The light cone of the telescope goes into the entrance slit of the spectroheliograph. The slit cuts out a fine strip, which is treated by the spectroscope. One sees on the figure that two sunspots of opposite polarity were bisected by the slit. The top vector field is plunging towards the interior of the Sun (red arrow) whereas the bottom one is emerging (blue arrow) .When the vector field comes towards the observer, i.e., it is emerging (blue case) then the component of shorter wavelength of the Zeeman doublet is constituted by circular vibrations of the same direction as the magnetizing current, which would produce this vector ( counterclockwise, or left). It is the opposite for the red case (clockwise, or right) . The light then meets a quarter wave plate of which we will the fast axis carried by Ox. The reference mark xOy is direct in its plan by the direction of the light . If the incidental light is right circularly polarized (clockwise) its Jones vector is written . The Jones matrix of the quarter wave plate is written: . At exit of the quarter wave plate the transmitted vibration is described by the Jones vector: .
If it is received by a linear polarizer whose axis forms an angle of +45° with Ox and thus from matrix which is written , then at exit the Jones vector of the luminous vibration is. The vibration is thus transmitted with an intensity equal to the intensity of the incidental vibration.
If on the contrary, it is received by a linear polarizer whose axis forms an angle of -45° respect to Ox and thus from matrix which is written then at exit of this one the vibration is described by the vector . It is stopped.
Let us take again this calculation on the assumption of a left circular
vibration arriving on the quarter wave plate which remains directed
with its fast axis carried by Ox.
. The vibration is transmitted with an intensity equal to the intensity of the incidental vibration.
It is completely equivalent to make a turn of 90° of the quarter
wave plate or of the polarizer as one can check it easily.
Our quarter wave plate results from the cleavage of a mica sheet, which is almost equal to the optical quality of a quartz plate but its cost is quite lower . Mica optical quality is good . It is rigorously quarter wave for 633nm . However it can be used without problem in a broad vicinity of the wavelength (between 400 and 700 Nm) because of its optical properties. I chose to use mainly the line of iron Fe I 6302.5Å, which offers a favorable factor of Landé g=2.5, or the line Fe I 5250.2Å (g=3.00) classically used in magnetography, for instance, with the Mount Wilson magnetograph (Mt. Wilson 150-Foot Solar Tower).
The polarizing device for solar magnetometry.
optical diagram. The revolving quarter wave plate is carried by the brassplated
Certain absorption lines of the solar spectrum, like
those quoted above and illustrated low, are sensitive to the longitudinal
component of the ambient magnetic field in the area where they occur (i.e.,
in photosphere or the lower chromosphere). This sensitivity is given by
the value of the Landé factor, noted g, ranging between 0 and 3.
It is supposed that the lines have a Gaussian spectral profile
the Stokes parameter V is given by:
The two components observed for the two positions of extinction of the analyzer are D=I +V and G=I - V . They make it possible to find et .
The two images below illustrate the two stages of the manipulation.On
the left one finds the principle of operation of the quarter wave
plate" plus " linear polarizer" with axis at 45° to
the axis of the plate. That makes it possible to separate two circular
polarizations from opposite directions and to filter them as indicated
in the preceding paragraph.
The image of the right-hand side illustrates the exploration of these
two series of spectral images. One applies to each one the usual processing
of rebuilding of a monochromatic solar image.
spectrogram by webcam.
Animation of the two positions of the mica 1/4 l .
|Notice the insensitivity of the atmospheric lines to the position of the quarter wave plate.
To calculate images BG, RG,BD,RD we consider the values of the intensity of the spectral line on both sides of its axis: I(-3), I(-2), I(-1) in the blue wing, I(0) at center, I(1), I(2), I(3) in the red wing.These points of measurement are represented on the spectral profiles below for the left wing of the Zeeman doublet or for the right wing of this one.
One simulated below a spectral
profile of the line FeI 5250Å such as it is observed in our SHG
where 1 pixel corresponds to 0.0037 angström. The profile can be
compared to Gaussian curve of following equation:
Is the intensity of the line to the wavelength l.
