Meteor Spectrum Calibration Example
Meteor spectra can give a lot of information about the meteor, such as composition and temperature. However, for amateurs the calibration of the spectra is not easy. Here a method is given for grating spectra recorded with a video camera, which produces linear spectra with constant dispersion. The method uses the orthographic projection, in detail described in meteor_spectroscopy_wgn43-4_2015.pdf. As an example a spectrum (M20171209_041224_JPMZ1)recorded by Koji Maeda with a Sony alpha 7S color camera is used (S20171208_191224_JPMZ1_HE_1080.mp4). The calibration, usually done with a calibration lamp or laser was done directly from the meteor spectral images. This requires the identification of known spectral lines over a large portion of the image area for a precise calibration. In the present spectra the yellow sodium lines are easily identified and used to determine the transformation parameters for the transformation of the images to an orthographic projection. In this fortunate case where the spectrum covers most of the image area, these transformation parameters may be used for other spectra recorded with the same camera – lens – grating combination.
For the recording of the spectrum a Sony Alpha 7S equipped with a Canon 24 mm F/1.4 lens (used at F/2) and a 600 L/mm grating were used. The meteor spectrum was captured as a 4K video (image size 3840 x 2160 pixels) at 30 images/sec with Sonotaco UFOCaptureHD. The meteor was observed for about 5 sec and reached magnitude -3.7m.
This is described in detail in meteorspectroscopy.org…processing-meteor-spectra-v15.pdf. In VirtualDub, the video file is converted into a series of BMP images for processing in IRIS.
The preprocessing is done in IRIS, which has a command line interface which allows to enter the commands and also some macros for simple command sequences.
The first step is to produce a background image by averaging the first 25 images of the video sequence. These are subtracted from the images containing the meteor spectra.
In order to get linear spectra all the images are transformed to an orthographic projection according to the equation:
r = r’*(1 + a3*r’^2 + a5*r’^4)
which transforms the distances r from the image center in the original images into distances r’ in the new image. This corresponds to a barrel distortion known from wide angle lenses. The determination of the transformation coefficients is the next step. It has to be done only once for each camera – lens – grating combination. It is important to note that this method only works if the grating is mounted perpendicular to the lens axis, otherwise a more complicated transformation equation results, which cannot be determined easily!
For the calibration several meteor images distributed over as much of the image area as possible are selected. The x/y-positions of the 3 to 4 orders of the sodium lines are measured in 6 spectra with the PSF tool in IRIS.
Measurement of line position with IRIS PSF tool (mark rectangle around selected line, right click, OK). The results are stored in output screen:
A fit of these line positions to a distorsion model in EXCEL gave the following values for the transformation parameters to the orthographic projection:
|scaling factor y/x (fixed value)||1.0000|
|center of symmetry x [pixel]||1869.7|
|center of symmetry y [pixel]||1089.3|
|3rd order coeff. a3||5.313E-08|
|5th order coeff. a5||1.396E-14|
In addition to the radial distortion parameters a3 and a5, also the axis position and the linear dispersion are calculated. Some care had to be taken to avoid lines at the very edge of the image and strongly saturated lines. The average root mean square error of 0.6 nm or < 1 pixel is reasonable, considering the size of the individual lines by the movement of the meteor and partial saturation of spectral lines. Details of the calculation are in M20171209calib_final (Macros in original are disabled in online version).
Image transformation to orthographic projection
The transformation parameters can be used in ImageTools to calculate the orthographic projection of the meteor images.
As a check, the image above is transformed with these parameters. As can be seen, the spectra are linear and parallel to each other. With closer inspection, it can also be seen that the yellow sodium lines are equally spaced in all spectra.
After this check all images are transformed and registered in order to eliminate the meteor movement. The resulting meteor spectra have been combined into a video showing that the spectra indeed have constant dispersion (constant separation of sodium lines in all spectra). The curvature of the spectra (hyperbolic shape) has been corrected as well. A small problem with registering occurs at the moments where the meteor splits into several fragments.
Extraction of spectra
In order to reduce the file size and for converting the 2D spectra to 1D-spectra it is advisable to convert the 4k images to b/w by adding the colour planes before transforming to the orthographic projection.
The meteor had a long duration; therefore it seemed worthwhile to treat the spectra in 5 groups of 1 sec intervals (30 images each). These are registered and analysed separately. For the different groups different spectral lines for registering were used, as some lines disappear at the edge of the image or saturate strongly. For the grouping the command reindex is useful, as IRIS commands always expect image indices starting from 1. The extraction of the raw spectra consisted of the following steps:
- Register the spectra
- Add images
- Subtract a background offset (residual background, not removed by pre-processing)
- Select image area containing spectrum (200 pixel height)
- Rotate the image to align the spectra with x-axis
- Remove the slant of the spectra, caused by the diagonal movement of the meteor during the exposure of each image
- Add the rows of the image containing the spectral information
- Save the resulting raw spectrum in *.DAT format (intensity versus column number)
All these steps were done in IRIS, but other software may be used as well.
These spectra are converted to wavelength (to be precise wavelength*order, with increasing values to the right, as this is expected by most spectroscopic analysis programs). For this step SpectroTools by Peter Schlatter was used http://www.peterschlatter.ch/SpectroTools/. A linear fit of the measured lines shows if the spectra are indeed linear, with small errors resulting from saturation of lines, overlap of neighbouring lines or movement of meteor. The spectra are calibrated by applying a linear function
λ = a0 + a1*x,
with the inverse dispersion a1 (@ 0.630 nm/pixel for the Sony Alpha 7S with the f = 24 mm lens and 600 L/mm grating). The spectra which are a function of wavelength*order may in addition be recalibrated into wavelength for each order separately with dividing by the order.
This is shown in the following diagram for the minus first and second order (most of these plots were created with Gnuplot):
For the -1st and -2nd order separately:
Notice how the stronger lines (Na and Mg) saturate at later times in the first order spectrum and the higher resolution of the second order spectrum.
For the third order spectrum only the last spectrum is fully within the image area:
notice the resolved splitting of the Mg-line at 517 nm, barely visible in 2nd order.