lehtinen, Saskatoon 3rd September 1996

1.  Introduction

The purpose of this report is to present various options for the wavelength calibration of the OSIRIS UV-VIS signals in Level 1 data. This is important as accurate wavelength assignment is required for the different data retrieval methods, especially DOAS. The DOAS iteration algorithm includes a correcting least-squares fit for wavelength shift and stretch. However, the algorithm requires an initial guess for the wavelength assignment of the spectrum; this estimate should be close to the correct value. The initial wavelength assignment must be carried out as part of the Level 1 to 2 processing. The York group has suggested that the accuracy requirement for the initial guess is about 1/4 of the pixel width (~ 0.1 nm). Wavelength accuracy of the order of a pixel (or less) is also desired for other analysis methods, such as aerosol retrieval. An essential use for the Level 1 calibration data is to check for wavelength shifts and distortions between CCD-rows.

2.  Methods

The in-flight wavelength calibration of OSIRIS data is entirely based on the following information:
•	Spectral structure in the measured signal, including solar spectral structure and atmospheric absorption/emission lines
•	Calibration data from previous flight measurements
The expected wavelength shifts and stretch in the OSIRIS data are quite small (typically less than 1-2 pixels) and are only slowly varying in time. Therefore, it has been assumed that one calibration per nod is sufficient. The result of the laboratory measurements, or a previous flight calibration, can be used as a first approximation for pixel-to-wavelength mapping and the spectral structure used to refine it.

Two techniques can be used for calibration:
1.	Locate the positions of individual spectral lines, or other narrow structures, whose wavelength positions are known. This will give a set of wavelength-to-pixel estimates. A straight line (or a low order polynomial) fit through the points will give the wavelength assignment over the entire spectrum. As an example, Figure 1 shows the locations of some solar Fraunhofer lines as identified in a measured OSIRIS sky spectrum.
2.	Use of the whole spectrum  (or at least a long section of it) to find the best fit with a simulated reference spectrum varying shift/stretch parameters.
This report concentrates mainly in the former technique and discusses the suitability of strong Fraunhofer lines for calibration.

Figure 1:  Some Fraunhofer lines in OSIRIS data. Circled lines are listed in Table 1.

3.  Use of Fraunhofer lines for calibration
 
Introduction

The solar spectrum contains a rich variety of absorption lines. They mainly originate in the cooler reversing layer above the solar photosphere. The absorption lines are known as Fraunhofer lines, after their discoverer Joseph Fraunhofer (1787-1826). The strongest visible lines are due to calcium, hydrogen and iron. OSIRIS can detect many of the stronger lines in the scattered solar light. Depending on the altitude and wavelength, these lines may be affected by atmospheric absorption. However, they are the strongest structures in the OSIRIS spectrum and, therefore, good calibration sources.

Selection of lines

The accuracy of calibration depends on the number and quality of lines available. Ideally, a suitable line for wavelength calibration is strong and isolated, and its shape can be modelled with an analytical function. For OSIRIS, the moderate resolution (about 1 nm in 280-450 nm and close to 2 nm in 450-800 nm) and the low sampling ratio (2.4 in 280-450 nm) strongly limit the number of usable Fraunhofer lines. The short list below attempts to give those strong lines which cover a region of at least 5 pixels, and for which the wavelengths are found in general literature (e.g., Allen: Astrophysical Quantities). This list was created with the help of the OSIRIS ground based measurements from March 1996. Figure 2 shows the lines in the measured spectrum. On-orbit data at high tangent altitudes are likely to contain more identified lines. The calibration report for GOME instrument (ESA contract no. 10346/93/NL/CN) lists a total of 34 strong lines in the wavelength range of OSIRIS. However, only some 20 of these lines could be identified in the Modtran3 solar spectrum with 1 nm resolution, and many of these are distorted by neighbouring lines. 

Table 1. Strong solar Fraunhofer lines.