On the image below on the left, the line (in black) is centered perfectly on pixel 20. On that of right-hand side on the contrary there is a shift of 0.010 angström respect to the axis of pixel 20.The problem is of knowing which is the impact of this shift on the value of I(-3)+I(-2)+I(-1)-I(1)-I(2)-I(3) =Blue - Red, who measures on each of the two Zeeman components this shift respect to pixel 20. This one is directly proportional to the value of the magnetic local field B.
Ideal case of a line (in black) centered on the column of pixels number 20 and its two wings of Zeeman duplicated by a local magnetic field of 1000 gauss.
Case of a line (in black) shifted of 0.019 angström compared to the column of pixels number 20 and its two wings of Zeeman duplicated by a local magnetic field of 1000 gauss.
|One thus simulated the variations of this measurement I (- 3) +I (- 2) +I (- 1) - I (1) - I (2) - I (3) = Blue-Red according to the values of the magnetic field B for various values of the off-centring of the axis of the line respect to pixel 20 . The values of between 0, 0.005, 0.010 and 0.015 angström are considered below.
B-R versus B for various values of off-centring.
Stokes's parameter calculated starting from the measurements simulated for a centered line (black) and for an shift of the line of 0.010 angström with a magnetic field of 1000 gauss.
notes the conservation of the linearity, with one slope independent
of the shift of the line respect to the lines of pixels. On the other
hand, this shift varies the ordinate at the origin of the approximations
closely connected of these curves in a range from -30 to
30 ADU for a side shift of the line varying of -1/2 pixel to 1/2 pixel.
Result of the calculation of the sums of differences BG-RG and BD-RD. I (- 3) +I (- 2) +I (- 1) - I (1) - I (2) - I (3) according to the various values of the magnetic field B.
The two blue dotted lines show the level of average noise on the final image of about 30 ADU what seriously limits the detection of fields of less than 100 gauss.
Intensity of the final image versus the value of the field.
|Note: ADU (Analogic Digital Unit) ,"pas codeur" in French.
Here some lines classically used for the study of the solar magnetic field and obtaining magnetograms.
They are characterized by their intensity, and their large Landé factors.
The differential of circular polarization is quite perceptible in the
middle of the spot
In the images below one tries to illustrate the principle and the sensitivity of the method of the differences.
image of left is obtained by making the difference of spectral image of
the line 5250.2Å and its symmetrical respect to a vertical axis for
left linear polarization. One thus obtains the blue minus red profile noted
for the area of the spot NOAA0898b on July 5, 2006. On the right the same
difference in right linear polarization BII-RII.
Note the inversion of intensity right/left after 1/4 l
mica rotated 90°.
In the center, photometric profile of this difference.
On the right this same difference for a zone except spot (more in the East).
Note: BI-RI, blue wing of the left linear polarizing component minus red wing of of the left linear polarizing component.
Note: BII-RII, blue wing of the right linear polarizing component minus red wing of the right linear polarizing component.
image of left is obtained by making the difference of spectral image in
left polarization and in right polarization: I-II.
On the right the image II-I.
This is for the area of the spot NOAA0898b on July 5, 2006.
On the right, photometric profile of this last difference for the line FeI 5250.2Å.
|R.B.Leighton announced the difficulty in the center of the spots (in the umbra) with images as strongly underexposed . The signal becomes of the same order as the noise, and the difference R-B give a uniform plage . In these areas of the magnetogram, the magnetic field is not correct any more, detected in spite of its great intensity .All must return in order if one wants the exposed images to be correctly exposed.
|Area of the correctly exposed spot. The umbra shows the same polarity well as the penumbra .The outside of the spot is over-exposed. See on the right the image difference R-B of the spectrum in the line Fe I 6302.5Å for the position of the slit indicated by the red vertical line..
I had waited for this favorable moment for several weeks Moment always delayed because of the unfavourable weather in this end of spring or because of the magnetic absence of activity of certain importance.
Finally a beautiful event arises on July 4, 2006.
The sky is not absolutely perfect, but the occasion is too beautiful to let pass!