CaII(K)	3933.7	
CaII(H)	3968.5	
H	4101.8	
CaI	4226.7	
G-band	4310	
FeI	4383.6	
H	4861.3	

The molecular G-band, which originates mainly from CH absorption, is included in Table 1 because it is one of the strongest structures in the solar spectrum. Its wavelength is not exactly defined, but it should be possible to define its peak with an accuracy of better than half a pixel. There are many other complex lines in the OSIRIS spectrum, which could also be used for moderate resolution wavelength calibration. However, one concern is the order sorter, which distorts the spectrum around pixel no. 650. There are two strong solar MgI lines in that region.

The origin of most solar lines can be described using the LTE (Local Thermodynamic Equilibrium) approximation. Line broadening is mainly caused by Doppler and collision broadening.This allows the lines shapes to be presented by the Voigt function. However, for the strong lines (e.g. those listed above) the LTE is not a good approximation. 

Figure 2: solar lines from Table 1 in OSIRIS sky spectrum, row 15 in the image.

Determination of the line positions in OSIRIS data

Requirement 

An accuracy of a fraction of the pixel requires either an interpolation or fitting method to determine the peak of the line in OSIRIS signal. Some possible methods are listed below.

Cubic spline interpolation

This is a simple method to find the peak of a smooth line which is sampled at discrete points. The advantage of this method is that it is very stable with respect to the background signal. The validity of the spline interpolation depends on the sampling ratio and the shape of the peak. An isolated, symmetric peak gives the best accuracy.

Fitting an analytic function

The peak position can also be found by fitting the lines with an analytic function, such as a parabola, a Gaussian or the Voigt function. None of these represent the strong Fraunhofer line shapes accurately, and therefore the result may have a relatively large error. The Gaussian and the Voigt functions are very sensitive to the successful removal of the background signal, which should be included in the fitting procedure. This is difficult in the case of the solar spectrum, where the background has a strongly varying structure.

Center of mass

One estimate of the peak position is the center of mass of the line shape. This method is also sensitive to the background removal, which should be carried out before the center of mass calculation. The small number of data points per line causes uncertainty in this method, as well as in the fitting methods.

Fitting the known line shape

Many of the solar lines are not symmetric around the peak, as adjacent lines contribute to the line shape. In this case, the spline or other function representation may give a biased result. One solution is to use a high-resolution solar spectrum to simulate the line as measured by OSIRIS. The best fit between the measured line and the simulated line indicates the wavelength position. This method requires a good knowledge of the instrument function and pixel response, as the simulated line must accurately represent the signal.
A more simple procedure is to use, for example, spline interpolation, and add a correction factor which is estimated from the known asymmetry properties of the line.

4.  Examples

Two Fraunhofer lines were used for testing the various methods for wavelength calibration. The lines were Ca(K) at 3933.7 and FeI at 4383.6 A. Both wavelengths are air values. Figure 3 is a high-resolution image of the lines. It is evident that the Ca line is stronger and more symmetric. Figure 3 also gives an idea of the complexity of the solar spectrum. This high-resolution spectrum was used to simulate a noiseless OSIRIS signal in the absence of atmospheric effects (e.g. Ring effect). The spectra were convolved with a triangular instrument function of 10 A FWHM and integrated over a single pixel. The resulting signals are shown with * symbols in Figures 4 and 5, and with a dashed line in Figure 6.

As expected, the parabola is not a good presentation for Fraunhofer lines (Figure 4). The error in the found peak position was 0.58 A for the Ca line and -0.72 A for the FeI line. The cubic spline interpolation represents the smooth line shape better (Figure 5). The range used in the interpolation was larger than shown in the figure to avoid end effects. The error in the derived peak position was 0.28 A for Ca and  -0.97 A for FeI. The result for Ca is acceptable. However, the fact that a better peak location algorithm gives a worse result for the FeI line suggests that the line shape is not symmetric. Indeed, Figure 3 suggests that the sharp peak of the FeI line is distorted by adjacent lines when the instrument has a low resolution. This interpretation is confirmed by the spline representation shown in Figure 5.

Figure 6 shows an attempt to match the simulated Ca and FeI lines with the corresponding lines in a measured OSIRIS DM sky spectrum. In the line simulation a linear wavelength calibration was assumed, where wavelength = 2694.38 + 3.96614*pixel (pixel < 650). This is based on calibration measurements made in Calgary by R. King. The simulation is not very successful. The Ca line shape is quite well reproduced, although the depth is incorrect. One reason for this is that the simulated spectrum represents a pure solar spectrum. The instrument function may also be too narrow. For the FeI line the match is poor. The line appears to be slightly shifted from the expected position.

Figure 3: a) Ca 3934 A and b) FeI 4384 A lines.

Figure 4: Parabolic fit to simulated OSIRIS signal at a) Ca and b) FeI lines.

Figure 5: Cubic spline interpolation to simulated OSIRIS signal at a) Ca and b) FeI lines.

Figure 6: OSIRIS DM sky-spectra, row15 (solid line) and simulated signal (dotted line) for a) Ca and b) FeI lines, for the triangular slit function discussed in the text.

5.  Other calibration options

Another calibration method mentioned in section 1 is to use atmospheric features, and then fit with a simulated reference spectrum. Typically, atmospheric absorption features are weaker than the solar Fraunhofer structure, and it is best to use them for wavelength calibration in the DOAS algorithm where the solar spectral structure can be ignored. An exception is the strong molecular oxygen absorption bands near 700 and 750 nm. These might be used to obtain a moderate resolution calibration in the same way as for the molecular solar bands. 

Fitting the measured spectrum with a reference spectrum (which is considered in more detail in “Wavelength Calibration of Odin Optical Spectrograph” by R. Lehtinen) has advantages when there are too few suitable strong lines. The reference spectrum method attempts to use all of the spectral information in the data, while the line-fitting method uses only the spectral data contained in the chosen lines. The result is dependent on the accuracy of the reference spectrum. 

6.  Database and programs

A number of  useful programs and data files have been collected in the course of the present work at the University of Saskatchewan. 

Solar spectrum

The high-resolution solar spectrum used to study the Fraunhofer lines was taken from the  “Solar Flux Atlas from 296 to 1300 nm” by Robert L.Kurucz, Ingemar Furenlid, James Brault, and Larry Testerman (National solar Observatory Atlas No. 1, June 1984). Due to its large size the spectrum has been divided into files each of which cover 4 nm. The files contain a residual spectrum and the actual measured irradiance in micro-watts per square centimeter per nanometer. Some files are combined to select the spectral region around strong Fraunhofer lines. The units can be converted into phot/(s cm2 nm) by multiplying the spectra with 5.03108wavelength[A]. Files so far created are found at the server of the Odin group in Saskatoon, in directory OSIRIS:\models\sunspectra\. The original Kitt Peak files are in the same directory, named as lm[nm]. The entire spectrum (all files 269 to 1300) can be obtained from me or from F. Hill (fhill@noao.edu).

Simulating the OSIRIS signal

The high-resolution spectrum is used to model the OSIRIS signal in the vicinity of Fraunhofer lines. This modelling involves two steps: 1) Convolution with an instrument function and 2) Integration of the convolved signal over pixels. A short Matlab m-file to do this task is found in OSIRIS:\software\matlab\linecalibration\linesim.m (*.m files are collections of Matlab commands, to be run from Matlab as a single procedure). The present instrument function is triangular, but this should be changed to the measured function.

Another m-file named OSIRIS:\software\matlab\linecalibration\wavecal.m calculates the best fit with OSIRIS DM sky spectra and a simulated spectrum for the CaII(K) or FeI lines in the least-squares sense. At the present time (see Figure 6) the agreement is poor. The OSIRIS DM sky spectrum used in this work is found in the same directory.

7. Conclusions

Table 1 and Figure 2 show strong Fraunhofer lines which are easily identified in the OSIRIS spectrum. Spline interpolation is probably the best means for locating the peak, as it does not require a removal of the baseline. For the OSIRIS spectral resolution many of these lines are not symmetric, and the location of the derived “peak” of the line may differ from the actual line position. A correction factor could be assigned to each line to compensate for this distortion. With all of these uncertainties in the peak location, and taking into account the small number of suitable lines, the accuracy of the Level 1 calibration is unlikely to be much better than one pixel. However, it is better to leave the calibration algorithm relatively simple, and achieve the required accuracy in Level 2 processing.