In the images below, the magnetograms obtained with our instrument are the images in red.
The beautiful spot of NOAA0898 is ideally located today at the center
of the solar disc, for a second test of magnetographic imagery.It is the
ideal configuration to detect the line of sight component of the magnetic
4 scan 060704_5250_x.avi,
A red left image(RG)
A blue left image(BG)
Sum of these images
|There is then composity of several magnetograms resulting from consecutive scans to obtain the final result.
|Comparison SOHO image of reference with full resolution on the left, and the image obtained on our SHG in spectromagnetography in the center, and on the right (two images). One can note the good agreement.
SEIT 171Å NOAA0898
SHG Juillan, Ha center line
Two active areas arised on July 8, 2006
SHG Juillan 10h13m UT
4 files 060708_5250_x.avi,
One sees above the various stages of construction
of a magnetogram by the method of the sums and differences derived from
that of R.B.Leighton.
|Above, on the left, comparative between
the results which we obtained in the city of Juillan, France (four images
top surrounded by red) and the reference documents of the professional observatories
(GONG and Wilson Mount). Dimensions of our images were reduced to bring
back them on a scale with those of the GONG and Wilson Mount. False colors
with the same palette which the Observatory of the Wilson Mount shows the
good agreement between the magnetogram obtained with Juillan and the magnetogram
of reference of the Wilson Mount using the same iron line.
Note: Juillan (N 43°12'28" E 00°01'33") in the south of France. Close to the Pyrenees.
At the top of the images on the left, the magnetogram of reference of SOHO MDI on July 24, 2006 to 0h35 UT.
Opposite the result of the treatment of the alternative scans "right
polarization"/ "left polarization" in the North-South direction
in the line Fe 6302.5Å (filer: 060724-6302-5).
Lastly, below, the image of professional reference: The 150-Foot Solar Tower Current Magnetogram. Image magnetogram of today.
|Animations showing in alternation a magnetogram of SHG Juillan like above and the magnetogram of the Mount Wilson with the same palette but two adjustments from the thresholds of visualization.
Comparison between our result with the SHG Juillan and the image of reference provided by the magnetogram SoHo MDI: satisfactory result.
|The cloudy passages with which it was necessary to find attic windows of 6minutes in order to take these magnetographic images did not enable me to also make images of the same area in H alpha.
Sky very cloudy , poor transparency and frequent cloudy passages! Our magnetogram lacks contrast and clearness.
The situation near limb does not make work easy
NOAA AR0905 is the only active area 29/08/2006.
Fields about +/- 100 gauss are detected. The image of reference SOHO MDI is in the center.
|I tried today a complete observation of active area NOAA 0905. In addition to the usual magnetogram, I observed the area in Ca II K, around Ha and make a dopplergram and a spectroheliographic image in the continum near Ha. The results are presented below.
Sun, on July 30, 2006, in white light.
The same area observed the same day in Ha and in Calcium CaII K3 (celestial north is at the top).
August 30, 2006, 13h17 UT, SHG Juillan: Exploration in wavelengths around line Ha.
SHG Juillan, August 30, 2006.
Translation of the dopplergram in speeds: One can measure
the spectral shift and thus deduce speeds from them on the parts of the
spectra corresponding to the green and red reference marks of the image
dopplergram presented opposite in two versions: false colors on the left
and B/W on the right.
On the left, median of 3 magnetograms SHG Juillan resulting from the file 061102_gd6302_3 to 10h18 YOU. On the right, the magnétogram of reference SoHo MDI smdi_maglc_fd_20061102_1605.gif
These results, which I did not dare to expect, confirm that solar magnetography
is possible for amateur observers by using a spectroheliograph of personal
theory : http://astrosurf.com/rondi/theo/polarisation/index.htm
Howard, Robert F., The Mount Wilson Solar Magnetograph: Scanning and Data System,Solar Physics, Vol. 48, June 1976.
Babcock, Horace W., The Solar Magnetograph, Astrophysical Journal, 118, 387 (1953)
The Magnetograph (Solar Physics, march 1963, pages 476 à 479)
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